Hybrid Composite Precast Systems: Numerical Investigation to Construction [1 ed.] 0081027214, 9780081027219

Table of contents :
Front Cover
Hybrid Composite Precast Systems: Numerical Investigation to Construction
Copyright
Contents
Preface
Chapter 1: Conventional precast assembly
1.1. Review of conventional precast concrete structures
1.1.1. Why precast concrete?
1.1.2. Quality control and facile installation
1.2. Conventional precast connection
1.2.1. Column-to-column connection
1.2.1.1. Cast-in-place connections for column-to-column joint with pour forms
1.2.1.2. Precast assembly using grouted splice sleeve connectors
1.2.1.3. Joints using shim bearing, dowel pin, welding
1.2.1.4. Stacked connections
1.2.1.5. Bolted column connections for fast and safe erection
1.2.1.6. Colum-to-foundation joints using sleeve
1.2.2. Beam-to-column connection
1.2.2.1. Concrete cast at beam-to-column joint; moment connection
1.2.2.2. Beam seated on corbels or steel inserts (haunches); pinned connections
1.2.2.3. Beam-to-column connections via hardware
1.3. Suggestion for the improvement of the precast joints
1.3.1. Use of the cast-in-place concrete
1.3.1.1. Construction waste and concrete pour forms at joints
1.3.1.2. Weakness of the precast connections
1.3.2. Why steel-concrete hybrid composite precast frames? Use of steel-concrete hybrid precast frames with reduced frame ...
References
Chapter 2: Experimental investigation of the precast concrete and the precast steel-concrete hybrid composite frames havi ...
2.1. Conventional bolted endplates used for steel frames
2.2. Description of the mechanical joints
2.2.1. Joint connection from an erection point of view
2.2.2. Column-to-column joint for the moment connections
2.2.2.1. Mechanical joints with the bolted metal plates for the precast columns
2.2.2.2. Mechanical joints with interlocking couplers for precast columns
2.2.3. Beam-to-column joint for the moment connections
2.3. Design of the mechanical joints
2.3.1. Column-to-column connection
2.3.1.1. Design of the column plates
2.3.1.2. Nominal bearing strength of the plates at the bolt holes
2.3.1.3. Design of the bolts
2.3.1.4. Design of the tension in bolts
2.3.1.5. Design of pretension in bolts
2.3.2. Beam-to-column connection and the design of the stiffness of the column plates and bolts
2.4. Verification of the structural performance of the joint via the numerical investigation
2.5. Experimental investigation of the structural performance of the column-to-column connections
2.5.1. Steel-concrete composite columns
2.5.1.1. Description of the tested specimen and test set-up
Metal filler
Concrete filler
2.5.1.2. Instrumentation of the test specimens
2.5.1.3. Test results and review with the design recommendations
Specimen C1
Specimens C2 and C6
Specimen C3
Specimen C4
Specimen C5
2.5.1.4. Strains evolution and the rate of strain increase
Load-displacement relationship
Influence of the metal and concrete plates on the rate of the strain increase of rebars
Influence of the metal and concrete plates on the rate of the strain increase of steel sections
Influence of the metal and concrete plates on the rate of the strain increase of concrete
Strength of the metal and concrete plates
2.5.2. Concrete columns without steel sections
2.5.2.1. Design of the test specimens; derivation of the equations based on strain compatibility
Design of the plates subjected to tensile forces
2.5.2.2. Fabrication of the test specimens
2.5.2.3. Test results
Specimen HC1
Specimen HC2
Specimen HC3
2.5.3. Conclusions of the column-to-column connections
2.6. Experimental investigation of the structural performance of the beam-to-column connections
2.6.1. Steel-concrete hybrid composite beams
2.6.1.1. Description of the tested specimen and test set-up
2.6.1.2. Instrumentation of the test specimens
2.6.1.3. Test results and review with the design recommendations
Specimen B1
Specimen B2
Specimen B3
Specimen B4
Specimen B5
Specimen B6
2.6.2. Conclusions of the beam-to-column connections
2.7. Test assembly
2.7.1. Significance of the connection
2.7.2. Assembly of the full-scale precast columns
2.7.3. Test assembly: Precast column splice implementing the mechanical joints having laminated metal plates
2.7.4. Test assembly
References
Chapter 3: The investigation of the structural performance of the hybrid composite precast frames with mechanical joints ...
3.1. Numerical investigation of the structural performance
3.1.1. Nonlinear inelastic finite element analysis
3.1.1.1. Plastic potential and yield surface
3.1.1.2. Plasticity model of damaged concrete; concrete crack models in the finite element analysis
3.1.1.3. Damaged plasticity model for concrete
Uniaxial tension and compression stress behavior
Damaged plasticity model for concrete (concrete damaged plasticity)
3.1.2. FEA parameters and their physical meanings
3.1.2.1. Material parameters for calibrations
3.1.2.2. Yield surface of concrete
3.1.3. Dilation angle
3.1.3.1. Volumetric dilatations
3.1.3.2. Definition of dilation angle
3.1.3.3. Drucker-Prager hyperbolic plastic potential function
Flow (plasticization) rule based on nonassociated plastic flow potential
Eccentricity,
Identification of dilation angles and damage variables for concrete section confined by T section steels
3.1.3.4. Viscosity parameter
3.1.3.5. Application of artificial damping factors to resolve the stability problems
Damping factor to solve numerical instability
Damping with steel structures
3.1.4. Fracture criterion
3.1.4.1. Pressure-independent yield criteria; von Mises and Tresca
3.1.4.2. Pressure-dependent yield criteria; Drucker-Prager and Mohr-Coulomb
3.1.5. Penetration of contact element
3.1.5.1. Definition of contact
3.1.5.2. Enforcement of contact compatibility to minimize penetrations
3.1.5.3. Linear and nonlinear penalty stiffness
3.1.5.4. Contact formulation
3.1.6. Modeling technique; types of contact elements in FEA
3.1.6.1. Embedded, tie elements and a geometric tolerance
3.1.6.2. Accurate contact model for steel-concrete hybrid composite members; bond-slip characteristics between concrete a ...
3.1.6.3. Limitation of the study for bond stress-slip characteristics of steel-concrete hybrid frames
3.2. Nonlinear finite element analysis of hybrid composite precast columns spliced by a mechanical metal plate
3.2.1. Finite element models for the mechanical joints with laminated plates
3.2.1.1. Mechanical joints with metal filler plates
Details of the tested specimens
Modeling of contact elements; definition of slave and master surfaces in a contact pair
Modeling of rebars and steels in steel-concrete hybrid composite members; embedded, tie (cohesive) model
Bond-slip method
Calibration of numerical data
Structural performance of Specimen C2
Structural performance of Specimen C5
Structural performance of Specimen C6 (monolithic specimen)
Plate deformation and strains
Conclusions
Nonlinear FEA model
Seismic performance of the precast concrete frames with mechanical joints having metal plates
3.2.1.2. Mechanical joints with concrete filler plates
FE models for mechanical connections using metal and concrete plates
Structural performance of Specimen C3
Influence of the thickness of concrete filler plates on the structural performance of Specimens C3 and C4
Calibration details
Influence of metal and concrete plates on the rate of strain increase of rebars
Influence of metal and concrete plates on the rate of strain increase of steel sections
Influence of metal and concrete plates on the rate of strain increase of concrete
Design recommendations
Conclusions
3.2.2. Numerical investigation of metal plates with high-yield strength steel splicing precast concrete columns
3.2.2.1. Description and calibration of the nonlinear finite element parameters
Numerical modeling of Specimen HC3 having monolithic joint
Numerical modeling of Specimens HC1 and HC2 having mechanical joints
3.2.2.2. Parameters defined for Specimens HC1, HC2, and HC3 having mechanical joint
3.2.2.3. Influence of high-yield metal plates on the flexural capacity
Influence of the high-yield strength of metal plates on the flexural strength of Specimen HC1 having mechanical joints
The height of column plates to avoid concrete degradation
3.2.2.4. The influence of headed studs on the flexural strength of the connection
3.2.2.5. Activation of strains of structural components attached to column plate
3.2.2.6. Conclusion
3.3. Nonlinear finite element analysis of the beam-to-column connections with mechanical metal plates for concrete/steel- ...
3.3.1. Finite element models for fully and partially restrained moment connections
3.3.1.1. With metal filler plates
Description of the numerical details
Nonlinear stress-strain relationship of unconfined and confined concrete; modeling techniques
Concrete damaged plasticity model
Modeling of contact elements
Mesh discretization, mesh density, mesh compatibility, and element distortion
Mesh discretization
Mesh density
Assigning material properties
Results and discussion
Monolithic specimen (B6)
Specimen B2; reflecting low cycle fatigue effect by reducing strain hardening behavior
Specimen B5; partially restrain moment connection
Contribution of the metal plates to the flexural capacity of the beams
Conclusions
3.3.1.2. With concrete filler plates
Numerical modeling
Mathematical model
Modeling of contact elements
Damaged plasticity model for concrete
Influence of the stiffness of metal and concrete plates on the structural performance
Load-displacement relationship
Influence of the stiffness of metal and concrete plates on the rates of the strain increase of concrete
Influence of the stiffness of metal and concrete plates on the rates of the strain increase of rebar
Influence of the stiffness of metal and concrete plates on the rate of strain increase of the steel sections
Strength of extended endplate and concrete filler plates
Influence of the stiffness of the metal plates on the load paths validated by numerical and experimental microscopic strains
Strain evolution of the structural elements of the hybrid joints
Influence of metal plate on strain-stress relationships of structural components
Fracture mode of concrete filler plate
Conclusions
References
Chapter 4: L-type hybrid precast frames with mechanical joints using laminated metal plates
4.1. Experimental investigation of the L-type hybrid precast frames using mechanical joints with laminated metal plates
4.1.1. Why L-type precast frames?
4.1.2. Specimen details and test preparation of Specimens LC1-LC3
4.1.3. Preparation of the test
4.1.4. Experimental investigations
4.1.4.1. Structural behavior and associated failure modes for Specimen LC3 (monolithic specimen)
4.1.4.2. Structural behavior and associated failure modes for Specimen LC1
4.1.4.3. Structural behavior and associated failure modes for Specimen LC2
4.1.4.4. Comparisons of the structural performance of the three specimens (LC1, LC2, and LC3)
4.1.4.5. Activation of the structural elements contributing to the flexural capacity of the hybrid precast column-column ...
4.1.5. Conclusion
4.2. Nonlinear finite element analyses of the L-type columns with mechanical joints
4.2.1. Selection of the elements and discretization
4.2.2. Defining interactions; surface-to-surface contact
4.2.3. Definition of the host, embedded elements, and constraints
4.2.4. FE models with a foundation; load application at a test center
4.2.5. Structural behavior of laminated metal plates
4.2.6. FE models without foundations
4.2.6.1. Load applied at a test center, not a shear center
4.2.6.2. Load applied at shear center
4.2.7. Strain evolution of L-type columns (monolithic and mechanical joints with no axial force) with/without foundation
4.2.8. Conclusions
4.3. Design verification of the beam-column frames
4.3.1. Nonlinear numerical model
4.3.1.1. Description of the numerical model
4.3.1.2. Modeling column-girder joints
4.3.1.3. Modeling the surface element
4.3.2. Design verification
4.3.2.1. Dynamic analysis of high-rise buildings with multibay L-type composite precast frames
4.3.2.2. Determination of the nominal strength at a concrete strain of 0.003 based on the concrete mesh under the average ...
4.3.2.3. Strain evolutions of the mechanical joints
4.3.2.4. Strain evolution of the structural components attached to plates
4.3.3. Conclusion
4.4. Test erection
4.4.1. Erection of irregular L-shaped frames
4.4.1.1. Significance of the test erection
4.4.1.2. Column-to-column connection
Connection mechanism
Erection test for column-to-column assembly
4.4.1.3. Girder-to-column connections
Connection mechanism
Erection test for column-to-beam assembly
Verification of the erection test
4.4.2. Conclusion
References
Chapter 5: Novel erection of the precast frames using interlocking mechanical couplers
5.1. Significance of the precast erection using interlocking mechanical joints
5.2. Assembly of the full-scale precast frame by interlocking couplers
5.2.1. Column-to-column connections
5.2.1.1. Using interlocking one-touch interlocking couplers to splice precast columns
5.2.1.2. Test erection
5.2.1.3. Replacing couplers
5.2.2. Girder-to-column connections and the test erection
5.3. Numerical investigation
5.3.1. Description of the mechanical connections for design verification
5.3.2. Finite element model of the proposed joint
5.3.3. Verification of the numerical analysis
5.3.4. Flexural capacity of the connection
5.3.5. Conclusions
References
Chapter 6: Novel precast frame for facile construction of low-rise buildings using mechanically assembled joint to replac ...
6.1. Introduction
6.1.1. Advantages and challenges
6.1.2. Methodology of joint details for low-rise frames; connections for column-to-column, column-to-girder, and girder-t ...
6.2. Design of the building with the mechanical joints
6.2.1. Design load combination and conventional design detail
6.2.2. Design of mechanically layered plates based on nonlinear finite element analysis
6.2.3. Numerical model and nonlinear finite element analysis parameters
6.2.3.1. Defining contact properties
6.2.3.2. Modeling of embedded elements (reinforcing bars and H-steels)
6.2.3.3. Discretization
6.2.4. Design of connection plates
6.2.5. Implementation of the extended endplates in girder-to-beam
6.2.5.1. Design of mechanical connections
6.2.5.2. Design of headed studs
6.2.6. Implementation of the extended endplates in column-to-girder connections
6.3. Design verification
6.3.1. Rates of strain increase and strain activation of the structural components at connection
6.3.2. Construction quantities
6.3.3. Reduction of construction period by mechanical connection
6.3.4. Reduction of energy consumption and CO2 emissions with the new precast frame
6.4. Results and conclusions
References
Chapter 7: Novel pipe rack frames with rigid joints
7.1. Overview of the pipe rack frames introduced in this chapter
7.1.1. The innovated pipe rack frames
7.1.2. Overall historical development, advantages and challenges of existing pipe rack frames
7.1.3. Significance of the pipe rack frames with rigid joints; motivations and objectives
7.2. Novel pipe rack frames with rigid joints
7.2.1. Precast concrete-based pipe rack frames with rigid monolithic beam-column connections
7.2.2. Precast concrete-based pipe rack frames with rigid mechanical joints
7.2.2.1. Frame module for easy assembly by the use of mechanical joints
7.2.2.2. Assembly sequence
7.2.2.3. Numerical investigation
7.2.3. Pipe-racks with prestressed frames
7.2.4. Rigid steel frames
7.3. Case study
7.3.1. Steel-concrete hybrid composite precast frames with moment connections
7.3.2. Dynamic characteristics
7.3.3. Suggestion for rapid construction based on the fast track using the proposed frames
7.3.4. Structural savings
7.3.5. Offsite modular construction with base template
7.4. Conclusions
References
Chapter 8: Application to the modular construction
8.1. Overview of the modular construction for low-rise buildings
8.2. Conventional modular construction
8.2.1. Structural and connection systems
8.2.2. Cellular-type modules and intra-module connection (Fig. 8.2.1) [3]
8.2.3. Inter-module connection [1]
8.2.4. Application of the modular construction to high-rise buildings
8.3. Implementation of the mechanical joints in precast connections for modular construction
8.3.1. High-rise building application
8.3.2. Application to special structures
8.4. Lateral stability of the hybrid composite precast frames with rigid mechanical joints
8.4.1. Seismic responses and fundamental period of the modular building
8.4.2. Modular steel building with braced frames
8.4.3. Precast concrete-based frames having mechanical joints
8.5. Conclusions
References
Chapter 9: Precast steel-concrete hybrid composite structural frames with monolithic joints
9.1. Why the precast steel-concrete hybrid composite with monolithic joints?
9.2. Structural behavior of the hybrid composite beams with monolithic joints
9.2.1. Wide steel flanges encased in concrete; the interaction between steel and concrete
9.2.1.1. Experimental investigation; flexural strength of the composite beam
9.2.1.2. Flexural moment capacity at the deflection of 1/360
9.2.1.3. Load bearing strength of the precast wings against construction loads
9.2.2. T-shaped steel section encased in concrete
9.2.2.1. Experimental investigation of the composite precast beams with T-shaped steel sections
9.2.2.2. Instrumentation and the test set-up
9.2.2.3. Numerical investigation
3D mesh for finite element analysis
Parameters for the nonlinear numerical model
9.2.2.4. Test results
9.2.2.5. Structural behavior of the unsymmetrical precast composite beams
9.2.2.6. Load-strain relationship using strain compatibility based method
9.2.2.7. Sensitivity of the dilation angles and damage variable to the nonlinear numerical behavior of the composite beams
9.2.2.8. Viscosity
9.2.2.9. Influence of the steel section on the activation of the rebars and concrete in compression for the damage assessment
9.2.2.10. Prediction of the propagation for the tensile cracks and compressive crushing; an evaluation of damage evolution
9.2.3. Seismic capacity of the hybrid precast beams
9.2.3.1. Strong column-weak beam frame
9.2.3.2. Story drift angle qualified as a special moment frame
9.2.4. Prestressed precast beam monolithically integrated with columns
9.2.5. Discussions and conclusions
9.2.5.1. Composite precast beam with T section steel
9.3. Analytical prediction of the nonlinear structural behavior of the steel-concrete hybrid composite structures
9.3.1. Conventional strain compatibility approach
9.3.2. Steel-concrete hybrid composite beams without axial loads
9.3.2.1. Analytical models of the concrete confined by transverse rebars and wide-flange steel sections based on an itera ...
9.3.2.2. Prediction of the nonlinear structural behavior of the steel-concrete composite beams
Equivalent confining factors
Idealization of the concrete confined by the structural steel sections
Influence of the buckling of the longitudinal bars and the structural steel
9.3.2.3. Formulation of the equilibrium at the yield and maximum load limit states based on an iterated strain compatibility
At the yield limit state
At the maximum load limit state
9.3.2.4. Verification analysis
Verification model
Nonlinear finite element analysis based on the concrete plasticity
Verification of the analytical model with the finite element analysis results
Influence of the buckling effect of the reinforcing steels on the flexural strength
Verification of the algorithm
Reduced beam depth using the composite beams
9.4. Assembly of the steel beam-column joints with a skewed beam section
9.4.1. Conventional steel erection
9.4.2. New erection method; splicing plates and bolting beyond critical path
9.4.2.1. Noncritical installation of the splicing plates and bolting
9.4.2.2. Preinstallation of the L-shaped pocket
9.4.2.3. Numerical evaluation of the proposed connections
9.4.2.4. Conclusions
9.4.3. Precast column spliced by the rebars extended in holes
9.5. Application of the hybrid composite precast frames with the beam depth reduction capability to high-rise buildings
9.5.1. Application to a 19-story building
9.5.1.1. Original design
9.5.1.2. Reduction in floor height
9.5.1.3. Design of the composite frames
9.5.1.4. Design summary
9.5.2. Erection and assembly of the hybrid composite beams
9.5.3. Descriptions of the selected buildings
9.6. Contributions
References
Chapter 10: Artificial-intelligence-based design of the ductile precast concrete beams
10.1. Concept and structure of the artificial neural networks
10.1.1. Analogy with the biological neuron model
10.1.2. ANNs for structural engineering
10.2. Multilayer perception
10.2.1. Weights and bias
10.2.2. Backpropagation by adjusting weights
10.2.3. Activation functions related to the structural-engineering applications
10.2.4. Initialization
10.2.5. Data normalization
10.2.6. Three ways to train ANNs in Matlab
10.2.6.1. Using neural-network toolbox fitting application
10.2.6.2. Using neural-network toolbox data manager
10.2.6.3. Writing Matlab code
10.3. Artificial neural network-based design of the ductile precast concrete beams
10.3.1. Generation of the big structural data; a ductile design of the doubly reinforced precast concrete beams
10.3.2. Supervised training
10.3.2.1. Numbers of datasets, hidden layers, neurons, and training functions
10.3.2.2. Factors influencing neural training
10.3.2.3. Training results and numbers of data values versus hidden layers
10.3.3. Test networks and the design results
10.3.4. Conclusions
References
Index
Back Cover

Citation preview

Hybrid Composite Precast Systems

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Woodhead Publishing Series in Civil and Structural Engineering

Hybrid Composite Precast Systems Numerical Investigation to Construction

Won-Kee Hong

An imprint of Elsevier

Woodhead Publishing is an imprint of Elsevier The Officers’ Mess Business Centre, Royston Road, Duxford, CB22 4QH, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom © 2020 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: (print) 978-0-08-102721-9 ISBN: (online) 978-0-08-102741-7 For information on all Woodhead publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisition Editor: Gwen Jones Editorial Project Manager: Emma Hayes Production Project Manager: Sojan P. Pazhayattil Cover Designer: Alan Studholme Typeset by SPi Global, India

Contents Preface

ix

1. Conventional precast assembly 1.1 Review of conventional precast concrete structures 1.1.1 Why precast concrete? 1.1.2 Quality control and facile installation 1.2 Conventional precast connection 1.2.1 Column-to-column connection 1.2.2 Beam-to-column connection 1.3 Suggestion for the improvement of the precast joints 1.3.1 Use of the cast-in-place concrete 1.3.2 Why steel-concrete hybrid composite precast frames? Use of steel-concrete hybrid precast frames with reduced frame weight implementing dry mechanical joints having bolted laminated plates References

1 1 1 1 1 8 12 12

12 14

2. Experimental investigation of the precast concrete and the precast steel-concrete hybrid composite frames having novel mechanical joints 2.1 Conventional bolted endplates used for steel frames 2.2 Description of the mechanical joints 2.2.1 Joint connection from an erection point of view 2.2.2 Column-to-column joint for the moment connections 2.2.3 Beam-to-column joint for the moment connections 2.3 Design of the mechanical joints 2.3.1 Column-to-column connection 2.3.2 Beam-to-column connection and the design of the stiffness of the column plates and bolts

15 16 16 16 19 20 20

28

2.4 Verification of the structural performance of the joint via the numerical investigation 2.5 Experimental investigation of the structural performance of the columnto-column connections 2.5.1 Steel-concrete composite columns 2.5.2 Concrete columns without steel sections 2.5.3 Conclusions of the column-tocolumn connections 2.6 Experimental investigation of the structural performance of the beam-tocolumn connections 2.6.1 Steel-concrete hybrid composite beams 2.6.2 Conclusions of the beam-tocolumn connections 2.7 Test assembly 2.7.1 Significance of the connection 2.7.2 Assembly of the full-scale precast columns 2.7.3 Test assembly: Precast column splice implementing the mechanical joints having laminated metal plates 2.7.4 Test assembly References

28

28 28 54 64

64 64 77 77 77 77

77 79 88

3. The investigation of the structural performance of the hybrid composite precast frames with mechanical joints based on nonlinear finite element analysis 3.1 Numerical investigation of the structural performance 89 3.1.1 Nonlinear inelastic finite element analysis 89 3.1.2 FEA parameters and their physical meanings 91 3.1.3 Dilation angle 94 3.1.4 Fracture criterion 103 3.1.5 Penetration of contact element 105 3.1.6 Modeling technique; types of contact elements in FEA 108 v

vi

Contents

3.2 Nonlinear finite element analysis of hybrid composite precast columns spliced by a mechanical metal plate 3.2.1 Finite element models for the mechanical joints with laminated plates 3.2.2 Numerical investigation of metal plates with high-yield strength steel splicing precast concrete columns 3.3 Nonlinear finite element analysis of the beam-to-column connections with mechanical metal plates for concrete/ steel-concrete composite frame 3.3.1 Finite element models for fully and partially restrained moment connections References

113

228 228 240 247

113

138

151

151 176

4. L-type hybrid precast frames with mechanical joints using laminated metal plates 4.1 Experimental investigation of the L-type hybrid precast frames using mechanical joints with laminated metal plates 4.1.1 Why L-type precast frames? 4.1.2 Specimen details and test preparation of Specimens LC1–LC3 4.1.3 Preparation of the test 4.1.4 Experimental investigations 4.1.5 Conclusion 4.2 Nonlinear finite element analyses of the L-type columns with mechanical joints 4.2.1 Selection of the elements and discretization 4.2.2 Defining interactions; surface-tosurface contact 4.2.3 Definition of the host, embedded elements, and constraints 4.2.4 FE models with a foundation; load application at a test center 4.2.5 Structural behavior of laminated metal plates 4.2.6 FE models without foundations 4.2.7 Strain evolution of L-type columns (monolithic and mechanical joints with no axial force) with/without foundation 4.2.8 Conclusions 4.3 Design verification of the beam-column frames 4.3.1 Nonlinear numerical model 4.3.2 Design verification 4.3.3 Conclusion

4.4 Test erection 4.4.1 Erection of irregular L-shaped frames 4.4.2 Conclusion References

179 179

179 180 183 193 195 195 196 198 198 203 206

206 209 214 214 219 226

5. Novel erection of the precast frames using interlocking mechanical couplers 5.1 Significance of the precast erection using interlocking mechanical joints 5.2 Assembly of the full-scale precast frame by interlocking couplers 5.2.1 Column-to-column connections 5.2.2 Girder-to-column connections and the test erection 5.3 Numerical investigation 5.3.1 Description of the mechanical connections for design verification 5.3.2 Finite element model of the proposed joint 5.3.3 Verification of the numerical analysis 5.3.4 Flexural capacity of the connection 5.3.5 Conclusions References

249 249 249 256 264

264 268 268 271 274 274

6. Novel precast frame for facile construction of low-rise buildings using mechanically assembled joint to replace conventional monolithic concrete frame 6.1 Introduction 6.1.1 Advantages and challenges 6.1.2 Methodology of joint details for lowrise frames; connections for columnto-column, column-to-girder, and girder-to-beam 6.2 Design of the building with the mechanical joints 6.2.1 Design load combination and conventional design detail 6.2.2 Design of mechanically layered plates based on nonlinear finite element analysis 6.2.3 Numerical model and nonlinear finite element analysis parameters 6.2.4 Design of connection plates 6.2.5 Implementation of the extended endplates in girder-to-beam 6.2.6 Implementation of the extended endplates in column-to-girder connections

275 275

275 277 277

278 280 280 286

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Contents vii

6.3 Design verification 6.3.1 Rates of strain increase and strain activation of the structural components at connection 6.3.2 Construction quantities 6.3.3 Reduction of construction period by mechanical connection 6.3.4 Reduction of energy consumption and CO2 emissions with the new precast frame 6.4 Results and conclusions References

292

292 297 297

298 299 300

7. Novel pipe rack frames with rigid joints 7.1 Overview of the pipe rack frames introduced in this chapter 7.1.1 The innovated pipe rack frames 7.1.2 Overall historical development, advantages and challenges of existing pipe rack frames 7.1.3 Significance of the pipe rack frames with rigid joints; motivations and objectives 7.2 Novel pipe rack frames with rigid joints 7.2.1 Precast concrete-based pipe rack frames with rigid monolithic beamcolumn connections 7.2.2 Precast concrete-based pipe rack frames with rigid mechanical joints 7.2.3 Pipe-racks with prestressed frames 7.2.4 Rigid steel frames 7.3 Case study 7.3.1 Steel-concrete hybrid composite precast frames with moment connections 7.3.2 Dynamic characteristics 7.3.3 Suggestion for rapid construction based on the fast track using the proposed frames 7.3.4 Structural savings 7.3.5 Offsite modular construction with base template 7.4 Conclusions References

301 301

331 332

334 334 336

338

338 340 340 345 345

301

302 304

304 304 314 314 314

314 321

321 321 328 329 329

8. Application to the modular construction 8.1 Overview of the modular construction for low-rise buildings 8.2 Conventional modular construction 8.2.1 Structural and connection systems 8.2.2 Cellular-type modules and intramodule connection

8.2.3 Inter-module connection 8.2.4 Application of the modular construction to high-rise buildings 8.3 Implementation of the mechanical joints in precast connections for modular construction 8.3.1 High-rise building application 8.3.2 Application to special structures 8.4 Lateral stability of the hybrid composite precast frames with rigid mechanical joints 8.4.1 Seismic responses and fundamental period of the modular building 8.4.2 Modular steel building with braced frames 8.4.3 Precast concrete-based frames having mechanical joints 8.5 Conclusions References

331 331 331 331

9. Precast steel-concrete hybrid composite structural frames with monolithic joints 9.1 Why the precast steel-concrete hybrid composite with monolithic joints? 9.2 Structural behavior of the hybrid composite beams with monolithic joints 9.2.1 Wide steel flanges encased in concrete; the interaction between steel and concrete 9.2.2 T-shaped steel section encased in concrete 9.2.3 Seismic capacity of the hybrid precast beams 9.2.4 Prestressed precast beam monolithically integrated with columns 9.2.5 Discussions and conclusions 9.3 Analytical prediction of the nonlinear structural behavior of the steel-concrete hybrid composite structures 9.3.1 Conventional strain compatibility approach 9.3.2 Steel-concrete hybrid composite beams without axial loads 9.4 Assembly of the steel beam-column joints with a skewed beam section 9.4.1 Conventional steel erection 9.4.2 New erection method; splicing plates and bolting beyond critical path 9.4.3 Precast column spliced by the rebars extended in holes

348 352

352 355 373

376 377

382 382 383 402 402

402 409

viii

Contents

9.5 Application of the hybrid composite precast frames with the beam depth reduction capability to high-rise buildings 9.5.1 Application to a 19-story building 9.5.2 Erection and assembly of the hybrid composite beams 9.5.3 Descriptions of the selected buildings 9.6 Contributions References

411 411 416 419 419 426

10. Artificial-intelligence-based design of the ductile precast concrete beams 10.1 Concept and structure of the artificial neural networks 10.1.1 Analogy with the biological neuron model 10.1.2 ANNs for structural engineering 10.2 Multilayer perception 10.2.1 Weights and bias 10.2.2 Backpropagation by adjusting weights

427 427 427 427 427 428

10.2.3 Activation functions related to the structural-engineering applications 10.2.4 Initialization 10.2.5 Data normalization 10.2.6 Three ways to train ANNs in Matlab 10.3 Artificial neural network-based design of the ductile precast concrete beams 10.3.1 Generation of the big structural data; a ductile design of the doubly reinforced precast concrete beams 10.3.2 Supervised training 10.3.3 Test networks and the design results 10.3.4 Conclusions References

Index

430 433 433 433

436

436 439 441 478 478

479

Preface The term precast concrete structure refers to an assemblage of the prefabricated members that, when jointed together, form three-dimensional frameworks for the structures that are able to resist gravity, wind, and seismic loads. In recognition of the fact that quite a few traditional precast frames require cast-in-place joints, this book has been designed to disseminate and elucidate how the joints of the precast frames can be simplified for a fast and facile joint assembly using the traditional steel used in the industry over the decades. The most important factor affecting recent trends in the area of the precast concrete structures has been a rapid and facile erection. A great deal of the research has been performed to upgrade the application of the precast concrete members, including studies carried out to facilitate the erection and installation process of the precast frames. This book provides various test erections and construction applications utilizing hybrid precast frames demonstrating a rapid and effortless assembly capability. The erection efficiency of the proposed dry joints for both steel-concrete composite precast and reinforced concrete precast frames is also elucidated. This book is dedicated to providing researchers and engineers with practical guidelines for the design of precast structures. The technological approach appeared in this book is committed to bridge gaps and break down barriers for the planning, designing, and building of sustaining and resilient infrastructures in the time of the climate changes for the academics, engineers, architects, contractors and city officials, who face the climate change issues. The author welcomes the further rectification of the hybrid precast technology proposed in this book. Chapter 1 introduces some precast practices found in the recent construction industry. The traditional precast joints including column-to-column/beam-to-column connections and their designs are briefly reviewed, even if much of the conventional precast construction with design methods are available in the literature. At the end of Chapter 1, how the conventional precast joints can be improved is suggested by utilizing the hybrid steel-concrete composite precast frames which can be implemented in dry mechanical joints having bolted laminated plates to reduce the erection times and frame weight. Chapter 2 presents both extensive experimental and numerical investigations of the novel hybrid precast systems utilizing beam-to-column and beam-to-beam connections that have been used for the steel frames. When the mechanical joints are implemented in both steel-concrete composite precast frames and reinforced concrete precast frames, the reduction of the construction period, cost efficiency, and fast erection of frames can be offered, on the top of the many advantages provided by the conventional precast frames, which have been widely adopted for many years. In this chapter, the structural stability of the proposed dry connections using laminated metal and concrete plates is verified with numerous experimental investigations. The nonlinear finite element analysis-based numerical investigations considering the concrete damaged plasticity are also successfully verified by the experimental data. At the end of this chapter, readers will appreciate how the construction methods implemented in steel frames can also be implemented in the hybrid precast steel-concrete or concrete frames, providing an innovative precast frame assembly, and removing drawbacks of the conventional precast methods. Chapter 3 introduces a nonlinear finite element analysis, which can serve as a useful guide to the numerical investigation of the novel precast frames showing complex joint behavior. Concrete and metals exhibit efficiently hybrid structural performances, whereas an understanding of the structural evolution via microscopic strains will not be possible without extensive and accurate numerical analysis tools. The hybrid composite precast frames are numerically modeled based on the calibrated parameters considering the damaged concrete plasticity to investigate the microscopic strains of the mechanical joints. Extensive experiments are also conducted to explore the structural evolution of the mechanical joints integrated with concrete, verifying the contribution of the mechanical joints to the flexural capacity of the hybrid precast frames. This chapter can be read separately from the other chapters on the first reading. Readers may choose to read this chapter when they are ready to delve into the numerical behavior of the proposed hybrid precast systems. Chapter 4 develops the L-shaped precast columns implementing the hybrid mechanical joints having laminated metal plates. The L-shaped columns are preferred by architects because of their architectural flexibility, fitting inside at the corners, replacing walls or rectangular columns in residential buildings. The performance of the L-type precast frames is explored experimentally and numerically, identifying structural elements that contributed to the flexural capacity.

ix

x Preface

The test erection of the irregular frames using hybrid mechanical joints is also presented by the online video abstract which shows the fast and easy assembly capabilities. In Chapter 5, one of the novel features of the precast frames is described with a full-scale erection test, utilizing interlocking couplers for the connections of the rectangular precast columns. Efficient and effortless assembly capabilities of the precast frames along with the corresponding cost are shown with the substantially reduced construction time compared with a conventional monolithic construction. This chapter also shows that stresses and strains numerically calculated based on the nonlinear FEA demonstrated the sufficient ductility and resistance against the loads for the precast frames assembled by interlocking couplers. Chapter 6 presents a design of a low-rise building using mechanically assembled joints to replace the conventional monolithic concrete frames. Well-designed novel and innovative precast joints with the laminated plates demonstrate the structural performance close to that of the monolithic joints, which can be applicable to column-to-column, column-to-girder, and girder-to-beam connections of the four-story building. This topic is of high scientific interest since interacting elements defining complex contact interfaces are developed, being recognized as a reference for the numerical analysis preventing penetrations at interfaces. Chapter 7 applies the mechanical connections with rigid joints to pipe rack frames, which are the well-known prefabricated open-frame steel structures with braces that are adopted for the modular construction of the industrial plants. The prestressed precast concrete frames with the detachable laminated joint plates contribute to both flexural strength and fireproofing, replacing the conventional steel pipe rack frames with braces. The advantages leading to multiple merits including the reduction of the construction quantities, and corresponding schedule, are verified. Chapter 8 disseminates the application of the proposed hybrid composite frames with the dry joints to high-rise modular constructions. The cast-in-place shear walls are used to resist lateral loads for the conventional modular constructions of the high-rise buildings. In this chapter, the upper modules can be stacked on the top of preinstalled modules via the bolted laminated plates introduced in Chapters 2 and 3, or one-touch interlocking couples shown in Chapter 5. The adequate connections between the modules for the high-rise stacks are provided not only to ease the erection process but also to create a moment connection between upper and lower columns. Chapter 9 is devoted to the fast erection of steel-concrete composite frames with rigid connections similar to that of the erection of steel frames, offering a rapid construction that is simple and straight-forward. However, the steel structures suffer from high cost and lower fire resistance than concrete. The advantages of the proposed hybrid modular construction demonstrate an erection speed with the assembly safety similar to those obtained by the steel frame, but with the lower construction costs as proved through the test erection. This chapter also introduces many construction applications of the high-rise buildings using hybrid composite beams with reduced beam depths. The interactive use of the steel members encased in the precast concrete reduces the weight of the precast frames when they are lifted and assembled. The precast steel-concrete composite frames are preferable over the conventional precast concrete practices since they are less heavy while achieving cost-efficient structural systems. An analytical model of the concrete confined by both transverse rebars and wide-flange steels section encased in the concrete was explored based on an iterated strain compatibility, and validated by an extensive nonlinear finite element analysis considering the concrete damaged plasticity. Chapter 10 presents the artificial neural network based-design of ductile precast concrete beams. The brief concepts of the neural networks are introduced, followed by the artificial neural networks for the structural engineering application, by which the real-world design of doubly reinforced precast concrete beams is conducted. This chapter shows how to quickly develop versatile AI-based neural networks for engineers who are not familiar with the neural networks. The readers will learn to formulate the artificial neural networks of their structures as fast as possible and to solve their engineering problems. The author would like to thank for their support of the Technology Transfer Center for a National R&D Program (TTC) grant funded by the Korean government (MSIP) (No. 2014K000239). He also appreciates the support by the Ministry of Land, Infrastructure, and Transport (MOLIT) of the Korean government and the Korea Agency for Infrastructure Technology Advancement (KAIA) (No. 14AUDP-B068892-02). The support by the Business for Cooperative R&D between Industry, Academy, and Research Institute funded by the Korea Small and Medium Business Administration in 2016 (Grant No. C0398455) is also gratefully acknowledged. The Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1A02937558) helped the author during the preparation of the book. The contribution of a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(No. 2019R1A2C2004965) is also appreciated by the author. The author would like to appreciate his students for preparing the illustrations at various stages. Some of them were J.D. Nzabonimpa, Nguyen Dinh Han, and Jisoon Kim, who are greatly appreciated for their contribution to the birth of this book. Finally, the author could not have published this book without the unflagging spiritual support of his wife Debbie and his son David. His parents and parents-in-law also have been with him during the tough time of the preparation of this book.

Chapter 1

Conventional precast assembly 1.1 Review of conventional precast concrete structures 1.1.1 Why precast concrete? A precast concrete structure is defined as an assemblage of prefabricated members, which, when connected together, form a three-dimensional framework for the structures including office buildings, parking lots, and schools that is able to resist gravity, wind, and seismic loads. The conventional precast frames consisted of prefabricated beams and columns that were manufactured in a plant. Good quality of mix, placement, and curing were ensured in a well-controlled casting environment when these members were manufactured, followed by the onsite assemblage to form a structural frame. For the past years, the construction industry extensively adopted the use of precast members over the conventional cast-in-place methods. This was because the precast concrete members offered many advantages, including the reduction of the construction period, cost efficiency, high-quality control, fast and accurate erection of members, and environmental protection. Precast members minimized onsite construction time while maintaining a high quality of the construction work. A great deal of the research has been performed to upgrade the application of the precast concrete members, including the studies that were carried out to investigate the erection and installation process of the precast frames. A study conducted by Proverbs et al. [1] suggested that the lifting and installation of precast frames have a significant impact on the construction period. The advantages of the precast concrete frames can be summarized as follows.

1.1.2 Quality control and facile installation With the offsite production giving better control of the manufacturing plant, the precast members are poured and cured in a well-controlled environment, being delivered to the job site. The erection of the precast members can offer a high-quality product with less onsite labor, and it has less impact on the construction site. The fabrication of the precast members does not heavily depend on the weather, eliminating weather delays, whereas the conventional, cast-in-place fabrications do. However, the erection of the precast members highly depends on the type of connections of the precast frames. The precast joints should be designed based on the consideration of effortless and rapid erection. Even if the precast concrete members demonstrate the rapid erection capability, the ductility and the stability highly depends on the types of the joints of the precast frames. Precast concrete members feature fireproof attributes. During a fire, the precast concrete members do not become so hot, and they do not light other materials—not catching fire while blocking the fast spreading of the fire. The modern construction industry prefers precast concrete members as great material for residential buildings due to these features.

1.2 Conventional precast connection 1.2.1 Column-to-column connection 1.2.1.1 Cast-in-place connections for column-to-column joint with pour forms One of the most traditional types of the column-to-column joint for precast frames is cast-in-place concretes with pour forms to form a moment connection, as shown in Fig. 1.2.1A [2]. Attention should be paid to the safety of the vertical joints, ensuring that the vertical rebars of the joints support the full construction load during the frame erection. Bumping precast members should also be avoided. The joint concrete must be cured with braces (refer to Fig. 1.2.1A-(1)) which support precast columns and beams before the further erection of the precast frames proceeds. Guan et al. [3] presented a beam-to-column moment connection for the precast concrete frames. They tested five specimens including one monolithic specimen under cyclic loads, and their findings indicated that the proposed moment connections (refer to Fig. 1.2.1A-(2)) were suitable for seismic regions because of their seismic resistance in terms of strength, ductility, and high energy dissipation capability. Parastesh et al. [4] Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00001-7 © 2020 Elsevier Ltd. All rights reserved.

1

2 Hybrid composite precast systems

FIG. 1.2.1, Cont’d

also performed an experimental investigation of the new ductile moment-resisting connection for the precast concrete frames in seismic regions requiring casting concrete at the joints, shown in Fig. 1.2.1A-(3).

1.2.1.2 Precast assembly using grouted splice sleeve connectors Having to use the pour forms—inevitable for the conventional, cast-in-place monolithic concrete frames—could delay the construction period. Proverbs et al. [1] suggested the overall delay of the construction period can be enhanced significantly by improving the lifting and installation processes of precast members. Many studies were conducted to ameliorate the application of precast members. Conventionally, sleeve connections were commonly used for precast columns. Elliot [5] detailed a wide range of joint types that were proposed to connect prefabricated concrete components. The joint design for

Conventional precast assembly Chapter

1

3

FIG. 1.2.1, Cont’d

precast members should comply with applicable building codes, and their structural safety should always be ensured. Connections were classified as pin, semi-rigid, and rigid categories, depending on their structural performance under various types of loadings. Elliot introduced the moment connections for precast concrete columns, as indicated in Fig. 1.2.1B-(1). Fig. 1.2.1B-(2) [6] shows a splice sleeve into which reinforcing bars are inserted, meeting approximately at the center of the sleeve. The precast columns were spliced by inserting the protruding bars halfway into the sleeves of the upper columns from the end of lower precast columns. Reinforcing bars spliced by a mechanical steel sleeve coupler with cylindrical shape

4 Hybrid composite precast systems

FIG. 1.2.1, Cont’d

provided full tension and compression between precast column connections. Fig. 1.2.1B-(2) to (4) illustrate the conventional sleeves that were embedded in the base of the upper precast columns at the precast plant. Tullini and Minghini [7] experimentally investigated column connections with grouted sleeve joints splicing precast concrete columns, shown in Fig. 1.2.1B-(4). Pipe splice sleeves for the use in precast beam-column connections and precast beams having splice sleeves for column rebars are found in Refs. [8] and [9], respectively. The sleeve connectors require the

Conventional precast assembly Chapter

1

5

FIG. 1.2.1, Cont’d

casting of either a nonshrinking high strength mortar or a high strength concrete around the longitudinal reinforcing bars. Enough bond must be provided between reinforcing bars for full anchorage bond length, resulting in the continuity of the longitudinal reinforcements of the columns. The reinforcing bars became continuous through the connection when the grouted nonshrinking high early strength mortar was cured, allowing further erection of the precast columns. However, some extended construction time should be allowed since each subsequent column is to be erected only after the joint concrete for the previous columns has been cured. In the traditional precast methods, the precast components may need temporary braces to support construction loads when the joint concrete was not cured, as shown in Fig. 1.2.1A-(1) [1], in which the braces are used to support the precast frames before the joint concrete was erected and cured. Rebars can be spliced directly by sleeves or dowel pin, as shown in Fig. 1.2.1C [10], where threaded rods were inserted into the sleeves embedded

6 Hybrid composite precast systems

FIG. 1.2.1 Typical precast column joints.

in the upper column. The clearance should be provided for the construction tolerances. Threaded rods and clearance were also grouted by nonshrinking high strength mortar.

1.2.1.3 Joints using shim bearing, dowel pin, welding Fig. 1.2.1D [10] shows column connections using plastic shims to accommodate construction tolerances. The clearance should be grouted by nonshrinking high strength mortar. Continuity was made by welding projecting rebars, as shown in Fig. 1.2.1E [5]. These connections were used to minimize the joint length in heavily reinforced areas, offering immediate structural strength for the connection. Welding quality should be well maintained to provide the moment connections between columns.

1.2.1.4 Stacked connections Stubbe’s precast [11] introduced splicing plates, as shown in Fig. 1.2.1F, which can also be implemented to splice precast columns. The plates installed to the upper column and dowel bars to attached the plates were anchored in the recess areas by threaded rods preinstalled in the lower columns. However, the vertical rebars must be anchored to the metal plates to transfer loads, whereas those rebars were not shown in detail (Fig. 1.2.1F). This connection type was interesting because the pour form at the column joints can be minimized.

Conventional precast assembly Chapter

1

7

1.2.1.5 Bolted column connections for fast and safe erection In Fig. 1.2.2, the precast column components are connected by bolts with endplates, contributing to easy, rapid, and safe column connections. The column connection shown in Fig. 1.2.2 should use the column plates with sufficient stiffness and strength. The axial loads and the moment must be transferred at the joints between the columns for moment connections, either partially or fully restrained. The structural behavior similar to those of rigid monolithic column joints would not be possible when the laminated mechanical joints fail to transfer the moment with considerable plate deformations. Chapters 2 and 3 provided the design examples appropriate for the use in the bolted column connections. The tolerances by the dimensional variations and variations in elevation should be compensated. In this type of connection, the bolted plates were assembled rapidly on-site and no temporary bracing was needed because the moment connection was made instantaneously.

1.2.1.6 Colum-to-foundation joints using sleeve Base plates, shown in Fig. 1.2.3, were traditionally used to connect for the column-to-foundation. In Ref. [12], reinforcing bars projecting from the end of the column passed into the sleeves preinstalled in a foundation block that were subsequently filled with grout. Columns were then placed into position.

FIG. 1.2.2 Column-to-column connections using bolted plate.

8 Hybrid composite precast systems

FIG. 1.2.3 Connections for column-to-foundation; typical column base plate.

1.2.2 Beam-to-column connection 1.2.2.1 Concrete cast at beam-to-column joint; moment connection In Fig. 1.2.1A-(3), Parastesh et al. [4] introduced a typical but novel ductile moment-resisting connection for the precast concrete frames in seismic regions without using column sleeves. This method created moment-resisting beam-to-column joints while reducing the use of pour form at joints. The longitudinal beam reinforcing bars were spliced at the joint before concrete was cast. Despite the cost of moment connections, these connections demonstrated the capability of reducing the depth of flexural members, improving the resistance to the progressive collapse of the precast members. The depth reduction enhanced the economy and the aesthetics of concrete structures. Some of the previous studies also attempted to develop moment connections for the precast concrete frames. In Fig. 1.2.1A-(2), Guan et al. [3] used column sleeves with the U-shaped precast beams for the beam-to-column moment connection, eliminating drawbacks similar to ones demonstrated by Fig. 1.2.4, where the pour forms at the beam-to-column joints were installed to form moment connections. Installing these pour forms was not easy due to the height, and entire works should be cautiously managed. Temporary supports were also required when concrete was cast and cured. Conventionally, the cast-in-place construction methods have been widely used for the precast beam-to-column connections over the past years. The concrete curing required a certain time for the concrete to reach the desired strength and durability. However, the conventional cast-in-place method was not attractive for some engineers since it may lengthen the construction period.

1.2.2.2 Beam seated on corbels or steel inserts (haunches); pinned connections Pinned connections were developed to reduce the cost of the joint for the precast concrete structures. These connections were formed to transfer shear forces at the joints. Elliot [5] outlined the geometric configuration of the conventional

FIG. 1.2.4 Pour forms for beam-to-column joints.

Conventional precast assembly Chapter

1

9

beam-to-column moment connections. Precast beams were placed on the top of the concrete corbel, as depicted in Fig. 1.2.5A, indicating that no connections such as metal angles were established between beams and columns. The beam sizes tended to be large because beams on corbels were simply supported. The fabricating corbels on the corner columns can be also complex [11]. In Fig. 1.2.5B [5], precast beams are installed on the corbels or the steel inserts (haunches). A bearing pad was necessary to distribute the weight over the bearing length (refer to Section 6.10 of PCI handbook, [13]). Bearing and shear joint using the metal angles on a bearing corbel is shown in Fig. 1.2.5C-(1) [5, 6, 13] (Section 6.10 of the PCI handbook) where the moment and shear were transferred through angles and bearings. In Fig. 1.2.5C-(2) [11], metal angles were not installed whereas vertical dowels (stainless steel pins) are fixed through the precast girders and column corbels (or walls) to prevent the slippage of the girders from the corbels, ensuring the stability of the joint; however, this joint detail did not offer the moment connections at the joints [11]. Fig. 1.2.5D shows slabs with a double tee, placed on the groove of the girders with pinned end conditions, demonstrating the precast frame system (refer to Fig. 1.2.5E) which is vulnerable against lateral loads including seismic impacts. In Fig. 1.2.5F, engineers had to add cast-in-place shear walls, providing a lateral resisting structural system for the precast frames. The steel props were also required to stabilize core shear walls when the floor height was more than 10 m. The extension of the construction schedule was necessary as the extensive shear walls were entirely cast on site. Some merits obtained by using the precast method were compensated by the construction of the extra lateral system, diminishing justification of using precast frames.

FIG. 1.2.5, Cont’d

10

Hybrid composite precast systems

FIG. 1.2.5, Cont’d

1.2.2.3 Beam-to-column connections via hardware One of the most common practices for the precast method is to utilize the hardware including bolts, clip angles, and plates with slots or oversized holes for the connections. Readers are recommended to refer to Architectural Precast Connection Guide (Architectural precast concrete all panels) published by NPCA [10]. In this manual, an assemblage of metal components with anchors was used to erect the precast frames. The construction tolerances were accommodated by sealant, which was used to fill in the joints around each of the precast panels. The panelized frames and the connection details commonly used with an architectural precast concrete was also presented in this manual. Chapter 6 of the PCI design handbook [13] also presented the practical design examples of the connections where the detailing taking into account of allowable tolerances was provided for a good fit between selected materials, avoiding an interference between strands or reinforcing steels and connection components. The diverse use of the hardware, including hanger connections and

FIG. 1.2.5 Beams installed on the prepared corbels or steel inserts (haunches).

12

Hybrid composite precast systems

embedded plates, was demonstrated as efficient connections of the precast components. Readers are referred to another beam-to-column joint, shown in Fig. 6.12.1 of the PCI handbook [13], which shows the moment connection of the precast frames using embedded plates. Metelli and Riva [14] proposed a dry moment connection between beam and columns. The connection was introduced to provide the seismic resistance of the prefabricated reinforced concrete frames. The negative moment was resisted by the upper high-strength steel bars while the shear strength resistance of the connection was controlled by the fiber-reinforced grout at the interface of beam and column units. The other role of the grout at the joint was to accommodate the construction tolerances. The interface and the erection tolerances, including minimum clearance between the precast concrete components and the structure, must be secured.

1.3

Suggestion for the improvement of the precast joints

1.3.1 Use of the cast-in-place concrete Despite the aforementioned advantages of the precast concrete members, the conventional precast members show drawbacks in the following aspects: (i) the use of the concrete pour forms at the joints delaying the erection of each subsequent frame and (ii) the lack of the structural continuity and redundancy in the load paths when beams are simply connected on the corbels without offering moment resisting capacity. Many studies report that the structural performance of the precast concrete structures depended on the stiffness of the connections. The geometric configuration of the connection affects a wide range of parameters, including stability, ductility, flexibility, constructability, and energy dissipation. The issues existing in the joints of the conventional precast concrete frames are discussed below.

1.3.1.1 Construction waste and concrete pour forms at joints The splice of the reinforcing rebars conventionally used in the construction of the traditional precast frames is depicted in Fig. 1.2.1A, where the various joint types for beam-to-column and column-to-column connections are illustrated. The use of the concrete pour forms to cast the concrete at the joints is commonly used in the construction of the precast concrete members, lengthening the construction period, and requiring the temporary braces to support the precast components, as shown in Fig. 1.2.1A-(1), before the joint concrete was cured. The overall construction quality should be carefully managed, and the ongoing erection process must not be hindered. The use of concrete pour forms, and temporarily braces were sought to be replaced for a fast erection process similar to that of the erection of steel frames.

1.3.1.2 Weakness of the precast connections Extensive numbers of the numerical and experimental studies were conducted to ameliorate the application of precast concrete members. Elsanadedy et al. [15] investigated the progressive collapse of the precast reinforced concrete frames. In their work, three specimens were loaded to failure to assess the failure modes of the connections, and the strength and ductility of the tested connections were explored when exposed to seismic loadings. They found that the ultimate load and dissipated energy of the monolithic specimen were significantly larger than those of the precast specimens. It was reported that the tested specimens experienced sudden failures, and they were vulnerable to the progressive collapse when the column was exposed to an extreme event. Elsanadedy et al. [15] concluded that the tested precast connections should be reinforced by adding steel angles, steel plates and metal studs to connect beam ends with the column and corbel. Besides, they recommended adding a nonshrinking mortar to fill up the gap between beams and columns. Previous studies [16–22] investigated the progressive collapse of the precast reinforced concrete structures under various conditions. A recent study conducted by Clementi et al. [23] verified the seismic performance of the prefabricated reinforced concrete buildings constructed with dowel pin connections. In their study, the joint behavior was extensively examined, and, some recommendations for upgrading the existing joint for the precast members were presented. Fig. 1.3.1A [24, 25] elucidates one of the examples of the collapse of the precast concrete structures caused by the lack of the proper connections, failing to transfer moments throughout the joints between members, which were designed as either pin or semi-rigid connections. The design of the joint connections for some precast members remained questionable. Collapse due to collision with a crane is also illustrated in Fig. 1.3.1B.

1.3.2 Why steel-concrete hybrid composite precast frames? Use of steel-concrete hybrid precast frames with reduced frame weight implementing dry mechanical joints having bolted laminated plates The traditional cast-in-place concrete for the erecting frames demanded ever more significant labor on the construction site (refer to Fig. 1.3.2, and Fig. 9.1.1 of Chapter 9). The weight of the precast concrete members can be significantly heavier for structures designed to carry heavy loads. The heavyweight of the precast members that must be lifted offsets a great deal of

Conventional precast assembly Chapter

1

13

FIG. 1.3.1 Structural failure of precast structures.

FIG. 1.3.2 Traditional column-tocolumn and beam-to-column connections requiring extensive pour forms and supports for conventional concrete frames.

the merits that were secured with the precast technology. The lifting and installation processes of the heavy precast members have a great impact on the construction period and cost. This has been one of the issues involved with the drawbacks of the present precast constructions related to the operation of the cranes. However, the interactive use of the steel members with the precast concrete can reduce the weight of the frames that were lifted and assembled. The precast steel-concrete hybrid composite frames are preferable over the conventional precast concrete practices since they are less heavy, achieving cost-efficient structural systems. The conventional steel connections can also be used for the precast column-to-beam joints, offering a rapid and facile erection similar to that of the steel frames with few crews on site. The additional expense of fireproofing was not required since the steel section was encased in structural concrete. The rapid erection for the column-to-column and beam-to-column joints, minimizing crane time, and enhancing safety can

14

Hybrid composite precast systems

be sought with the mechanical connections proposed in Chapters 2 and 3. The advantages similar to those found in the steel structures can be obtained in on-site construction, which is more effective than that provided by the conventional precast construction. The erection test of these hybrid technologies was performed and described in the following chapters, including Chapter 4. In Chapters 2 and 3, the precast-based mechanical joints, having versatile laminated steel plates interconnected by bolts (which were traditionally used for the assembly of the steel frames, refer to AISC 358 [26]), are implemented for both the assembly of reinforced concrete precast frames and the steel-concrete hybrid composite precast frames. Tension and compression force couples are transferred at the joints, providing moment connections.

References [1] D.G. Proverbs, G.D. Holt, P.O. Olomolaiye, Factors impacting construction project duration: a comparison between France, Germany and the UK, Build. Environ. 34 (2) (1998) 197–204. [2] J.D. Nzabonimpa, W.K. Hong, J. Kim, Mechanical connections of the precast concrete columns with detachable metal plates, Struct. Des. Tall. Spec. Build. (2017). [3] D. Guan, Z. Guo, Q. Xiao, Y. Zheng, Experimental study of a new beam-to-column connection for precast concrete frames under reversal cyclic loading, Adv. Struct. Eng. 19 (3) (2016) 529–545. [4] H. Parastesh, I. Hajirasouliha, R. Ramezani, A new ductile moment-resisting connection for precast concrete frames in seismic regions: an experimental investigation, Eng. Struct. 70 (2014) 144–157. [5] K.S. Elliott, Precast Concrete Structures, Butterworth-Heinemnn, 2016 (An imprint of Elsevier Science). [6] R.E. Englekirk, Seismic design of reinforced and precast concrete buildings, John Wiley & Sons, 2003. [7] N. Tullini, F. Minghini, Grouted sleeve connections used in precast reinforced concrete construction—experimental investigation of a column-tocolumn joint, Eng. Struct. 127 (2016) 784–803. [8] Y.M. Kim, A Study of Pipe Splice Sleeves for Use in Precast Beam-Column Connections, Master’s Thesis, University of Texas at Austin, 2000. [9] Splice Sleeve North America, Inc. https://www.youtube.com/channel/UC5ExN7iRN3L3PStib-rM3eA. [10] Architectural Precast Connection Guide (Architectural Precast Concrete all Panels) Published by NPCA. [11] https://www.stubbes.org/file_uploads/Columns_Beams.pdf. [12] N. Buratti, L. Bacci, C. Mazzotti, Seismic behaviour of grouted sleeve connections between foundations and precast columns, in: 15th World Conference of Earthquake Engineering (WCEE), Lisbon, Portugal, September, 2012, pp. 24–28. [13] PCI design handbook, 7th, PCI. [14] G. Metelli, P. Riva, Behaviour of a beam to column “dry” joint for precast Concrete elements, in: The 14th World Conference on Earthquake Engineering, October, 2008, pp. 12–17. [15] H.M. Elsanadedy, T.H. Almusallam, Y.A. Al-Salloum, H. Abbas, Investigation of precast RC beam-column assemblies under column-loss scenario, Constr. Build. Mater. 142 (2017) 552–571. [16] Y. Bao, S.K. Kunnath, S. El-Tawil, H.S. Lew, Macromodel-based simulation of progressive collapse: RC frame structures, J. Struct. Eng. 134 (7) (2008) 1079–1091. [17] M. Sasani, M. Bazan, S. Sagiroglu, Experimental and analytical progressive collapse evaluation of actual reinforced concrete structure, ACI Struct. J. 104 (6) (2007) 731. [18] J. Yu, K.H. Tan, Experimental and numerical investigation on progressive collapse resistance of reinforced concrete beam column sub-assemblages, Eng. Struct. 55 (2013) 90–106. [19] M. Li, M. Sasani, Integrity and progressive collapse resistance of RC structures with ordinary and special moment frames, Eng. Struct. 95 (2015) 71–79. [20] T. Wang, Q. Chen, H. Zhao, L. Zhang, Experimental study on progressive collapse performance of frame with specially shaped columns subjected to middle column removal, Shock Vibrat. (2015) 2016. [21] R.B. Nimse, D.D. Joshi, P.V. Patel, Behavior of wet precast beam column connections under progressive collapse scenario: an experimental study, Int. J. Adv. Struct. Eng. (IJASE) 6 (4) (2014) 149–159. [22] S.B. Kang, K.H. Tan, Behaviour of precast concrete beam–column sub-assemblages subject to column removal, Eng. Struct. 93 (2015) 85–96. [23] F. Clementi, A. Scalbi, S. Lenci, Seismic performance of precast reinforced concrete buildings with dowel pin connections, J. Build. Eng. 7 (2016) 224–238. [24] B. Zoubek, T. Isakovic, Y. Fahjan, et al., Cyclic failure analysis of the beam-to-column dowel connections in precast industrial buildings, Eng. Struct. 52 (12) (2013) 179–191. [25] M.H. Arslan, H.H. Korkmaz, F.G. Gulay, Damage and failure pattern of prefabricated structures after major earthquakes in Turkey and shortfalls of the Turkish Earthquake code, Eng. Fail. Anal. 13 (4) (2006) 537–557. [26] AISC 358, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications, AMERICAN INSTITUTE OF STEEL CONSTRUCTION, 2016.

Chapter 2

Experimental investigation of the precast concrete and the precast steel-concrete hybrid composite frames having novel mechanical joints 2.1 Conventional bolted endplates used for steel frames The endplates connection is a popular beam-to-column and beam-to-beam connection that has been in use since the mid1950s for steel frames. The bolted extended endplates used for the conventional steel moment joint are depicted in [1]. Fig. 2.1.1 shows the mechanical moment connections for the joints of the steel frames described by AISC 358 [1], which were modified and implemented in both steel-concrete composite precast frames and reinforced concrete precast frames. Conventional connections for the steel frames commonly used the bolted endplates with either endplates or cover plates to transfer both axial forces and moments exerted on the two parts of steel column components. These connections designed to act as rigid connections transfer loads either via the direct bearing through the endplates or by the tension and compression in the cover plates. In most situations, bolts were subjected to both shear and tension. Steel-frame structures can utilize bolted extended endplates with pinned, semirigid or fully rigid connections. The rigidity of the bolted end connections depended on many parameters including plate thickness, bolt diameter, and bolt positioning with grade and size. The behavior of the extended endplates connections for the steel frames subjected to monotonic and cyclic seismic loads has been extensively explored over the past decades. Despite wide applications to the steel frames, the applications of the extended endplates to precast concrete-based frames including steel-concrete composite precast or reinforced concrete precast members are largely absent from the industry. The following sections are devoted to understanding of the behavior of the bolted connections implemented in the precast concrete-based frames, capable of transferring loads at the frame joints [2–7]. The structural behaviors of the joint components with laminated plates including load capacities and failure modes were identified by the experimental and numerical investigations [2,3].

FIG. 2.1.1 Mechanical concrete joint: installation test of the full-scale steel-concrete composite precast column-beam connection using a laminated metal plate (see Chapter 4).

Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00002-9 © 2020 Elsevier Ltd. All rights reserved.

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2.2

Hybrid composite precast systems

Description of the mechanical joints

2.2.1 Joint connection from an erection point of view The mechanical joint with endplates and metal filler plates illustrated in Fig. 2.2.1A, which is capable of transferring moment at the joints between the lower and upper column plates, was implemented in the precast frames. Two endplates (lower and upper column plates) were interconnected by high-strength bolts. The threaded end of the vertical reinforcing bars was anchored to the endplates, as illustrated in Fig. 2.2.1B and C. In Fig. 2.2.1D, a rapid assemblage similar to that of the steel frames is exhibited by a full-scale installation test of the precast columns. The readers are referred to Section 2.7.4 of this chapter for the test erection using the mechanical joints for the typical precast steel-concrete composite frames.

2.2.2 Column-to-column joint for the moment connections The geometric configurations of the typical column-to-column connections for the steel-concrete composite precast and concrete precast frames are illustrated in Fig. 2.2.2. The laminated column plates are designed to transfer both tension and compression forces at the joints. Rebars of the tension side of the plates exert tensile forces on the column plates, and subsequently, these metal plates transfer forces to the high-strength bolts, and the tensile forces from the high-strength bolts are received by the lower column plates, which then transfer forces to the embedded rebars in the lower column. On the compression side, the concrete block of the upper column exerts bearing pressures on the metal plates, and the compressive forces from the metal plates are then resisted by the concrete block of the lower concrete column. The mechanical rigid joints consisting of the laminated steel plates are interconnected by the high-strength bolts for the precast concrete column units. The laminated steel plates with stiff enough enabled loads to be transferred at the joints, creating rigid connections. The precast concrete-based mechanical joints for the column-to-column connections are depicted in Fig. 2.2.2A–D. The joint of the proposed connection consists of the two laminated endplates (the lower and upper column plates shown in Fig. 2.2.2A and B), nuts, and high-strength bolts. The steel sections and reinforcing bars should be connected appropriately to the layered column plates. The nuts are incorporated to connect the threaded end of the vertical reinforcing bars at the rear face of the endplates, as illustrated in Fig. 2.2.2C. The precast concrete-based mechanical joints can be used for both the reinforced concrete precast and the steel-concrete composite precast frames as illustrated in Fig. 2.2.2A and B, where the details of the mechanical moment connections are elucidated with the pipe rack applications (refer to Chapter 7). The steel sections of the composite beams are welded to the column plates. The high-strength bolts are designed based on either the bearing type or slip-critical type, providing the moment connections for the column-to-column assemblies by transferring Side view (beam side) Steel plates Top plate A Filler plate A⬘

Beam section (A-A⬘)

(A) FIG. 2.2.1 See figure legend on opposite page.

Bottom plate

Drawing implementing mechanical joints with laminated column plate [2, Chapter 1].

Experimental investigation of the precast concrete Chapter

2

17

FIG. 2.2.1 Erection verification.

moments through the interconnected lower and upper column plates. Fig. 2.2.3 demonstrates the full-scale installation test of precast columns using the mechanical joints with the metal plates, exhibiting a rapid assemblage similar to that of the steel frames. The details of the erection test with the mechanical joints for the typical precast steel-concrete composite frames will be described in Chapter 4. This mechanical joint can also contribute to assembling modular offsite construction, including buildings and heavy industrial plants. The important design parameters include the stiffness of column plates, the sizes and locations of bolts to transfer loads between columns, resisting moment at joints. The stiffness and strength of the laminated metal plate should be sufficient to preclude the prying action of plates, contributing to the moment transfer through joints. The prying actions of the column plates can also be effectively minimized by locating the high-strength bolts either inside or outside the composite column sections.

2.2.2.1 Mechanical joints with the bolted metal plates for the precast columns The extended endplates were originally introduced in the steel structures to transfer loads at the joints. The design of the column base plate must consider the bending of the metal plate and bearing pressure on the support material. Based on the AISC design guide [8], design equations were provided to determine the required bolt diameter and plate thickness

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Hybrid composite precast systems

FIG. 2.2.2 Connection details for columns.

for the extended endplates subjected to axial loads and moments. However, these equations cannot be used to determine the thickness of the metal plate for precast columns. This is because the structural behavior of the joint depends on the behavior of the concrete material, making it difficult to predict the concrete characteristics in both nonlinear and plastic regions. The nonlinear finite element analysis considering damaged concrete plasticity was performed to obtain the required plate

Experimental investigation of the precast concrete Chapter

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19

FIG. 2.2.3 Assembly of the precast columns via the mechanical joint for the steel-concrete composite precast frame.

thickness, exploring stresses and strains to ensure that the metal plates did not fail under the design loads. This chapter outlines some design equations which can be used to estimate the required number of bolts for the column-to-column mechanical joint. The number of bolts with their positioning was also calculated based on the bearing-type connections introduced by AISC. Tests showed that the selection of the plates with sufficient stiffness provided a required structural strength while the plates with insufficient stiffness experienced large deformations, failing to transfer the moments as the rigid joints via the interconnected elements.

2.2.2.2 Mechanical joints with interlocking couplers for precast columns Fig. 2.2.4 illustrates the rigid mechanical joints with interlocking couplers (refer to Chapter 5) by which the column rebars are spliced for the connections of the precast concrete columns. Couplers are designed to be interlocked by the weight of the upper column having weights heavy enough to push the vertical rebars into the couples located at the lower part of the upper column, providing a monolithic joint for the connected concrete columns. The vertical rebars pass through the metal plates attached to the upper and lower columns as shown in Fig. 2.2.4. The assembly process of the proposed connection is rapid and simple; the upper column having couplers is lifted and positioned on the rebars of the bottom column. The upper column with the couplers is then released downward to anchor the bottom rebars. The rebars (male part) are then inserted into the couplers (female part) via the pressure generated by the weight of the upper column. The assembly process is completed when the rebars are completely interlocked into the couplers. The metal plates are not used as structural elements. These plates are used only for the erection purposes. The flexural capacity of the connection with one-touch couplers does not depend on the stiffness of the metal plates. Instead, the axial loads and moments are directly transferred at the joints via the rebars and the couples. Throughout the numerical investigations, metal plates 5–10 mm thick provided the structural strength similar to that of the monolithically designed model. It will be demonstrated in Chapter 5 that the assembly method using the couplers significantly reduces the assembly time for precast frames.

2.2.3 Beam-to-column joint for the moment connections Rigid beam-to-column joints for the precast frames using the extended beam endplates and plates embedded on the column face are presented in Fig. 2.2.5A and B [2]. The mechanical joints can be fully or partially restrained moment connections for either steel-concrete composite precast frames or reinforced concrete precast frames. The connection consisting of plates and high-strength bolts is intended to transfer force couples (tension and compression) to create moment connections.

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Hybrid composite precast systems

FIG. 2.2.4 Connection details for “interlocking” columns with one-touch couplers.

The top beam rebars with the threaded ends are anchored via the nuts on the rear face of the extended beam endplates. The steel sections for the steel-concrete composite precast beams are welded to the extended endplates as shown in Fig. 2.2.5D(3). The details of structural elements for the joints including couplers, threaded rebar, and anchor rebar are illustrated in Fig. 2.2.5C and D. Fig. 2.2.5E shows the extended beam endplates that have been assembled to the column plates embedded in a column unit via bolts and couplers. The column plates are anchored by the rebars in a column unit. The sufficient stiffness of the extended endplates and the positioning of bolts with sizes prevents the prying action of the endplates from taking place, permitting rigid joints. The coupled forces of the tension and compression shown in Fig. 2.2.6 are transferred, enabling the moment connection through the laminated plates. The procedures introduced in Section 2.3.1 are used to design the mechanical joints for the beam-to-column connections. The designs of the plates and bolts are verified based on a nonlinear inelastic finite element analysis in Chapter 3. The tensile forces are transferred from the beam reinforcements to the reinforcing bars anchored in columns when the beam endplates are designed with sufficient stiffness.

2.3

Design of the mechanical joints

2.3.1 Column-to-column connection 2.3.1.1 Design of the column plates The design of the stiffness of the column plates and bolts is described in Section 2.5.2, where the neutral axis and corresponding force components at the design load limit are calculated based on the profile of the strains and stresses.

2.3.1.2 Nominal bearing strength of the plates at the bolt holes In Fig. 2.3.1A, the neutral axes for the beam-to-column and the column-to-column connections are illustrated and the nominal bearing strength at the bolt holes is depicted in Fig. 2.3.1B [3]. The design procedure of the mechanical connections of Specimen C4 (see Fig. 2.5.7) is described in this section. The edge distance from the center of the standard hole to the edge of the connected part is indicated by Le in Fig. 2.3.1. The edge distance of the specimens is 50 mm, which is greater than the 34 mm specified in AISC Table J3.4 [9]. The distance between the standard, oversized, and slotted hole centers of the specimens is 120 mm, which is not less than 53.3 mm (2 23 times the nominal diameter (20 mm) of the fastener), which is required by AISC J3 section 3 (minimum spacing). The available bearing strength at the bolt holes (kN) is calculated using fRn ¼ f(1.2LctFu)  f(2.4dtFu), where Lc is the clear distance in the direction of the force between the edge of the hole and the edge of the adjacent hole or the edge of the material (mm). Specimen C4 is fabricated with the thinnest thickness (two laminated plates with 32 mm). For the bolts shown in Fig. 2.3.1B, the available bearing strength at each bolt hole (kN) is calculated based on the following equations, where Fu is the specified minimum tensile strength of the connected material (MPa) and h is the diameter of the bolts. The bearing strength at each bolt hole is calculated by Eqs. (2.3.1)–(2.3.4). The total bearing strength of the plates is then estimated by Eqs. (2.3.5), (2.3.6). h Lc1 ¼ Le  ¼ 50  11 ¼ 39 mm 2

Experimental investigation of the precast concrete Chapter

2

21

FIG. 2.2.5 See figure legend on page 24.

Lc2 ¼ 120  h ¼ 120  22 ¼ 98 mm

(2.3.1)

fð1:2Lc1 tFu Þ ¼ 0:75ð1:2Þð39 mmÞð32 mmÞð490 MPaÞ ¼ 550:4 kN=bolt

(2.3.2)

fð1:2Lc2 tFu Þ ¼ 0:75ð1:2Þð98 mmÞð32 mmÞð490 MPaÞ ¼ 1383:0 kN=bolt

(2.3.3)

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Hybrid composite precast systems

FIG. 2.2.5, Cont’d

fð2:4dtFu Þ ¼ 0:75ð2:4Þð20 mmÞð32 mmÞð490 MPaÞ ¼ 564:5 kN=bolt

(2.3.4)

Eqs. (2.3.5), (2.3.6) verify that the available bearing strength at the bolt holes could resist the load on the specimens. The column end shear of the monolithic column (Specimen C6, Vu ¼ 394.6 kN) (see Fig. 2.5.5A-(2)) must be less than the bearing strength (fRn) of the holes shown in Eq. (2.3.5). fRn ¼

550:4 kN 564:5 kN  6 bolts +  2 bolts ¼ 9043:2 kN bolt bolt Vu ¼ 394:6 kN  fRn ¼ 9043:2 kN

(2.3.5) (2.3.6)

2.3.1.3 Design of the bolts The use of the column-to-column steel connections was extended to the precast concrete column connections. The design of the moment-resisting endplate connections requires the determination of the bolt size, the plate thickness, and the weld details. The design of the bolts and the welds for the steel connections is a straightforward application, but the determination of the plate thickness becomes quite complicated for the connections with concrete. The number and location of the bearing-type connection bolts are determined based on the shear, bearing, and tension strengths that are checked against the required moment demand at the joints. The pretension introduced in the bolt shaft to prevent the slippage within the contact elements should be confirmed by a torque gauge. The bolts sufficient to resist the column shear force (Vu) with

Experimental investigation of the precast concrete Chapter

2

23

FIG. 2.2.5, Cont’d

394.6 kN for Specimen C6 (see Fig. 2.5.5A-(2)) should be provided in the compression side on the horizontal shear plane of the mechanical joint as shown in Eq. (2.3.7). The bolts are 20 mm-diameters having a high yield strength of 1000 MPa. Vu  fV n,bolt

(2.3.7)

where fVn,bolt is the design shear strength of the bolts provided on the compression side of the steel plate. The neutral axis of the joint is shown in Fig. 2.3.1B. The design shear strength of the eight bolts located on the compression side of the plate is calculated as in Eq. (2.3.8). The eight bolts provide sufficient shear strength to meet the shear demand.

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Hybrid composite precast systems

FIG. 2.2.5 Moment connections for the precast steel-concrete composite frames.

fV n, bolt ¼ 0:75  Fnv  Ab  Number of Bolts ðwhere Fnv ¼ 0:4 ∙ Fu Þ ¼ 0:75  400 MPa  314 mm2  8 bolts ¼ 753:6 kN

(2.3.8)

;Vu ð 394:6 kNÞ  fV n,bolt ð753:6 kNÞ

2.3.1.4 Design of the tension in bolts In Eq. (2.3.9), the number and the location of the bolts required for the tension to resist the moment demand in the specimen are determined as follows: Mt + Mflange + Mweb  fMn, bolt

(2.3.9)

where the required moment demand on the column plate represented by Mt + Mflange + Mweb is calculated from the overturning moments exerted by the rebars, flanges, and webs of the steel section welded to the column plates as shown in Table 2.3.1A and Eq. (2.3.10): Mt + Mflange + Mweb ¼ 425:0 kN  m

(2.3.10)

where Mt, Mflange, and Mweb are the moments exerted by the rebar in tension, steel flange, and steel web, respectively. The strain levels (in rebar, steel flange, and steel web for the specimen) and the neutral axis subjected to the tension are calculated in Table 2.3.1A, demonstrating that most of them yielded. The stresses and strains shown in Table 2.3.1A are obtained based on the strain compatibility (Section 9.3 of Chapter 9). In Table 2.3.1B, Mn,bolt, calculated using Eq. (2.3.11) and shown in boldface is the nominal flexural moment strength of the bolts provided on the tension side of the plate to resist the moment demand (425 kN-m); fMn,bolt ¼

X

f  Fnt  Abolt  d ¼ 565:2kN  m

(2.3.11)

where d is the distance between the centroid of the tensile bolt group and the neutral axis. The left side of the neutral axis is subjected to the tension as demonstrated in Fig. 2.3.1. The design of the bolts required for the flexural moment is given by Eq. (2.3.12): ;Mt + Mflange + Mweb ð425:0 kN  mÞ  fMn, bolt ð565:2 kN  mÞ

(2.3.12)

The nonlinear inelastic finite element analysis will be performed in Chapter 3 to determine the stiffness of the column plates for enabling the transfer of the loads between columns.

Experimental investigation of the precast concrete Chapter

2

25

Bolt

50 mm

Rebar Flange h–c Web

Tension

Flange Flange Rebar

c = 122.16 mm 50 mm

Bolt

Compression

(B)

RC connection [2]

FIG. 2.2.6 Design of plates and bolts resisting force couples.

2.3.1.5 Design of pretension in bolts No-slip behaviors were caused by the shear force in the column as exhibited in Fig. 2.3.2A for both specimens without/with filler plates. The slippage between the laminated metal plates ought to be resisted by the friction generated by the pretension introduced in the high-strength bolt shaft. A pneumatic torque wrench as shown in Fig. 2.3.2B generating up to 900 N-m was used to apply the pretension into the high-strength bolt 22 mm in diameter resulting in the rigid joints. Fig. 2.3.2B shows the torque gauge reading of 600 N-m for one of the bolts installed to connect the column plates. The average torque coefficient of 0.14 for the 22 mm-diameter bolts in the specimen was used. The nonlinear finite element analysis also indicated that no slips between the metal plates were observed when the couplers and bolts were modeled to share the same nodes. The design of the bolt positioning and the plate thickness of the specimens were verified by the nonlinear finite element analysis.

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Hybrid composite precast systems

FIG. 2.3.1 Nominal bearing strength at the bolt holes of Specimen C4 (see Fig. 2.5.7).

Experimental investigation of the precast concrete Chapter

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27

TABLE 2.3.1 Design of connection plate (Specimen C4, Fig. 2.5.7) [3]. (A) Strains exerted on rebar, steel flange, and steel web Neutral axis

163.32 mm (from right)

Moment

601.42 kN-m

Compressive rebar

0.001815194

Compressive flange (top)

0.000703886

Compressive flange (bottom)

0.000446721

Tension flange (top)

0.993631178

Tension flange (bottom)

0.003888342

Tension rebar

0.005036399

(B) Required moment demand on the column plate Fc

Ft0

Fflange0

Fweb0

Ft

Fflange

Fweb

kN

1305.2

375.4

402.7

9.8

506.7

1137.5

448.8

4186.1

31.2%

9.0%

9.6%

0.2%

12.1%

27.2%

10.7%

50.0%

50.0%

2093.0

Mc

Mt0

Mflange0

Mweb0

Mt

Mflange

Mweb

kN-m

125.5

37.8

12.8

0.2

138.9

232.8

53.3

601.4

20.9%

6.3%

2.1%

0.0%

23.1%

38.7%

8.9%

70.7%

425.1

29.3%

2093.0

176.3

FIG. 2.3.2 No-slip behaviors caused by the shear force in the plates.

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Hybrid composite precast systems

2.3.2 Beam-to-column connection and the design of the stiffness of the column plates and bolts The design procedure similar to that introduced for the column-to-column connections is implemented in the column-tobeam connections, as shown in Fig. 2.2.6. The loads exerted on the extended beam endplates are identified in Fig. 2.2.6A where the compressive (refer to Eqs. 2.3.13 and 2.3.13a) and tensile (refer to Eqs. 2.3.14 and 2.3.14a) forces were found based on the strain compatibility. The flexural strengths of the joints in the compression and tension zones are also presented in Eqs. (2.3.13b), (2.3.14b), respectively. The area of the bolts required to resist the moment demands is then calculated in Eqs. (2.3.13c), (2.3.14c). Bolts with an area of 1548.4 mm2 for the steel-concrete composite beams are provided as shown in Eq. (2.3.15). Mt + Mf + Mweb < ’Mn, bolt

(2.3.13)

Mt + Mf + Mweb ¼ 0:9  59:9 kN  m

(2.3.13a)

’Mn ¼ fy  Ab  d ðdistance between bolts and neutral axisÞ ¼ 400 Mpa  Ab,required  172:16 mm

(2.3.13b)

¼ 53:91 kN  m Ab, required ¼ 782:8 mm2

(2.3.13c)

Mt + Mf + Mweb < ’Mn, bolt

(2.3.14)

Mt + Mf + Mweb ¼ 0:9  118:9 kN  m

(2.3.14a)

’Mn ¼ fy  Ab  d ðdistance between bolts and neutral axisÞ ¼ 400 Mpa  Ab,required  257:84 mm

(2.3.14b)

¼ 107:1 kN  m Ab, required ¼ 1038:4 mm2   Bolts required : 4  D22 Abolts ¼ 1548:4 mm2 > Ab, required ¼ 1038:4 mm2

(2.3.14c) (2.3.15)

2.4 Verification of the structural performance of the joint via the numerical investigation The extensive strain data and hysteresis curves for the columns having different types of the mechanical joints are collected by the full-scale test under the monotonic and cyclic loads. In Chapter 3, the nonlinear finite element analysis with wellestablished models will enable the micro-strains of the proposed connection to be provided, eliciting further insight into the failure modes. Factors influencing the structural performance of the proposed joints were also be identified. The results obtained from the FE models well match the test results, indicating that numerical investigation could serve as an alternative to the full-scale experiment for the investigation of the structural performance of the proposed mechanical joints.

2.5 Experimental investigation of the structural performance of the column-to-column connections 2.5.1 Steel-concrete composite columns 2.5.1.1 Description of the tested specimen and test set-up Metal filler The nine test specimens [2–5,7], including three specimens having plates with the high-yield-strength splicing precast columns [6], were manufactured and tested as demonstrated in Figs. 2.5.1 and 2.5.12. Tables 2.5.1 and 2.5.3 present the material properties and component dimensions. This section is devoted to the mechanical joints of 325 MPa yieldstrength for the assembly of the precast columns encasing the steel sections. Table 2.5.1 presents the material properties including the column plates, exterior bolts interconnecting plates, rebars, and steel columns. The dimensions of the

Experimental investigation of the precast concrete Chapter

2

29

structural components consisting of the mechanical connections for columns are also described. Specimens C1, C3, and C5 were 20 mm thick, and the plate thickness of C4 was 16 mm. Specimens shown in Fig. 2.5.1 were loaded to failure to investigate the structural performance of the proposed column-to-column joints. Specimens C1–C5 were constructed with the bolted endplates, whereas Specimen C6 was a conventional monolithic steel-concrete composite column having no endplates. In Fig. 2.5.1A, the rebars are fillet-welded to the column plates for Specimen C1. Neither threaded ends for the rebars nor the filler plates between the column plates were prepared for the mechanical joints. Specimen C2 was fabricated with the two thick plates, each having a thickness of 45 mm without the metal filler plate as shown in Fig. 2.5.1B-(1) and (2). The use of the thick plates in Specimen C2 was intended to accommodate the nuts anchoring the column reinforcing bars to the lower and upper plates as shown in Fig. 2.5.1B-(1), demonstrating the mechanical connection details including the nuts installed in the counterbore of the column plate. The vertical rebars were fastened by the nuts via the threaded rebar ends at the rear side of the column plates as shown in Fig. 2.5.1B-1 for Specimen C2. Specimen C5 in Fig. 2.5.1C had a metal filler plate with a thickness equivalent to the height of the two nuts to accommodate the nuts connecting the columnreinforcing bars to the lower and upper plates. The upper and lower plates were manufactured with a thickness of 20 mm each, while the filler plate was fabricated with a thickness of 44 mm. The filler plates were thick enough to accommodate and protect the nuts completely. The nuts of the mechanical joint installed in Specimens C3 (see Fig. 2.5.2A-(1) and (2)) were protected in the concrete filler plates. In Fig. 2.5.1C-(3), the mechanical connection details for Specimen C5 were exposed on the face of the column plate, followed by the installation of a metal filler plate to encase the exposed nuts in Fig. 2.5.1C-(4). In Figs. 2.5.1D and 2.5.5A-(2), a maximum load capacity of 394 kN at a stroke of 68 mm (390 kN, 51 mm) was observed from Specimen C6, which was the monolithic cast-in-place specimen fabricated with the rebars having a diameter of 25 mm without column plates. The precast concrete columns having the mechanical connections were tested to investigate the structural performance of the proposed connections in terms of their failure modes. Via experimental observations, it was found that the tested mechanical joints depended mainly on the stiffness of the metal plates. Specimens having the plates with sufficient stiffness were able to transfer the moments at the joint, creating fully restrained moment connections while the specimens with the column plates having insufficient stiffness experienced large plate deformations, creating partially restrained moment connections. The structural performance of the column connection stiffened with the internal bolts and ribs shown in Column C7 of Table 2.5.1 will be explored in Chapter 4. The performance of the connection stiffened by additional interior stiffeners was significantly improved, enabling to achieve the practical design while reducing the thickness of the connecting plates. Concrete filler The 44-mm thick concrete filler plate with a wire mesh layer was fabricated for Specimens C3 and C4 as shown in Fig. 2.5.2A and B, where the mechanical joint fabricated by a pair of metal plates and concrete filler plate between them is illustrated. Threaded ends of the rebars and steel sections were fixed to the column plates. Table 2.5.1 summarizes the material properties of the precast concrete-based mechanical joints with the concrete filler plates for the partially restrained moment connections. The concrete filler plates with a thickness of 44 mm were used for Specimens C3 and C4, whereas the different thicknesses were implemented in the metal column plates. The concrete filler plates transferred the axial loads from and to the laminated metal plates, protecting the nuts threaded on the rebar end. The connections of the two specimens were fabricated with the metal plates with a thickness of 20 mm and 16 mm for Specimen C3 and Specimen C4, respectively. The partially restrained moment connections of the joints were established due to the stiffness of the column plates for Specimens C3 and C4 which are not stiff enough for the rigid connections. A wire mesh layer was used in the concrete

FIG. 2.5.1 See figure legend on page 32.

FIG. 2.5.1, Cont’d

Experimental investigation of the precast concrete Chapter

FIG. 2.5.1, Cont’d

2

31

32

Hybrid composite precast systems

FIG. 2.5.1 Fabrication of specimen with metal filler plates and instrumentation.

filler plates to resist the vertical loads at the joints efficiently. The wire-meshes offered the bearing strength to support the compressive bearing loads, and to sustain the compressive loads better.

2.5.1.2 Instrumentation of the test specimens Fig. 2.5.3A depicts the full-scale column connected by the mechanical plates with a loading protocol (Fig. 2.5.3C) [3,10,11] to obtain the structural data including strains and stresses in the plates. Both monolithic specimen and the specimen having the mechanical joints were instrumented with 60 strain gauges and five linear variable differential transformers (LVDTs),

TABLE 2.5.1 Summary of material properties (test values (*); E: Young’s modulus; fy: yield strength; the density of steel: 7850 kg/m3; Poisson’s ratio of steel: 0.3; density of concrete: 2354 kg/m3; Poisson’s ratio of concrete: 0.16) Material properties and design parameters

Specimen C3

Specimen C4

Specimen C5

21 (* 21)

21 (* 21)

21 (* 21)

21 (* 21)

21 (* 21)

21 (* 21)

E, MPa

21,540

21,540

21,540

21,540

21,540

21,540

Size, mm

500  500

500  500

500  500

500  500

500  500

500  500

Rebar

fy, MPa

500 (*550)

500 (*550)

500 (*550)

500 (*550)

500 (*550)

500 (*550)

E, MPa

206,000

206,000

206,000

206,000

206,000

206,000

Standard

4-D25

4-D25

4-D25

4-D25

4-D25

4-D25

Hoops and stirrups

fy, MPa

400

400

400

400

400

400

E, MPa

206,000

206,000

206,000

206,000

206,000

206,000

Standard (spacing)

HD10 (@200)

HD10 (@200)

HD10 (@200)

HD10 (@200)

HD10 (@200)

HD10 (@200)

Steel

fy, MPa

325 (*350)

325 (*350)

325 (*350)

325 (*350)

325 (*350)

325 (*350)

E, MPa

205,000

205,000

205,000

205,000

205,000

205,000

Size Standard

H2502509 14

H2502509 14

H250250 914

H250250 914

H250250 914

H250250 914

Upper/lower plates

fy, MPa

325 (*350)

325 (*350)

325 (*350)

325 (*350)

N/A

650 (high yield metal plate)

E, MPa

205,000

205,000

205,000

205,000

205,000

Size, mm

700  700

700  700

700  700

700  700

700  700

Thickness, mm

45

20

16

20

20

Concrete filler plate (concrete + wire mesh, thickness: 44 mm)

fc0 , MPa

N/A

21 (* 21)

21 (* 21)

N/A

E, MPa

21,540

21,540

Size, mm

700  700

700  700

fc0 ,

MPa

N/A

N/A

2

Continued

Experimental investigation of the precast concrete Chapter

Specimen C2

Characteristics Concrete

Specimen C7 (numerical model with interior bolts)

Specimen C6 (monolithic specimen)

33

34

Material properties and design parameters

Characteristics Metal filler plate (thickness: 44 mm)

Exterior bolts

Interior bolts

Nuts (22 mm height)

fy, MPa

Specimen C2

Specimen C3

Specimen C4

Specimen C5

Specimen C6 (monolithic specimen)

N/A

N/A

N/A

325 (*350)

N/A

Specimen C7 (numerical model with interior bolts) 325

E, MPa

205,000

205,000

Size, mm

700  700

700  700

Thickness, mm

44

44

fy, MPa

900

900

900

900

N/A

E, MPa

206,000

206,000

206,000

206,000

206,000

Size Standard

20-M22-F10T

20-M22-F10T

20-M22-F10T

20-M22-F10T

20-M22-F10T

fy, MPa

N/A

N/A

N/A

N/A

N/A

900

900

E, MPa

206,000

Size Standard

6-M27

fy, MPa

900

900

900

900

900

E, MPa

206,000

206,000

206,000

206,000

206,000

Size Standard

4-M22

4-M22

4-M22

4-M22

4-M22

Hybrid composite precast systems

TABLE 2.5.1 Summary of material properties (test values (*); E: Young’s modulus; fy: yield strength; the density of steel: 7850 kg/m3; Poisson’s ratio of steel: 0.3; density of concrete: 2354 kg/m3; Poisson’s ratio of concrete: 0.16)—cont’d

FIG. 2.5.2 Fabrication of a specimen with concrete filler plates and instrumentation.

36

Hybrid composite precast systems

shown in Fig. 2.5.3B with their locations. The drift angles (rad) with the associated lateral displacements and the number of cycles applied for each stroke are indicated in Fig. 2.5.3C where the applied lateral displacements were obtained by multiplying the inter-story drift angle (rad) by the height of the specimen measured from the base. The readings of strains and displacements will be compared with the numerical results in Chapter 3. AISC (2005) suggested simulating the effects of the seismic loads for qualifying moment connections of the composite column frames. The structural behavior of the joint with the metal plate connection and their hysteretic behavior could be monitored by a quasi-static testing under the displacement control followed by the cyclic loading protocol of two or three cycles for each stroke length as shown in Fig. 2.5.3C.

2.5.1.3 Test results and review with the design recommendations The cyclic load was applied at 1.5 m from the base (Fig. 2.5.3A) to explore the hysteretic behavior of specimens according to the loading protocol (Fig. 2.5.3C). The loading conditions were kept the same for all specimens. Dimensions and material properties of the tested columns are presented in Table 2.5.1. The test results were obtained to help design the precast composite frames having the mechanical joints, providing photos to illustrate the failure mechanism. The important design parameters that influenced the structural behavior were also reviewed. Test results, describing the plate deformations, the failure modes and the maximum/minimum strength measured during the test with corresponding strokes are presented in Table 2.5.2 [3]. Specimen C1 In Table 2.5.2A and Fig. 2.5.4C, the deformations of 2 mm and 12 mm from the upper and lower plates of Specimen C1 were found to be smaller than those of Specimens C3 and C5, despite having the same plate thickness, owing to a welding failure. The fillet-welding fractures of the rebars initiated a stroke of 51 mm prior to the yielding of the rebars, as depicted in Table 2.5.2B and Fig. 2.5.4A and B. The fracture of fillet-welding for rebars accompanied a rapid load reduction as shown in Fig. 2.5.4A; therefore, the fillet-welding was not recommended for the mechanical joint. Specimens C2 and C6 Specimen C2, shown in Fig. 2.5.5A-(1), designed with 45-mm-thick column plates, successfully transferred the moments between the upper and lower columns, creating a rigid joint for the moment connection. In Fig. 2.5.5A-(2), Specimen C6 with the monolithic cast-in-place joint without column plates fabricated with 25-mm-diameter rebars demonstrated a maximum load capacity of 394 kN at a stroke of 68 mm (390 kN, 51 mm). The plates of Specimen C2 designed with sufficient stiffness were able to provide the structural behavior similar to that of the conventional monolithic column Specimen C6. A load reduction was caused by the necked rebars and the crushing failure of concrete due to compression. The test of Specimen C2 was terminated with the crushing of the concrete observed as the loading increased to the maximum load limit

FIG. 2.5.3 See figure legend on page 38.

Experimental investigation of the precast concrete Chapter

2

37

state, as depicted in Fig. 2.5.5B-(1). In Fig. 2.5.5B-(2)–(4), no deformations of the detached joint plates of Specimen C2 were observed, whereas large deformation was exhibited with the column plates with 16 and 20 mm thicknesses, regardless of the filler plate type. Concrete crushed at the base of the column for Specimen C6 is illustrated in Fig. 2.5.5C. Specimen C3 In Fig. 2.5.6A, the load-displacement relationships are shown for Specimen C3 fabricated with 20 mm thick laminated column plates and a 44 mm thick concrete filler plate between the column plates. The failure modes of Specimen C3

FIG. 2.5.3, Cont’d

38

Hybrid composite precast systems

Height of the column: 1.7 m Interstory Lateral Number drift angle displacement of cycles (rad) (mm)

6.0%

0

0

0

4.0%

0.005

6.3

6

2.0% 1.5% 1.0%

0.0075

8.5

6

0.010

12.75

6

0.015

17

4

0.02

25.5

2

0.03

34

2

0.04

51

2

0.05

68

2

0.06

85

2

0.07

102

2

0.08

119

2

0.09

136.3

2

0.1

153.4

2

0.75% 0.5% 0.375%

(C)

6

6

6.4

8.5

0.75% 6

12.8

6.0%

0.5%

4.0%

Displacement (mm)

0.375%

2.0%

Cycles

N

Number of cycles

1.5%

Story drift angle (% rad)

8.0%

4

2

2

2

2

17.0

26.0

1.0%

68.0 34.0

8.0% 2

136.0 102.0

Loading protocol [3, 10, 11]

FIG. 2.5.3 Test preparation.

are identified at strokes of 153 mm and 170 mm, as shown in Fig. 2.5.6B-(1) and (2). The nuts started to slip off the rebar threading at the maximum load of 200 kN and a stroke of 102 mm; it was observed that the nuts collided with the concrete filler plate in the positive load direction as shown in Fig. 2.5.6B-(3) and (4). The load reduction was initiated at the interface between the column plate and the concrete column at around a stroke of 119 mm (Fig. 2.5.6A) after reaching the maximum load in the positive load direction. A decrease in the load-resisting capacity was caused because the forces holding the rebars decreased. Further separation of the interface between the column plate and the concrete column continued up to a stroke of 153 mm. A significant separation at the interface, exposing the thread of the rebar was found at a stroke of 170 mm as shown in Fig. 2.5.6B-(2), damaging nuts with the load reduction. Sudden drops in the loads terminated the test, as shown in Fig. 2.5.6A. In Fig. 2.5.6A, however, the maximum load was maintained until the end of the test in the opposite direction. The two nuts were not damaged in the opposite direction of the loads, indicating that load degradation was not observed in the load-displacement curve. These nuts resisted the loading relatively well, which contributed to the flexural capacity of the specimen until the end of the experiment without the loss of the loads, as shown in Fig. 2.5.6A. It is recommended to use the nuts with a head length that is sufficiently extended to prevent the threads from being displaced. The nuts’ holes must made with sufficient room so as to avoid beating against the filler plates. Fig. 2.5.9A displays the strokes of Specimens C3, C4, and C5 where the nuts started to slip off the threaded rebar end. The load drop for the Specimen C5 with a metal filler plate (represented by the stiffness loss (3) shown in the load-displacement relationship indicated by Legend 1 of Fig. 2.5.8A and Legend 5 of Fig. 2.5.9A-(1)) was observed at a stroke of around 60–70 mm, which was earlier than the stroke of 115–120 mm for Specimen C3 with a concrete filler plate (represented by stiffness loss (2) shown in shown in the displacement relationship indicated by Legend 1 in Fig. 2.5.6A and Legend 3 of Fig. 2.5.9A). The strength can be gained when the additional stiffeners including interior bolts and rib plates were used to stiffen the column plates. The similar load-bearing capacities between the two specimens with metal and concrete filler plates having the same plate thickness were displayed up to the stroke before any of the nuts of either specimen was displaced. The edges and corners of the concrete filler plate were crushed due to the compression; however, in general, the filler plate was not completely damaged, as shown in Fig. 2.5.6C-(1). The column plates deformed about 8 mm at a stroke of 136 mm. At the end of the test, the plate deformation range of 15  23 mm was measured on the lower plate, whereas the upper plate demonstrated a deformation range that spanned 12 18 mm, as can be seen in Fig. 2.5.6C-(2) and Table 2.5.2A. Specimen C4 Specimen C4, fabricated with column plates 16 mm thick and a concrete filler plate 44 mm thick between the column plates, exhibited a maximum load capacity of 148 kN at a stroke of 187 mm (164 kN, 202 mm), as depicted in Fig. 2.5.7A. The tension exerted by the rebars and the steel sections welded to the plates persisted plate deformations from the beginning of the test up to the maximum load limit state. A constant load-bearing capacity within the stroke range of 110–180 mm was maintained, after which the load decreased by the nuts slipped off the threaded rebar end, followed by the nut fracture at a

TABLE 2.5.2 Test summary [3].

Category

Specimen C1 (two 20 mm plates)

Specimen C2 (two 45 mm plates)

Specimen C3 (two 20 mm plates)

Specimen C4 (two 16 mm plates)

Specimen C5 (two 20 mm plates)

Specimen C6 (monolithic specimen)

(A) Plate deformations at maximum load limit state [3] N/A

No filler plate (Nuts in counterbores)

Concrete filler plate

Concrete filler plate

Metal filler plate

Monolithic

Plate deformation

2 mm (top plate) 12 mm (bottom plate) (premature failure at rebar welding)

No deformations *Fully restrained: No prying action

1218 mm (top plate), 1523 mm (bottom plate) *Partially restrained: with prying action

1520 mm (top plate), 1725 mm (bottom plate) *Partially restrained: with prying action

3–5 mm (top plate), 15–20 mm (bottom plate) *Partially restrained: with prying action

N/A

Fixity

Partially restrained

Fully restrained

Partially restrained

Partially restrained

Partially restrained

Fully restrained

Noted failure modes

Premature failure of welding (partially restrained)

No nut slippage

Nut slippage at 119 mm of stroke

Nut slippage at 187 mm of stroke

Nut slippage at 67 mm of stroke

Concrete crushing at base

Max. stroke reached (mm)

(+) 119 () 120

(+) 155 () 159

(+) 170 () 174

(+) 206 () 207

(+) 153 (1) 153

(+) 123 (1) 119

Max. strength (kN); Stroke (mm)

(+) 208, +51 () 215, 68

(+) 382, +102 () 392, 102

(+) 200, +102 () 208, 136

(+) 148, +187 () 164, 202

(+) 188, +68 () 206, 102

(+) 394, +68 () 390, 51

Specimen

Max. rebar strains measured during experiment (yield strain of rebar)

Rebar status

Load level compared with nominal moment capacity (Mn) of column

(B) Strains of selected rebars: tensile strength 5 500 MPa, yield strain 5 0.0025 [3] C1 (plate t ¼ 20 mm)

0.0015 (0.0025)

Not yielded

Less than

C2 (plate t ¼ 45 mm)

0.0037 (0.0025)

Yielded

Reached

C3 (plate t ¼ 20 mm)

0.0010 (0.0025)

Not yielded

Less than

C4 (plate t ¼ 16 mm)

0.0011 (0.0025)

Not yielded

Less than

C5 (plate t ¼ 20 mm)

0.0018 (0.0025)

Not yielded

Less than

C6 (control: without plate)

0.0036 (0.0025)

Yielded

Reached

Experimental investigation of the precast concrete Chapter

Filler plate

2 39

40

Hybrid composite precast systems

TABLE 2.5.3 Fabrication of the test specimens with the high-yield strength plate. Specimen (plate thickness) HC1 (two 26-mm plates)

HC2 (two 26-mm plates)

HC3

Embedded nut

Embedded nut

Control specimen

Deformation

Material

Size

Property

No deformation

Concrete

300  300 (mm)

fc0 ¼ 33 MPa

Rebar

HD-25

Fy ¼ 600 MPa

Plate

500  500 (mm)

Fy ¼ 650 MPa

Bolt

M22-F10T

Fu ¼ 1000 MPa

Stud

M13

Fy ¼ 400 MPa

Concrete

300  300 (mm)

fc0 ¼ 33 MPa

Rebar

HD-25

Fy ¼ 600 MPa

Plate

500  500 (mm)

Fy ¼ 650 MPa

Bolt

M22-F10T

Fu ¼ 1000 MPa

Concrete

300  300 (mm)

fc0 ¼ 33 MPa

Rebar

HD-25

Fy ¼ 600 MPa

No deformation

–

stroke of 204 mm, as shown in Fig. 2.5.7B-(1). The separation of the interface between the column plate and the concrete column face took place due to the slippage of the nuts at a stroke of 204 mm and at the end of the test, as shown in Fig. 2.5.7B-(1) and (2). The nut completely slipped off the thread end of the rebars at a stroke of 204 mm, accompanying a sudden decrease of the load capacity. The flexural strength of the section was finally lost when the rebars were unable to transfer the tension onto the metal column plate, terminating the test shortly after the fracture of a nut, as shown in Fig. 2.5.7B-(3) and (4). The exposed thread of the rebar shown in Fig. 2.5.7B-(2) caused a significant separation between the interfaces. However, the flexural capacity of the specimen was well exhibited up until the end of the experiment because the three nuts resisted the loading relatively well in the opposite direction, as shown in Fig. 2.5.7A and B-(3). The nuts of Specimen C4 were more sustainable than those of Specimen C3, as illustrated in Fig. 2.5.9A-(1), showing an extended stroke of 187 mm for Specimen C4 because of the low rebar strain level of Specimen C4 (Legend 2 of Fig. 2.5.9B-(2)) compared with that of Specimen C3 (Legend 1 of Fig. 2.5.9B-(2)). The concrete filler plate was crushed due to the compression with the noticeable deterioration; however, in general, the filler plate was not completely damaged, as shown in Fig. 2.5.7B-(5). The concrete filler plate of Specimen C4 showed the fracture modes similar to those in Specimen C3. In Section 3.2.1.2 of Chapter 3, the rates of the strain increase in Specimens C3 and C4 will be explored in order to evaluate the influences of the strength of the metal and the concrete plates on the rates of the strain increase of the rebars and steel sections as the over-turning moments increase. Plate deformations of 9 mm and 14 mm of the upper and lower plates at a stroke of 187 mm gradually increased to 15 20 and 17  25 mm at the end of the test, as can be seen in Fig. 2.5.7B-(6) and (7) and Table 2.5.2A. The structural degradation with energy dissipation was concentrated on the column plates. Specimen C5 Damages to the mechanical connections with metal plates including failure modes and plate deformations for Specimen C5 will be explored in detail in this section. Specimen C5, fabricated with the column plates of the limited stiffness (having a thickness of 20 mm and a steel filler plate 44 mm thick between them), demonstrated the structural degradation in the steel plates. This structural degradation of the metal plates was initiated by pulling the column plates off in the stroke range of 80–120 mm, as depicted in Fig. 2.5.8A. The rebars were pulled from the nuts in this stroke range, and were responsible for the nuts’ fractures. The deformation of 15–20 mm in the column plate did not allow a fully restrained moment connection to be created between the two columns, as shown in Fig. 2.5.8B-(2) and (3), where the deformations of 3–5 and 15–20 mm from the upper and lower column plates were measured at the end of the test, respectively. In Fig. 2.5.8B-(1) and C, the deformation of the column plates in Specimen C5 caused the nuts to be displaced and slip off from the rebar threading, decreasing the flexural capacity below 150 kN at 102 mm. When the nuts slips off the thread, collisions between the nuts and adjacent metal plates must be avoided by providing sufficient room in the bolt holes for the nuts to move freely. In contrast, Specimen C2, having sufficient plate thickness, showed no deterioration of the column plates, and demonstrated no plate deformations. The shear strength of C5 with 206 kN was smaller than that of the shear strength of the monolithic

Experimental investigation of the precast concrete Chapter

2

41

FIG. 2.5.4 Failure modes for Specimen C1.

Specimen C6 with 394.6 kN. However, the stroke exhibited by Specimen C5 was larger than that of Specimen C6 due to the rotation of the mechanical joint with Specimen C5, as shown in Fig. 2.5.8D. The displacement of 150 mm was reached for Specimen C5 whereas Specimen C3 reached a smaller stroke of 119 mm. It was found by the experimental and numerical investigations that a plate with at least 45 mm thickness was required to bring the stiffness of the plate to a level that makes the flexural capacity of the column with the plate equivalent to that of monolithic concrete columns (Specimen C6). Specimen C2 successfully reached the load level that was similar to that of the monolithic column with this thickness. However, the option with a 45-mm-thick plate is too impractical and uneconomical to be adapted in practice, while a stiffened column plate with interior stiffeners can increase the flexural stiffness of column plates by reducing the deflection of the plate effectively. Fig. 2.5.9A-(2) shows that the additional internal stiffness (interior bolts and rib stiffeners) added to the 20 mm thick plates enabled the mechanical joint to gain the strength with the extra flexural capacity equivalent to that of monolithic concrete columns (Specimen C6). The numerical investigation to verify the contribution of the internally stiffened plates will be described in Chapter 3.

2.5.1.4 Strains evolution and the rate of strain increase The measured strains are shown in Fig. 2.5.9 in which the structural behavior of the precast column connected by the metal plates and concrete filler plates, as well as the influence of the stiffness of the metal plates on the strains of the structural components (including rebars, steel flanges, and concrete columns), are explored.

42

Hybrid composite precast systems

Load-displacement relationship The load-deflection relationships of the monolithic connections are compared with that of specimens with the connection plates of both having fully and partially restrained moment connections in Fig. 2.5.9A. The displacement is marked at a concrete strain of 0.002. The displacements at which the nuts fractured were indicated in the load-displacement relationships of Specimens C3 and C4. Alternatively, Specimen C2 showed no noticeable deterioration and no rapid drop in the loads, indicating that the stiffness degradation was not initiated by the failure of nuts or the specimen itself. Specimen C2 showed compressive failure modes, which were observed as the loading increased to the maximum load limit state, as depicted in Fig. 2.5.9A. It was worth noting that the specimen with the concrete filler plate provided a lateral load-bearing strength similar to that of the metal plates until the nuts in Specimen C5 slipped off the rebar end at 67 mm. The nuts in Specimen C3 were fractured at 119 mm. Specimens C3 and C5 had the same plate thickness, while concrete and steel filler plates were used for Specimens C3 and C5, respectively. The extensive experimental investigation showed that the structural behavior of the column components connected with the laminated plates having sufficient stiffness and strength (Specimen C2) exhibited the structural behavior similar to those of the conventional monolithic columns, whereas those having the plates with insufficient stiffness and strength (Specimens C3, C4, and C5) demonstrated less capacity.

FIG. 2.5.5 See figure legend on page 44.

Experimental investigation of the precast concrete Chapter

2

43

Plates incapable of providing sufficient stiffness and strength demonstrated large deformations which result in the failure to create rigid joints. Fig. 2.5.9A compares the load-deflection relationship of the monolithic column-to-column connection to those of the columns connected with the plates of varied stiffness. Specimen C4, which was assembled with a connecting plate of 16 mm and a concrete filler plate, demonstrated substantial strength reduction of the moment-resisting capacity as indicated by Arrow 1, indicating a decrease in the strength observed between the monolithic specimen and the specimen with thin plates with insufficient stiffness. Specimens C3 (20 mm, concrete filler plate) and C5 (20 mm, metal filler plate),

FIG. 2.5.5, Cont’d

44

Hybrid composite precast systems

FIG. 2.5.5 Failure modes for Specimens C2 and C6.

assembled with insufficient stiffness of the plates, failed to transfer the forces with the strength lost being similar to each other. They yielded noticeable plate deformation, failing to form rigid joints as a fully restrained moment connection. However, a rigid joint for a moment connection was created for Specimen C2, which was assembled with 45 mm thick plates. Table 2.5.2 summarizes the deformation of the specimens. The discrepancy of the structural performance between Specimens C2 and C6 indicated by Arrow 4 in Fig. 2.5.9A is due to the difference in the rebar diameters. Specimen C2, prefabricated with a mechanical joint, used rebars of 25 mm diameter with a threaded end of 20 mm diameter whereas Specimen C6 used rebars of 25 mm diameter without the thread end. Adequately designed column plates with sufficient stiffness and strength contributed to the transfer of axial loads and moments at joints, providing a structural performance similar to that of monolithic columns. Influence of the metal and concrete plates on the rate of the strain increase of rebars The rate of the strain increase of the structural components consisting of the mechanical joint is also elicited in Fig. 2.5.9B(1) and (2), presenting recommendations for the design of the mechanical joints. Significant deformation of the column metal plates occurred in Specimens C3 and C4, while the metal plates of Specimen C2 did not undergo any noticeable deformation due to the sufficient stiffness of the plate, as stated in Table 2.5.2. The rebar strains observed in Specimen C6 were larger than those of Specimens C3 and C4; this was the case because the strain energy was absorbed by the metal plates of Specimens C3 and C4 due to their insufficient stiffness. In Fig. 2.5.9B-(2) these results indicated that the rebar strains were not fully activated in Specimens C3 and C4, which were less than those of the strains of the control specimen reaching 0.0025. The measured rebar strains of Specimen C4 (reaching 0.0014) were less than those of Specimen C3 (0.002) because more strain energy was absorbed by the 16-mm-thick metal plates of Specimen C4 than by the 20mm-thick metal plates of Specimen C3, indicating that the rebar strains of Specimen C4 were less activated than those of Specimen C3. The loads increased up until the maximum load capacity of 200 kN at a stroke of 102 mm (positive load direction) and 208 kN, 136 mm (negative load direction) for Specimen C3; this was followed by the rapid load reduction since the force holding the rebars started to decrease. The rates of the strain increase of Specimens C3 and C4 decreased to very small values after a stroke of 40 mm, resulting in the structural behavior that was similar to the rigid body rotational mode for Specimens C3 and C4; here, the active participation of the rebars to resist the loads was not possible, as shown in Fig. 2.5.9B-(2). This also implied that the rebars and metal column plates of Specimens C3 and C4 were able to help resist the loads when the loads were small in the beginning; however, the column plates deformed while resisting lateral loads as the applied loads progressed, limiting the ability of the rebars to resist the lateral loads. The rate of the strain increase relative to the stroke of the control column increased consistently to 0.0025 up to the failure of the specimens. It was also observed that steel flanges (Fig. 2.5.9C-(2)) of Specimen C2 reached levels of the strain similar to those of the control specimens, implying that the proposed metal joint yields similar flexural capacity to the monolithic column as long as the metal plates used in Specimen C2 offered sufficient stiffness. Specimens C3 and C5 displayed similar strain-stroke relationships, indicating that the concrete filler plates provided the bearing strength against vertical loads that were similar to the bearing strength of the metal plates. Fig. 2.5.9C-(2) also compares the numerical strain-stroke relationships with the test data.

Experimental investigation of the precast concrete Chapter

2

45

FIG. 2.5.6 See figure legend on next page.

Influence of the metal and concrete plates on the rate of the strain increase of steel sections The strain evolution of the steel flanges was similar to that of the rebar, as shown in Fig. 2.5.9B and C. The flange strains observed in Specimens C2 and C6 were larger than those of Specimens C3 and C4 as shown in Fig. 2.5.9C-(1) and (2). These results indicated that the steel flange strains were not fully activated in Specimens C3 and C4. The strains of the

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Hybrid composite precast systems

FIG. 2.5.6 Failure modes for specimen C3.

monolithic column and Specimen C2 reached 0.0016. The measured steel flange strains of Specimen C4 reached 0.0008, which was slightly less than those of Specimen C3 (0.001) because more strain energy was dissipated by the 16-mm-thick metal plates of Specimen C4 than by the 20-mm-thick metal plates of Specimen C3. This indicated that the steel section of Specimen C4 was less activated than that of Specimen C3 due to the plate deformation of Specimen C4. The rates of the strain increase of Specimens C3 and C4 decreased to very small values after a stroke of 40 mm, demonstrating the structural

FIG. 2.5.7 See figure legend on page 48.

Experimental investigation of the precast concrete Chapter

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47

FIG. 2.5.7, Cont’d

behavior that was similar to the rigid body rotational mode, in which the steel flanges did not actively participate to resist loads after a stroke of 40 mm (Fig. 2.5.9C-(2)). However, the column plates deformed as the applied loads increased, limiting the contribution of the steel sections to resisting lateral loads, as shown in Fig. 2.5.9C-(2). The rate of the strain increase of the steel flange of Specimen C2 was gradually reduced before suddenly decreasing at a stroke of 90 mm; this drop corresponded to the formation of the plastic hinges. The strain levels of the rebars and steel flanges of Specimen C2 were similar to those of the monolithic specimen, alluding that the structural elements of the steel-concrete composite columns were activated as long as the metal column plates offered sufficient stiffness. Influence of the metal and concrete plates on the rate of the strain increase of concrete The column plates of Specimen C4 were more deformable, preventing the concrete from being fully activated, as shown in Fig. 2.5.9D-(1) and (2). As shown in Fig. 2.5.9D, the concrete of Specimen C4 was activated least due to the concentration of the deformations on the thin column plates. The concrete behaviors of Specimen C2 and the monolithic column are similar. The findings on the damages and stiffness degradations in Fig. 2.5.9D can be implemented into the nonlinear finite element model considering concrete damaged plasticity. The dilation angle of the numerical model can also be determined based on the rate of the strain increase.

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Hybrid composite precast systems

FIG. 2.5.7 Failure modes for Specimen C4.

Strength of the metal and concrete plates Fig. 2.5.9E shows that the measured strain of the upper metal column plate in Specimen C3 reached 0.0037. However, the plate on Specimen C2 only reached a strain of 0.0019, indicating that the 45-mm-thick column plate of Specimen C2 did not undergo noticeable deformation, as was observed during the experiment, leading to the full stress activation of the other structural elements attached to the column plates. The rate of the strain increase of the column plates of Specimen C3 was greater than that of Specimen C2. Plates without sufficient stiffness are more vulnerable to deformation, as shown in Fig. 2.5.9E-(1). The strains of the rebars, steel flanges, and concrete (shown in Fig. 2.5.9B-(2), C-(2), and D-(2)) of the precast column (Specimen C3) fabricated with a 20-mm-thick were greater than those of the precast column (Specimen C4) fabricated with a 16-mm-thick endplates. From the strain data, an increased strength in the column plates led to a greater amount of the activation in the other structural elements. The measured strain of the lower metal column plates of Specimen C3 shown in Fig. 2.5.9E-(2) reached 0.0015. However, the plate on Specimen C2 only reached a strain of 0.0012 with a low rate of the strain increase. The rates of the strain increase for the upper and lower column plates of Specimens C3 and C4 were greater than those of Specimen C2.

Experimental investigation of the precast concrete Chapter

FIG. 2.5.8 See figure legend on page 51.

2

49

FIG. 2.5.8, Cont’d

FIG. 2.5.8 Failure modes of joint plates for Specimen C5.

FIG. 2.5.9 See figure legend on page 53.

FIGURE 2.5.9 , Cont’d

FIGURE 2.5.9 Performance of the mechanical joints; rate of strain increase.

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Hybrid composite precast systems

2.5.2 Concrete columns without steel sections Detachable precast concrete column joints for fully restrained moment connection between the bottom and top of adjacent columns using high-strength steel plates were presented. In earlier sections, the precast columns fabricated with steel plates of 325 MPa yield strength were tested to investigate the influence of the thickness of plates on the flexural resisting capacity of the steel-concrete precast columns. A fully restrained moment connection having 45-mm-thick plates with 325-MPayield-strength steel was found to create rigid joints. In this section, the optimum plate thickness of 650-MPa steel with connecting bolts of 900-MPa high-yield-strength for the connections of the precast columns was discussed [6]. Experiments showed that plates 26 mm thick were capable of providing the required stiffness and strength for the precast columns, exhibiting the structural behavior similar to the conventional cast-in-place monolithic reinforced concrete columns. The structural behavior with and without headed studs was also compared. A nonlinear finite element model with concrete damaged plasticity was implemented in ABAQUS [12], which yielded analytical results similar to the test data in Chapter 3, Section 3.2.2. These results demonstrated the possibility of using high-yield-strength steel plates to form rigid joints for the precast column connections. Fig. 2.5.15E and F shows how the metal plates were disassembled to examine the surfaces of the plates and bolts after the test.

2.5.2.1 Design of the test specimens; derivation of the equations based on strain compatibility Specimens HC1 and HC2 shown in Fig. 2.5.10A and B were spliced by plates interconnected by high-strength bolts. In Eqs. (2.5.1)–(2.5.10) [6], the equations to determine the tensile loads exerted by the rebars on the splicing plates are derived based on the strain compatibility.

B

e cm = 0.003 e r1

D

C

CC

Neutral axis

T

e r2

Fr2

e r3

Fr3

Strain compatibility

(B)

gc

Fr1

Rebar

c

Concrete

Internal force contribution

Neutral axis and corresponding force components at the design load limit with profile of strains and stresses

FIG. 2.5.10 See figure legend on opposite page.

Experimental investigation of the precast concrete Chapter

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55

FIG. 2.5.10 Test specimens of an RC section with splicing column plates [6].

The neutral axis, c, is calculated using the equilibrium equations given in: Faxial ðzero when there is no axial loadsÞ + Cc + FRcomp: ¼ FRtension

(2.5.1)

Faxial ¼ FRtension  Cc  FRcomp:

(2.5.2)

or:

where the internal forces on the column plates contributed by the structural components of the section are shown in Eqs. (2.5.3)–(2.5.5). c  d1 c d c + Ar3  fyR FRtension ¼ Ar2  Er  ecm  2 c FRcomp: ¼ Ar1  Er  ecm 

Cc ¼ a  c  B  fc0

(2.5.3) (2.5.4) (2.5.5)

The mean stress factors a and the centroid factors g obtained by Eqs. (2.5.6), (2.5.7) are used to calculate the compressive forces of concrete, Cc, and nominal moment capacity. ð ecm fc dec (2.5.6) a¼ 0 0 fc ecm

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Hybrid composite precast systems

ð ecm

g¼1

ec fc dec ð ecm ecm fc dec 0

(2.5.7)

0

The nominal moment strength at the maximum load limit state is then obtained using Eq. (2.5.8): Mnominal ¼ MR=centroid  M

Conc centroid

(2.5.8)

where the flexural moment capacities provided by the structural components, with respect to the centroid, are shown as follows: MR=centroid ¼ Ar2  Er  ecm 

d2  c c  d1  ðd2  dc Þ + Ar3  fyR  ðd3  dc Þ  Ar1  Er  ecm   ð d1  dc Þ c c MConc=centroid ¼ a  c  B  fc0  ðg  c  dc Þ

(2.5.9) (2.5.10)

The calculation procedure is summarized in Fig. 2.5.10C. Readers are referred to Section 9.3 of Chapter 9 for further formulation based on an iterated strain compatibility.

Design of the plates subjected to tensile forces The tensile forces of the first layer (top) and the second layer (middle) shown in Fig. 2.5.10B were calculated as 883.12 and 226.88 kN, respectively, using Eqs. (2.5.3), (2.5.4). The total tensile force (PTension) was then 1110 kN. AISC Manual Part 9 (pp. 9–10) and Steel design guide 24 were used to calculate the thickness of the plates for Specimens HC1 and HC2. A number of bolts in tension (n), b0 and p were 9, 89, and 100 mm, respectively. Table 2.5.3 lists the geometric details and the material properties used in the design of the specimen. Plate thickness of 27 mm and the locations of the bolts shown in Fig. 2.5.10A are determined using Eq. (2.5.11) [8], as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4:44ðPu =nÞb0 ¼ 27 mm (2.5.11) tp  tmin ¼ pFyp A plate thickness of 26 mm similar to one calculated shown in Eq. (2.5.11) was verified by the finite element analysis presented in Section 3.2.2 of Chapter 3. The Matlab-based design procedure presented in this section was implemented for the design of the plates splicing the concrete column components. Eqs. (2.5.1)–(2.5.10) can also be used for a manual calculation including the flexural strength of the column plates required to resist tension exerted by rebars.

2.5.2.2 Fabrication of the test specimens Column joints were designed without a filler plate for the experiment, as shown in Fig. 2.5.11. The nuts threaded with vertical rebars were located in the counterbores prepared in the column plates, and the column plates were thick enough to hide the nuts completely. Fig. 2.5.11A shows the plate holes with and without nuts installed. The column plate provided sufficient flexural strength to resist the tension exerted by the rebar, contributing to the stability of the column joints. Two precast test specimens (HC1 and HC2) and one precast conventional monolithic specimen (HC3) were prepared to validate whether the plate joints formed fully restrained moment connection shown in Fig. 2.5.11B and C, respectively. The influence of the headed studs on the flexural resisting capacity of the cold joints for Specimen HC1 between the steel plates and concrete was explored. Specimen HC2 did not use headed studs. Columns above and below the plates were manufactured separately and connected using high-strength bolts, as illustrated in Fig. 2.5.11B. Specimens HC1 and HC2 were connected using column plates 26 mm thick, while HC3 was a monolithic specimen fabricated without plates. The instrumented specimen and test setup for the application with a load at 1.5 m from the base were shown in Fig. 2.5.12. The specimens were subjected to a displacement-controlled cyclic loading protocol described in Fig. 2.5.13 [6,10,11] to study a hysteretic behavior. A displacement-controlled cyclic loading protocol (based on the FEMA-SAC loading protocol) was applied to the specimens. In Fig. 2.5.14, gauges to measure strains were affixed at several locations of the interest to characterize the structural behavior. Finally, Section 3.2.2 of Chapter 3 will introduce a nonlinear and inelastic finite element analysis based on a concrete compressive strength of 33 MPa. The numerical results were compared with the test data.

FIG. 2.5.11 Prefabrication of the test specimens.

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Hybrid composite precast systems

FIG. 2.5.12 Test specimens HC1, HC2, and HC3, with instrumentation.

FIG. 2.5.13 Cyclic displacementcontrolled loading protocol [6,10,11].

8.0%

4.0% 2.0% 1.5% 0.75% 1.0% 0.5% 0.375%

Displacement (mm)

0.75% 6

5.6

7.5

11.25

1.0% 4

6.0%

0.5% 6

4.0%

0.375% 6

2.0%

Cycles

2

2

2

2

15.0 22.5

60.0 30.0

FIG. 2.5.14 Gauge installation.

N

Number of cycles

1.5%

Story drift angle (% rad)

6.0%

8.0% 2 120.0

90.0

Experimental investigation of the precast concrete Chapter

2

59

2.5.2.3 Test results Specimen HC1 Table 2.5.3 summarizes the material properties used in the test including the yield strength of column plates, connecting bolts and rebars. Fig. 2.5.15A shows the agreement between test data and a nonlinear inelastic finite element analysis, calculated with and without the inclusion of the damaged plasticity of concrete. The detailed numerical investigation will be presented in Section 3.2.2 of Chapter 3. In Fig. 2.5.15B, the initial tensile cracking at a stroke of 7 mm observed from the interface between the upper plate and concrete column in Specimen HC1 was followed by the cracks having widths of 0.3– 0.4 mm at a stroke of 15 mm and a load of 39 kN. At a stroke of 45 mm and a load of 100 kN, the width of the tensile cracks grew to 2 mm accompanying a rapid load reduction as shown in Fig. 2.5.15C. At a concrete strain of 0.00684, the compression failure of the concrete column below the plates (refer to Fig. 2.5.15D) at a stroke of 60 mm and a load of 108 kN (or at a stroke of 60 mm and a load of 116 kN in the other direction) was observed with a loud sound. The plates and mechanical joints were disassembled, showing both nuts and bolts to be undamaged, as exhibited in Fig. 2.5.15E, where no deformation in either plate after the test indicated that the plate stiffness was sufficient to provide a fully restrained moment connection (refer to Fig. 2.5.15F). The undamaged headed studs provided at the construction joints of Specimen HC1 indicated that the rebar alone provided enough shear resistance at the cold joints between the steel plates and concrete, as shown in Fig. 2.5.15G. The hysteretic envelope shown in the load-deflection relationships of columns HC1 and HC2 (see Fig. 2.5.16A) was also not influenced by the absence of headed studs. In Fig. 2.5.15A (see Section 3.2.2 of Chapter 3), the experimental test data including the flexural resisting capacity match well the numerical load-displacement relationships plotted up to a concrete strain of 0.021 and 0.017 with and without damaged plasticity, respectively. Load-displacement curve 150

(60.0 mm, 115.5 kN)

Load (kN)

100

(Concrete strain : 0.00684)

50

0

–50 1. Experimental analysis 2. Analytical analysis based on ABAQUS

–100

–150 –100

3. Analytical analysis based on ABAQUS (with damaged plasticity of concrete)

(-57.5 mm, -119.4 kN) –80

–60

–40

–20

0

20

40

60

80

100

Displacement(mm)

(A) Comparison of experimental and numerical (ABAQUS) investigations

FIG. 2.5.15 See figure legend on next page.

FIG. 2.5.15 Failure modes for Specimen HC1.

Experimental investigation of the precast concrete Chapter

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61

Specimen HC2 The initial cracks of 0.3–0.4 mm widths between the upper plate and concrete at a stroke of 15 mm and a load of 44 kN increased to 0.6 mm at a stroke of 30 mm (a load of 70 kN), and 0.8 mm at a stroke of 45 mm (a load of 97 kN). The crack widths further opened to 1.2 mm at a stroke of 60 mm and a load of 115 kN, followed by a rapid load reduction accompanied by a loud sound at a stroke of 70 mm and a load of 118 kN, as illustrated in Fig. 2.5.16B. Cracks of 8 mm were observed at the end of the test. Fig. 2.5.16C shows that the nuts were undamaged, enabling the tension to be transmitted to the column plates. Fig. 2.5.16D shows no deformation in either plate, indicating that the plate stiffness was sufficient to provide a fully restrained moment connection. Both Specimens HC1 and HC2 with sufficient plate stiffness did not display any noticeable plate deformation. Specimen HC2 was identical to the Specimen HC1 except for the presence of headed studs, demonstrating the flexural capacity of Specimen HC1 with headed studs, similar to that of Specimen HC2 without headed studs. Headed studs can be removed because sufficient shear capacity between the two cold joints was provided by the rebar in

FIG. 2.5.16 See figure legend on next page.

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Hybrid composite precast systems

FIG. 2.5.16 Failure modes for Specimen HC2.

both test specimens. The maximum load of 118.2 kN (120.2 kN) at a stroke of 65.4 mm (60 mm) measured for Specimen HC2 (refer to Fig. 2.5.16A) was exhibited to be similar to the maximum load of 115.5 kN (119.4 kN) at a stroke of 60 mm (57.5 mm) measured for Specimen HC1 (refer to Fig. 2.5.15A). Specimens HC1 and HC2 also provided the flexural capacity similar to that of a conventional monolithic column.

Experimental investigation of the precast concrete Chapter

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63

Specimen HC3 In Fig. 2.5.17A, a maximum load capacity of 120.1 kN at a stroke of 38.8 mm was demonstrated by Specimen HC3, a monolithic column fabricated without the column plates. Fig. 2.5.17B and C illustrate the test results which were terminated with the compressive failure modes observed at a stroke of 60 mm. The conventional columns without connecting plates exhibited a similar flexural strength to the columns with plates, demonstrating that adequately designed column plates with Load-displacement curve for Specimen HC3 200

150

(36.3 mm, 124.8 kN)

Load (kN)

100

50

0

–50

–100

1. Experimental analysis

(-38.8 mm, -120.1 kN) –150 –80

–60

–40

2. Analytical analysis based on ABAQUS –20

0

20

40

60

Displacement (mm)

(A)

Load-displacement relationships for Specimen HC3

FIG. 2.5.17 Failure mode at a stroke of 60 mm for Specimen HC3.

80

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Hybrid composite precast systems

FIG. 2.5.18 Activation of the rebars, steel sections, and metal plates at a stroke of 50 mm, based on the FEA results [5].

Tensile strain in the rabar: 0.0051 = 2ey

Tensile strain in the steel flange: 0.0021 = 1.2ey

No noticeable plate deformation for C2

Considerable plate deformation for C3

Tension

Nut

Tensile strain in the rabar: 0.0038 = 1.5ey

Compression

Tension

Assumed netural axis

Tensile strain in the metal plate (45-mm thick) : 0.0009 = 0.5ey

Tensile strain in the steel flange: 0.0018 = 1 ey

Compression

Nut Assumed netural axis Tensile strain in the metal plate (20-mm thick) : 0.006 = 3.5ey

Specimen C2

Specimen C3

sufficient stiffness and strength can transfer loads between connected columns. Test data matched the numerical loaddisplacement relationships up to a concrete strain of 0.01 without considering damage variable, as depicted in Fig. 2.5.17A, except for in the high-strain region where the concrete degrades rapidly. The experiments showed that precast concrete columns jointed with 26-mm-thick plates of high-yield-strength (650 MPa) and 900 MPa high-strength bolts were capable of providing sufficient stiffness and strength. This study also demonstrated a sustainable moment-resisting joint provided for a precast concrete frame allowed both assembly and disassembly as quickly as for a steel frame, enabling faster and facile precast modular offsite construction of buildings and heavy industrial plants.

2.5.3 Conclusions of the column-to-column connections Fig. 2.5.18 shows that the stresses and strains of the rebars and steels in Specimen C2 were more effectively activated than those in Specimen C3 at a stroke of 50 mm, based on the FEA results [5]. Table 2.5.2B shows how effectively the rebars and the steel sections with Specimen C2 similar to Specimen C6 were activated, demonstrating that the rebars of Specimens C2 and C6 have yielded, and the nominal moment capacities (Mn) of these columns have been reached. However, the rebars of the remaining specimens did not yield owing to the deformation and inelastic energy, which was concentrated on the plates with insufficient stiffness rather than on the rebars, leading to the specimens not being able to reach the nominal moment (Mn) of columns.

2.6 Experimental investigation of the structural performance of the beam-to-column connections 2.6.1 Steel-concrete hybrid composite beams 2.6.1.1 Description of the tested specimen and test set-up Six specimens [2,7] and [16, Chapter 3] that had beam plates were fabricated to test the mechanical beam-to-column connection as demonstrated in Fig. 2.6.1. The details of the specimens are presented in Table 2.6.1, which sets out the dimensions and material properties of the beam plates used in the test. The high-strength bolts interconnecting the beam endplates to the embedded column plates were anchored to the U-shaped rebars in the column unit by the couplers as shown in Fig. 2.6.2A and B. The couplers were tack-welded to the column plates to ensure the locations of couplers and the anchor rebar. The mechanical joints for the steel-concrete composite beams showing the connection details between the column plates and couplers are shown in Fig. 2.6.2C and D. A description of all connecting components used in the experimental investigation is provided in Fig. 2.6.3. The extended beam plate with a thickness of 45 mm was used in Specimen B2, while Specimens B1, B3, and B5 had plate thicknesses of 20 mm. The plate thickness of Specimen B4 is 16 mm. No endplates were used in Specimen B6, which was fabricated as a conventional monolithic steel-concrete composite column. The design for the mechanical beam-to-column connections should take into account the erection tolerances between the beam

FIG. 2.6.1 Fabrication and instrumentation of the specimens with extended beam endplates.

TABLE 2.6.1 Dimensions and material properties of the beam plates (Ec: Young’s modulus of concrete; Es: Young’s modulus of steel; fy: yield strength; fc0 : Concrete compressive strength; Poisson’s ratio of steel: 0.3; Poisson’s ratio of concrete: 0.16). Category

Size

Material properties

Beam section

300  330 mm

Concrete, fc0 : 21 MPa, Ec ¼ 21,540 MPa, density: 2354 kg/m3

Column section

500  500 mm

End-plate for B2

500  530  45 mm

End-plate for B3

500  530  20 mm

End-plate for B4

500  530  16 mm

End-plate for B5

500  530  20 mm

B6 (no end-plate)

300  330 mm

Concrete, fc0 ¼ 21 MPa, Ec ¼ 21,540 MPa, density: 2354 kg/m3

Column plate

500  530  10 mm

SM490, fy ¼ 325 MPa, Es ¼ 205,000 MPa, density: 7850 kg/m3

Steel section for all specimens

H-200  100  4.5  7

SM490, fy ¼ 325 MPa, Es ¼ 205,000 MPa, density: 7850 kg/m3

Steel section for column

H-250  250  9  14

Beam rebar

4-HD25

Column rebar

4-HD25

Hoops and stirrups

HD10@200

fy ¼ 235 MPa, Es ¼ 206,000 MPa, density: 7850 kg/m3

Nut

M22-F10T

fy ¼ 900 MPa, Es ¼ 206,000 MPa, density: 7850 kg/m3

High-strength bolts

M20-F10T

Concrete filler for B3 and B4

500  530  22 mm

Concrete, fc0 : 21 MPa, Ec ¼ 21,540 MPa, density: 2354 kg/m3

Metal filler plate for B5

500  530  22 mm

SM490, fy ¼ 325 MPa, Es ¼ 205,000 MPa, density: 7850 kg/m3

SM490, fy ¼ 325 MPa, Es ¼ 205,000 MPa, density: 7850 kg/m3

fy ¼ 500 MPa, Es ¼ 206,000 MPa, density: 7850 kg/m3

FIG. 2.6.2 Fabrication of a beam-to-column joint for testing.

FIG. 2.6.3 Load application for the test specimen for the beam-tocolumn joints.

Category Typical beam specimen layout Beam Size: (300 × 330 mm)

Beam (section size: 300 × 330; mm)

Cyclic loading

Column Size: (500 × 500 mm)

1.5 m Column support

Column (500 × 500 × 2,400; Unit: mm)

Concrete compressive strength: 21 MPa

Column rebars, beam rebars

4-HD25, fy = 500 MPa

Beam stirrups, column hoops

HD10@200 mm ( fy = 235 MPa

1.8 m Column support

Material properties

H-steel for beam Size: H- 200 × 100 × 4.5 × 7, mm

SM490, fy = 325 MPa

H-steel for column Size: H- 250 × 250 × 9 × 14, mm High-strength bolts

M20-F10T, fy = 900 MPa

Nuts

4-M22-F10T, fy = 900 MPa

Beam end plates Size: 500 × 530, mm Thicknesses: 16, 20, 45 mm

SM490, fy = 325 MPa

Column plate Size: 500 × 530, mm Thicknesses: 10 mm

SM490, fy = 325 MPa

and column units. These considerations should permit sufficient variations and minimum clearance for the interface between the precast concrete components and the structures. The dimensional variations of the mechanical connections between the beam-to-column units were compensated by providing the erection tolerances. Either metal (Specimen B5) or concrete filler plate (Specimens B3 and B4) was used between the beam endplates and column plates to account for these erection tolerances. Maximum stresses and strains at the anticipated clearance ought to be considered with an appropriate analysis. The 44-mm-thick concrete filler plate with a wire mesh layer was fabricated for Specimens B3

Experimental investigation of the precast concrete Chapter

2

67

and B4. The nuts anchoring rebars to the beam plates of Specimens B3 and B4 were protected in the concrete filler plates. In Specimen B5, the nuts were placed in the metal filler plates. The filler plates had a thickness equivalent to the height of two nuts. However, for Specimen B2, the nuts were accommodated in 45-mm-thick plates similarly to Specimen C2, as shown in Fig. 2.5.1B-(1) and (2).

2.6.1.2 Instrumentation of the test specimens Fig. 2.6.4 shows the cyclic loading protocol that was applied to the test specimens to explore the structural performance and the hysteretic behavior of the mechanical joints. Beams instrumented with extensive gauges are illustrated in Fig. 2.6.5, which presents the locations of gauges and the LVDTs to measure the strains and displacements caused by the loading. Fig. 2.6.5 illustrates the locations of the approximate 60 strain gauges and five LVDTs for both monolithic specimen and the specimen with the mechanical joints. The strain readings were compared with the numerical results in Chapter 3.

2.6.1.3 Test results and review with the design recommendations This section is primarily devoted to the comprehensive description of the structural behavior of the beam-column joints of the steel-concrete precast observed experimentally. The behavior of the composite precast frame joints with the extended beam plates is far more complex than that of the steel frame joints. The mechanical joints introduced in this section can be used for the precast beam-column joints of both composite and concrete frames. The mechanical joints consisting of couplers, anchor rebars in the column, extended beam plates, column plates, and high-strength bolts interconnecting the plates were subjected to cyclic loadings to explore the structural behavior of the mechanical beam-to-column joint. The loading conditions were kept the same for all specimens. The deformations and strains of the beam endplates were investigated to understand the influence of the stiffness of the mechanical joints on the activations of the structural components attached to the plates. In Fig. 2.6.1, the beam plates with 20 mm (Specimen B3) and 16 mm (Specimen B4) thickness deformed regardless of the type of filler plates. These plates formed partially restrained moment connections. The strains measured from the test specimens subjected to the cyclic loadings were used to estimate the structural performance of the beam-tocolumn joint with the concrete filler plates, including the deformations, the stresses of the beam plates, and the failure mode of the frame joints. Specimen B2 with the beam plates of 45 mm thickness transferred loads at the joint, forming a rigid moment connection. The failure modes based on the varied stiffness of the plates were also identified to prevent unexpected fractures of the connections. The design recommendations for the extended beam endplates were proposed for the steelconcrete composite frames. The test data including the strains of the reinforcing bars/steel and beam plates will be used to calibrate the numerical analysis in Chapter 3, enabling the predictions of the performances of the extended beam endplates and high strength bolts. In Chapter 3, the influence of the beam plate deformations on the flexural capacity of the specimens will also be numerically investigated by comparing them with the test data. The important test observations were reviewed with numerous photos to prevent undesirable structural behavior of the beam-to-column connections for the use in the design of the precast composite frames. Test results, uncovering the plate deformations, the failure modes, and the maximum/minimum strength measured during the test with corresponding strokes are summarized in Fig. 2.6.6 and Table 2.6.2. FIG. 2.6.4 Test set-up and loading protocol [2,10,11].

Loading point: 1.5 m 8.0%

Story drift angle (% rad)

6.0% 4.0%

0.75% 0.5%

Beam

2.0% 1.5% 1.0%

1.5 m

0.375%

N

Number of cycles

Displacement (mm)

0.75% 6

5.6

7.5

11.25

1.0% 4

6.0%

0.5% 6

4.0%

0.375% 6

2.0%

Cycles

1.5%

Column

2

2

2

2

15.0 22.5

8.0% 2

60.0 120.0 90.0 30.0

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Hybrid composite precast systems

FIG. 2.6.5 Gauge locations.

Specimen B1 Fig. 2.6.7A and B shows Specimen B1 damaged at a stroke of 50 mm shortly after 77 kN with the premature fillet-welding fracture of the rebars attached to the endplates. The rebars were prematurely detached from the plate, preventing the strain in the steel section and rebars from reaching the yield strain. No noticeable plate deformation was observed at the time of fracture. The flexural strength was not contributed effectively due to the separation of the column concrete from the beam plate occurred by the welding failure. An early brittle failure mode accompanying the significant strength reduction of the

Experimental investigation of the precast concrete Chapter

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69

FIG. 2.6.6 Performance of the mechanical joints: extended beam plates with fully and partially restrained moment connections [2].

TABLE 2.6.2 Observed plate deformations. Max. load (max. displacement)

Specimen (plate thickness)

Deformation

Prying action

B1 (20 mm)

Welded rebar

No deformation (premature failure at rebar welding)

Welding fracture

+77.4 kN (45 mm) 87.7 kN (45 mm)

B2 (45 mm)

Embedded nut

No deformation

No (fully restrained)

+137 kN (95 mm) 133 kN (90 mm)

B3 (20 mm)

Concrete filler plate

14–18 mm

Yes (partially restrained)

+84 kN (105 mm) 85 kN (75 mm)

B4 (16 mm)

Concrete filler plate

15–20 mm

Yes (partially restrained)

+72 kN (225 mm) 73 kN (150 mm)

B5 (20 mm)

Metal filler plate

13–17 mm

Yes (partially restrained)

+84.7 kN (105 mm) 92 kN (105 mm)

B6

Control monolithic specimen

–

–

+158 kN (90 mm) 174 kN (90 mm)

composite Beam B1 was dominant during the degradation. The fillet-welded rebars were not recommended for the use in the mechanical connection unless the welding quality is ensured. Specimen B2 In Fig. 2.6.8A and B, Specimen B2 with a 45-mm-thick beam endplates displays the ductile behavior up to a 100 mm stroke followed by the fracture of the steel section and rebars. The circles in the photo indicate the necked rebars. Fig. 2.6.8A depicts Specimen B2 which exhibited the maximum load capacity of 137 (133) kN at a stroke of 90–100 mm. No noticeable plate deformation was observed during the test. The plate embedded in the column had no noticeable surface damage. A flexural capacity of Specimen B2 similar to that of the monolithic concrete frame without joint plates was observed, indicating that the stiffness of the mechanical joint of Specimen B2 was sufficient enough to suppress the deformation and to transfer the tensions exerted from the rebar to the column. The structural degradation of the joint plates did not occur; instead, the steel beams and reinforcing bars were fractured by the tension before the structural degradation occurred in the joint plates, as shown in Fig. 2.6.8B. Specimen B2 had the failure modes similar to those of the monolithic beam-column joint. In Fig. 2.6.6, the tested hysteretic load-displacement relationships of the monolithic beam (Specimen B6) were compared with those of the specimens having plates of 45 mm (Specimen B2) and 16 mm (Specimen B4). The stiffness of the beam plates insufficient to transfer loads at the joints having the 16-mm plate (Specimen B4) resulted in a large strength

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FIG. 2.6.7 Failure modes for Specimen B1.

FIG. 2.6.8 See figure legend on opposite page.

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71

FIG. 2.6.8 Failure modes for Specimen B2.

reduction of the beam. Specimen B2 built with a stiff plate was prefabricated with a rebar of 20 mm diameter whereas Specimen B6 (refer to Fig. 2.6.13) with a rebar diameter of 25 mm had a conventional monolithic beam-column joint. The strength difference due to the rebar difference is indicated by Arrow #1 of Fig. 2.6.6. The strength similar to each other likely would have been obtained when the rebars of the same diameter were used in these two specimens. Specimen B3 Specimen B3 was fabricated with a 20-mm-thick endplates and a concrete filler plate between the beam and column plate. In Fig. 2.6.9A, the maximum load capacity of 84 kN at a stroke of 105 mm (85 kN, 75 mm, in the other load direction) and the degradation at a stroke of 150 mm (see Fig. 2.6.9B and C) is demonstrated. In Fig. 2.6.9A, the slippage of the nuts off the threaded ends of the rebar begins at the stroke of 135 mm, causing a rapid load reduction after reaching the maximum load. Fig. 2.6.9C and Table 2.6.2 show the plate deformed as much as 14–18 mm due to insufficient stiffness of the beam endplates. The displaced nuts began to collide with the concrete filler plate at the stroke of 120–135 mm, causing significant failures to appear at the interface between the beam plates and concrete beam. At the stroke of 135 mm and 150 mm when forces holding the rebar decreased, a significant separation between the interface and the exposed threaded end of the rebar (Fig. 2.6.9A and E) was exhibited with the reduction of the load resisting capacity at the end of the test. Such slippage and the beating of the nuts against the filler plates can be prevented by providing nuts with enough head length and nuts’ holes large enough in diameter. The specimen with the steel filler plate demonstrated a slightly higher load-bearing capacity than the one with the concrete filler plate up to the stroke of 100 mm as shown in Legends 4 and 2 in Fig. 2.6.6. These two specimens have beam endplates of the same thickness. However, better ductility from the beam-column joint with the concrete filler plate was observed, as shown in Fig. 2.6.6. The bearing failure modes with the compression failure were found from the beam-column joint with the concrete filler plate, but, in general, the nuts were protected well, indicating that the filler plate was not completely damaged. In Fig. 2.6.9C and D, the final failure modes indicate that the beam plate of the disassembled specimen deformed as much as 14–18 mm at a stroke of 150 mm. In Fig. 2.6.9E, a numerical investigation predicts the tested plate deformation, which was as much as 18 mm for Specimen B3. The contribution of the beam plate to the flexural strength was prevented because the inelastic energy was dissipated through the gradual deformation of the plate prior to the fracture of steel flange. In Section 3.2.3 of Chapter 3, additional interior bolts are implemented to reduce unsupported length between the bolts. The internally stiffened plates will increase the stiffness of the beam plates, and decrease the deformation of the plates.

FIG. 2.6.9 Failure modes for Specimen B3.

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73

Specimen B4 Fig. 2.6.10A shows that a maximum load capacity of 72 kN in a stroke range of 120–225 mm (-73 kN, 150 mm) was demonstrated in Specimen B4, fabricated with a 16-mm endplate and a concrete filler plate between the beam and column plates. The structural degradation with energy dissipation was concentrated on the beam plate, causing a constant loadbearing capacity in this stroke range. Any noticeable deterioration or strains were noticed from the concrete section when the deformation of the beam plate gradually increased as much as 15–20 mm at a stroke of 150 mm. This was because the plates experienced substantial deformation with all the damage being concentrated on plates, as observed in Fig. 2.6.10B. No noticeable deterioration and structural degradation of the structural elements attached to the beam endplate including concrete, rebars, and steel section, were not apparent since all the damage was concentrated on the plate. The deformed plate pushed nuts off the rebar thread plane, displacing those nuts during the transfer of the tension exerted by the rebars. Either minimizing the twisted distortion of the plates or providing sufficient gaps between the nuts and the holes prepared in the plates may prevent the unexpected distortions of the nuts leading to the failure at the threaded ends of the rebar. The least flexural strength among all the test specimens was observed in Specimen B4 due to the beam plate with the least stiffness with only 16 mm thickness. The plate deformation of as much as 15–20 mm was responsible for the significant reduction of the flexural strength of the specimen, as found in Fig. 2.6.10B and Table 2.6.2. In Fig. 2.6.11B-(2) and C-(2), the strains of the rebar and steel section of Specimens B3 and B4 were smaller than those of Specimen B2 and the monolithic specimen

FIG. 2.6.10 Failure modes for Specimen B4.

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Strain-stroke curve (concrete)

Load-strain curve (concrete) 180 160 B2

120

Strain

Load (kN)

140

B3

100 80

B4 (malfunction)

60 40

B6

20 0

0

0.002 0.004 0.006 0.008

0.01

0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0

B2 B3 B4 B6

0

20

(A)

(1) Load-strain curve

Strain

Load (kN)

B3 B4 B6

(B)

0.001

80

Strain-stroke curve (rebar)

B2

0

60

(2) Strain-stroke curve

Concrete

Load-strain curve (rebar) 180 160 140 120 100 80 60 40 20 0

40

Stroke (mm)

Strain

0.002

0.003

0.004

0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0

B2 B3 B4 B6 0

50

100

150

200

Strain

Stroke (mm)

(1) Load-strain curve

(2) Strain-stroke curve Rebar Strain-stroke curve (steel)

Load-strain curve (steel) 0.0025 B2 B3 B4

0.002

Strain

Load (kN)

180 160 140 120 100 80 60 40 20 0

B6

0.0015

B2

0.001

B3

0.0005

B4

0 0

0.0005

0.001

0.0015

0.002

0.0025

B6 0

50

200

Strain

Stroke (mm)

(2) Strain-stroke curve

250

Steel section Strain-stroke curve (plate)

Load-strain curve (plate) 0.005 0.004 B2 B3

Strain

Load (kN)

150

(1) Load-strain curve

(C) 160 140 120 100 80 60 40 20 0

100

B4 0

0.001

0.002

0.003

0.004

0.005

B3

0.001

B4 0

20

40

60

80

100 120 140 160

Stroke (mm)

(1) Load-strain curve

(D)

0.002

0

Strain

B2

0.003

(2) Strain-stroke curve Metal plate

FIG. 2.6.11 Rate of the strain increase [7].

B6, whereas the strains of the beam endplate of Specimens B3 and B4 were greater than those of Specimen B2, as shown in Fig. 2.6.11D-(2). Fig. 2.6.10B shows how the deformed plate pushed the nuts off the rebar threads during the transfer of the tension exerted from the rebar, causing the nuts to be displaced. Specimen B5 A 20-mm-thick endplate and metal filler plate between the beam and column plates were used in Specimen B5, which exhibited a maximum load capacity of 84.7 kN at a stroke of 105 mm (92 kN, 105 mm, in the other load direction), as depicted in Fig. 2.6.12A. Specimens B3 and B5 had a plate of the same 20 mm thickness, but differed in that a metal filler

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75

FIG. 2.6.12 Failure modes for Specimen B5.

plate was used in Specimen B5 whereas a concrete filler plate was used in Specimen B3. A constant load-bearing capacity of Specimen B5 similar to those of Specimen B3 and B4 was apparent in this stroke range because the inelastic energy inducing structural degradation was substantially absorbed in the beam plate. For the same reason observed in Specimen B4, there was no noticeable deterioration and structural degradation of the structural elements attached to the beam endplate. In Fig. 2.6.12B, the deformation of 13–17 mm of the beam plate at a stroke of around 150 mm (see Table 2.6.2) is observed. The measured deformation and the force-displacement relationship of the plate in Specimen B5 were similar to those of Specimen B3, as shown in Table 2.6.2 and Fig. 2.6.6. However, the flexural strength of Specimen B5 was found to be 5% larger than that of Specimen B3 due to the steel filler plate in Specimen B5 providing larger bearing stiffness under the compression.

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Hybrid composite precast systems

Specimen B6 Specimen B6 having a monolithic joint of a conventional beam-to-column connection for a steel-reinforced concrete composite frame was fabricated. The measured hysteretic load-displacement relationships with a maximum load capacity of 158 kN at a stroke of 90 mm (174 kN, 90 mm) are shown in Fig. 2.6.13A. In Fig. 2.6.13B, a comparison of the loaddisplacement relationships [2] of the tested beams is presented with the numerical predictions (see Chapter 3). Fig. 2.6.13C depicts the failure modes in the compression observed at the maximum load limit state.

FIG. 2.6.13 Failure modes for Specimen B6.

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77

2.6.2 Conclusions of the beam-to-column connections The structural performance similar to the monolithic joints was obtained for Specimen B2 having plates with sufficient stiffness and strength to transfer the tensile forces exerted by rebars and steel beams against the bending moment. Specimens B3, B4, and B5 with 16 and 20 mm plates demonstrated a constant load-bearing capacity and large energy dissipation concentrated at the beam plates, preventing full strain activations of the structural elements attached to the beam endplate. The strength loss of the beam with plates (Specimen B5) shown in Figs. 2.6.6 and 2.6.13B, found by comparing it with a monolithic joint, presents the stiffness of the mechanical joints necessary to attain the strength of the beam equivalent to that of the monolithic beam (Specimen B6). Fig. 2.6.6 compares the structural behavior with the hysteretic envelope of the load-deflection relationship of the monolithic beam-to-column joint with the beams having the extended endplate with varied stiffnesses. Specimens B3, B4, and B5 demonstrated the strength loss of the flexural moment resistance; among them, the largest strength reduction was noticed in Specimen B4. The strength reduction of the moment resistance obtained from Specimen B4 assembled with a beam plate of 16 mm and concrete filler is indicated by Arrow 1. A strength reduction similar to Specimen B4 was observed in Specimen B3 (20 mm, concrete filler, Arrow #2) with the endplate of the insufficient stiffness in which the load-bearing capacity of Specimen B4 with a 16 mm plate was slightly smaller than that of the Specimen B3 with a 20 mm endplate. In Fig. 2.6.10 displaying the failure modes of Specimen B4, the slips of the nuts are accompanied by the separation of the interface between the beam plate and the embedded concrete plate from the stroke of 165 mm. The rebar could, then, no longer exert tension onto the metal beam plate, causing a decrease in the load resisting capacity when the nut fracture continued. The threaded rebar ends completely slipped off at the stroke of 225 mm. A sudden drop in the load was found when the test was terminated at the 250 mm stroke. The nuts in Specimen B4 were less susceptible to the failure owing to the low rate of the strain increase of the rebar (see Fig. 2.6.11B). The concrete filler plate of both Specimens B3 and B4 showed the similar fracture modes. But in general, no significant compressive failures of the concrete filler plates were exhibited. The prying actions at the beam endplate were minimized by providing an endplate stiff enough (by adjusting the positioning of bolts and sizes) to transfer the moments properly from beams to columns.

2.7 Test assembly 2.7.1 Significance of the connection In this section, the test assembly implementing the rigid mechanical joints having the laminated metal plates was conducted for precast concrete columns. Rigid mechanical joints were proposed as a time- and cost-saving alternative to the conventional monolithic cast-in-place joints. The test assembly was performed to investigate the generalizability of the erection for both steel-concrete composite precast frames and reinforced concrete precast frames using the mechanical joints. The efficiency and simplicity of the erection were demonstrated. The construction time compared with the conventional assembly was significantly reduced when the mechanical joints with the laminated steel plates were used. Pour forms and curing times required for the conventional monolithic concrete frames were eliminated completely, reducing the assembly time for one pair of precast columns to approximately 10–20 min.

2.7.2 Assembly of the full-scale precast columns Fig. 2.7.1A and B introduces the two types of the modular precast connections, implementing interlocking couplers and the laminated metal plates interconnected via high-strength bolts. In this section, the test assembly of the rectangular precast column shapes was conducted using the laminated metal plates interconnected via high-strength bolts as shown in Fig. 2.7.1B. The flexural capacity of this type of the connection depends mainly on the plate stiffness and bolt positioning with the size of the diameter. Extensive numerical investigations to identify the strain levels and failure modes of the structural elements at the joints will be presented in Chapter 3, where the structural performance of the bolted metal plates will be verified. Test assembly with irregular shapes will be also introduced in Chapter 4.

2.7.3 Test assembly: Precast column splice implementing the mechanical joints having laminated metal plates Connection details with the bolted metal plates are demonstrated for the frame modules as shown in Fig. 2.7.1. Three types for the column-to-column connections are summarized in Figs. 2.7.2–2.7.4. The rebars from the upper and lower columns are fixed to the column plates via nuts. In Fig. 2.7.2, all rebars are bent to avoid the nuts of the different columns from running into each other in the filler plate. The locations of the nuts and size of the nuts’ holes are determined so as not to bump into the filler plates during the deformation of the column plates. In Fig. 2.7.2A and B, the nuts from both the

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Hybrid composite precast systems

FIG. 2.7.1 Connection details for the column modules; bolted metal plates.

upper and lower columns occupy all of the holes in the filler plate after the columns are connected. A metal filler plate with a thickness sufficient to encompass the height of one nut is used in this type; however, the costs for bending all vertical rebars are required. The filler plate is not used as a structural element; instead, it is used only to hide the nuts connecting the column rebars to the metal plates. In Fig. 2.7.3A and B with the second type of connection, the nuts threaded with the rebars are accommodated in the counterbores of the column plates without using a filler plate. The column plates encasing the nuts should be thick enough to encase and protect the nuts completely. A bent rebar is not necessary because the nuts are kept in the column plates, not in a filler plate. The counterbores of the plates with and without nuts are shown in Fig. 2.7.3B. The stability of this type of column joints is contributed by the neck of the flexural strength of the plates having counterbores. The third type of the connection is installed on the top of each other, requiring the filler plates twice as thick (equivalent to the height of the two combined nuts) as those of the first type shown in Fig. 2.7.2A. Fig. 2.7.4A and B highlight the use of the thick plates to accommodate the upper and lower nuts when the counterbores are not required in the plate. The filler plates do not contribute to the flexural strength of the joints, whereas the costs for the bending rebars and making counterbores in the column plates are saved. The first type with the thinnest plate without the section loss of the filler plate at the cost of bending vertical rebars was selected for the test assembly in this section. The constructability and generalizability were demonstrated during the test assembly.

Experimental investigation of the precast concrete Chapter

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79

FIG. 2.7.2 Filler plate with bent rebars [2, Chapter 1].

2.7.4 Test assembly Fig. 2.7.5 shows both fabricated specimens and test assembly using a pair of steel plates. Three laminated metal plates with the upper, middle (filler plate), and lower plates are presented in Fig. 2.7.5A-1. In Fig. 2.7.5A-(2), the rebars and column plates for the upper and lower columns are placed ready for the concrete casting. The bent rebar placed in the lower column (refer to Fig. 2.7.5A-2) was anchored by the nuts at the plate (refer to Fig. 2.7.5B), avoiding the conflict with the rebars from the upper column in the metal filler plate, whereas the rebar of the upper column was not bent. The nuts from both upper and lower columns were enclosed at the different locations in the metal filler plate placed between the column plates, ensuring the structural integrity of the vertical rebar. In Fig. 2.5.9 of Section 2.5.1, the stiffness of the plate was investigated to

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Hybrid composite precast systems

Upper column plate Nut from upper column

Nut from lower column

Lower column plate

(A)

Second type of connection Pits prepared in the column plates

Rebar threaded with nuts inside the pit prepared in the column plates

(B)

Nuts intalled in the pit of the column plate

FIG. 2.7.3 Nuts accommodated in the counterbores of the column plates [2, Chapter 1].

suppress the deformation of the column plates, transferring the moments at the joints by preventing a prying action. Loads are transferred by the nuts anchored to the threaded ends of the rebar on the rear side of the column plates, as shown in Fig. 2.7.5B and C. The protection of the nuts must be ensured for the load transfer. In Fig. 2.7.5D–F, the lower column having the column plates is being assembled to the plate attached to the upper column. The material properties of the full-scale proto-model for the assembly are summarized in Table 2.7.1. In Fig. 2.7.5G and H, the filler plate encloses and protects the nuts anchored on the surface of the column plates. In the filler plate, the nuts of the different columns did not run into each other due to the bent rebars. A nonlinear finite element analysis using ABAQUS [12] was performed to determine the locations and sizes of the holes in the filler plates. Fig. 2.7.5G and H shows that the nuts from the lower columns are completely enclosed, whereas empty holes in the filler plate were reserved for the nuts from the upper columns and bolts. The full-scale test assembly presented in this section verified the merits and economy of the proposed installation. In Fig. 2.7.6A and B, the column plates are laminated in which the nuts were encased in the holes prepared in the filler plate.

Experimental investigation of the precast concrete Chapter

2

81

Upper column plate Nut from upper column

Nut from lower column Lower column plate

(A)

Third type of connection

Filler plate

(B)

Connection of third type

FIG. 2.7.4 Filler plate with straight rebars [2, Chapter 1].

The laminated steel plates (two column plates and one filler plate) were subsequently interconnected by high-strength bolts, as depicted in Fig. 2.7.6C. Fig. 2.7.6D illustrates the high-strength bolts connecting the two plates and the filler plate. The torque coefficient was estimated to prevent an over-tightening. A 600 N-m torque based on the torque coefficient of 1.4 was used to introduce a pretension to the bolts. Beams were supported on the column plate at the floor level, as shown in Fig. 2.7.6E. The completely assembled column units are presented in Fig. 2.7.6F. The costs of the metal sections (twocolumn plates and one filler plate) to assemble the upper and lower columns with a weight of 2.8 kN were insignificant when compared with the cost in the conventional erection methods. The constructability and generalizability of using the mechanical joints with the steel plates was verified for both steel-concrete composite precast frames and reinforced concrete precast frames. The bolt holes were accurately aligned for the bolt installations, improving an assembly efficiency. In Fig. 2.7.7A, a full-scale test assembly of the precast columns demonstrates that an assembly time for the precast columns of less than 10 min was observed, leading to a significant reduction in the construction. Fig. 2.7.7B and C illustrates the beamto-column assembly with vertical and horizontal directions implementing the mechanical joints. In Fig. 2.7.7D, the facile beam-to-column connection of the full-scale steel-concrete composite precast frame using the laminated metal plates is demonstrated. A more demonstration of the test assembly can be found in Chapter 4. The time for the total precast frame joint assembly with the mechanical joints shown in Fig. 2.7.7B–D was approximately 1 h. Following the conventional method, 7–10 days are expected to require for the erection of one floor frame. The proposed assembly method was proven for the use in the precast industry.

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Hybrid composite precast systems

FIG. 2.7.5 See figure legend on opposite page.

FIG. 2.7.5 Preparation of the joint connection of columns [2, Chapter 1].

TABLE 2.7.1 Properties of the full-scale erection mock-up model [2, Chapter 1]. Size

Material properties

Concrete

500  500 (mm  mm)

fc0 ¼ 27 MPa

Top plate

700  700 (mm  mm) (thickness ¼ 20 mm)

Fy ¼ 325 MPa; ey ¼ 0.0016

Filler plate

700  700 (mm  mm) (thickness ¼ 25 mm)

Fy ¼ 325 MPa; ey ¼ 0.0016

Bottom plate

700  700 (mm  mm) (thickness ¼ 20 mm)

Fy ¼ 325 MPa; ey ¼ 0.0016

Rebar

HD-25 and HD-19

Fy ¼ 500 MPa; ey ¼ 0.0025

Bolt

M22-F10T

Fu ¼ 1000 MPa; ey ¼ 0.0045

Descending column onto filler plate

Inserting nuts from the upper column into the holes

(A)

(B)

FIG. 2.7.6 See figure legend on opposite page.

Experimental investigation of the precast concrete Chapter

FIG. 2.7.6 Dry connection of the precast concrete columns using column plates [2, Chapter 1].

2

85

FIG. 2.7.7 See figure legend on opposite page.

Beam

Connected via bolts

Column Embedded column plate

(C)

Beam plate

Beam-to-column joint details [2, Chapter 1]

(D) FIG. 2.7.7 Assembly of the precast frames using mechanical joints.

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Hybrid composite precast systems

References [1] ANSI/AISC 358-16 (An American National Standard), Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications, American Institute of Steel Construction, 2016. [2] J.D. Nzabonimpa, W.K. Hong, S.C. Park, Experimental investigation of dry mechanical beam-column joints for precast concrete based frames, Struct. Des. Tall Spec. Build. 26 (1) (2017). [3] J.Y. Hu, W.K. Hong, S.-C. Park, Experimental investigation of precast concrete based dry mechanical column-column joints for precast concrete frames, Struct. Des. Tall Spec. Build. 26 (5) (2016). [4] J.D. Nzabonimpa, W.-K. Hong, Structural performance of detachable precast composite column joints with mechanical metal plates, Eng. Struct. 160 (2018) 366–382. [5] J.D. Nzabonimpa, W.K. Hong, Use of laminated mechanical joints with metal and concrete plates for precast concrete columns. Mater. Struct. 51 (2018) 76, https://doi.org/10.1617/s11527-018-1207-y. [6] J.D. Nzabonimpa, W.K. Hong, Experimental and nonlinear numerical analysis of precast concrete column splices with high-yield metal plates, J. Struct. Eng. (ASCE) 145 (2) (2019). [7] J.D. Nzabonimpa, W.K. Hong, Experimental and non-linear numerical investigation of the novel detachable mechanical joints with laminated plates for composite precast beam-column joint, Compos. Struct. 185 (2018) 286–303. [8] AISC design guide, [design-guide-24-hollow-structural-section-connections]. [9] Minimum Edge Distance Table AISC ANSI 360, AISC Table J3.4, American Institute of Steel Construction. [10] Protocol for fabrication, inspection, testing, and documentation of beam-column connection tests and other experimental specimens, SAC Joint Venture, 1997. [11] FEMA, State of the Art Report on Connection Performance, FEMA-355D, FEMA, Washington, DC, 2000. [12] Abaqus, Dassault Syste`mes, ABAQUS Analysis User’s Manual 6.14-2, Providence, RI, USA, Dassault Syste`mes Simulia Corp, 2014.

Chapter 3

The investigation of the structural performance of the hybrid composite precast frames with mechanical joints based on nonlinear finite element analysis 3.1 Numerical investigation of the structural performance 3.1.1 Nonlinear inelastic finite element analysis 3.1.1.1 Plastic potential and yield surface The structural performance of the hybrid composite precast frames with the mechanical joints was numerically performed based on a nonlinear FEA considering the damaged concrete plasticity. The theory of linear elasticity or hyperelasticity is used to calculate the elastic strain while the plastic behavior of the concrete and the plastic part of the strain are estimated based on a plastic potential energy (flow rule). As described in Section 3.1.3.3 of this chapter, plastic behavior of the material is obtained by a flow rule that determines the direction of plastic straining. The hardening rule describes the yield surface that defines the onset of plasticity. The yield surfaces are established, resulting in the progressive changes of yielding criteria with stress status for subsequent loading and progressive yielding. Two hardening rules (isotropic hardening and kinematic hardening) are available. The center of the initial yield surfaces does not alter for isotropic hardening, but the initial area of yield surfaces changes as the plastic strains develop. For kinematic hardening, the initial area of yield surfaces does not change, whereas the center of the initial yield surfaces moves in stress space with progressive yielding. The structural performance of the proposed hybrid frames was explored, demonstrating acceptable structural strength numerically and experimentally.

3.1.1.2 Plasticity model of damaged concrete; concrete crack models in the finite element analysis Abaqus [12, Chapter 2] provides three crack models to predict the nonlinear behavior of concrete material, considering a concrete damaged plasticity model, a smeared crack concrete model, and a brittle cracking concrete model. The smeared crack model assumes that cracking is the main failure mechanism of concrete in compression under low confining pressures, not tracking individual “micro” cracks during the analysis. Alternatively, the plasticity model of concrete damage represents the behavior of the concrete material based on the two major failure mechanisms: plastic tensile cracking and compressive crushing. According to the Abaqus documentation [12, Chapter 2], the directions of the crack surface normal to the existing cracks were propagating, closing, and reopening, when the tensile strength of the brittle material was exceeded by the maximum principal tensile stress, according to the constitutive equation. Rebar elements were defined as embedded in oriented concrete based on the one-dimensional strain theory. The rebars were superposed on a mesh of plain concrete with elastoplastic material behavior, assumed to be independent of the concrete cracking. In Fig. 3.1.1, a damaged concrete plasticity model was described with the stress-strain response under uniaxial compression based on the Kent-Park model. The stress-strain response behaves in a linear elastic fashion until it reaches the initial yield stress, sc0. These stresses are formed to replace the microcracks in the concrete material. This stage is followed by strainsoftening, which shows the typical uniaxial constitutive relationship of concrete in compression with damaged plasticity. In Abaqus [12, Chapter 2], the onset of the plasticity of the inelastic stress-strain relationship was also demonstrated. The first pair of the inelastic stress-strain relationship corresponds to the onset of plasticity, which was represented by the stiffness softening for compression corresponding to 0.4sc and ec ¼ 0.0005 (refer to Point A) for the concrete with a compressive Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00003-0 © 2020 Elsevier Ltd. All rights reserved.

89

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Hybrid composite precast systems

sc

scu = 21 MPa

scu st st0

B

E0 = 21,540 MPa

0.4sc

E0

(1 – dc)E0

A E0

E0 e~tck pl e~t

e~0tel

et

Point A sc = 8.4 MPa dc = 0 e~cin = 0 ec = 0.0005

Point B sc = 21 MPa dc = 0.55 ~ ecin = 0.0015 ec = 0.002 E0 = 21,540 MPa

(8.4 MPa)

(1 – dt)E0

Compression

0.0001

et

0.002

e~cin

e tel

e~cpl st0 = 2.1 MPa Tension

el e~0c = 0.0005

ec

ecel

st

FIG. 3.1.1 Concrete damaged plasticity model [5, Chapter 2].

strength of 21 MPa. In Fig. 3.1.1, the cracking behavior of concrete observed in the experiments was represented by parameters defining the constitutive law in compression and tension. The tensile cracking and compressive crushing in the complete nonlinear and inelastic failure mechanisms of concrete were reflected by the plasticity model of damaged concrete, including the hardening behavior of concrete. In this chapter, the strain-stress constitutive law for cracked concrete defined the postfailure of stress-strain relationship that existed between the microcracks of the composite precast frames having mechanical joints, shown in Fig. 2.2.2 of Chapter 2.

3.1.1.3 Damaged plasticity model for concrete Uniaxial tension and compression stress behavior In Chapter 3, most of the numerical investigations for the proposed hybrid precast frames introduced in Chapter 2 were based on Abaqus software package. This section summarized the damaged plasticity model for concrete and related theoretical background of the finite element analysis from Abaqus manual. The strain rates coupled by damage and plasticity were decomposed additively, as seen in Eq. (3.1.1) and Fig. 3.1.1. e_ ¼ e_ el + e_ pl

(3.1.1)

The failure mechanics of concrete in tension and in compression for low levels of confinements was investigated based on the stiffness degradation and inelastic deformations. In Eq. (3.1.1), where e_ is the total strain rate, e_ el is the elastic strain rate, and e_ pl is the plastic strain rate, the stress-strain relationship is written as indicated in Eq. (3.1.2).
 pl el pl (3.1.2) s ¼ ð1  dÞDel 0 : e  ev ¼ D : e  e el el Based on scalar damaged plasticity where Del 0 is the undamaged elastic stiffness of the material. D ¼ (1  d)D0 is degraded elastic stiffness and d is the scalar stiffness degradation variable. The damaged stress-strain relationships under uniaxial tension and compression loading shown in Fig. 3.1.1 becomes Eqs. (3.1.3), (3.1.4), respectively, when E0 is the undamaged elastic stiffness of the material. The unloading response with degraded elastic stiffness of the concrete is defined by the two damage variables, dt and dc, which are the functions of plastic strains governing the damaged response of concrete in tension and compression. The degradation of elastic stiffness is significantly different between tension and compression, the effect of which becomes more pronounced as the plastic strain increases.
 (3.1.3) st ¼ ð1  dt ÞE0 et  e_ pl t
 sc ¼ ð1  dc ÞE0 ec  e_ pl (3.1.4) c

The failure surface is also estimated based on the effective tensile and compressive cohesion stresses. These stresses are respectively calculated as:

The investigation of the structural performance of the hybrid composite precast frames Chapter

  st pl ¼ E0 e t  e t ð 1  dt Þ   sc pl ¼ E 0 ec  e c sc ¼ ð 1  dc Þ st ¼

3

91

(3.1.5) (3.1.6)

Constitutive relationship of concrete in uniaxial tension and compression with damaged plasticity of concrete is presented in Fig. 3.1.2, where the damage variables for compression and tension are defined by dc and dt, respectively. Readers are referred to Abaqus manual [12, Chapter 2] for details of descriptions. Damaged plasticity model for concrete (concrete damaged plasticity) ck ck The postfailure stress-strain relationships expressed as a function of the cracking strains (e t and e c ) characterize the postfailure behavior with plastic strains for reinforced concrete. In Fig. 3.1.1, these plastic strains were calculated as the difference between the total strain and the elastic strain corresponding to the undamaged material. During the analysis, Abaqus converts the cracking strain to plastic strain using Eqs. (3.1.5), (3.1.6). Compressive and tensile cracking under low confining pressures governs the failure of the concrete according to the concrete damaged plasticity rule. Both compressive and tensile behavior of concrete is modeled by concrete damaged plasticity, being discretized to ensure the accurate result, in the model for the numerical analysis of this chapter. The behavior of concrete in tension and strain-stress characteristics for cracked concrete are assigned in two ways: (1) defining a postfailure stress-strain relationship existing between microcracks and (2) applying a fractured energy cracking criterion [1]. The uniaxial tensile response of concrete with damaged plasticity is defined by a postfailure stress-strain relationship subjected to tension forces as illustrated in Fig. 3.1.1.

3.1.2 FEA parameters and their physical meanings Abaqus requests the users to define some parameters to represent the behavior of the concrete and steel materials. The concrete parameters defined to simulate the structural performance of the proposed mechanical joints shown in Fig. 2.2.2 of Chapter 2 can be summarized into two categories: (1) In the elastic region, both the density and Young’s modulus (E) were defined, and (2) in the plastic region, the damaged plasticity model of concrete was introduced. The damaged plasticity model of concrete was assigned by defining compressive behavior, tensile behavior, and plasticity parameters, including dilation angle, eccentricity, fb0/fc0 value, Kc value, and viscosity. The compressive behavior of concrete was predicted using stress-strain curve including Kent-Park and Mander [2] in this chapter, and the tensile behavior was defined by assuming the tensile concrete strength equivalent to 1/10 of the compressive strength of concrete. However, the definition with the physical meaning of these FE parameters for concrete plasticity is discussed in the following sections.

3.1.2.1 Material parameters for calibrations The parameters commonly used in nonlinear finite element analysis considering damaged concrete plasticity include plastic tensile cracking and compressive crushing as the two major failure mechanisms. The typical parameters defined in damaged plasticity of concrete for the calibration included a density, Young’s modulus (E), a Poisson’s ratio, viscosity parameter, an eccentricity with dilation angles, and Kc. The default value of eccentricity is 0.1, and Kc is defined as the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian. All parameters must be determined reflecting the structural environment, structural type, boundary conditions, structural material so that the best structural behavior can be obtained. The dilation angle for steel-concrete precast composite beams was sought to best match the behavior of test data based on the parameter sensitivity analysis. Table 3.1.1 summarizes the parameters used to model hybrid composite members of the numerical analysis in this chapter.

3.1.2.2 Yield surface of concrete This section summarizes the yield surface of concrete described in the Abaqus manual [12, Chapter 2]. The yield function proposed by Lubliner et al. [3], which was modified by Lee and Fenves [1], was implemented in the yield model of the Abaqus to account for different evolution of strength under biaxial tension and compression. In the yield criteria [3], tension and compression stresses instead of J3 shown in Eq. (3.1.7) were calculated based on maximum principal effective stress ^max ) and an invariant function of the state of stress, showing that the yield is independent of the intermediate principal (s stress. Different yield values in tri-axial tension and compression were observed by the concrete material.

92 Hybrid composite precast systems

FIG. 3.1.2 Constitutive relations with damaged plasticity of concrete; scalar stiffness degradation variable for damaged plasticity of concrete [4, Chapter 2].

The investigation of the structural performance of the hybrid composite precast frames Chapter

3

93

TABLE 3.1.1 Parameters used for the calibration of FE models. Parameter

Specified values in FE runs

Default values

Dilation angle

30 degrees

N/A

Eccentricity (E)

0.1

0.1

Ratio fb0/fc0

1.16

1.16

K-value

2/3

2/3

Viscosity

0.003

0.0

Damping factor

0.0002

0.0002

F¼

 pl       1   ^max  g s ^max  sc e pl q  3ap + b e s c ¼0 1a

(3.1.7)

where hxi ¼ 12 ðjxj + xÞ: With 

 =sc0  1  a¼  ;0  a  0:5 2 sb0 =sc0  1 sb0

(3.1.8)

 pl   sc e c b ¼ pl  ð1  aÞ  ð1 + aÞ, st e t g¼

(3.1.9)

3ð1  Kc Þ 2Kc  1

(3.1.10)

The ratio (a) of the initial equibiaxial compressive yield stress (sb0) to the initial uniaxial compressive yield stress (sc0) shown in Eq. (3.1.8) should not be less than 0 and not greater than 0.5. The a increases, resulting in decreasing the yield function when the difference between biaxial and uniaxial compressive yield stress increases. Oliver showed that a value of a between 0.08 and 0.12 was yielded when experimental values of sb0 =sc0 lie between 1.10 and 1.16. Abaqus analysis used 1.16 as the default value of sb0 =sc0 . The values of sb0 =sc0 other than the default values can be used to determine the a value that best describes the postyield behavior of the composite 2 and 4. The  beam with mechanical joints shown in Chapters   pl

pl

ratio of the effective compressive cohesion stresses, s c e c , to the effective tensile cohesion stresses, st e t , denoted as  pl   pl    b in Eq. (3.1.9), becomes 7.68 when a ¼ 0.12 and sc e c =st e t ¼ 10:0.

Increasing the difference between the effective compressive and the effective tensile cohesion stresses, resulting in the effective compressive cohesion stresses that are larger than the effective tensile cohesion stresses, increases the yield function F. The shape of the yield surface is defined by g, shown in Eq. (3.1.10), when the maximum effective principal ^max ) is negative. The shape of the yield surface in the three-dimensional space shown in Fig. 3.1.3A is also defined stress (s by the ratio (Kc) of the second stress invariant in the tensile meridian to that of the compressive meridian, which must satisfy the condition 0.5 < Kc  1.0. The default value of Kc in the Abaqus analysis is 2/3. The yield function in-plane in plane stress subjected to biaxial stresses is shown in Fig. 3.1.3B. The value of the ratio fb0/fc0 (ratio of initial equibiaxial compressive yield stress to initial compressive stress, values of sb0 =sc0 in Fig. 3.1.3B) was set to the default value of 1.16 in most of the numerical analyses in this chapter. The increase of sb0 =sc0 ðfb0/fc0) ratio is related to the increase of the flexural capacity of reinforced concrete members. However, this value may be adjusted to study its influence on the confining effects of concrete members. The ratio sb0 =sc0 ðfb0/fc0) was kept as default to avoid the overestimation of the structural response of the frames with mechanical joints shown in this chapter.

94

Hybrid composite precast systems

FIG. 3.1.3 Yield surface of concrete [12, Chapter 2].

^ 1 – – + bs– (q - 3a p 2) = sc0 1-a

s^2 s10 s^1

Kc = 2/3

–S2

Uniaxial tension

–S1

Uniaxial compression Biaxial tension

Kc = 1

^ 1 – – + bs– (q - 3a p 1) = sc0 1-a

(T.M.)

sc0

(sb0,sb0)

(C.M.) –S3

1 – (q - 3a p– ) = sc0

Biaxial compression 1-a

(A)

Typical yield surfaces for the linear model in the deviatoric (3D) plane, [12, Chapter 2]

(B)

Yield surface in plane (2D) stress [12, Chapter 2]

3.1.3 Dilation angle 3.1.3.1 Volumetric dilatations The angle of dilation, which is assumed constant during plastic yielding, controls an amount of plastic volumetric strain developed during plastic shearing. Soils such as clays (regardless of overconsolidated layers), which are characterized by a very low dilation, do not change volume during shearing. A dilation angle can be estimated by uniaxial and biaxial stress tests, shown in Fig. 3.1.4 [4], where volumetric strains are compared with uniaxial compressive strain for various dilation angles. In the numerical analysis shown in Fig. 3.1.4 [4], the negative volume changes were observed for the dilation angles of 0°, 5°, and 15° when the uniaxial compressive strain was applied, while the volume change started to become positive at around 0.0017 of uniaxial compressive strain for the dilation angle of 30°. Numerical computations with values of dilation angles between 0° and 30° provided larger volumetric strains than those of Kupfer [4], indicating that experimental volumetric strains of Kupfer were negative within entire strains e11. The numerical volumetric strains shown in Fig. 3.1.4 [4] FIG. 3.1.4 Influence of dilation angles on concrete damaged plasticity models; volumetric dilatations and dilation angle [5].

The investigation of the structural performance of the hybrid composite precast frames Chapter

3

95

were also found negative with the dilation angles in range 0° and 15°. The default value of 30° was used in Abaqus because the volumetric strains for the prediction of concrete plasticity for reinforced concrete members in general were well represented by the dilation angle of 30°.

3.1.3.2 Definition of dilation angle The dilation angle, c, indicates the volume change caused by the confining pressure within the material, and it is used to predict the plasticization of the sections, which comes from the nonassociated flow rule. The dilation angles for brittle behavior of concrete were determined based on the theory proposed by Malm et al. [5], shown in Fig. 3.1.4. The inelastic strains caused by the plastic distortion for a brittle material such as concrete can cause significant volume change, called dilatancy. In Fig. 3.1.4, Malm et al. studied the influence of dilation angles in the range between 10° and 56.3° on concrete damaged plasticity models, suggesting that dilation angles between 30° and 40° provided the best fit for the numerical investigations of reinforced concrete structures. Brittle behavior was observed for low values of the dilation angle, while higher values of dilation close to 56° provided ductile behavior [5]. In this chapter, the nonlinear behavior of concrete with the mechanical joints introduced in Chapter 2 was investigated based on a dilation angle of 30° to 40°, indicating that numerical result with 30° provided an acceptable match with test data in general.

3.1.3.3 Drucker-Prager hyperbolic plastic potential function Flow (plasticization) rule based on nonassociated plastic flow potential In ABAQUS, the dilatancy in damaged plasticity concrete was modeled by the dilation angle in Drucker-Prager [5, 6] hyperbolic plastic potential function shown in Eq. (3.1.11) and Fig. 3.1.5A [12, Chapter 2] where the slope of the plastic potential at high confining pressures was defined by the dilation angles. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi GðsÞ ¼ ðEst0 tancÞ2 + q2  ptan c (3.1.11) The dilatancy (dilation angle) and the interlocking concept are originally formulated by the volume change of the soil. Frictional soil behavior and strength is primarily influenced by frictional resistance between soil particles based on positive (for dense sand) or negative (negative dilation angle for loose sand) volume change caused by the interlocking when

Hardening

q-

Î Eccentricity

(A)

e× p

y

Hyperbolic Drucker-Prager flow potential p-

Drucker-Prager nonassociated plastic flow potential [12, Chapter 2], [5], [6]

Nonassociated plastic flow potential vs. associate flow with yield function

(B) FIG. 3.1.5 Nonassociated plastic flow potential.

[7]

96

Hybrid composite precast systems

shear stress is applied to particles. The volume increases with shearing for dense sand because sand expands due to the confining pressure. The apparent externally mobilized angular friction of soil on horizontal friction (f) can be defined as [7]: f ðstrengthÞ ¼ fu ðinternal frictionÞ + b ðdilatancyÞ

(3.1.12)

Where f is an angle of sliding friction between particle surfaces (apparent externally mobilized angle of friction on horizontal planes), depending on the nature of packing of the soil (b) and friction (fu). The friction (fu) is mostly constant for given soils while dilatancy (b) will vary depending on how densely the soils are packed. The f (angle of sliding friction) becomes higher as the soil becomes denser. fu is an angle of friction that is determined for soils, resisting sliding on the inclined planes. b is the function of dilatancy of the soil, which increases with the packing of soil (making dense soil) because more work needs to be done to overcome the effect of the interlocking. The soil’s strength is then determined based on the angle of friction (fu) and dilatancy (b). The dilation angle for granular soils like sands can also be determined based on the angle of internal friction. Clays, regardless of the degree of overconsolidation, are defined by a very low dilation angle (b  0). For noncohesive soils (including sand and gravel) with the angle of internal friction (fu) greater than 30°, the dilation angle can be estimated as b ¼ fu  30°. A negative value of the dilation angle is acceptable only for rather loose sands [8]. Concrete with large confinement will demonstrate higher sliding friction angle than concrete with less confinement because of higher dilatancy with the interlocking (b). Dilation angles define the direction of the plastic increment vector. Three types of models— linear, hyperbolic, and exponential—were suggested in Abaqus software [12, Chapter 2]. In this chapter, the concrete damaged plasticity model was constructed based on a nonassociated hyperbolic function, shown in Fig. 3.1.5A [12, Chapter 2] to reproduce the change in volume. Dilation caused by plastic distortion was reproduced by the plastic potential function G, by Lublinear et al. [2]. The evolution of the inelastic displacement in the fracture process zone was determined by the flow rule defined as, e_ pl ¼ l_ ∂G∂sðsÞ, shown in Eq. (3.1.13). Plastic flow (plasticization represented by plastic strain vector) develops along the normal to the plastic potential function, not to the yield surface for a nonassociated flow [9]. The nonassociated plastic potential function reaches the asymptotic line of the linear Drucker-Prager flow potential at high confining pressure stress, which intersects hydrostatic pressure axis at 90°, not intersecting the yield surface, as shown in Fig. 3.1.5B [7]. The direction of the plastic strain flow is normal to the yield surface for an associated flow. In most cases, the plastic potential functions follow the nonassociated flow rule. The rate of plastic strain (_e pl ) is defined as being proportional to the derivative of the plastic flow potential function with respect to the effective stress. Thus, the direction of the rate of plastic strain (_e pl ) is defined by the effective stress. The plastic potential and yield function are the same when associated plasticity is used whereas they are different when nonassociated plasticity is implemented. Plastic deformation of some ceramics, concrete, and clay are determined based on the nonassociated flow rule, whereas metals and alloys follow the associated flow rule. The _ which varies length of the strain increment vector, e_ pl , is governed by a scalar hardening parameter denoted as l, depending on the straining process [10]. A scalar hardening parameter, in Fig. 3.1.5, indicates the length of the strain increment vector. ∂GðsÞ e_ pl ¼ l_ ∂s

(3.1.13)

The parameters of the nonassociated plastic flow potential are shown in Fig. 3.1.5. The hydrostatic pressure is represented by p ( I1/3 ¼  (s11 + s22 + s33)/3) where I1 is the first stress invariant. The von Mises equivalent effective stress is also qffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 3 governed by q 3J2 , where J2 (s211 + s222  s11s22) represents the second deviatoric stress invariant for 2S : S ¼ biaxial loading and S (PI + sÞ represents the effective deviatoric stress tensor. c is the dilatation angle measured in the p-q plane at high confining pressure stress [12, Chapter 2]. Eccentricity, e The eccentricity, E, in Eq. (3.1.11) is the rate, letting the hyperbolic plastic potential function approach the asymptote at the uniaxial tensile stress, st0. The dilation angle increases more rapidly at the lower confining pressure when an eccentricity is large, as shown in Fig. 3.1.5. The lager curvature is provided to the flow potential for a larger eccentricity. However, almost the same dilation angle with constant curvature is used over the wide range of the confining hydrostatic pressures when an

The investigation of the structural performance of the hybrid composite precast frames Chapter

3

97

eccentricity is small. When eccentricity is equal to zero, the constant dilation angle with constant curvature is obtained over the entire range of the confining hydrostatic pressures, leading to flow potential that is independent of the uniaxial tensile stress. The failure criteria can be determined by Mohr circle. The role of eccentricity is to provide the rate at which the asymptote for the plastic potential function is evaluated. The default for the eccentricity value of 0.1 is set for the flow potential so that almost the same dilation angle with constant curvature is used over the wide range of the confining hydrostatic pressures. In this chapter, the default value of 0.1 was used for the eccentricity to construct the flow potential function. The dilation angle, c, indicates the volume change caused by the confining pressure within the material, and it is used to describe the flow rule, which comes from the nonassociated flow rule. Identification of dilation angles and damage variables for concrete section confined by T section steels Confinements provided by a T steel section in the compression zone, shown in Fig. 3.1.6A, were explored to identify the dilation angles and damage variables of the concrete sections in a previous study of the author [11]. The structural characteristics differed based on the direction of T steel section since the specimens were not symmetrical. The evaluated structural response of the specimens is presented in Fig. 3.1.6B where a good correlation between numerical estimation and test observation was found. In the 1st quadrant, where no steel flange was available to confine the concrete section in the compression zone, the numerical estimation of the specimens represented by load-displacement relationship indicated by

FIG. 3.1.6 Composite beam with T steel section [11].

98

Hybrid composite precast systems

Legend 6 were in agreement with test data when a dilation angle of 30°, a full damaged plasticity and a viscosity of 0.001 were used in the 1st quadrant. However, the load-displacement relationship represented by Legend 6 is too small relative to the test data in the 3rd quadrant because of the large damage variable, where a steel flange was available for confining the concrete section in the compression zone, as shown in Fig. 3.1.6B. The load-displacement relationship represented by Legend 4 was in agreement with the test data in the third quadrant, which demonstrated that the accurate composite action with the concrete was captured in the numerical model when the damage variable was reduced to 10% with the same dilation angle of 35°. The numerical analysis yielded greater load-displacement relationship (refer to Legend 4) than the experimentally observed data with a large discrepancy in the first quadrant when the 10% damaged plasticity model with a dilation angle of 35° was implemented, as shown in Fig. 3.1.6B. This result indicated that small damage variable were not preferable for composite beam sections where concrete sections were not strongly confined by wide flange and web sections. The scientific combination of lower dilation angle and larger damage variable was referable, reflecting brittle failures of concrete that was less confined. Both the brittle failures of concrete and dilatancy of the concrete should be modeled based on the combinations of the dilation angles and damage variables, respectively, as illustrated in the load-displacement relationship as shown in Fig. 3.1.6. The small damage variable was considered in the calculations of the load-displacement relationships (Legends 4 and 5) for concrete fully confined by steel sections whereas the large damage variable was implemented in those (Legends 6 and 7) for concrete less confined by steel sections.

3.1.3.4 Viscosity parameter The viscoplastic strain rate tensor expressed in Eq. (3.1.14) was originally proposed by Devaut-Lions [12] to stabilize the concrete damaged plasticity model: e_ pl v ¼

1
pl pl  e  ev m

(3.1.14)

where m denotes the viscosity parameter which relaxes the viscoplastic systems to calculate the plastic strains in the inviscid model. The plastic flow rate is significantly reduced when viscosity (m) increases (refer to Eq. 3.1.15), which will, then, decrease both the plastic degradation and the rate of the plastic fracture of the structural member. A good convergence of the nonlinear analyses is achieved as a result of the application of viscosity (m). The viscosity parameter (viscous stiffness degradation variable for the viscoplastic system) also controls the rate of degradation variable for the viscoplastic system, which can be written as: 1 d_ v ¼ ðd  dv Þ m

(3.1.15)

where d represents the degradation variable for the viscoplastic system. The convergence of the numerical process is enhanced by increasing viscosity parameter, m, which decreases the rate of the plastic fracture. The stress-strain relationship of the viscoplastic model with the viscous stiffness degradation variable is obtained by Eq. (3.1.16) whereas the damage variable considering viscosity parameter m is defined as dv.
 pl (3.1.16) s ¼ ð1  dv ÞDel 0 : e  ev The rate of convergence of the model in the softening region can be improved by the viscoplastic regularization with a small value compared to the time increment without compromising analysis results. Change of viscosity does not influence analysis results significantly for the specimen under consideration with mechanical joints introduced in Chapter 2. The viscosity parameter of 15% of the time increment step was proposed by Fenves to overcome severe convergence difficulties for highly weakened structural systems. The value of viscosity parameter, 0.001, was used in the analysis of this chapter when no severe convergence difficulties are expected for investigating the structural behavior of the precast hybrid composite beam with mechanical joints. A default value of 0.0 is suggested as the input for the viscosity parameter in Abaqus. However, the viscosity parameter may be adjusted to improve the rate of convergence, especially when dealing with complex numerical models. It should be noted that the concrete materials demonstrate complex behavior with continuous cracking that is caused by tensile stresses and strains. The FE models are more likely to undergo converging difficulties once these cracks are being formed, leading to premature termination of the analysis.

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99

3.1.3.5 Application of artificial damping factors to resolve the stability problems Damping factor to solve numerical instability The automatic addition of volume-proportional damping with constant factor is issued to the model to stabilize the nonlinear procedures when numerical instabilities occur with FE models. In Eq. (3.1.17), the numerical problems were treated by an automatic mechanism, adding viscous forces (Fv ¼ cMv) to the global equilibrium equations. A damping factor, an artificial mass matrix calculated with unit density, and the vector of nodal velocities were represented by c, M, and v, respectively. In ABAQUS, updated damping factors were recalculated based on the declared damping intensity and the solution of the first increment of the step. The damping factors were modified at the beginning of the steps, and automatic stabilization was implemented in the subsequent steps to remove potential convergence difficulties. Applied damping factors varied with time to account for changes in the analysis depending on the degree of numerical instability. When the model was stable, artificial damping did not vary any more, not affecting viscous forces. The amount of dissipated viscous energy was, then, very small. However, when numerical instability occurred, the applied damping dissipated the strain energy, increasing viscous forces. The damping factor can change the consequences of the run when the dissipated energy is too large. P  I  Fv ¼ 0

(3.1.17)

It is recommended in Abaqus that the energy dissipation due to damping (ALLSD, ALLCD, and ALLVD) be limited to less than 2% of the total internal energy (ALLIE). The level of the dissipated energy should be checked when the damping factor is applied during the analysis. A minimum value of the damping factor is recommended to improve convergence when encountering numerical instabilities. In Abaqus, the initial default the damping factor of 0.0002 is used for automatic stabilization. The viscosity introduced in Section 3.1.3.4 is applied when the run is terminated during the analysis due to concrete damages, whereas damping may have to be used to overcome the initial convergence difficulties when the model is not stable from the beginning of the runs. Damping with steel structures Fig. 9.4.2A of Chapter 9 shows a column bracket with a skew cut, the guide angles consisting of a pair of L-shaped channels (refer to Figs. 9.4.3 and 9.4.4A of Chapter 9), and stiffener plate (refer to Figs. 9.4.4B and C of Chapter 9) that were installed beneath the lower flange of the column bracket to help place the steel beam section with the skew web cut into the L-shaped channels. However, in Fig. 3.1.7 [13], numerical errors were identified at nodes #1 and #2, which were in the neighborhood of the sharp edges of structural steel joint, indicating that the convergence difficulties and numerical instability were caused by the irregular structural configuration. In Fig. 3.1.8, the internal and external forces failed to balance the residual force (Rb) as time elapsed, leading to the cyclic analysis, which did not converge. In Fig. 3.1.9 [13], the moment-displacement relationships without damping ratios are compared with that based on the damping ratios of 1.0  104 to 2.0  104. As shown in the computation represented by Legend 3 (refer to Fig. 3.1.9), the numerical computation for the cyclic

FIG. 3.1.7 Convergence difficulties and numerical instability; locations of numerical instability [13].

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FIG. 3.1.8 Iteration in ABAQUS [12, Chapter 2].

FIG. 3.1.9 Cyclic analysis results without damping/with damping ratios of 1.0  104 to 2.0  104 [13].

load-displacement relationship was terminated prematurely at a stroke around 60 mm when a damping factor was not assigned. The computed strokes of cyclic analysis results without damping (refer to the moment-displacement relationships by Legend 3 in Fig. 3.1.9) were substantially short compared with those obtained by implementing a damping factor of 0.0001 (refer to the moment-displacement relationships by Legend 4 of Fig. 3.1.9) in which the damping factor enhanced the analysis results and convergence. In the moment-displacement relationship represented by Legend 4 in Fig. 3.1.9, the numerical instability was resolved by an application of default damping factor. However, the computed lateral load-resisting strength (refer to Legends 4 and 5 of Fig. 3.1.9) of the section was much higher than that obtained monotonically when the default damping factor was not implemented. The manual process of trial and error was required until a converged solution with an optimal damping factor was obtained. The energy dissipated by viscous damping (ALLSD) increased to overcome numerical instability; however, the dissipated stabilization energy (ALLSD) should be sufficiently small. In Fig. 3.1.10 [13], the computation was extended beyond that without a damping factor when the cyclic analysis results were performed with damping factors of

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FIG. 3.1.10 Cyclic analysis results with damping ratios of 1.0  106 to 4.0  106 [13].

1.0  106 to 4.0  106. However, the damping factors should be increased because the instability of the numerical calculation in the positive regime did not subside. In Fig. 3.1.11 [13], the numerical instability subsided when damping factors increased to values of 1.0  105 to 5.0  105. The damping factors were determined in such a way that the dissipated energy for a given increment similar to the first increment was a small fraction of the strain energy that was applied at nodes to satisfy the equilibrium. In the last cycle (highlighted by a solid line) of Fig. 3.1.12A [13], the moment-displacement relationship with a damping factor of 5.0  105 is most accurately matched with the monotonic moment-displacement relationship. Fig. 3.1.12B [13] illustrates locations of the errors caused by the instability during the analysis when damping factors of 2.0  105 and 5.0  105 were implemented. The two errors, including (1) maximum contact force error and (2) maximum residual force error were observed. Fig. 3.1.12B indicates that the maximum contact force error occurred at the interface between the bolt head FIG. 3.1.11 Cyclic analysis results with damping ratios of 1.0  105 to 5.0  105 [13].

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FIG. 3.1.12 Best prediction of the moment-displacement relationship [13].

and the stiffener plate. Penetration between two surfaces during contact caused this type of convergence error, suggesting that the bolt head penetrated the stiffener plate. In most cases, the penetration errors were removed by either re-assigning the contact properties between the elements in contact (bolt-stiffener plate) or adjusting the mesh. The convergence error with a residual force was generated, leading to an abnormal termination, when force equilibrium was not achieved. A lack of equilibrium between the external and internal forces causing the maximum residual force error can be fixed by assigning an artificial damping factor to stabilize the analysis.

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FIG. 3.1.13 Comparison of viscous damping (ALLSD) and total strain energy (ALLIE) [12, Chapter 2].

The damping factors must be increased if the convergence behavior is problematic, whereas the damping factors should be decreased if they distort the solution. The stabilization energy (ALLSD) dissipated by viscous damping (ALLSD) should be less than the total strain energy (ALLIE), ensuring that viscous force stabilization (VF) be sufficiently low, as shown in Fig. 3.1.13 [12, Chapter 2]. ALLSD in ABAQUS will stop increasing when a converged solution is obtained.

3.1.4 Fracture criterion 3.1.4.1 Pressure-independent yield criteria; von Mises and Tresca The pressure independent yield criteria, such as von Mises and Tresca [14] yield criterion, are generally used to describe the behavior of ductile materials such as steels because confining pressures do not influence shear strength and volumetric changes of metals. The von Mises and Tresca, shown in Fig. 3.1.14, are widely used to predict the failure mechanism of ductile materials. Once the material yields under tension forces, stresses are no longer proportional to the strains, and the plastic deformation is caused by the molecular rearrangement in the material. It is so important to have a full understanding of the yielding and fracture of the material. The fracture is driven by the normal stresses, which act to separate molecules, and if the bond between molecules fails, then molecules cannot reform in new positions. Alternatively, the yielding of material is controlled by shear stresses causing the sliding of one plane along with another. However, the broken molecules are allowed to reform in new positions. Tresca yield criterion assumes that the yielding of materials starts when the maximum shear stress in the material reaches the maximum shear stress at yielding in a given simple test. It should be noted that the maximum shear stress is equivalent to half of the difference between the largest and smallest principal stress, implying that the shear yield stress is half the axial yield strength. The von Mises yield criterion states that yielding of material begins when the maximum distortion energy in material reaches the maximum distortion at yielding in a given simple tensile test. The distortion energy is estimated based on the change in volume and shape of the material. Tresca and von Mises yield criteria do not depend on hydrostatic pressures. von Mesis is more accurate in describing ductile materials in terms of ductile plastic deformation, such as steel and aluminum. von Mesis closely agrees with most conventional ductile materials. von Mesis generally works

FIG. 3.1.14 Pressure independent yield criterion; von Mises and Tresca [14].

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very well, avoiding plastic failure. However, brittle failure is not very well defined by these two models (von Mesis and Tresca). These two methods are widely used to determine the failure points of ductile materials. The yield surface of the von Mesis is located outside than that of Tresca, indicating that the resisting strength of the von Mesis is larger (overestimate) than that of Tresca. The von Mesis criterion is only a mild overestimate of yielding of the ductile metals, steel, copper, and aluminum because larger strength is used for design. The yield criterion and design are also mildly less conservative. Reaching the yield criteria with the von Mesis yield criterion is more difficult than that with the Tresca yield criterion, predicting lower effective stresses for a given stress status. This consideration leads to lower loads-displacement. However, reaching the yield criteria with the Tresca yield criterion is easier (underestimate) than that with the von Mesis yield criterion, predicting higher effective stresses for a given stress status. This leads to higher loads-displacement. Tresca is an underestimate of yielding of the materials, leading to conservative yield criterion and design because lower strength is used for design. In the hybrid composite beams with T steel sections [11], load-displacement relationship computed with von Mesis yield criteria was slightly lower than that based on Tresca criteria in the same state of stress. The postyield behavior based on von Mesis yield criterion for steel section was compared with that obtained using Tresca model, as shown in Fig. 3.1.15, where von Mesis model predicts lower effective stress (lower actual comparison to the yield strength) than Tresca for a given status of stress. The load-displacement relationship represented by Legends 4–7 were obtained using von Mesis yield criterion based on various parameters, whereas those indicated by Legend 8 was calculated based on Tresca yield criterion. The Tresca model was not used in the present model since this model underestimates yield strength of the materials. The von Mises yield criterion was selected to determine the strength of ductile elements, including rebars, embedded L-shaped steels, metal plates, bolts, and nuts. As discussed in Section 3.1.3.2, the dilations angle of 30° was recommended for reinforced concrete. The dilation angle increased when confining effects were provided by stirrups, hoops, and steel section encased in structural concrete. The damage variable can be implemented with dilation angle to model damaged plasticity of concrete. The internal friction angles little higher than dilation angle can be used in Tresca yield criterion. However, the internal friction angle and dilation angle of 0° were used for the yield prediction of the ductile materials such as steels when Tresca yield criterion was implemented in computation by Legend 8 of Fig. 3.1.15. This was because that shear strength and volumetric changes did not occur even if confinement was provided to steels sections.

3.1.4.2 Pressure-dependent yield criteria; Drucker-Prager and Mohr-Coulomb The strength of ductile metals, steel, copper, and aluminum can be predicted using yield criterion, such as von Mesis and Tresca criterion, which are independent of confining pressures due to the low volumetric-dilatational characteristics

FIG. 3.1.15 Test data versus nonlinear numerical results (Specimen PS1) [11].

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FIG. 3.1.16 Drucker-Prager and Mohr-Coulomb failure criterion.

of the materials. The shear strength of metal does not change due to the confining effect. However, pressure-dependent yield criterion such as Drucker-Prager, shown in Fig. 3.1.16, should be used to evaluate the strength of concrete because the strength of concrete is greatly affected by confining pressures. Coulomb yield criterion is usually used for the prediction of the shear strength of the brittle geotechnical materials such as sand and rock, which need some conservatism in the analysis. The Mohr-Coulomb yield criterion (MC) is used as a pressure-sensitive constitutive model in engineering practices, especially in geotechnical engineering. The failure criterion is controlled by three crucial parameters, which include friction angle ’, cohesion c, and the dilation angle c. The dilation angle c is used to describe the flow rule, which comes from the nonassociated flow. The plastic theory defines the flow rule as the evolution law for plastic strain rates. The flow rule is referred to associated flow rule when the plastic function is similar to the yield function. However, if they are different, the flow rule is no longer associated flow rule; instead, it is referred to nonassociated flow rule. The associated flow rule is widely used to model the behavior of the materials having significant negative dilatancy while the nonassociated rule is used to represent the behavior of materials having both negative and positive dilatancy. Rani et al. [15] criticized the application of MC despite its advantages. It was concluded that the MC criterion underestimates the yield strength of materials in many cases. Rani et al. stated that the MC criterion demonstrated two drawbacks, which can be summarized as follows: (1) the major principal stress s1 is independent to the intermediate principal stress s2, which underestimates the yield strength of material in many cases; and (2) the irregular hexagon of the MC yield surface harms the convergence in flow theory due to the presence of six sharp corners. The Drucker-Prager yield criterion (DP) is considered as a pressure-dependent model, which is used to determine if a material failed or underwent plastic yielding. Similarly, the DP yield criterion is defined based on two parameters, which govern the failure criteria. Parameters, including internal friction angle and cohesion are considered to define the yield surface of the DP yield criterion. The DP model is a simplified version of MC model, where the hexagonal shape of the failure cone was changed to a simple cone, as shown in Fig. 3.1.16. This model is often used to model soil behavior. Drucker Prague model is a pressure-dependent J2 (von Mesis) model, and Mohr Coulomb model is Tresca model with pressure dependence. The difference between MC and DP failure criteria is that MC yield criterion does not consider the intermediate principal stress, which leads to underestimating the yield strength of materials leading to a conservative design. The MC yield criterion was not used to study the concrete behavior of the proposed mechanical joints of this chapter. The DP yield criterion was chosen to simulate the failure mechanism of concrete columns; concrete columns were modeled based on concrete damaged plasticity models constructed using DP failure criterion.

3.1.5 Penetration of contact element 3.1.5.1 Definition of contact In the finite element analysis, independent contact surfaces exist with no related stiffness relationship defined between the surfaces in contact, uncoupling the stiffness matrix of the surfaces. They can overlap over the adjacent surface when the displacement of one element reaches further than the surface of another element. This overlapping destroys equilibrium between contacting elements to lead to convergence difficulties, which are common during numerical analysis. In Abaqus

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FIG. 3.1.17 Penetrations without contact compatibility.

applications, the contact stresses called penalty stiffness across the contacting area should be transferred, not being dissipated via penetrations, as shown in Fig. 3.1.17. The compressive normal stresses and tangential friction force are caused when they collide into each other, but tensile normal stresses should not act between the surfaces when they are apart. Slip model should define surface-to-surface contact, which is used for the slip interaction. With slip model, a contact surface was defined as hard contact in the normal direction, which is generally specified for the interface, allowing the separation of the interface in tension and no penetration of that in compression by applying penalty stiffness (refer to Section 3.1.5.3). However, the tangent contact is simulated by the friction coefficients, assuming there is little or no slip between the surfaces in contact.

3.1.5.2 Enforcement of contact compatibility to minimize penetrations The contact analysis aims to predict actual behavior between contact areas while the overlapping between elements is prevented. This can be achieved by assigning appropriate contact forces between the contacts when they collide, so that they expel each other, preventing the contacted meshes from being overlapped. In Fig. 3.1.18, the contact forces are applied to the contact surfaces (nodes and segments), enforcing contact constraints in compression to prevent overlapping of the surfaces. The penetrations are minimized by controlling contact forces, which are determined by the stiffness of contact elements. The stresses across the contacting area are artificially applied on the other surface to push the contacted surfaces back to the tangential surfaces of the elements, avoiding overlapping or penetrations between the contacted surfaces. The relationship between contacting surfaces to prevent interpenetration is achieved by enforcing contact compatibility. Contact compatibility was developed in the finite element formulation of the mechanical joints for no overlapping between contacts. However, pushing/sliding with some resistance was permitted between the contacted surfaces shown by gN and gT in Fig. 3.1.19. The finite normal contact force is calculated in Eq. (3.1.18) where Kn is called contact stiffness. Fn ¼ Kn  dp

(3.1.18)

Penetration (dp) decreases when the penalty stiffness increase with finite normal contact force. The penetration, dp, is small, leading to accurate solutions due to the small penetrations when the contact stiffness, Kn, is high. When penetration (dp) is zero, contact stiffness in Eq. (3.1.18) is infinite, which is numerically diverging. The penetration, dp, is big when the contact

FIG. 3.1.18 Contact compatibility.

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FIG. 3.1.19 Use of stiff springs in two directions to establish contact formulation.

stiffness, Kn, is small, leading to the convergence difficulties. One of the simplest methods to establish contact formulation is to use a stiff spring between two contacts, as shown in Fig. 3.1.19 [12, Chapter 2]. This method is based on contact stiffness (penalty stiffness) of the connecting elements.

3.1.5.3 Linear and nonlinear penalty stiffness In this section, the linear and nonlinear penalty stiffness was summarized from Abaqus manual [12, Chapter 2], including the contact properties between the two surfaces in contact that must be defined with one another. The penalty method was selected to represent the constraint enforcement to calibrate FE models. The contact stiffness behavior should be assigned with either linear or nonlinear characteristics to enforce contact compatibility. Abaqus prevented numerical instabilities by introducing the four regimes shown in Fig. 3.1.20A, which depicts the variation of contact stiffness in terms of contact pressure-overclosure relationships. The nonlinear penalty stiffness with a nonlinear pressure-overclosure relationship increases from the initial stiffness (0.1 Kin or 10% of the initial stiffness) to the final stiffness (denoted as 10 Kin), whereas the linear penalty method is constant. Four distinct regimes for the nonlinear penalty method are illustrated in Fig. 3.1.20A and B. Nonlinear behavior for the contact stiffness, which is defined based on two parameters (i.e., the nonlinear penalty stiffness and clearance C0), was chosen for the analysis of specimens with mechanical joints in this chapter. (1) Inactive contact regime (clearance greater than C0); the contact forces remains zero. The default setting of C0 is zero in Abaqus. (2) Constant initial penalty stiffness regime; the contact forces start increasing linearly with a slope of contact stiffness equal to constant Ki to remove penetrations in the range between  C0 and e. The default initial penalty stiffness, Ki, is equal to the representative underlying element stiffness. The default value of e is 1% of the characteristic length computed by Abaqus to represent a typical facet size. FIG. 3.1.20 Nonlinear penalty pressureoverclosure relationship [12, Chapter 2].

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(3) Stiffening regime; when contacts with zero C0 collide, the contact pressure increases rapidly in a quadratic manner causing penetrations in the range between e and d. Contact stiffness is increased in a slow manner to prevent infinite contact forces at zero C0. The contact penalty stiffness increases linearly from Ki to Kf to prevent overlapping. The penetration can be avoided by assigning small contacts forces prior to the contacts. The default final penalty stiffness, Kf, is 100 times the representative underlying element stiffness (Ki). The default value of d is 3% of the characteristic length used to compute e. (4) Constant final contact stiffness regime; the contact forces vary linearly again with final constant contact stiffness of a slope equal to Kf to remove penetrations greater than d. Low initial penalty stiffness typically results in better convergence of the Newton iterations and better robustness, while the higher final stiffness keeps the overclosure at an acceptable level as the contact pressure builds up. However, the high contact stiffness jeopardizes convergence as well due to the numerical instability when hard surfaces contact each other at high speed. The contact area and penalty stiffness should be reduced when the convergence difficulties occur due to high penalty stiffness. However, the penetration should be monitored to ensure that penalty stiffness was not kept too low. In Abaqus modeling, parameters defining a nonlinear pressure-overclosure relationship can be established by default values as follows. (1) Scale factor; the default scale factor for the final nonlinear penalty stiffness or for the final nonlinear penalty stiffness if specified in the first field of the data line. The default is one. (2) Initial/final stiffness ratio; the ratio of initial penalty stiffness (Ki) over the final penalty stiffness (Kf). The default is 0.01. (3) Upper quadratic limit scale factor; scale factor for the upper quadratic limit d, which is equal to the scale factor times the characteristic contact facet length. The default is 0.03. (4) Lower quadratic limit ratio; ratio (e  c0)/(d  c0) that defines the lower quadratic limit e. The default is 0.33333 (1/3, ratio of between C0 and e over C0 and d). (5) Clearance at which contact pressure is zero.

3.1.5.4 Contact formulation Complex contacts between elements that slide over one another during the analysis were formulated to characterize geometric configurations of the mechanical joint. The contact properties between two surfaces were defined by a surface-tosurface method due to the reliable results compared with the node-to-surface method. Each constraint considers one slave node but also covers adjacent slave nodes because the surface-to-surface approach imposes contact conditions in an average sense over the areas that neighbor the slave nodes. In Fig. 3.1.21, contact between the two surfaces was defined by choosing the slave and master surfaces in a contact pair containing the surfaces. When selecting these surfaces, the following guidelines are used: (1) between the surfaces in contact, the larger should be a master surface, (2) if they have the same size, the stiffer body should act as a master surface, and (3) if the surfaces have the same size and stiffness, then the one with the coarse mesh should be selected as the master surface [12, Chapter 2]. The slave body cannot penetrate into the master element; however, the master element can penetrate into the slave element These useful guidelines should be followed when defining contact formulations because failing to define a proper master or slave surface can lead to undesirable penetration among bodies in contact.

3.1.6 Modeling technique; types of contact elements in FEA 3.1.6.1 Embedded, tie elements and a geometric tolerance The components consisting of a mechanical joint, including H-steel sections, reinforcing bars, couplers, and stirrups, can be modeled as one of elements including tie, cohesive, bond-slip, and embedded elements. In a embedded region

FIG. 3.1.21 Definition of master and slave nodes.

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FIG. 3.1.22 Defining constraint.

(A)

Embedded region [16]

Nodes on the host elements Nodes on the embedded elements Edges of the host elements Edges of the embedded elements

(B)

Exterior tolerance for embedded elements [12, Chapter 2]

technique, the elements were embedded in “host” elements, allowing a perfect bond between embedded elements and host elements, as depicted in Fig. 3.1.22A. Possible translational degrees of freedom of the embedded nodes are prohibited when Abaqus tracks the geometric relations between nodes of embedded and host elements. In Abaqus, the geometric tolerance defined as 5% of the length of nonembedded elements is allowed to specify how far an embedded node can lie outside of the host element during analysis with a default value of 0.05. The node on the host element was precisely located based on the position of the embedded nodes, as indicated in Fig. 3.1.22B. Abaqus will issue an analysis error when the embedded node is located outside of the tolerance zone. A geometric tolerance of 0.1 was used in the analysis of mechanical joints. A surface-based tie constraint ties two surfaces (both in the horizontal and normal direction) together for the duration of simulation only with surface-based constraint definitions. A tie constraint allows an interface to fuse together two regions even though the meshes created on the surfaces of the regions may be dissimilar. During the analysis, the tie model constrains each of the nodes on the slave surface to have the same motion and the same value of temperature and pore pressure on the master surface to which it is closest. Rotational degrees of freedom were allowed between the two materials. Additional application of tie and cohesive model technique are explained in the subsequent sections.

3.1.6.2 Accurate contact model for steel-concrete hybrid composite members; bond-slip characteristics between concrete and rebar, steels As many as 32 runs were performed to calibrate, and all numerical runs with calibration history are described in Fig. 3.1.24 for the specimen C6 shown in Fig. 3.1.23 (refer to Fig. 2.5.5 in Section 2.5.1.2 of Chapter 2) [16, 17] tested by the author. Numerical runs with all models, including bond-slip characteristics between concrete and steels (wide flange steel sections and rebars) were performed. The parameters for all calibrations were also summarized in the legends of

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FIG. 3.1.23 Experimental investigation of the hybrid column [17].

Fig. 3.1.24A. A total of 32 runs were classified according to the models to demonstrate the influences of the models on the structural responses. It is noteworthy that the numerical model based on the tie or default cohesive model represented by Legends 2 and 4 of Fig. 3.1.24B, respectively, led to the closest correlation with the test data. The load-displacement relationship based on tie model (refer to Legend 2 in Fig. 3.1.24B) similar to that obtained by default cohesive contact (refer to Legend 4 in Fig. 3.1.24B) model was observed when the rotational influence by the foundation was included. The rotational degrees of freedom were allowed between the two materials in both runs with the tie and default cohesive contacts shown in Fig. 3.1.24B. The load-displacement relationships indicated by Legends 5 and 6 of Fig. 3.1.24A were underestimated when the cohesive contacts with inaccurate parameters were implemented. The rotational components of the base were not included in the numerical prediction indicated by Legend 3. The composite frames

FIG. 3.1.24 See figure legend on next page.

FIG. 3.1.24, Cont’d

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FIG. 3.1.24 Calibration of the steel-concrete composite member.

with tie (cohesive) model had two contacts, contact between concrete/wide flange steel members and concrete/rebars. The bond-slip characteristics with bond strengths and elastic slippages shown in Fig. 3.1.24C [18] were used in numerical analysis; the bond strength (τmax) for 35-MPa concrete was determined between 15 and 23 MPa depending on the rebar sizes (36-, 43-, and 57-mm bars by Murcia-Delso et al. [18]). The models with bond-slip characteristics shown in Fig. 3.1.24C did not represent test data as close as the those by tie model (refer to Legend 2 of Fig. 3.1.24B) and default cohesive contact model (refer to Legend 4 of Fig. 3.1.24B), implying that the bond effects between concrete and wide flange steel sections were insignificant, and should not be considered. The load-displacement relationships indicated by Legends 15–20 of Fig. 3.1.24A were obtained implementing Tresca yield criterion with bond-slip characteristics, yielding larger load-displacement relationship than those by von Mesis criterion (refer to Section 3.1.4.1). This was because the yield surface of the Tresca was located inside than that of von Mesis, indicating that reaching the yield criteria with the Tresca yield criterion was easier than that with the von Mesis yield criterion, predicting larger effective stresses for a given stress status. Loads were overestimated when Tresca yield criterion was implemented as shown in the load-displacement relationships indicated by Legends 15–20 of Fig. 3.1.24A.

3.1.6.3 Limitation of the study for bond stress-slip characteristics of steel-concrete hybrid frames Many test programs related to bond stress-slip response found in the literature have been performed with specimens having one-rebar or few rebars, where only one rebar was, thus, pulled out. This type of test showed the limited results to predict the bond effects when multiple rebars and steel members were embedded in concrete like one of the studies in this section.

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Besides, the multiple rebars and steel sections were anchored at the base in the proposed specimens of this chapter, implying the test conditions were quite different from those of the specimens found in references including [19]. The finite element analysis (Abaqus) of the author has shown that the structural behaviors were better demonstrated when contact between concrete and rebars/steel sections was modeled as tie or cohesive contact element as shown in Fig. 3.1.24B. Further study may be needed to understand the bond stress-slip response when multiple rebars and steel members are embedded in concrete, however, the bond effects of multiple rebars and steel members with embedding concrete can be small.

3.2 Nonlinear finite element analysis of hybrid composite precast columns spliced by a mechanical metal plate 3.2.1 Finite element models for the mechanical joints with laminated plates 3.2.1.1 Mechanical joints with metal filler plates Precast steel-concrete hybrid composite frames are preferable over conventional precast concrete practices since they are less weight, achieving cost-efficient structural systems that offer rapid and facile erection. Structural behavior of the novel hybrid composite precast frames having mechanical joints with metal plates was investigated by the nonlinear finite element analysis in this chapter. The flexural strength and behavior of the mechanical column connections with fully or partially restrained moment joints numerically calculated was compared well with experimental results, showing that the FE models were accurately constructed and calibrated. Nonlinear finite element analyses were used to seek failure modes, deformations of the column plates, and damages occurred to the proposed novel mechanical connections. The FEA parameters used in the concrete damaged plasticity model including parameters suitable for the design of proposed composite columns jointed by metal plates were identified. The numerical investigations of nine specimens subjected to cyclic loadings introduced in Chapter 2 were performed to validate and calibrate the numerical parameters for damaged concrete plasticity. The stiffness of the column metal plates required to create rigid joints was identified. Recommendations based on the nonlinear behavior of the joints were made for the practical and optimal design of the mechanical column connections for the precast industry. Details of the tested specimens FE models were developed based on the geometric configuration of rectangular column Specimens (C1–C6), shown in Fig. 3.2.1. Precast concrete column joints for fully-restrained moment connection using high-strength steel plates were also numerically investigated in Section 3.2.2. Specimens C1, C2, C3, C4, and C5 were constructed with metal plates, while Specimen C6, having no plates, was fabricated as a monolithic cast-in-place steel-concrete hybrid composite column. Specimen C1 was manufactured with a pair of metal plates, each having a thickness of 20 mm. In Specimen C1, column rebars were filet-welded to the column plates. Specimen C2 was equipped with two thick plates, each having a thickness of 45 mm. The use of thick plates in Specimen C2 was to accommodate endnuts that connected column bars to the lower and upper plates. However, thick plates were not used in Specimens C3, C4, and C5; instead, filler plates (metal plates or concrete filler plates with wire mesh layer) having thicknesses equivalent to the height of two combined nuts were installed to accommodate the endnuts connecting column rebars to the lower and upper plates. In Specimens C3 and C5, the upper and lower plates were manufactured with a thickness of 20 mm each, while the filler plate was fabricated with a thickness of 44 mm. Specimens C3 and C4 used the concrete filler plates while a metal filler plate was used in Specimen C5. Specimens C3 and C4 were designed with 20 and 16-mm thick column plates, respectively. This chapter was devoted to the investigation of the influence of the plate thickness on the flexural capacity of the proposed mechanical joint. Table 2.5.1 of Chapter 2 shows the sizes of elements along with their material properties that were used in the experimental and numerical investigations of rectangular columns. Modeling of contact elements; definition of slave and master surfaces in a contact pair C3D8R elements, one-node integration elements, were chosen to model the proposed mechanical joints. In Fig. 3.2.2A(1), Specimen C6 was modeled as a monolithic column having no plates, with 185,836 elements and 225,494 nodes. Specimens C2 and C5 (Fig. 3.2.2A-(2)) with discretized mesh for the typical layout of the mechanical joint were modeled with 214,799 and 259,918 elements, respectively. The proposed mechanical joint featured advanced treatment of contact formulations between surfaces. Contact properties were assigned between the following contact pairs: concrete-metal plate, metal plate-concrete filler plates, bolts-metal plates, bolts-concrete filler plates, bolt-metal filler plates, and nutsmetal plates. The master and slave surfaces are chosen as depicted in Fig. 3.2.3B. The surfaces of the H-steels and

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FIG. 3.2.1 Geometric configurations of Specimens C1–C6.

reinforcing bars are defined as master surfaces, whereas the concrete surface is defined as a slave surface. In Fig. 3.2.2B, the contacts in the Abaqus FE models were represented by a total of nine interactions. Elements in contact were well partitioned so that only the targeted surfaces were assigned to have contact properties. A small degree of sliding between the bolt shank and plate holes (Int-9) was allowed by a tracking approach to control the movement of bodies in contact, whereas finite sliding was assigned to the remaining interactions (Int-1 to Int-8). With a small degree of sliding, large deformations were restrained, only allowing for a small sliding between the surfaces. A surface-to-surface approach, instead of a node-to-node contact approach, was considered to obtain accurate results. A symmetric modeling technique (SXM ¼ U1 ¼ UR2 ¼ UR3 ¼ 0, see Fig. 3.2.2A-(1) and (2)) was employed in this FEA model to reduce the number of degrees of freedom (DOFs). A static load controlled by displacements (refer to the loading protocol shown in Fig. 2.5.3C of Chapter 2) was exerted at the height of 1700 mm above the foundation, as can be seen in Fig. 3.2.2A-(1) and (2). Boundary conditions (constraints #1 and #2) were assigned at the foundation to prevent any possible movement of the foundation from occurring during the application of the lateral load. Modeling of rebars and steels in steel-concrete hybrid composite members; embedded, tie (cohesive) model Modeling of steel-concrete hybrid composite members requires a proper understanding of the interactions between the surfaces in contact. The use of the “embedded region” technique can be used to define interactions between embedded elements (rebars and H-steels) and host element (concrete). This method assumes a perfect bond between embedded elements and host element (refer to Fig. 3.2.3A). The Abaqus user needs to place the embedded elements (reinforcing bars and steels) into the host elements (concrete) to define an embedded region. The Abaqus tracks the embedded elements that are then constrained by the response of the host elements. In the case the embedded elements lie within the host region, Abaqus eliminates the translational DOFs of the nodes; these nodes are referred to embedded nodes. The translational movement of embedded elements is controlled by the host elements. Another alternative is to use a tie model for the prediction of the structural behavior of the proposed mechanical joints, in which reinforcing bars and H-steels are tied to the concrete surface. The assigned cohesive constraint method ties these two surfaces together so that relative motion between them does not occur; however, rotational degrees of freedom are allowed. The tie approach introduced in this chapter is a technique that can be used to model steel beams encased by concrete members under seismic loadings to prevent the overestimation of the structural behavior when embedded region technique is employed. The “embedded region” technique is not

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115

used for Specimens C2 and C6 since it tends to overestimate the flexural strength of the proposed steel-concrete members, as it is seen in Legend 3 of Fig. 3.2.4A for and in Legend 3 of 3.2.10A for Specimen C6 in which the embedded effects overestimated the flexural strength of Specimens C2 and C6 when mechanical plates with sufficient stiffness were implemented. However, in Fig. 3.2.5, the cohesive (tie) model implemented in Specimen C5 provided prediction similar to that by embedded model, because the structural elements attached to column plates were not fully activated, causing the embedded bond effects to be insignificant.

rebars and concrete

(1) Monolithic column; Specimen C6

(2) Column with metal plates; Specimen C5 (A)

Developed FE models

FIG. 3.2.2 Finite element meshes with contact elements (Specimen C5) [4, Chapter 2]. (Continued)

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Hybrid composite precast systems

Interaction type

Master surface Jig

Slave surface

Interaction type

Upper column

Master surface Upper rebar, nut

Slave surface Plate holes for rebars, nuts

Int-6

Int-1

Upper plate Upper plate

Lower rebar, nut

Upper column

Int-2

Lower plate

Int-7

Upper plate

Filler plate

Int-3

Upper nuts

Lower nuts

Int-8

Lower plate

Filler plate

Exterior bolts

Plate holes for bolts

Int-4 Int-9 Lower plate

Lower column

Int-5

Surface-to-surface interactions (B) FIG. 3.2.2, Cont’d

Bond-slip method The model based on bond-slip characteristics was described in Section 3.1.6.2. Readers may refer to this section for further information.

Calibration of numerical data Structural performance of Specimen C2 Modeling for contacts: Specimen C2 was designed with joint plates to form a fully restrained moment connection equivalent to that of conventional monolithic steel-concrete composite moment frames. The embedded model does not allow the rotational degrees of freedom, whereas the cohesive (tie) model does. The bond effects between concrete and wide flange steel sections on the postyield behavior of the composite beams was insignificant in Specimen C2, and thus, can be ignored. Calibration details: Specimen C2 [6, Chapter 2], with a thick plate of 45 mm, reached a maximum load capacity of 382 kN at a stroke of 102 mm, as can be seen in Fig. 3.2.4A. FE models were developed to provide further insights into the failure modes of the proposed joint. The load-displacement relationship obtained based on tie model with dilation angle of 30° implementing no damage parameter was designated by Legend 2 in Fig. 3.2.4A. The model implemented a viscosity of 0.003. Dilation angle similar to that used for the monolithic Specimen C6 was suggested to represent the behavior of the Specimen C2, indicating that the ductility and plastic strain rate observed in Specimens C2 and C6 during the test were similar. The best fit was found with a dilation angle of 30° with no damage parameter, as presented in the load-displacement relationship denoted by Legend 2 in Fig. 3.2.4A. The default value of the ratio fb0/fc0 in the Abaqus analysis was set to 1.16 for concrete structures.

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(A)

(B)

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117

“Embedded region” technique

“Tie modeling” technique

FIG. 3.2.3 Modeling of reinforcing bars and steels in steel-concrete composite members.

The major failures of Specimen C2 were the necking of column rebars and the embedded H-steels, followed by the concrete crushing in compression. However, metal plates did not deform (refer to Fig. 3.2.4B-(1)), proving that the joint was stiff enough to fully transfer the moment via the interconnected splicing elements. Fig. 3.2.4B exhibits the numerical failure modes of Specimen C2, the necking of rebars caused by large tensile forces, similar to experimentally observed failure modes. The von Mises failure stresses of structural elements comprising the mechanical joints are illustrated in Fig. 3.2.4B, where the failure modes of rebars and bolts interconnecting plates are illustrated. A small separation of

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4 mm was observed between metal plates, as shown in Fig. 3.2.4B-(1), at a stroke of 170 mm. Unlikely the tested specimens (Specimens C3, C4, and C5) in which large deformations at metal plates were measured, only Specimen C2 (45 mm plate) was able to provide enough structural strength that was similar to that of the monolithic column (Specimen C6). The metal plate of Specimen C2 (45 mm plate) did not demonstrate noticeable deformation at the end of the test (refer to Table 2.5.2 of Chapter 2). The flexural capacity of Specimen C2 was compared to that of Specimen C6 (monolithic column), and the

Separation between plates (4 mm) Upper concrete Tension Compression LE, LE33 (Avg: 75%) +6.879e-01 +6.168e-01 +5.457e-01 +4.746e-01 +4.035e-01 +3.323e-01 +2.612e-01 +1.901e-01 +1.190e-01 +4.791e-02 –2.320e-02 –9.431e-02 –1.654e-01

Z

X Lower concrete

Necking of rebar due to large tensile force

(1) No noticeable deformation of plates FIG. 3.2.4 Structural performance of Specimen C2.

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Upper steel Upper plate (45 mm plate)

Lower plate (45 mm plate)

Lower steel

S, Mises (Avg: 75%) +3.526e+02 +3.233e+02 +2.939e+02 +2.645e+02 +2.352e+02 +2.058e+02 +1.764e+02 +1.471e+02 +1.177e+02 +8.832e+01 +5.895e+01 +2.958e+01 +2.155e–01

Upper column rebars Nuts connecting rebars to plates

Necking of column rebars

Lower column rebars

LE, LE33 (Avg: 75%) +6.879e–01 +6.237e–01 +5.594e–01 +4.952e–01 +4.309e–01 +3.667e–01 +3.025e–01 +2.382e–01 +1.740e–01 +1.098e–01 +4.553e–02 –1.871e–02 –8.294e–02

(2) Failure models of rebars

Bolts

S, Mises (Avg: 75%) +9.620e+02 +8.819e+02 +8.017e+02 +7.216e+02 +6.414e+02 +5.612e+02 +4.811e+02 +4.009e+02 +3.208e+02 +2.406e+02 +1.604e+02 +8.027e+01 +1.074e–01

(3) Failure models of bolts inter-connecting plates (B)

Failure modes of the joint at 170 mm of stroke

FIG. 3.2.4, Cont’d

results indicated that Specimen C2 reached a maximum load capacity of 382 kN at a 102 mm stroke while Specimen C6 reached a maximum load of 394 kN at a stroke of 102 mm (positive direction). In a negative direction, Specimen C2 attained a maximum load capacity of 392 kN at a stroke of 102 mm while Specimen C6 reached a maximum load capacity of 390 kN at a 51 mm stroke. Structural performance of Specimen C5 Calibration details: In Fig. 3.2.5, Specimen C5, equipped with 20 mm-thick plates and 44 mm-thick metal filler plate between them, demonstrated a maximum load capacity of 188 kN at a stroke of 68 mm (refer to the positive direction). In a negative direction, a maximum load of 206 kN was recorded at a stroke of 102 mm. The measured deformations of 3–5 and 15–20 mm from the upper and lower column plates at the end of the test

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FIG. 3.2.5 Load-displacement relationships for Specimen C5 compared with nonlinear plastic FE analysis (influence of penetration between surfaces on the load-displacement relationship of C5) [4, Chapter 2].

were well compared with numerical simulation of the mechanical joint based on nonlinear FEA with damaged concrete plasticity at a maximum load limit state, as shown in Fig. 3.2.6A and B, and in Table 2.5.2 of Chapter 2. The failure patterns with numerical stress-strain relationships of the bolts and extended endplates in microscopic level are also elicited in Fig. 3.2.7A and B, respectively. The strains of bolts and plates in column-to-column connections were 0.0036 and 0.0024 at a concrete strain of 0.003, respectively, for Specimen C5. These stresses and strains are important for the design. Stresses in column plates and high-yield strength bolts should be ensured suitable when they are used in structural frames for high-rise buildings. The strength degradation of this specimen was caused by two main failures; (1) large deformations in column plates (see Fig. 3.2.8A) and (2) the slippage of nuts connecting column rebars to the metal plates (see Fig. 3.2.8B and C). In Specimen C5, column plates were unable to create a fully restrained moment connection between the upper and lower columns. The FE models developed in Fig. 3.2.8E provide more insight into the actual behavior of the tested specimens, and identify a variety of parameters influencing the performance of mechanical column-to-column joints. The two important failure modes, including deformations of plates, rebars, and bolts, are shown in Fig. 3.2.8F. In Fig. 3.2.9A, premature termination of the analysis resulted due to the endnuts that penetrated a lower plate. Penetration issues (Int-7 in Fig. 3.2.2B) were corrected by defining the proper master and slave surfaces, as demonstrated in Fig. 3.2.9B. The master surfaces were assigned to the nuts ( fy ¼ 900 MPa) of Int-7, shown in Fig. 3.2.2B, since they were stiffer than the column plates ( fy ¼ 350 MPa). Displaced nuts impeded the transition of the tensile forces from rebars to column plates, resulting in losing their functions as connectors. The numerical model demonstrated that the penetrated nuts failed to transfer loads at connections. Fig. 3.2.9 shows nuts that slipped off the threaded rebar ends, showing the penetration of bolts into adjacent filler plates (refer to Fig. 3.2.9A) similar to displaced nuts observed in the test. In the numerical model of Specimen C5, the overall flexural moment capacity of the specimen with nuts slipped off the threaded rebar ends (refer to load-displacement by Legend 5 of Fig. 3.2.5) was predicted lower than that obtained without the penetrations of nuts. Nuts that were displaced during the test of Specimen C5 were reflected in the nonlinear inelastic finite element analysis using a dilation angle of 30°, as presented in the loaddisplacement by Legend 5 of Fig. 3.2.5, which was obtained based on the model shown in Fig. 3.2.9A. With penetration during the test, the lower plate was deformed by as much as 15–20 mm, while deformation of 3–5 mm at the end of the test was measured at the upper plate (see Fig. 3.2.6B, and Table 2.5.2 of Chapter 2). The deformations of plates with penetration observed in the experimental investigations relatively well-matched numerical failure mode of Specimen (numerically 16.7 and 5.3 mm at the lower plate and upper plate, respectively, as shown in Figs. 3.2.6B and 3.2.8E) obtained from numerical investigations. Sufficient room for bolt holes must be provided for nuts to move freely, avoiding collisions between the nuts and adjacent metal plates.

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FIG. 3.2.6 Numerical prediction of the plate deformation with penetration for Specimen C5; well correlated with test data.

The test data were compared with the numerical load-displacement relationship by Legend 4 of Fig. 3.2.5 with a dilation angle of 30°. The upper column plate deformed as much as 11 mm while the lower column plate demonstrated a deformation of 19 mm when penetration of nuts did not occur into adjacent filler plate, as can be seen in Fig. 3.2.8D and F. The numerical model without penetration of nuts into adjacent filler plate demonstrated deformation larger than that measured during the test. This was because the more effective transition of the loads exerted by rebars to column plates was possible, indicating that greater deformation was generated when penetration of the upper plate was removed from the numerical model. The von Mises stresses are illustrated in Fig. 3.2.8F, where the necking of the tensile rebars was experienced when penetration of nuts was prevented. The overall structural strength of Specimen C5 was smaller compared to that of

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Stress-strain curve

Stress (MPa)

1000

S, Mises (Avg: 75%) +1.022e+03 +9.373e+02 +8.521e+02 +7.669e+02 +6.817e+02 +5.965e+02 +5.112e+02 +4.260e+02 +3.408e+02 +2.556e+02 +1.704e+02 +8.521e+01 –3.000e–03

(A)

800 704.5

Concrete strain: 0.003

600 400 200

0.0036

0 0

0.002 0.004 0.006 0.008

0.01

0.012

Strain Yield stress for bolt: 900 MPa Yield strain for bolt: 0.00437

Stresses in the high strength bolts for column-to-column joint of Specimen C5 Deformation of 11 mm Stress-strain curve

S, Mises (Avg: 75%) +3.521e+02 +3.227e+02 +2.934e+02 +2.641e+02 +2.348e+02 +2.055e+02 +1.761e+02 +1.468e+02 +1.175e+02 +8.816e+01 +5.884e+01 +2.952e+01 +1.978e–01

(B)

Deformation of 19 mm

Stress (MPa)

370 400 350 300 250 200 150 100 50 0

Concrete strain: 0.003

0.0024 0

0.01

0.02

Yield stress for metal plate: 325 MPa Yield strain for metal plate: 0.00158

0.03

0.04

0.05

0.06

Strain

Stresses in the laminated column plates

FIG. 3.2.7 Numerical stress-strain relationships for joint plates of Specimen C5; without penetration.

Specimen C6 (monolithic specimen), indicating that the mechanical joint failed to create a rigid joint. FE model with the viscosity of 0.003 developed for Specimen C5 denoted by Legends 2 and 3 of Fig. 3.2.5 experienced convergence difficulties at a stroke of 99 mm regardless of the application of damage parameter of 50%. Abaqus issued an error message (maximum residual force error between metal filler plate and bottom plate) at a stroke of 99 mm, leading to the premature termination of the analysis. The FE model with the damage parameter of 50% was re-submitted with an increased viscosity parameter from 0.003 to 0.005, as indicated in the load-displacement relationship denoted by Legend 4 of Fig. 3.2.5. The increase of viscosity enhanced the convergence of the analysis, and the run was able to reach the required stroke of 152 mm. It should be noted that the increase of viscosity parameter from 0.003 to 0.005 did not compromise FE results. The loaddisplacement relationships for FE models with viscosity parameters of 0.003 and 0.005 were identical, as can be seen in Fig. 3.2.5. Structural performance of Specimen C6 (monolithic specimen) Modeling for contacts: Specimen C6 [6, Chapter 2], fabricated as a monolithic column without metal plates, exhibited a maximum load of 394 kN at a stroke of 68 mm (refer to the positive direction). In a negative direction, a maximum load of 390 kN was observed at a stroke of 51 mm (see Fig. 3.2.10A). The flexural capacity of specimen C6 was compared with that of the specimens having mechanical joints; FE models constructed based on cohesive (tie) and embedded region techniques were compared to test data. The cohesive (tie) model allowed the buckling or necking of the rebars by permitting rotations. In Fig. 3.2.10A, the load-displacement relationships with cohesive (tie) model (refer to Legend 2) were obtained smaller than those with the embedded model

The investigation of the structural performance of the hybrid composite precast frames Chapter

(A)

(C)

Plate deformation measured at the end of the test

(B)

Nut slipped off the rebar threaded end [4, Chapter 2]

Nut displaced on the filler plate [4, Chapter 2] (D)

Nut not displaced on the filler plate [4, Chapter 2]

[4, Chapter 2]

3

123

FE mesh with penetration with tie model [4, Chapter 2] (E) FIG. 3.2.8 Failure modes of joint plates for Specimen C5. (Continued)

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Hybrid composite precast systems

Nut

No penetration between nuts and column plates

Metal plate Separation between plates (11 mm)

Upper steel Upper plate (20 mm plate)

S, Mises (Avg: 75%) +3.500e+02 +3.209e+02 +2.917e+02 +2.626e+02 +2.335e+02 +2.043e+02 +1.752e+02 +1.461e+02 +1.169e+02 +8.780e+01 +5.867e+01 +2.954e+01 +4.039e–01

Lower plate (20 mm plate)

Metal filler plate (44 mm plate) Lower steel

Separation between plates (19 mm)

(1) Plate deformation

S, Mises (Avg: 75%) +7.303e+02 +6.695e+02 +6.086e+02 +5.478e+02 +4.869e+02 +4.261e+02 +3.652e+02 +3.044e+02 +2.435e+02 +1.827e+02 +1.218e+02 +6.098e+01 +1.292e–01

S, Mises (Avg: 75%) +1.030e+03 +9.444e+02 +8.586e+02 +7.729e+02 +6.871e+02 +6.013e+02 +5.156e+02 +4.298e+02 +3.440e+02 +2.583e+02 +1.725e+02 +8.675e+01 +9.815e–01

Necking of rebars

Bolts

(2) Failure modes of the joint at the end of the analysis (F) FIG. 3.2.8, Cont’d

FE model without penetration

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FIG. 3.2.9 Improper and proper contact pair definitions [4, Chapter 2].

(refer to Legend 3), demonstrating that cohesive (tie) model accurately predicted the structural behavior of Specimen C6 while the embedded region technique overestimated the flexural strength of the specimen. The difference was significant because the rotation effects between concrete, rebar, and steel sections were not activated within the embedded model. The FE model shown in Fig. 3.2.10B was established based on the cohesive (tie) approach, allowing the accurate prediction of the structural behaviors of rebars and H-steels. Calibration details: The failure modes of the Specimen C6 were obtained numerically as shown in Fig. 3.2.10B where the von Mises stresses of H-steels and rebars were predicted. It was found that the steel section and rebars experienced buckling in compression and necking in tension. A better correlation with the test data was demonstrated with the cohesive (tie) model than the results obtained using the embedded model. In Fig. 3.2.11, the influence of the damage parameter on the postyield structural behavior was explored. The load-displacement relationship with dilation angle of 30° implementing no damage parameter (denoted by Legend 2) was predicted higher than that with 50% damage parameter (denoted by Legend 3). The concrete viscosity was 0.003 in the numerical analysis. One of the best correlations with the test data was shown in the load-displacement relationship represented by Legend 2 of Fig. 3.2.11 which was based on dilation angle of 30°, without considering damage parameter. The load-displacement relationship similar to the test data at a large lateral displacement, as an evident softening effect can be observed both in the experimental and numerical investigation.

Plate deformation and strains Noticeable plate deformation with a significant loss in strength was caused by insufficient metal plate stiffness provided for Specimen C5 (20-mm plate), since a fully restrained moment connection was not created by these plates, being unable to transfer forces between columns. However, a joint similar to a rigid moment connection was created between the two columns when a thickness of 45 mm was used. In Table 3.2.1, strain levels measured at rebars were compared with those calculated numerically. The rebars yielded in Specimens C2 similarly to those of C6, resulting in reaching nominal moment capacities (Mn). Strength loss was noticed with Specimen C5, which did not reach the nominal moment (Mn); this was due to the strains of rebars in Specimen C5, which did not yield. This was because the deformation was concentrated on the plates, which dissipated more energy, preventing rebars from yielding. The metal column plates with sufficient stiffness activated structural elements attached to the column plates more efficiently. In Fig. 3.2.12, the locations of the good strain comparison for testing and numerical investigation of Specimen C2 are depicted. Fig. 3.2.13 identifies the numerical strains and stresses of the selected structural components at a concrete strain of 0.003 on the load-displacement relationships of Specimens C2 and C5. The contribution of the metal plates to the flexural capacity of the columns is exhibited by these data. Fig. 3.2.14 demonstrates the plate deformation of Specimen C5 numerically calculated, which increased rapidly as the stroke of the specimen increased, whereas that of Specimen C2 did not vary much regardless of the stroke. Figs. 3.2.15 and 3.2.16 show that the plates of Specimen C5 with insufficient stiffness were more vulnerable to deformations, suggesting that the rate of strain increase of the upper and lower column plates of Specimen C5 was greater than those of C2.

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S, Mises (Avg: 75%) +3.542e+02 +3.247e+02 +2.953e+02 +2.658e+02 +2.364e+02 +2.069e+02 +1.775e+02 +1.480e+02 +1.186e+02 +8.912e+01 +5.967e+01 +3.023e+01 +7.781e–01

LE, LE33 (Avg: 75%) +3.836e+01 +3.514e+01 +2.192e+01 +2.869e+01 +2.547e+01 +2.225e+01 +1.903e+01 +1.581e+01 +1.259e+01 +9.365e+02 +6.143e+02 +2.922e+02 –3.000e+03 –1.009e+01

Buckling of steel

Necking of steel

(1) von Mesis stress of steel section

Necking of rebar

Buckling of rebar S, Mises (Avg: 75%) +5.600e+02 +5.133e+02 +4.667e+02 +4.200e+02 +3.734e+02 +3.267e+02 +2.801e+02 +2.334e+02 +1.868e+02 +1.401e+02 +9.344e+01 +4.678e+01 +1.287e–01

(2) von Mesis stress of rebars

(B) FIG. 3.2.10 Structural performance of Specimen C6.

Failure modes

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127

FIG. 3.2.11 Prediction of Specimen C6 with tie model [4, Chapter 2].

TABLE 3.2.1 Strains of selected rebars (Yield strength: 550 MPa, Yield strain: 0.0027). Concrete strain

Specimens Specimen C2 (45-mm thick plates)

Specimen C5 (20-mm thick plates)

Specimen C6 (control: without plates)

Rebar strain at concrete strain of 0.0025 (Test data)

0.0037 (yielded)

0.0018 (not yielded)

0.0036 (yielded)

Rebar strain at concrete strain of 0.0025 (Abaqus)

0.0043 (yielded)

0.0017 (not yielded)

0.0033 (yielded)

FIG. 3.2.12 Locations of strain comparison for test and numerical investigation for C2 [4, Chapter 2].

Fig. 3.2.15A–D verifies the full stress activation of the concrete, rebars, steel sections, and bolts of Specimen C2, yielding strains larger than those of Specimen C5. In Fig. 3.2.15E and F, no noticeable deformation was found for the column plate of Specimen C2, according to the numerical estimate. The rates of strain increase shown in Fig. 3.2.16A and B exhibited the full stress activation of rebars and steel sections similar to those found in Fig. 3.2.15A and B. On the other hand, the rates of strain increase shown in Fig. 3.2.16C and D demonstrate plate strains of Specimen C5 increased more rapidly than those of Specimen C2.

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Hybrid composite precast systems

FIG. 3.2.13 Strains and stresses of the selected structural components at concrete strain of 0.003 [4, Chapter 2].

Lower plate: plate deformation-stroke curve

Plate deformation (mm)

25 20 15

1. Specimen C5 (20 mm plate, without peneration of nuts)

10 2. Specimen C5 (45 mm plate) 5 0

0

25

50

75 100 125 Stroke (mm)

150

175

FIG. 3.2.14 Contribution of the metal plates to the flexural capacity of the beams; plate deformation versus stroke [4, Chapter 2].

Conclusions Nonlinear FEA model The use of the cohesive (tie) model allowed no relative motions between the materials, but also, by permitting rotational degrees of freedom, the buckling or necking of the rebars. The embedded model did not allow the buckling or necking of both the rebars and steel sections embedded in concrete. For the columns having mechanical joints with sufficient stiffness (Specimen C2) and monolithic Specimen C6, the cohesive (tie) model provided a better correlation with the test data than the results obtained using the embedded model, which overestimated. However, for Specimen C5, cohesive (tie) model provided predictions similar to those of embedded models because the joint plates deformed, resulting in the insignificant embedded bond effects. The structural elements attached to column plates were not fully activated. 1. The experimental investigations verified the numerical (nonlinear FEA) model, which proposed to predict structural performance with postyield structural behavior of the steel-concrete hybrid composite precast columns with mechanical joints having metal plates.

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129

FIG. 3.2.15 Stress-strain relationships [4, Chapter 2].

2. Parameters for the prediction of the connection behavior of the specimens were calibrated with test results subjected to cyclic loadings, successfully predicting nonlinear structural behavior of column-to-column joints of the precast composite frames. The nonlinear FEA parameters including dilation angle, concrete damage factor, and concrete viscosity of the damaged concrete plasticity were found suitable for the prediction of the proposed hybrid precast columns. The dilation angles similar to those of concrete structures were adequately used to model the behavior of the composite columns. The stiffness of the column metal plates required for rigid joints was also identified. For all of the columns with mechanical connections, the nonlinear model and the load-displacement relationship obtained numerically with a dilation angle of 30° and a concrete viscosity of 0.003 was well compared with test data, whereas the influence of the damage parameters on the nonlinear behavior of the columns was insignificant.

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Hybrid composite precast systems

Stress-strain curve

0.008 0.006

Strain-stroke curve

Concrete strain: 0.008 Concrete strain: 0.003

1. Specimen C2-FEA (45 mm plate)

Concrete strain: 0.008

0.002

0.006

1. Specimen C2-FEA (45 mm plate)

0.005 0.004 0.002

Concrete strain: 0.003

0

25

50

75

Concrete strain: 0.003

0.001 100

0

Rebar

0

Concrete strain: 0.003 Stroke (mm)

(D)

100

125

Strain-stroke curve Concrete strain: 0.008

0.014 Tensile strain

Tensile strain

50 75 Stroke (mm)

Concrete strain: 0.008

H-steel 0.016

0.02 Concrete strain: 0.008 0.018 0.016 0.014 Concrete strain: 0.003 1. Specimen C5-FEA (20 mm plate, 0.012 without penetration of nuts) 0.01 0.008 2. Specimen C2-FEA (45 mm plate) 0.006 0.004 Concrete strain: 0.008 0.002 0 0 25 50 75 100

Lower plate

25

(B)

Strain-stroke curve

(C)

2. Specimen C5-FEA (20 mm plate, without penetration of nuts)

Concrete strain: 0.003

0.003

Stroke (mm)

(A)

Concrete strain: 0.008

0.007

2. Specimen C5-FEA (20 mm plate, without penetration of nuts)

0.004

0

0.008 Tensile strain

Tensile strain

0.01

0.012 Concrete strain: 0.003

0.01 0.008

1. Specimen C5 (20 mm plate, without penetration of nuts)

0.006

2. Specimen C2-FEA (45 mm plate)

0.004 0.002 0

Concrete strain: 0.008

0

25

50

Concrete strain: 0.003

75

100

Stroke (mm)

Upper plate

FIG. 3.2.16 Strain-stroke relationships [4, Chapter 2].

3. The behavior of precast composite columns interconnected by bolted column plates was also investigated, based on parameters representing the clearance of the contact surfaces and penalty stiffness. The surface-to-surface interface elements of metal plates contacted by concrete and nuts threaded with rebar end were defined. 4. The flexural strength of the structures and the load-displacement relationship similar to test data was exhibited as the stroke increased in the simulation. The softening effect was attained both in the experimental and numerical investigation.

Seismic performance of the precast concrete frames with mechanical joints having metal plates 1. Flexural strength of mechanical metal plates was verified by both the finite element analysis based prediction and the test data. The calibrated FE models accurately predicted the seismic performance of the mechanical column-to-column joint, demonstrating the conventional precast joints such as traditional sleeve connection can be replaced. 2. The rates of strain increase of the upper and lower column plates of the specimen with 45-mm thick column plates were smaller than those of the specimen with 20-mm thick column plates, since the plates with sufficient stiffness were not vulnerable to deformations, as where those of the specimen with 20-mm thick column plates. 3. Recommendations for the practical and optimal design of the mechanical column connections were presented based on the nonlinear behavior of the joints. The rapid increase of the plate deformation of the specimen with a 20-mm thick column plate retarded the activations of steel section with strains only reaching 0.001. The strains in the steel section of the specimen with 45-mm thick plates reached between 0.002 and 0.0021 at the concrete strain of 0.008. Stresses and strains at the interface between column concrete and plates were also obtained by the numerical model for the design of the proposed connections. Retarded activation of the structural elements attached to the column plates was avoided by the column plates with sufficient stiffness.

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4. The failure modes and deformations including damages to the mechanical connections of composite precast columns were numerically explored whereas the failure modes were difficult to observe by experiments. Nuts of Specimen C5 were displaced off the threaded rebar end, recommending sufficient rooms for plate holes be provided to accommodate nuts to move freely. Collisions between the nuts and adjacent metal plates should be avoided. 5. The deformations of both the upper and low plates with displaced nuts for a specimen with 20-mm thick column plate were accurately estimated by allowing the nuts to penetrate into the adjacent column plate in the nonlinear inelastic finite element analysis, reflecting the displaced nuts of the test. The numerical models presented in this chapter were expected to contribute to rapid and accurate design of the mechanical joints with laminated metal plates.

3.2.1.2 Mechanical joints with concrete filler plates The influence of the stiffness of steel and concrete filler plates on the load-displacement relationship and plate deformation of the joints was explored by nonlinear finite element analyses considering concrete damaged plasticity. Rates of strain increase of the structural components attached to the column plates were also investigated to understand how effectively the structural components were activated relative to the stiffness of the metal and concrete plates. The bearing capacity of the concrete filler plates was ensured to transfer loads at joints, and to protect nuts that were threaded on the rebar end. The concrete filler plates were verified to offer the advantages similar to those obtained by metal-filler plates via both the observed test data and extensive numerical investigation. The degradation variables for concrete filler plates were implemented in the finite element model to estimate the rate of degradation, and its influence on the overall degradation of the mechanical connections. The higher strains of structural elements that were attached to plates with sufficient stiffness were found than those of the structural elements that were attached to plates with insufficient stiffness. These evident strains in the nonlinear finite element analyses and experimental investigations demonstrated that the conventional precast connections can be replaced by the laminated mechanical plates with metal and concrete plates.

FE models for mechanical connections using metal and concrete plates The concrete damaged plasticity model with the damage parameter was implemented in numerical analysis of the mechanical joints with concrete filler plates. The joints of the specimens were partially restrained moment connections with 20 mm (Specimen C3) and 16 mm (Specimen C4) thick plates. The concrete compressive strength of 21 MPa was used in this analysis. The embedded H-steel and reinforcing bars with yield strengths of 325 MPa and 500 MPa were implemented, respectively (refer to Table 2.5.1 of Chapter 2). Elasto-hardening and elasto-plastic rules were used for steel sections and reinforcing bars in both compression and tension regions. Steel sections reached 490 MPa at the ultimate strength. In Fig. 3.2.17, the difference between the two numerical predictions by cohesive (tie) and the embedded model for both Specimens C3 and C4 was not as significant as the difference obtained for Specimens C2 and C6, shown in Figs. 3.2.4A and 3.2.10A, respectively. The overall load-deflection relationships of Specimens C3 and C4 were closely correlated with test data based on both embedded and cohesive (tie) model, as shown in Fig. 3.2.17, where the loaddeflection relationships estimated with embedded model for Specimens C3 and C4 similar to that obtained by cohesive (tie) model were predicted. Embedded effects between concrete, steels, and rebars were insignificant because the structural elements attached to columns plate were not fully activated, showing modes close to the rotating rigid body due to the insufficient stiffness of the column plate. The flexural strength calculated with embedded regions was not different from that obtained by cohesive (tie) model when the stiffness of the column plates was not sufficient, preventing the strains of rebars and steel sections encased in concrete from being fully activated. For Specimens C2 and C6, however, the greater load-deflection relationships were found based on embedded model (refer to Legend 3) than those calculated by cohesive (tie) model (refer to Legend 2), as shown in Figs. 3.2.4A and 3.2.10A, respectively. Specimen C2 was fabricated with sufficient plate stiffness, whereas Specimen C6 was a monolithic specimen, both fully activated the strains of rebars and steel sections encased in concrete. The embedded model did not represent the behavior of Specimens C2 and C6, overestimating flexural strength of the columns. The cohesive (tie) models were recommended for the finite element analysis in this type of column connections, showing the embedded effects should not be considered. In Fig. 3.2.18, the plate deformation of Specimen C3 with deformed meshes was obtained at the maximum load limit state based on the nonlinear finite element analysis with concrete damaged plasticity. Degradation of the metal and concrete plates at the end of the test with a stroke of 170 mm for Specimen C3 in Fig. 3.2.18A and B was evaluated, and agreed well with test observations presented in Table 2.5.2 of Chapter 2,

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(A)

(B)

Specimen C4 (16 mm thick column plates); tie and embedded models

FIG. 3.2.17 Numerical load-displacement relationships of specimens having concrete filler pates.

demonstrating that the influence of the concrete filler plate on the lateral load-bearing capacity of the specimen was well evaluated. The high-cost and full-scale testing can be replaced by the nonlinear numerical analyses performed based on concrete plasticity. Structural performance of Specimen C3 Specimen C3 [6, Chapter 2] was designed with 20-mm thick plates with a concrete filler plate between them, exhibited a maximum load capacity of 200 kN at 102 mm stroke (negative direction: 208 kN; 136 mm). In this specimen, load began dropping at a stroke of 108 mm due to the nut slippage, as shown in Fig. 3.2.17. The flexural capacities of the Specimen C3

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FIG. 3.2.18 Plate deformations of Specimens C3 and C4. (Continued)

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FIG. 3.2.18, Cont’d

corresponding to the compressive strains of the filler concrete to 0.003 and 0.008 were represented by Points A and B in Figs. 3.2.17A, 3.2.18A, and 3.2.20. The strains of column concrete were 0.00218 and 0.00234 (Fig. 3.2.20) at these strains (Points A and B) of concrete filler plate. Fig. 3.2.19A and B also illustrate that the concrete filler plate contributed to the structural behavior of the mechanical joints up to the column concrete strain of 0.0022 whereas the contribution retarded after the column concrete strain of 0.0022. The stresses of 20 MPa (Point A of Figs. 3.2.18A and 3.2.20) and 6 MPa (Point B of Figs. 3.2.18A and 3.2.20) were identified at the concrete filler plate at the stroke of 15.7 and 16.6 mm. The strains in the concrete filler plate increased rapidly from a stroke of 15.4 mm that corresponded to the column strain of 0.0022 for

FIG. 3.2.19 Contribution of the concrete filler plate to the flexural strength at the joint.

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FIG. 3.2.20 Strains of concrete filler plate vs. column concrete for Specimen C3 based on FEA results [5, Chapter 2].

Specimen C3, as shown in Fig. 3.2.20. The analytical and experimental damage evolution including failure modes of the concrete filler plate at Points A and B were comparable. The specimen was pushed more to reach a stroke of 170 mm, as shown in Fig. 3.2.18A and B. The numerical, experimental failure modes and the complex crack patterns on the concrete filler plate at the end of the test (at a stroke of 170 mm) were well correlated, as shown in Fig. 3.2.18B, which also illustrates the damaged edges of the concrete filler plate at the end of the test. The concrete filler plate crushed due to large compressive forces exerted between the metal plates of the two columns. The specimens were capable of providing sufficient stiffness to transfer loads up to the end of the test, showing that only the peripherals of the concrete plate were degraded due to the compression. Both the numerically deformed shapes and the test photograph illustrate cracks propagated inside the specimens towards the rebars. The influence of the bearing strength of the concrete filler plates on both the hysteretic behaviors and flexural capacities of the proposed column-column joints with concrete filler plates was similar to that with the metal filler plate before sudden dissipation of strain energies by the concrete filler plate was observed at the stroke of 15.4 mm. The rates of strain increase of the lower metal plate measured from Specimen C3 similar to those of Specimen C5 (refer to Fig. 2.5.9E-(2)) were identified until a stroke between 15.4 mm. However, the rate of strain increase of the lower metal plate measured from Specimen C3 displayed sudden decrease at between 15 and 20 mm, causing retarded deformation of the metal column plate. This consideration indicated that strain energies were absorbed by the concrete filler plate, whereas the rate of strain increase of the lower metal plate measured from Specimen C5 displayed constant increase at the stroke beyond 15 mm, allowing larger deformations of metal column plate. The deformations of 12–18 and 15–23 mm (refer to Table 2.5.2 of Chapter 2) were measured at the end of the test for upper and lower plates, respectively, for Specimen C3. The deformations of the column plates estimated numerically at the end of the test were 18.3 and 22.8 mm at the upper and lower plates (refer to Fig. 3.2.18B and C), respectively, and were close to the test data.

Influence of the thickness of concrete filler plates on the structural performance of Specimens C3 and C4 Calibration details The structural behavior of the precast column spliced with mechanical joints having concrete filler plates was investigated via multiple gauges attached at rebars, steel sections, column plates, and concrete, as can be seen in Fig. 2.5.3B of Chapter 2. The loading protocol used for these specimens is shown in Fig. 2.5.3C of Chapter 2. The loaddisplacement relationships shown in Fig. 2.5.9A-(1) of Chapter 2 were extracted from experimental data to study the influence of the concrete filler plates on the ductility of the column connections. The concrete and steel filler plates were used for Specimens C3 and C5, respectively, but they had the same thicknesses for the column plates, equal to 20 mm. The displacement was marked at a concrete strain of 0.002. The strokes were also marked in the load-displacement relationships of the Specimens C3 and C5, identifying the fracture of the nuts. The same flexural strength was exhibited for the two specimens until the stroke that led to the displacement of any of the nuts of either specimen. However, loads that decreased

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with different patterns were observed for the specimens with the metal and concrete filler plates. In Fig. 2.5.9A-(1) of Chapter 2, the load-displacement relationship represented by Legend 5 of Specimen C5 indicates the damages of the nuts of the specimen with a metal filler plate occurred at strokes within the range of 60–70 mm, whereas the damages of Specimen C3 with a concrete filler plate were identified in the load-displacement relationship by Legend 3 in Fig. 2.5.9A-(1) of Chapter 2 at later strokes in the range of 115–120 mm. Specimens C5 and C3 displaced off the rebar end at 67 mm and fractured at 119 mm, respectively, demonstrating the specimen with the concrete filler plate provided a flexural strength similar to those obtained by the steel plates until the nuts displaced. Influence of metal and concrete plates on the rate of strain increase of rebars The activation of structural elements comprising mechanical joints was represented in Fig. 2.5.18 of Chapter 2, where the activation of the mechanical joint was recorded at a stroke of 50 mm. The strain of the upper column plate in Specimen C2 reached a value of 0.006. However, the plate in Specimen C3 only reached a strain value of 0.0009. The strains of the structural elements fabricated with a 20-mm thick end-plate (Specimen C3) were smaller than those of the rebars, steel flanges, and concrete attached to the column plate with a thickness of 45 mm (Specimen C2), which were fully activated to a greater degree when sufficient plate stiffness was provided. This indicated that the column plate of Specimen C2 did not undergo noticeable deformation as observed during the experiment shown in Chapter 2. The rates of strain increase for the upper and lower column plates of Specimens C3 having 20-mm thick plate were greater than those for Specimen C2 with 45-mm thick plate. Plates with insufficient stiffness were more vulnerable to deformation, as shown in Fig. 2.5.18 of Chapter 2. In Fig. 2.5.9B–E, the influence of the stiffness of the metal plates on the displacements and strains of the structural components (including rebars, steel flanges, and concrete columns) are shown with strains measured over sixty locations reported relative to strokes. Specimens C3 and C4 underwent significant deformation of the column plates, whereas the plates of Specimen C2 did not show any noticeable deformation due to the sufficient stiffness of the plate, as stated in Table 2.5.2 of Chapter 2. FEA results show that stresses and strains of rebars and steels in Specimen C3 were less effectively activated than those in Specimen C2 at a stroke of 50 mm, as shown in Fig. 2.5.18 of Chapter 2. Fig. 2.5.9B illustrates test data at the design limit state for rebars corresponding to the concrete strain of 0.003 (at a stroke of 15 mm). The smaller strains were apparent for the rebars of Specimens C3 (Legend 4, a strain of 0.0008 based on tests) and C4 (Legend 7, a strain of 0.00035 based on tests) compared with those of the monolithic Specimen C6 (Legend 11, a strain of 0.00149 based on tests). Fig. 2.5.9B also verifies that column plates with less stiffness are responsible for less activation of the structural elements which are attached to column plates. At a stroke of 15 mm, the plates of Specimen C3 were less stiff at higher strains (strain of 0.0011 based on tests by Legend 5, and strain of 0.0011 based on FEA by Legend 6) than those of Specimen C2 (strain ¼ 0.00025 based on tests by Legend 2, and strain of 0.00049 based on FEA by Legend 3). Fig. 2.5.9C depicts strains for the steel sections similar to those of rebars. The strains of the steel section of Specimens C3 (strain of 0.00036 based on tests by Legend 2, and 0.000268 based on FEA by Legend 3) and C4 (strain of 0.00019 based on tests by Legend 4) were also found to be small compared with those of Specimens C2 (strain of 0.0005 based on tests, by Legend 1) and C6 (strain of 0.0011 based on tests by Legends 7, and strain of 0.00138 based on FEA by Legend 8). More of the strain energy was absorbed by the metal plates of Specimens C3 and C4 than by the metal plates of Specimens C1 and C2, due to their insufficient stiffness, indicating that the strains of either the rebars or the steel sections in Specimens C3 and C4 were not fully used. The rebar strains of Specimen C3 were more activated than those of Specimen C4, as shown in Fig. 2.5.9B, which exhibits the smallest rebar strains of Specimen C4, reaching a value of 0.0014, than those of Specimen C3, reaching strain of 0.002. This was because less inelastic strain energy was dissipated, leading to smaller strain and deformation by the metal plates of Specimen C3 with a thickness of 20 mm than that of the metal plates of Specimen C4 with a thickness of 16 mm. The rates of strain increase of the structural components attached to 20-mm thick column plates (Specimen C3) with concrete filler plates were, thus, higher than those of the precast column frame fabricated with 16-mm thick column plates (Specimen C4). The loads increased until the maximum load capacity of 200 kN was reached for Specimen C3 at a stroke of 102 mm (208 kN, 136 mm) with a positive load direction. This was followed by a rapid load reduction at 119 mm since the force holding the rebars started to decrease. Structural behaviors similar to a rigid body rotational mode for Specimens C3 and C4 were observed when the rates of rebar strain increase of Specimens C3 and C4 decreased to very small values after a stroke of 40 mm. In the beginning, during the periods when the loads were small, the rebars and metal column plates of Specimens C3 and C4 provided the ability to resist the lateral loads. However, the deformed column plates prevented the rebars and steel sections from further resisting the lateral loads, leading to the retarded participation of the rebars to resist the loads, as the load application progressed, as shown in Fig. 2.5.9B. The rebar strains of 0.0025 were reached by the monolithic specimen, as observed in

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Fig. 2.5.9B. The rate of strain increase relative to the stroke of the monolithic Specimen C6 increased consistently, to 0.0025, until the failure of the specimens. Strains similar to those of the monolithic specimens were reached at the rebars (refer to Fig. 2.5.9B) and at the steel flanges (refer to Fig. 2.5.9C) of Specimen C2. Flexural capacity of the metal joint with concrete filler plates similar to the monolithic column was yielded in instances when the metal plates maintained sufficient stiffness. Specimen C3 displayed strain-stroke relationships similar to those of Specimen C5, indicating that the concrete filler plates provided compressive bearing strength against the vertical loads that was similar to that of the steel plates. Influence of metal and concrete plates on the rate of strain increase of steel sections An evolution of the strain of steel flanges similar to that of the rebar has been demonstrated, as shown in Fig. 2.5.9C. The steel flange strains were not fully activated in Specimens C3 and C4, demonstrating that flange strains for Specimens C2 and C6 larger than those of Specimens C3 and C4 were observed. The maximum strains reached by Specimens C2 and C6 were 0.0016, whereas those reached by Specimens C3 and C4 were only 0.001 and 0.0008, respectively. The metal plates of Specimens C3 and C4 dissipated more strain energy due to their insufficient stiffness, inducing deformation of the column plates with insufficient stiffness, which then hindered the activations. The steel section of Specimen C3 was more activated than that of Specimen C4, implying that less plate deformation was caused by Specimen C3 with a thickness of 20 mm than by Specimen C4 with a thickness of 16 mm. Fig. 2.5.9C shows the rates of flange strain increase of Specimens C3 and C4 decreased gradually at strokes beyond 40 mm. The structural behavior similar to the rigid body rotational mode was demonstrated, preventing the steel flanges from actively participating to resist loads for strokes beyond 40 mm. This also suggested that the deformed column plates limited the contribution of the steel sections to resisting lateral loads, even if the steel flanges and metal column plates of Specimens C3 and C4 contributed to resisting loads at the beginning when the loads were small. The formation of the plastic hinges of the steel flange of Specimen C2 was found at the stroke of 90 mm, beyond which the rate of strain increase was gradually reduced prior to the sudden strain decrease. Strain levels of the rebars and steel flanges of Specimen C2 similar to those of the monolithic Specimen C6 were observed, implying that the metal column plates with sufficient stiffness activated the structural elements attached to column plates. Influence of metal and concrete plates on the rate of strain increase of concrete The influence of the stiffness of the metal plates with concrete filler plates on the activation of the structural components (tensile rebars, tensile steel sections, and concrete in compression) was identified for the overturning moments being progressed. The deformable column plates of Specimens C3 and C4 prevented the concrete from being fully activated, leading to less contribution than that by Specimen C2 and the monolithic Specimen C6. In Fig. 2.5.9B–D, the lowest contribution of the rebars, steel flanges, and concrete attached to the column plate with a thickness of 16 mm (Specimen C4) were observed due to the largest deformations occurring at the thin column plates. The largest contribution of the structural components of Specimen C2 similar to that of the monolithic Column C6 was demonstrated. Plates with insufficient stiffness for Specimens C3 and C4 were more vulnerable to deformation than those of Specimen C2, as can be seen in the rates of strain increase for the upper and lower column plates, shown in Fig. 2.5.18 of Chapter 2 and Fig. 2.5.9E. The findings pertaining to the damages and stiffness degradations were implemented in the nonlinear parameters that accounted for the plasticity of damaged concrete. The rate of strain increase can be used to determine the dilation angle. The plate in Specimen C2 reached a strain value of 0.0012 with a low rate of strain increase whereas the strain in metal plates in the lower column of Specimen C3 reached 0.0015, as shown in Fig. 2.5.9E. The upper plate in Specimen C2 reached a strain of 0.0019 while the strain of 0.0037 was reached at the upper metal column plate in Specimen C3. The column plate of Specimen C2 with a thickness of 45 mm with unnoticeable deformation fully activated the stress of the structural elements attached to the plate. Design recommendations The activations of the structural elements attached to column plates were evident by strain data retrieved from full-scale experiments. Concrete filler plates were verified to have similar advantages to those observed using metal filler plates, serving as an alternative to metal filler plates. The concrete filler plates delayed the fracture of nuts for a longer period of time than the metal filler plates, as validated by experimental investigations. The cushions were provided by the concrete filler plates for nuts when they were displaced and collided with the concrete filler plates.

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Conclusions This section was devoted to performing nonlinear finite element analyses of mechanical column-to-column joints with concrete filler plates under cyclic loadings, exploring how loads were transferred at precast concrete-based mechanical column joints. 1. The numerical investigations with the nonlinear model considering the damaged concrete plasticity were proposed to predict postyield structural behavior of the steel-concrete composite precast columns, being verified by experimental investigations for the specimens subjected to cyclic loadings. The proposed modeling of joint connections of rectangular column specimens was successfully calibrated with test results, resulting in recommended parameters that can be used to predict nonlinear structural behavior of the precast composite column-to-column joint. The recommended parameters included the calibrated dilation angle, concrete damage factor, and concrete viscosity. The material parameters of the damaged concrete using a plasticity model were found suitable for the prediction of the proposed precast columns. 2. The influence of the concrete filler plate on the lateral load-bearing capacity of the specimen was also explored. The numerical models with the proposed parameters provided dependable design alternatives. The predicted damage evolution of the metal plate and the complex crack patterns of the concrete filler plate were consistent with the observed failure modes. 3. The required stiffness of the column metal plates for rigid joints was identified. The validation of FE models against experimental results was successfully achieved. The effective way to increase the activation of the structural elements including rebars and steel sections attached to column plates was presented.

3.2.2 Numerical investigation of metal plates with high-yield strength steel splicing precast concrete columns Concrete in compression for Specimen HC1 was modeled with Kent-Park constitutive equation. The first part of the curve is the linear-elastic region, which ends at the stress level corresponding to sc0 ¼ 0.4fc0 , as shown in Fig. 3.1.1 of this chapter. The compression damage parameter for concrete under uniaxial compression loading used to model concrete damaged plasticity is implemented in finite element analysis. The stiffness degradation variable is presented in Fig. 3.1.2 of this chapter, which occurs in the softening range of compression after reaching the end of the linear portion of the constitutive relation of concrete, shown in Fig. 3.1.1, where tensile constitutive relationships for concrete and damaged plasticity defining softening part of the tensile constitutive relationship are also shown. In this section, the failure mode and strain data observed in experiment suggest the use of damaged plasticity model with the confined stress-strain relationship in the region where concrete degradation is expected. The nonlinear plastic behavior of the proposed columns with high-yield strength mechanical joints was accurately predicted by the finite element analysis, which can be implemented to determine the stiffness of joint plates and the optimum sizes, locations of high-strength bolts, achieving proper moment transfer, and preventing plates from deforming.

3.2.2.1 Description and calibration of the nonlinear finite element parameters Specimens HC1 and HC2 were a precast column having a mechanical joint with high-yield strength and Specimen HC3 was a cast-in-place column constructed as a monolithic specimen, as shown in Fig. 2.5.12 of Chapter 2. In Fig. 3.2.21A–C, finite element descriptions with meshes for the HC1, HC2, and HC3 specimens are presented with a column, foundation, rebars, and stirrups, in which the numbers of elements used in specimens HC1 and HC2 were 47,975 and 46,815, respectively. The selected surface-to-surface details are depicted in Fig. 3.2.21D, showing details of contact elements with contacts established by master and slave surfaces. Surface-to-surface contact details are summarized in Table 3.2.2. The symmetry plane was established by restraining the displacement degree of freedom (DOF) in the normal direction (U2) of the plane to specify boundary conditions. All of the displacement degrees of freedom were restrained at the sides and bottom of the foundation for simulating fixed support. Numerical modeling of Specimen HC3 having monolithic joint The load-displacement relationships obtained by the embedded, tie, cohesive, and slip models are compared based on a dilation angle of 30° in Fig. 3.2.22. In the monolithic runs designated by Legends 2–4 in Fig. 3.2.22, the load-displacement relationships similar to those of the test data were predicted by all nonlinear models except one with slip effects when damage variables were not considered. In Fig. 3.2.23, the cyclic kinematic model with the slip-effect of the rebars estimates

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FIG. 3.2.21 Element description for numerical analysis [6, Chapter 2].

TABLE 3.2.2 Surface-to-surface contact details [6, Chapter 2]. Master surface

Slave surface

1

Connection plates (upper and lower)

Bolts

2

Lower connection plate

Upper connection plate

Continued

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TABLE 3.2.2 Surface-to-surface contact details [6, Chapter 2]—cont’d Master surface

Slave surface

3

Upper connection plate

Top concrete

4

Lower connection plate

Bottom concrete

5

Upper connection plate

Top rebars and nuts

6

Lower connection plate

Bottom rebars and nuts

7

Bottom rebars and nuts

Top rebars and nuts

FIG. 3.2.22 Comparison of experimental and numerical investigations for monotonic loads; dilation angle of 30° [6, Chapter 2].

Specimen HC3: Load-displacement curve 150 1. C3-Test data 100 2. C3-FEA-Tie model—no damage

Load (kN)

50

0 3. C3-FEA-Cohesive model—no damage –50

4. C3-FEA-Slip model (bond stress: 20 MPa, Elastic slip: 0.1 mm)—no damage

–100

–150 –60 –60 –20 –80 (–0.05) (–0.04) (–0.026) (–0.013)

0 0

20 40 60 (0.013) (0.026) (0.04)

80 (0.05)

Displacement (mm) Drift ratio

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FIG. 3.2.23 Experimental and numerical investigations under monotonic and cyclic loads; monolithic column (HC3) [6, Chapter 2].

the flexural capacity smaller than that of the test data and models which was based on the cohesive and embedded model. For the Specimen HC3, cyclic behaviors implementing kinematic hardening behavior were well predicted for the hysteretic evaluation of the precast column with the mechanical joints up to 30 mm corresponding to the concrete strain of 0.0095, as shown in Fig. 3.2.23. Numerical analysis with Abaqus element (C3D8R) did not well predict the area under the hysteretic loop measured by test beyond a stroke of 30 mm because the softening and pinching effects were not well treated for hysteresis analysis. According to Wan et al. [20] and Ali et al. [21], who presented similar conclusions, to model the pinching effect of concrete during cyclic loading using Abaqus was quite difficult in the region with large deflections. A customized hysteresis model or user-defined stress-strain relationship for cyclic behavior should be implemented when the pinching effect of concrete in cyclic loading is to be explored in Abaqus. However, in Figs. 3.2.22, 3.2.24A, and 3.2.25A, monotonic load-displacement relationships and envelope of hysteretic response for entire deflections similar to the measured ones were obtained by the finite element analysis. Numerical modeling of Specimens HC1 and HC2 having mechanical joints Specimen HC1 was fabricated with joint plates and headed studs to form a fully or partially restrained moment connection. In Fig. 3.2.24A, load-displacement relationships numerically estimated based on the embedded model with full damage were well matched with experimental test data up to a stroke of 60 mm, corresponding to a concrete strain of 0.021 when dilation angles similar to those used for Specimen HC3 were implemented. A dilation angle of 30° with full damage variable (a damage factor of 0.8 for the full damage) provided the best fit with test data, as shown in the load-deflection relationships by Legends 1 and 2 for a specimen having a plate with high-yield strength (HSA 800, 650 MPa). Flexural capacity with plates having yield-strength of 325 MPa (SM490) and 100% damage was compared by load-deflection relationships (refer to Legend 3) obtained using high-yield strength (HSA 800, 650 MPa). In Fig. 3.2.24B, hysteresis cycles of Specimen HC1 were also numerically obtained, and compared with the test data when with full damage and dilation angle of 30° were implemented, demonstrating that the maximum numerical forces in each cycle agreed well with their corresponding experimental load prior to 60 mm. In Fig. 3.2.24C, sudden concrete fracture occurred with loud noise at a stroke of 60 mm. The cracking and crushing of concrete initiated the convergence failure at 60 mm, leading to the numerical instability when damage factor of 0.8 and viscosity of 0.003 were implemented. The convergence was improved when the damage factor of 0.7 and viscosity of 0.004 were applied. The failure modes for Specimen HC1 are shown in Fig. 3.2.24C–E. In Fig. 3.2.25A (refer to Legend 2), the load-displacement relationship of Specimen HC2 under monotonic loads were numerically calculated and matched well with test data up to a concrete strain of 0.0197 based on the full damage variable (determined based on failure mode shown in Fig. 3.2.25B) and a dilation angle of 30° with the embedded model. The influence of axial loads on flexural strength was also identified in Fig. 3.2.25A where the flexural strength of the Column HC2 without axial loads (refer to Legend 2) was

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FIG. 3.2.24 Numerical investigation and failure modes for Specimen HC1 [6, Chapter 2].

Moment: 126 kN m Displacement: 23.3 mm Concrete strain: 0.008 (2.7ec) Rebar strain: 0.0011 (0.4ey)

Moment: 196 kN m Displacement: 20 mm Concrete strain: 0.008 (2.7ec) Rebar strain: 0.0012 (0.4ey)

Moment: 211.3 kN m Displacement: 48 mm Concrete strain: 0.022 (7ec) Rebar strain: 0.0035 (1.2ey)

200

Load (kN)

Moment: 91.1 kN m Displacement: 26.4 mm Concrete strain: 0.00819 (2.7ec) Rebar strain: 0.00376 (1.3ey) Upper plate: 0.00239 (0.7ey) Lower plate: 0.00180 (0.6ey)

1. HC2-Test data—no axial load 150

2. HC1-FEA-Embedded model— no damage

100 50

3. HC2-FEA-Tie model—no damage—30% of axial load

0 –100

–80

–60

–40

–20 –50 –100 –150

0

20

40

60

80

100

Displacement (mm) Moment: 73.2 kN m Displacement: 19.4 mm Concrete strain: 0.00301 (1.0ec) Rebar strain: 0.00256 (0.8ey) Upper plate: 0.00178 (0.6ey) Lower plate: 0.00138 (0.4ey)

–200 (–0.067) (–0.05) (–0.04) (–0.026) (–0.013) (0) (0.013) (0.026) (0.04) (0.05) (0.067)

(A)

4. HC2-FEA-Tie model—no damage—60% of axial load 5. HC2-FEA-Slip model—no damage—0% of axial load

Drift ratio

Comparison of experimental and numerical investigations, Specimen HC2 (full damage and dilation angle of 30°); influence of axial loads

FIG. 3.2.25 Numerical investigation and failure modes for Specimen HC2 [6, Chapter 2].

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smaller than that of the column with both 30% (refer to Legend 3) and 60% (refer to Legend 4) of nominal axial strength of the columns. Greater ductility was demonstrated with lower axial loads, whereas the flexural capacity increased when the column was under compression with axial loads. The column plates transferred axial loads and moments successfully. At the compressive strain of 0.008, flexural moment strengths of 196, 126, and 91.1 kN-m were observed by columns with 60%, 30%, and 0% axial loads (refer to Legends 4, 3 and 2), respectively. Columns spliced by plates also exhibited stable performance up to deformations of 20, 23.3, and 26.4 mm for 60%, 30%, and 0% axial loads, respectively. No deformation was observed in either plate or nuts as can be seen in Fig. 3.2.25C.

3.2.2.2 Parameters defined for Specimens HC1, HC2, and HC3 having mechanical joint The structural behavior of the mechanical connections splicing precast concrete columns was investigated based on the FE parameters considering concrete damaged plasticity. In Figs. 3.2.22–3.2.25, the calibrated FE models with a dilation angle of 30° under monotonic loads were well implemented to match the test data. The convergence difficulties and premature termination of the analyses owing to the concrete cracks were overcome by increasing viscosity parameters (from 0.004 to 0.005 in this section) while not compromising the FE results. Convergence can be also improved by decreasing the damage index.

3.2.2.3 Influence of high-yield metal plates on the flexural capacity Influence of the high-yield strength of metal plates on the flexural strength of Specimen HC1 having mechanical joints Fig. 3.2.26 presents the load-displacement relationships of all specimens and the influence of the yield-strength of metal plates on the flexural capacity. Maximum plastic strains and von Mises stresses of laminated plates with 650 and 325 MPa yield strengths for Specimens HC1 and HC1-1 were also indicated at concrete strains of 0.003 and 0.008, as shown in Fig. 3.2.27, in which larger plastic strains (refer to 0.0034 and 0.0064 at concrete strains of 0.003 and 0.008, respectively) were observed for the plates with 325 MPa yield-strength than those of the plates with 650 MPa yield-strength. Plates with 650 MPa were elastic, whereas those with 325 MPa yield strength were in the plastic region at strains of 0.003 and 0.008. Table 3.2.3 presents the real-world behavior of the proposed column joints numerically calibrated to test data at the microscopic level. Fig. 3.2.28A depicts the influence of the metal plates with high-yield strength (650 MPa) on the flexural capacity of the proposed connection, which was compared with that of the metal plates with a yield-strength of 325 MPa, shown in Fig. 3.2.28B, when the strains of the columns reached 0.003. The flexural capacity (63.3 kN, moment of 76.0 kN-m) of the column having plates with a 650 MPa yield-strength increased by 1.8% relative to that having a metal plate with 325 MPa yield-strength, which can resist the lateral loads of 62.2 kN and moment of 74.6 kN-m.

Moment: 73.2 kN m Displacement: 19.4 mm Concrete strain: 0.00301 (1.0ec) Rebar strain: 0.00256 (0.8ey) Upper plate: 0.00178 (0.6ey) Lower plate: 0.00138 (0.4ey) Bolt: 0.00290 (0.6ey)

160 1. HC1-FEA-Embedded model—full damage

140

2. HC2-FEA-Embedded model—full damage

120

Load (kN)

Moment: 76.0 kN m Displacement: 19.8 mm Concrete strain: 0.00302 (1.0ec) Rebar strain: 0.00233 (0.8ey) Upper plate: 0.00172 (0.7ey) Lower plate: 0.00133 (0.4ey) Bolt: 0.00301 (0.7ey) Headed stud: 0.00075 (0.4ey)

Moment: 96.6 kN m Displacement: 27.7 mm Concrete strain: 0.00805 (2.7ec) Rebar strain: 0.00336 (1.1ey) Upper plate: 0.00236 (0.4ey) Lower plate: 0.00178 (0.5ey) Bolt: 0.00397 (0.9ey) Headed stud: 0.0009 (0.5ey)

Moment: 91.1 kN m Displacement: 26.4 mm Concrete strain: 0.00819 (2.7ec) Rebar strain: 0.00376 (1.3ey) Upper plate: 0.00239 (0.7ey) Lower plate: 0.00180 (0.6ey) Bolt: 0.00373 (0.8ey)

100

3. HC3-FEA-Cohesive model—no damage

80 4. HC3-FEA-Tie model—no damage 60 5. HC2-2: FEA-Tie model—no damage -Plate located at the half of column length

40 20 0 0

10

20

30

40

50

Displacement (mm)

60

70

80

Concrete strain of 0.003 Concrete strain of 0.008

FIG. 3.2.26 Influence of the location of column plate on the flexural capacity of the specimens with dilation angle of 30° [6, Chapter 2].

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FIG. 3.2.27 Maximum plastic strains and von Mises stresses of the plates for Specimen HC1 (650 MPa) and HC1-1 (325 MPa) at concrete strains of 0.003 and 0.008 [6, Chapter 2].

No noticeable differences of stress-strain relationships between Specimens HC1 (yield strength of 650 MPa) and HC1-1 (yield strength of 325 MPa) were indicated on the load-displacement relationships represented by Legends 2 and 3 of Fig. 3.2.24A. Fig. 3.2.28 and Table 3.2.3 also elucidate that the influence of the yield-strength of the column plates on the strains of concrete, rebars, headed studs, and bolts connecting column plates was insignificant at the concrete strain of 0.003. Numerical results of Specimen HC1-1 are presented in Table 3.2.3, indicating that the selection of yield strength did not affect the flexural strength of the column with mechanical plate joints at a concrete strain of around 0.003. The contribution of the column plates was more controlled by their thickness. Rates of strain increase were exhibited with respect to yield-strength of the metal plates, as shown in Fig. 3.2.29 where the concrete strain of 0.003 was marked. Fig. 3.2.29C and D present the rates of plate strain increase relative to stroke of specimens having plates with 650 MPa yield strength, which were similar to those having plates with yield strength of 325 MPa until a stroke of 20 mm, whereas the rapid increase of plate strain with yield strength of 325 MPa were observed from a stroke of 20 mm (at strains greater than 0.003). The rate of strain increase of the plates with high-yield strength was kept from rising (Fig. 3.2.29C and D), demonstrating the activation of structural elements attached to the plates at large strokes (Legends 1 and 3 of Fig. 3.2.29A and B), while the stress activation of structural elements attached to the column plates with limited flexural strength became retarded after the specimens reached 20 mm, as shown in Legend 2 of Fig. 3.2.29A and B. Stiffness and strength sufficient to exhibit stable structural behavior similar to those of monolithic concrete columns were offered by laminated metal plates with high-yield strength at large deformation and ultimate load limit state.

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TABLE 3.2.3 Strains and stresses of the mechanical joints for the yield strength of metal plates with 650 and 325 MPa at the concrete strains of 0.003; refer to Figs. 3.2.24A and 3.2.25A [6, Chapter 2]. Numerical values Specimen

Material

Strain

Stress

Test data, strain

HC1 (with studs) (Plate—HSA800) (Fy ¼ 650 MPa)

Concrete (allowable design strain, ec ¼ 0.003)

0.00302 (ec)

30.6

0.00297 (ec)

Rebar (ey ¼ 0.003)

0.00233 (0.78ey)

498.2

0.00269 (0.9ey)

Upper plate (ey ¼ 0.00325)

0.00172 (0.53ey)

349.6

0.00162 (0.5ey)

Lower plate (ey ¼ 0.00325)

0.00133 (0.41ey)

279.1

0.00121 (0.4ey)

Bolt (ey ¼ 0.0045)

0.00301 (0.67ey)

618.0

N/A

Headed studs (ey ¼ 0.002)

0.000749 (0.37ey)

167.1

0.000630 (0.3ey)

Concrete (allowable design strain, ec ¼ 0.003)

0.00299 (ec)

30.4

N/A

Rebar (ey ¼ 0.003)

0.00219 (0.73ey)

465.6

N/A

Upper plate (ey ¼ 0.00159)

0.00196 (1.236ey)

237.9

N/A

Lower plate (ey ¼ 0.00159)

0.00147 (0.92ey)

244.2

N/A

Bolt (ey ¼ 0.0045)

0.00299 (0.66ey)

614.4

N/A

Headed studs (ey ¼ 0.002)

0.000755 (0.38ey)

167.5

N/A

Concrete (allowable design strain, ec ¼ 0.003)

0.00301 (ec)

30.4

0.00300 (ec)

Rebar (ey ¼ 0.003)

0.00256 (0.85ey)

30.7

0.00259 (0.9ey)

Upper plate (ey ¼ 0.00325)

0.00178 (0.55ey)

358.5

Lower plate (ey ¼ 0.00325)

0.00138 (0.43ey)

286.5

0.00132 (0.41ey)

Bolt (ey ¼ 0.0045)

0.00289 (0.64ey)

593.9

N/A

HC1-1 (with studs) (Plate—SM490) (Fy ¼ 325 MPa)

HC2 (without studs) (Plate —HSA800) (Fy ¼ 650 MPa)

Table 3.2.3 and Fig. 3.2.29C and D elucidate the strains of the metal plates in Specimen HC1 with high-yield strength (650 MPa) plates, which were found to be lower than those of Specimen HC1-1 with a yield strength of 325 MPa. Table 3.2.3 also demonstrates rebars and concrete attached to the plates with larger stiffness were more activated, whereas a larger deformation was induced at the plates with less stiffness. It is noteworthy from Fig. 3.2.29E and F that no noticeable differences of rates of strain increase between Specimens HC1 and HC1-1 were found at connecting bolts and headed studs. Strains of 0.00301 and 0.00299 were identified at the bolts connecting column plates of high-yield strength (650 MPa) for Specimen HC1 and of yield strength of 325 MPa for Specimen HC1-1, respectively. The total tension forces required to place the columns both above and below in positions were similar regardless of the yield strength of the column plates.

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FIG. 3.2.28 Influence of the yield strength of metal plates on the flexural capacity [6, Chapter 2].

In Table 3.2.3, microscopic strains in the structural elements of the mechanical joints were presented as verified by the experimental investigation for both Specimens HC1 and HC2. In Fig. 3.2.30, strains and stresses of the structural elements including concrete, rebar, column plates, and connecting bolts at a concrete strain of 0.003 were well compared at the same locations of gauges and corresponding meshes. The height of column plates to avoid concrete degradation Premature concrete damage was caused by the substantial compression forces exerted by metal plates on the concrete below the metal plates during overturning, leading to the underestimated stiffness and strength of concrete. Nearly 1.5 times greater stiffness and 1.2 times greater strength of the Specimens HC1 and HC2 were obtained by the monolithic column without column plates. The plates compressed a short length of sandwiched precast concrete section between the basement and the steel connection plate, resulting in the concrete which failed under compression. Fig. 3.2.24C shows that Specimens HC1 failed between metal plates and foundation with a loud sound at the stroke of 60 mm. Fig. 3.2.25B, the failure modes similar to those observed for the Specimen HC1 were also observed by Specimen HC2. The stress and rate of strain increase similar to those observed for the monolithic specimen were found from rebars of the Specimens HC1 and HC2 with mechanical joints. Rebars of Specimens HC1 and HC2 underwent strains at the microscopic level similar to those of Specimen HC3.

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FIG. 3.2.29 Numerical strain-stroke relationship of HC1, HC2, and HC3 [6, Chapter 2].

FIG. 3.2.30 Gauges and mesh locations for comparison between the test results and FEA for Specimen HC1 [6, Chapter 2].

The mechanical joints including rebars attached to plates were not responsible for the strength reduction found in the specimens with mechanical joints, as can be seen in Fig. 3.2.24D and E for Specimen HC1, and in Fig. 3.2.25C for Specimen HC2. Concrete degradation was avoided by adjusting the location of column plates, as in Specimen HC2-2 (refer to Legend 5), shown in Figs. 3.2.26 and 3.2.31, where the load-displacement relationship was evaluated again for Specimen HC2-2, having the same connection type, but relocated in a higher location than near the column bottom, particularly on the column mid-length. Lower field compression stress was exerted on the sandwiched concrete since the length of

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149

FIG. 3.2.31 Overturning moments at plate locations [6, Chapter 2].

the precast concrete column was longer now. The numerical load-displacement relationship obtained from the Specimen HC2-2 (refer to Legend 5 of Fig. 3.2.26) was closer to that of the monolithic specimen represented by Legends 3 (cohesive) and 4 (tie) of Fig. 3.2.26 than that obtained by Specimens HC1 and HC2 (refer to Legends 1 and 2), which were located near the column bottom with the embedded model with damage variable. The premature concrete damage and the concrete bearing crushes observed in Specimens HC1 and HC2 could have been avoided when the column plates had been spliced not too close to the column base, higher than those of the test specimens. The location of mechanical plates should be determined to prevent concrete failure under all load combinations. No concrete damage was implemented in the numerical model when concrete degradation and crushing damage was not expected to occur between the relocated plates and the foundation. Eqs. (3.2.1), (3.2.2) were used to calculate the compressive stress exerted on the column between the plates and the base based on overturning moment acting at the plate level, when the plates were located at h/2 of column height (refer to Fig. 3.2.31). M1 ¼ 122 kN  0:75 m ¼ 92 kN  m s¼

Mðkd Þ ¼ 31 MPa Icr

(3.2.1) (3.2.2)

It was ensured that the design compressive strength of concrete (33.1 MPa) was greater than the compressive stress occurring in a column, inducing no concrete failure under compression. The capacity of the column with the mechanical joint at h/2 (refer to Legend 5 of Fig. 3.2.26) similar to that with monolithic columns was verified by the load-displacement relationship with Legends 3 and 4 of Fig. 3.2.26.

3.2.2.4 The influence of headed studs on the flexural strength of the connection Strains in headed studs were slightly smaller at HC1 with a 650 MPa yield strength plate than those of HC1-1 having metal plates with a 325 MPa yield strength, because headed studs were more engaged to provide additional stiffness for the joints with lower yield strength plates. In Table 3.2.3, strains and stresses of the mechanical joints for Specimen HC1 with headed studs were compared with Specimen HC2 without headed studs at the concrete strain of 0.003 when considering concrete damaged plasticity. Strains and deformation of the metal plates in Specimen HC2 of 650 MPa yield strength without headed studs were slightly larger than those of Specimen HC1 of the same yield strength with headed studs, resulting in less activation of rebars and concrete attached to the plates of Specimen HC2 with lower flexural capacity. However, the influence of the stiffness of metal plates installed in Specimen HC1 similar to that of Specimen HC2 on the strain-stroke relationship up to the concrete strain of 0.003 was identified in Fig. 3.2.29. Rates of strain increase for the mechanical joints were also similar to one another regardless of the inclusion of headed studs.

3.2.2.5 Activation of strains of structural components attached to column plate In Fig. 3.2.29A–D, the rebars and concrete of Specimens HC1 and HC2 were activated similarly to those of monolithic concrete column due to the sufficient stiffness of the plates. In Fig. 3.2.29B, column plates with high-yield strength deformed less activated rebars attached to the column plates more effectively up to a concrete strain of 0.008. In Fig. 3.2.29C and D, the rate of strain increase relative to the stroke was also shown for upper and lower column plates, respectively. The column plates of HC1 and HC2 demonstrate small strains and low rates of strain increase, resulting

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Hybrid composite precast systems

FIG. 3.2.32 Numerical deformation-stroke relationship for the plate of HC1, HC2 (dilation angle of 30° and full damage) [6, Chapter 2].

in the metal plates of both Specimens HC1 and HC2 not yielding when concrete strain reached 0.003, while upper plate with HC1-1 of SM 490 plate yielded. The strain rates found from plates with high-yield strength of 650 MPa (Specimen HC1 with HSA 800) were smaller than those of conventional steel plates with a yield strength of 325 MPa (Specimen HC1-1 with SM 490). The ductility and plastic strain rate obtained from Specimen HC1 similar to those of HC3 were also observed. In Fig. 3.2.32A and B, the deformations of 0.666/0.686 mm for upper plates and 0.759/0.771 mm for lower plates were found at the concrete strain of 0.003 for HC1 and HC2, respectively. The strains and deformations of the plates HC1 and HC2 with no noticeable deformation at the termination of both test specimens were small enough to activate the concrete and rebars installed on the plates. Considerable drawbacks engaged in the cost and handling were inevitable when thicker conventional steel plates were used, thus not recommended, whereas the thin plates with highyield strength can be used to ensure no yielding or lower damage in the plate. Strains of column plates and their influence on the activation level of the rebars attached to the column plates should be traced accurately to control the damage level of splicing plates.

3.2.2.6 Conclusion This section presented the design and application of the 26-mm thick mechanical joint plates with the high-yield strength to provide the required stiffness and strength. The structural behavior of the proposed hybrid mechanical joint with high-yield strength, splicing precast concrete components was investigated in both nonlinear and plastic regions. The numerical analysis that included consideration of damaged concrete plasticity was verified by the data retrieved from the experimental investigations, exploring the structural performance of the mechanical joints for the precast concrete columns. This section also presented direct comparisons of the measured strains with those calculated numerically based on the finite element parameters including calibrated dilation angles and viscosity regulation, demonstrating real-world behavior on the microscopic level with acceptable reliability and accuracy. The failure modes were investigated with strain evolution of the column joints and deformation of the metal plates. Both strains/stresses and flexural capacity of the bolted column-tocolumn joint with high-yield strength were also predicted. The numerical evaluation of the load-displacement relationship, and the flexural load capacity were performed, estimating strains in the structural components comprising the mechanical joint subjected to monotonic loads, which well matched the test data at the microscopic level. The damage concrete parameters must be implemented in the numerical model when the concrete degradation is expected. The appropriate plate thickness, size of bolt, and their positioning were determined by understanding the structural performances based on the concrete plasticity, along with damage characteristics of the concrete. This section provided how the structural elements including metal plates were interacting with the concrete section to offer resistance to the cyclic loads relative to the varied yield strengths of metal plates. The connections may fall into the semirigid category even if bolted column plates were primarily designed to act as rigid connections when the structural elements attached to the joint plates were not integrated well with column plates due to the insufficient stiffness of the mechanical joint. In the design phase, the location of the mechanical plates should be determined to eliminate the premature failure of concrete, not causing substantial concrete degradation by locating the column plates not too low and not too close to the column base. Length of the sandwiched concrete column between the column plate and base should be long enough to prevent high compressive stresses in the sandwiched concrete. Mechanical joints can be installed and encased in floor slabs with slab concrete.

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151

3.3 Nonlinear finite element analysis of the beam-to-column connections with mechanical metal plates for concrete/steel-concrete composite frame 3.3.1 Finite element models for fully and partially restrained moment connections 3.3.1.1 With metal filler plates The conventional bolted beam-to-column connections widely used in steel-frame structures were modified by implementing mechanical joints for the use in both steel-concrete composite precast frames or reinforced concrete precast frames. The primary application of these extended endplates was to provide rapid erection for precast frames, as shown in Fig. 3.3.1, where moment connection of steel frame with extended endplates (AISC) [1, Chapter 2] was compared with the proposed joint for the precast frame. Extended bolted endplates, column plates embedded in the column, and concrete or metal filler plates placed between them accommodating nuts are shown in Fig. 3.3.2, replacing the conventional steelconcrete frames that require pour-forms. The upper rebar of the beams with threaded ends was anchored on the rear face of the beam endplates by nuts. Steel sections encased in concrete were welded to the endplates. Beam endplates were interconnected by high-strength bolts to transfer loads at joints. The design of the moment connections entails a determination of the stiffness of the beam endplates and the positions of the bolts to preclude prying action at the joint, enabling full or partial moments to be transferred at the joints. The details of mechanical moment connections with an extended endplates for the column-to-beam joint assembly are shown in Figs. 2.2.2.5 and 2.2.6.2 of Chapter 2, and Fig. 3.3.3 of this section. The structural behavior of the extended endplates connections was explored by the extensive experimental and numerical studies to explore the influence of endplate stiffness on the design parameters, including bolt diameters and grades, positioning of bolts, and column and beam steel sizes. The contributions of endplates stiffness to the precast frame connections, as either fully rigid or semirigid joints, were also investigated. The filler plates were thick enough to completely accommodate and protect the nuts. Additional structural elements for the joints included couplers, and anchor rebars placed in the column to transfer tension and compression couples to create moment connections. In Figs. 2.2.2.5 and 2.2.6.2 of Chapter 2, and Fig. 3.3.3 of this section, the couplers connect anchor rebar in a column unit to the beam endplates by high-strength bolts, offering moments connections between the beam and the column plates. An assemblage of precast frames similar to the steel construction was exhibited during the

FIG. 3.3.1 Detachable mechanical joints with laminated plates for hybrid composite precast beam-column joint [7, Chapter 2].

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Hybrid composite precast systems

full-scale erection test (refer to Fig. 4.4.5 of Chapter 4). The erection of the frame connection constituted the procedures including: (1) lift beams, (2) place beams between column plates, and (3) connect beam and column plates by bolts. Description of the numerical details The geometric configuration for each specimen shown in Figs. 3.3.2–3.3.5 was established in finite element (FE) models. The geometric characteristics for Specimen B2 similar to those of Specimen B5 were illustrated, with the exception that Specimen B2 was fabricated with a 45-mm thick endplate. For Specimen B2, the protruding endnuts were accommodated in the 45-mm thick plate, thereby eliminating the use of a filler plate, as shown in Fig. 3.3.2. In Figs. 3.3.3 and 3.3.4, a steel filler plate was placed between the column plate and a 20-mm thick beam endplate for Specimen B5. The column plates and the C-type steel anchoring them, which were discretized as a 3D FE model, are shown in Fig. 3.3.3A and B, respectively. In Fig. 3.3.4, the filler plate for Specimen B5 was used to accommodate the protruding nut, whereas Specimen B6 was designed, having monolithic beam-column joint, as depicted in Fig. 3.3.5. Nonlinear stress-strain relationship of unconfined and confined concrete; modeling techniques The typical stress versus strain relationships of the Kent-Park model for both unconfined and confined concrete is shown in Fig. 3.3.6A [22]. In Fig. 3.3.6B, Grassl et al. [23] presented an equibiaxial compression model, which was also compared with experiments carried out by Kupfer et al. [4]. The axial strength confined by stirrups was measured as 1.2 times the strength without confinement. In Fig. 3.3.6C, the constitutive relationship retrieved from the model predicted by Grassl et al. [23] compared as higher than that with unconfined constitutive relationships by the Kent-Park model. This comparison

FIG. 3.3.2 Abaqus model of specimen B2 [16].

FIG. 3.3.3 Modeling of C-type rebars [16].

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153

FIG. 3.3.4 Abaqus model of Specimen B2 [16].

FIG. 3.3.5 Abaqus model of Specimen B6 (monolithic specimen) [16].

was based on tested and nominal properties. The concrete behavior with the confinement model of Grassl et al. [23] and their hardening law for concrete was not related only to a descending softening curve but also to the maximum compressive and tensile strength ( fc, ft) changes coherent to the confinement condition, as shown in Fig. 3.3.6B and C. In Fig. 3.3.6D, the calibration of the numerical models in this section was performed based on the low cycle fatigue of the material under cyclic loading for different strain amplitude, which was reported by Roy et al. [24]. Campbell et al. [25] presented the elastoplastic and elasto-softening behavior of the material under cyclic loading for different strain amplitude, in which the dependency of peak tensile stress on the number of cycles and strain amplitude versus the number of cycles (N) is shown. Cyclic softening led to continually increasing strain ranges and early fracture. The idealized elasto-softening behavior of the steel and rebars was implemented to predict the load-displacement relationship of the mechanical connection of this section. In Fig. 3.3.6E, the elasto-softening model considering low cycle fatigue was compared with the strain hardening model. The stress levels were softened to 5% and 1% of fy at the strain of 5ey [16].

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Hybrid composite precast systems

Concrete damaged plasticity model Concrete should be well discretized to ensure accurate results, simulating actual concrete behaviors with the specified compressive strength. In Fig. 3.3.7, the stress-strain curve for concrete (compressive strength of 21 MPa) and the damage parameter for full, half, and 10% degradations were implemented in the concrete damaged plasticity model of the unconfined concrete proposed by Kent and Park [22]. For the constitutive model of concrete shown in Fig. 3.3.7, the softening of concrete in the compression region began from the end of the linear region (equivalent to 0.4fc0 ). The damages in the tension region initiated after the concrete reached its maximum tensile stress, st0, which is equivalent to 1/10 of the compressive strength of concrete, scu. Modeling of contact elements Two surfaces in contact with each other were defined to assign surface-to-surface contacts. Undesirable penetration between the two surfaces in contact was avoided by adjusting the mesh sizes of the master and slave surfaces. Six types of interactions (Int-1 to Int-6) for beam-column joints are defined based on surface-to-surface method, as illustrated in Fig. 3.3.8. Surface-to-surface contact properties were then defined by assigning tangential and normal behavior. The penalty method and hard contact for pressure-overclosure explained in Section 3.1.5.3 (refer to Fig. 3.1.20) were used to define the normal behavior, whereas the tangential behavior was assigned to be frictionless. In the proposed mechanical

(A)

(B)

Proposed stress-strain model for confined and unconfined concrete by Kent and Park [22]

Equibiaxial compression tests (s 11/s 22 = 1.0/1.0) reported by Kupfer et al. [4] compared to the model prediction by Grassl et al. [23]

FIG. 3.3.6 Material properties implemented in numerical investigation.

Concrete : stress-strain curve 30

Grassl model (test material data)

25 MPa

Kent Park model (test material data)

25

Stress (MPa)

21 MPa 20 15 10 5 0 0

0.001

0.002

0.003 Strain

0.004

0.005

0.006

Comparison of concrete compressive constitutive relationships between [New Grassl et al. [23] and Kent-Park [22]] model based on nominal and actual material data (C) 500 Tensile Stress Amplitude, MPa

±1.0% ±0.8%

400 ±0.6% ±0.5% ±0.4% ±0.3%

300

200

316 L(N) SS Room Temperature Strain Rate: 3x10–3 s–1

100 1

(D)

10

100 1000 No. of Cycles, N

10000

Cyclic stress response curve of 316L(N) SS [24] Stress-strain curve

600 Rebar (tested material data, elasto-plastic behavior)

Stress (MPa)

500

Rebar (tested material data, elasto-softening behavior: 0.99 fy at 5 ey)

400

Rebar (tested material data, elasto-softening behavior: 0.95 fy at 5 ey)

300

Steel (tested material data, elasto-hardening behavior)

Steel (tested material data, elasto-plastic behavior)

200

5*ey (steel)

100

0

5*ey (rebar)

Steel (tested material data, elasto-softening behavior: 0.99 fy at 5 ey) Steel (tested material data, elasto-softening behavior: 0.95 fy at 5 ey)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Strain

(E) FIG. 3.3.6, Cont’d

Constitutive relationship for steel and rebars

[16]

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Hybrid composite precast systems

FIG. 3.3.7 Constitutive relations with the damaged plasticity of concrete [16].

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FIG. 3.3.8 Interaction properties; surface-to-surface contact [16].

joint, a linear penalty method with default values of 1 and 0 for the stiffness scale factor and initial contact pressure(Kin), respectively, was considered for the analysis. Five interactions (Int-1 to Int-4 and Int-6) were formulated as finite-sliding elements, whereas Int-5, between the bolt shank and the holes of endplate was defined as small sliding to improve contact movement between the bolts and endplate. The contact surfaces having nonmatching meshes were required to be adjusted. A kinematic constraint can be issued to prevent the nodes located on the slave surface from penetrating the master surface.

Mesh discretization, mesh density, mesh compatibility, and element distortion Mesh discretization Elements of type C3D8R, reduced integration elements, which were suitable for nonlinear static analysis, were preferred because the integration was performed on a single integration point to reduce the running time. Alternatively, a rigid body (jig) was modeled by elements of type R3D4. A reference point on which a monotonic load was exerted was located for a rigid body jig. The average 183,450 nodes and 157,176 elements were used to model both Specimens B2 and B5, while Specimen B6 was modeled by 31,017 nodes and 27,160 elements. All specimens were simplified with symmetry to reduce the DOFs, enhancing the convergences and accuracies.

Mesh density Fig. 3.3.9 depicts finer meshes, which were assigned in areas of importance and at locations where stress concentrations were expected to occur. Coarse meshes were used elsewhere. The region with the most interest was the mechanical connection consisting of laminated plates, bolts, couplers, rebars, nuts, and U-shaped anchor rebars, where finer meshes were implemented to obtain accurate analysis results including strains and stresses.

FIG. 3.3.9 Completed 3D mesh for a mechanical joint (Specimen B2) [16].

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Assigning material properties Yield stresses of 550 and 400 MPa were used for main reinforcing bars in all specimens (B2, B5, and B6) and the stirrups, respectively. The concrete compressive strength of 21 MPa was used for all specimens. The following parameters were implemented to model the specimens: a concrete density of 2.354 ton/m3; Young’s modulus of 24,854.2 MPa; Poisson’s ratio of 0.167; dilation angles of 30°, 45°, 55°, and 56°; eccentricity of 0.1; fb0/fc0 (ratio of initial equibiaxial compressive yield stress to initial compressive stress) of 1.16; Kc value of 0.6667; and viscosity parameter of 0.001. Steel plates with an initial yield stress of 350 MPa and a Poisson’s ratio of 0.3 were used for Specimens B2 and B5. High-strength bolts with an initial yield stress of 900 MPa and a Poisson’s ratio similar to that of the steel plates were implemented in the FE analysis. Similarly, an initial yield stress of 900 MPa and a Poisson’s ratio of 0.3 were also implemented to model nuts. Young’s moduli of 206,000 MPa were implemented for reinforcing bars, couplers, and nuts for all specimens whereas Young’s modulus used for the steel plates was 205,000 MPa. The density of the steel material was 7.85 ton/m3. The von Mises yield criterion after isotropic strain hardening of the steel material was applied to define plastic strains and stresses for each material. Results and discussion Monolithic specimen (B6) Modeling contacts: The load-displacement relationships obtained for varied dilation angles with cohesive (tie) model in Fig. 3.3.10B were smaller than those with the embedded model, shown in Fig. 3.3.10A. The difference would be more significant without damage parameter with the embedded model. Cohesive (tie) model allowing the rotational degrees of freedom contributed to the release of the loads, whereas embedded model yielded greater loads because the rotational degrees of freedom between concrete and rebar, steel sections were not accounted. The difference is expected to be more significant when bond-slip characteristics are used in the FEA as shown in Fig. 3.3.10B. The loaddisplacement relationships were better predicted by the embedded model than by cohesive (tie) and bond-slip models for frames with beam-to-column connections, indicating that neither bond slippage nor rotation took place between steel section and concrete for the monolithic joint. Calibration details: In Fig. 3.3.10A, the full damage parameter and a dilation angle of 56° were implemented in the numerical model of Specimen B6 when elements including H-steel sections, reinforcing bars, couplers, and stirrups were modeled as embedded elements. Stiffness degradation was more prominent in the first quadrant than in the third quadrant as shown in unsymmetrical the load-displacement relationship of the Specimen B6. In Fig. 3.3.10A, load-displacement relationship in each quadrant was predicted relatively well by either constitutive property even if elasto-plastic steel property provides a better match for a the load-displacement relationship in the third quadrant (refer to the load-displacement relationship by Legend 2) whereas elasto-softening steel property defined in Fig. 3.3.6E offers a closer correlation with test data in the first quadrant (refer to the load-displacement relationship by Legend 3). Specimen B2; reflecting low cycle fatigue effect by reducing strain hardening behavior Modeling for contacts: The load-displacement relationships with the embedded model shown in Fig. 3.3.11A were greater than those with cohesive (tie) model in Fig. 3.3.11C, which demonstrates the flexural strength calculated smaller when bond-slip characteristics are used in the FEA. The embedded model yielded greater loads by accounting neither rotations nor the slip effects between concrete, rebar, and steel sections. The difference would be more significant when the damage parameter with the embedded model was not implemented. The embedded model provided a better prediction of the load-displacement relationships than cohesive (tie) and bond-slip models did for beam-to-column connections with sufficient plate stiffness, indicating that neither rotation nor bond-slippage characteristics was not evident for Specimen B2 because the concrete was unlikely displaced from the surface of the rebars and steel sections encased in the concrete. Calibration details: Joint plates to form a fully restrained moment connection equivalent to conventional monolithic steel-concrete composite moment frames were fabricated with Specimen B2. In Fig. 3.3.11A, a dilation angle of 55° represented the behavior of the B2 specimen, similar to that of B6 specimen, reflecting the ductility and the high rate of strain increase of the structural concrete attached to the column plates relative to displacement that were observed during testing. A better comparison was sought with 100% damage parameter, representing the failures that occurred on the concrete attached to the plates. The column plates did not undergo much deformation during cyclic loading. Strain hardening behavior at large displacement ductility level shown in Fig. 3.3.11B was removed in Fig. 3.3.11A by reflecting low cycle fatigue effect. The better correlation between monotonic numerical data and cyclic experimental data at large strains (ductility) was obtained as shown in Fig. 3.3.11A when elasto-plastic steel property (refer to Fig. 3.3.6E) was used, instead of the strain hardening model. An improved match (refer to the elasto-plastic steel property, Fig. 3.3.11A) with test data along with both direction of loadings in the 1st and 3rd quadrants of the plot was obtained, whereas the flexural loads obtained based on the strain hardening behavior grow at large displacement ductility level as indicated by the curves shown in

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(A)

(B)

Load-displacement relationships with tie, cohesive, bond-slip model

FIG. 3.3.10 Calibration of the monolithic model for B6.

Fig. 3.3.11B. Fig. 3.3.11A demonstrates the flexural load-bearing capacities with nominal material properties shown in Table 2.6.1 of Chapter 2, which were slightly underestimated compared to the capacities with tested material values. Both Grassl and Kent-Park models, shown in Fig. 3.3.6B and C, provided the flexural load resisting capacity, which is closely correlated with test data, as demonstrated in Fig. 3.3.11A and B. Specimen B5; partially restrain moment connection Modeling for contacts: Tie (cohesive) model indicated by Legend 2 of Fig. 3.3.12A provided a better prediction of the load-displacement relationships than the embedded model shown by Legend 4 of Fig. 3.3.12A did when elasto-plastic material property was implemented in rebars and steel sections. However, the difference between the two (tie and embedded) numerical predictions for Specimen B5 was not as significant as the difference obtained for Specimens B2 and B6 shown in Figs. 3.3.10 and 3.3.11, respectively. The noticeably smaller loaddisplacement relationships of the beam-to-column connections of Specimens B2 and B6 having sufficient plate stiffness were obtained based on the cohesive (tie) model than those with the embedded model which overestimated the flexural strength. For Specimen B5, the structural elements attached to column plates having insufficient plate stiffness were not fully activated with insignificant strain changes, resulting in the large deformation on the thin beam endplates due to the mode similar to rigid body rotation of the structural elements attached to the beam end-plates. Slip-bond effect within

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FIG. 3.3.11 Calibration of the monolithic model for B2.

FIG. 3.3.12 Test observation compared with the numerical prediction for Specimen B5. (Continued)

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(C)

Experimental and numerical failure modes

FIG. 3.3.12, Cont’d

the model between concrete, steels, and rebars were, thus, neither insignificant nor evident due to the rotational mode as shown in Fig. 3.3.12A–C. The load-displacement relationship with full damage for concrete beam and column is indicated by Legend 3, demonstrating that the beam and column sections did not undergo any significant concrete degradation because the joints plate absorbed most of the inelastic energy, preventing damages of concrete sections. Calibration details: The prediction of B5 without a damage parameter was well-matched with the test data when a dilation angle of 30° was used, unlike specimen B2 where a damage parameter was implemented with a higher dilation angle. The 20-mm thick beam plate absorbed most of the fracture energy, preventing the structural elements attached to column plates from contributing to flexural stiffness for the specimen. No significant tensile concrete fracture or substantial concrete crushing was displayed at the end of the experiment. Implementing elasto-softening model considering low cycle fatigue enhanced analysis accuracy significantly (refer to the load-displacement relationship indicated by Legend 4 of Fig. 3.3.12A). The elasto-softening steel and rebar properties provided better correlations with test data than elastoplastic property did for the composite beam. The nonlinear finite element model with deformed meshes of mechanical joint details for Specimens B5 presented in Fig. 3.3.12B well matched the measured deformation of the beam endplate shown in and Fig. 3.3.12C, predicting the plate deformation of 13–17 mm of the mechanical joint, as shown in Table 2.6.2 of Section 2.6.1.3 of Chapter 2. Experimental and numerical investigations enable the retrieval of a reliable strain evolution of the structural components at the joints including the column plates assembled by high strength bolts. The structural behavior in the microscopic level of bolts and endplates are shown in Fig. 3.3.13A and B, respectively. Stresses in high strength bolts and extended beam endplates provided important data for the design of precast concrete-based mechanical joints. The strains of bolts were 0.0029 at a concrete strain of 0.003 for the Specimen B5, as shown in Fig. 3.3.13A. The strains of plates were also computed as 0.0015 at a concrete strain of 0.003, as shown in Fig. 3.3.13B. The strains found in plates and bolts were considered as being suitable for the use in the structural frames including those implemented in high-rise buildings. Contribution of the metal plates to the flexural capacity of the beams Substantial strength loss and noticeable plate deformation were displayed with plates having endplate of insufficient stiffness. Specimen B5 with 20-mm thick plate was unable to transfer forces as a fully restrained moment connection. However, Specimen B2 with 45 mm-thick beam plates created a rigid joint for a moment connection, transferring loads at beam-to-column joints. The substantial plate deformation (rather than with the rebars) of Specimen B5 was due to the inelastic energy dissipation concentrated on plates, preventing rebars from being structurally activating. Fig. 3.3.14A shows the strains and stresses of Specimens B2 and B5 marked at a concrete strain of 0.003 for the selected structural components. In Fig. 3.3.14B, the plate deformation of Specimen B5 increases substantially, whereas the deformation of B2 does not vary, contributing to the flexural capacity of the beams by fully activating the rebars and steel sections attached to the plates. In Table 3.3.1, strains of the tensile rebar

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FIG. 3.3.13 Numerical simulation of the mechanical joint.

measured from the gauge are indicated in Fig. 3.3.15A which are similar to those obtained numerically at the rebar elements shown in Fig. 3.3.15B. Acceptable reliability and accuracy representing real-world behavior in microscopic level of strains calculated numerically were well correlated with the measured strains of the tensile rebars and the H-steel section at a concrete strain of 0.0025 for Specimens B2, B3, B4, B5, and B6. Strains of the rebars (0.0025) and H-steel section (0.0024) of specimens B2 and B6 were comparatively greater than the strains of the rebars (0.0013) and H-steel section (0.0011) for Specimen B3. The nominal moment capacity (Mn) of the Specimens B2 and B6 was reached, whereas Specimen B5 was not able to reach the nominal moment (Mn), as summarized in Table 3.3.1. The strains of rebars in Specimens B2 and B6 were found substantially greater than those of Specimen B5. In Figs. 3.3.16 and 3.3.17, Specimen B2 (based on the load-displacement by Legend 3 of Fig. 3.3.11A) activated the strains of rebars, steel section, and bolts more effectively than those of Specimen B5 (based on the load-displacement by Legend 4 of Fig. 3.3.12A), offering sufficient strength similar to that of the monolithic beam-column joint (Specimen B6). Fig. 3.3.16 shows the stress and strain data retrieved from the load-displacement relationships represented by Legend 3 of Fig. 3.3.11A and Legend 4 of Fig. 3.3.12A. The rates of strain increase relative to the displacement of the rebars, steel sections and metal plates for Specimens B2 and B5 are also explored in Fig. 3.3.17. Severe deformations of endplate in Specimen B5 were undergone with high rates of strain increase relative to displacement, failing to provide a rigid joint. Rates of strain increase observed from the numerical investigation were well correlated with ones experimentally obtained in Fig. 3.3.17C.

Load-displacement curve (Moment: 240 kN-m) 160

140 120 100

Load (kN)

Load: 84.4 kN Displacement: 12.1 mm Concrete - strain: 0.003 - stress: 18.0 MPa Rebar - strain: 0.0046 (1.7e y) - stress: 554 MPa Steel section - strain: 0.0017 (1.0e y) - stress: 363 MPa Beam end plate - strain: 0.0008 (0.5e y) - stress: 208.0 MPa - deformation: 0.44 mm Bolt - strain: 0.0031 (0.7e y) - stress: 668.2 MPa

80 60

Specimen B2 (Fig. 3.3.11A)

40 20

Specimen B5 (Fig. 3.3.12A) 0 0

20

40

60

80

100

Displacement (mm)

120

140

Load: 51.5 kN Displacement: 13.5 mm Concrete - strain: 0.0030 - stress: 18.4 MPa Rebar - strain: 0.00241 (0.9e y) - stress: 492.0 MPa Steel section - strain: 0.0015 (0.8e y) - stress: 296.4 MPa Beam end plate - strain: 0.0031 (1.8e y) - stress: 366.1 MPa - deformation: 1.21 mm Bolt - strain: 0.0021 (0.5e y) - stress: 435.1 MPa

Strains and stresses of the selected structural components at a concrete strain of 0.003

(A)

Plate deformation-stroke curve Plate deformation (mm)

18 16 14 12 10 8 6

Specimen B5 (Fig. 3.3.12A)

4

Specimen B2 (Fig. 3.3.11A)

2 0 0

20

40

60

80

100

120

140

Stroke (mm)

(B)

Plate deformation vs. stroke

FIG. 3.3.14 Contribution of the metal plates to the flexural capacity of the beams [16].

TABLE 3.3.1 Microscopic strains of selected rebar (fy 5 500 MPa, yield strain: 0.0025) and steel sections (Fy 5 325 MPa, yield strain: 0.001625). Experimental investigation

Computational investigation

Specimens

(a) Rebar strains at a concrete strain of 0.0025

Connection type

B2 (plate t ¼ 45 mm)

0.0025 (yielded)

0.00252 (yielded)

Fully restrained Legend 3 of Fig. 3.3.11A

B3 (plate t ¼ 20 mm)

0.0013 (not yielded)

0.00174 (not yielded)

Partially restrained

B4 (plate t ¼ 16 mm)

Strain gauge malfunctioned

0.00161 (not yielded)

Partially restrained

B5 (plate t ¼ 20 mm)

0.00180 (not yielded)

0.00203 (not yielded)

Partially restrained Legend 2 of Fig. 3.3.12A

B6 (monolithic: no plate)

0.00250 (yielded)

0.00242 yielded (almost)

Fully restrained Legend 3 of Fig. 3.3.10A

Specimens

(b) H-steel strains at a concrete strain of 0.0025

H-steel status

B2 (plate t ¼ 45 mm)

0.00241 (yielded)

0.00201 (yielded)

Fully restrained Legend 3 of Fig. 3.3.11A

B3 (plate t ¼ 20 mm)

0.0011 (not yielded)

0.00103 (not yielded)

Partially restrained

B4 (plate t ¼ 16 mm)

Strain gauge malfunctioned

0.00073 (not yielded)

Partially restrained

B5 (plate t ¼ 20 mm)

0.00131 (not yielded)

0.00112 (not yielded)

Partially restrained Legend 2 of Fig. 3.3.12A

B6 (monolithic: no plate)

0.00247 (yielded)

0.00213 (yielded)

Fully restrained Legend 3 of Fig. 3.3.10A

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FIG. 3.3.15 Locations of strain comparison for the experimental and numerical investigations of Specimen B1 [16].

Conclusions Nonlinear numerical simulations of the beam-to-column connections for the steel-concrete composite precast frames were performed. Concrete damage plasticity was considered for concrete with embedded and cohesive(tie) elements. The contact formulations for the mechanical connection of a precast beam-to-column connection were also established. Parameters including dilation angle, concrete damage, eccentricity, clearance of the contact surfaces, and penalty stiffness were identified to explore the endplate behavior connecting the precast beam-to-column frames. The von Mises yield criterion was used as the yield criterion of steel. The following points summarized the proposed nonlinear model. (1) The numerical modeling of the mechanical connections was successfully calibrated with test results. Strain evolutions in structural elements attached to beam endplate were explored. Higher rates of strain increase relative to displacement were exhibited with full composite actions for the concrete and steel members in Specimens B2 and B6. Specimen B5 did not activate full-composite actions due to the beam plates subjected to significant deformation. (2) A dilation angle of 56° and 100% damage with embedded region technique were successfully implemented in the monolithic specimen which displayed ductile behavior and prevent much compressive crushing or tensile fracture of the concrete section from occurring. Acceptable comparisons with the test data were not possible with dilation angles less than 50°. The structural behavior with the cohesive (tie) model was found substantially less than that by embedded model. (3) The beam plates of Specimen B2 did not undergo any noticeable deformation during the application of cyclic loading. The flexural load-bearing capacity for Specimen B2 was contributed by the structural elements attached to beam plate. The structural behavior with the cohesive (tie) model was found substantially less than that by embedded model. (4) The structural elements including concrete section attached to 20-mm thick beam plates (B5) did not contribute significantly to the flexural load-bearing capabilities. Most of the fracture energy was dissipated by the plates, preventing full composite actions among these components. The use of higher dilation angles was not necessary for Specimen B5, whereas the concrete section of the Specimen B2 contributed significantly to the flexural strength, requiring the application of the damage parameters and a large dilation angle to describe the beam response accurately. Low dilation angles are recommended when the confining pressures of the concrete section were not much activated. Alternatively, high dilation angles can be implemented when the concrete sections were subjected to the high confining pressures caused by large strains.

3.3.1.2 With concrete filler plates Numerical modeling Mathematical model The identical material properties to those used to design the test specimens shown in Table 2.6.1 of Chapter 2 were implemented to explore the structural behavior of the connections concrete filler plates (Specimens B3 and B4). The surface-to-surface contacts between the metal and the concrete plates were modeled to avoid penetrations. The influence of the strength of the metal beam endplates and concrete filler plates on the flexural capacity of the connection was attained by identifying failure modes of both the metal and concrete plates. The structural behavior having the mechanical joint with concrete filler plates similar to that seen with steel filler plates was observed.

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FIG. 3.3.16 Stress-strain relationships; retrieved from Legend 4 of Figure 3.3.12A [16].

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FIG. 3.3.17 Strain-stroke relationships; retrieved from Legend 4 of Fig. 3.3.12A [16].

Modeling of contact elements Warnings and numerical errors can be caused by improper meshes, resulting in premature termination or inaccurate results. 3D solid elements of type (C3D8) representing three degrees of freedom at each node (translations in the x, y, and z directions) were implemented to model the mechanical joint shown in Fig. 3.3.18, where Specimen B3 was modeled by a total of 157,176 elements and 183,450 nodes. Fig. 3.3.19 illustrates a total of six interactions (Int-1 to Int-6), which were defined based on tangential and normal behavior, representing interaction properties for two surfaces (master surface and slave surface). Finite sliding was assigned to the interactions of Int-1 to Int-4, and Int-6, whereas small slides between the bolt shank and the plates’ holes (Int-5) were allowed for the remaining interactions. The master surface (bolt) did not penetrate into the slave surface (plate) by a kinematic constraint when a small sliding approach (Int-5) was selected to adjust contact surfaces with nonmatching meshes. Assigning a little sliding between the holes of plates and bolts restrained large deformations in Int-5. In both Fig. 2.6.9C and Table 2.6.2 of Chapter 2, joint failure modes between beam-end metal and concrete plate for Specimen B3 were observed based on the six interactions (Int-1 to Int-6) where the calculated plate deformation (18 mm) was well correlated with test data (14 to 18 mm). Damaged plasticity model for concrete The stress-strain constitutive relationship proposed by Kent-Park [22] was used to establish the damaged plasticity of concrete, which was implemented only in the concrete filler plate. The damage factor (dc) for compression starting from the end of the linear region corresponding to 0.4fc0 was assigned as indicated in Fig. 3.3.20A and B. Fig. 3.3.20C and D introduced the damage factor (dt) in tension when the concrete reaches its maximum tensile stress (st0). The maximum tensile stress of concrete of 2.1 MPa, and the maximum compressive stress of concrete of 21 MPa were used for all specimens.

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FIG. 3.3.18 3D FE model for Specimen B3 [7, Chapter 2].

FIG. 3.3.19 Interaction properties; surface-to-surface contact [7, Chapter 2].

Influence of the stiffness of metal and concrete plates on the structural performance Load-displacement relationship The stroke at which the nuts were displaced from the threaded end of the rebar was indicated in the load-displacement relationship of B3. However, for B2, no deterioration with no stiffness degradation and no rapid drop of loads up to the stroke of 100 mm were noticed in the load-displacement relationship identified in Fig. 2.6.6 of Chapter 2, where load and displacements were marked at the concrete strain of 0.002 and 0.003. Compressive failure modes for the concrete and tensile failure modes for the rebar/steel section were only observed for Specimen B2 at the maximum load limit state. The load-displacement relationships with cohesive (tie) model for Specimen B3 in Fig. 3.3.21 were well correlated with test data. The influence of embedded model on the flexural strength of Specimen

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FIG. 3.3.20 Constitutive relations with proposed damaged plasticity of concrete [4, Chapter 2]. FIG. 3.3.21 Calibration of the proposed model with test data for B3 and B5 [7, Chapter 2].

B3 was similar to that of cohesive (tie) model because slip-bond effect between concrete, steels, and rebars was not significant when the structural elements attached to columns plates were subjected to rigid body modes. Influence of the stiffness of metal and concrete plates on the rates of the strain increase of concrete The load paths and the influence of the stiffness of the metal and concrete plates on the strains in the structural components, rebar, steel flange, and concrete beam evaluated experimentally were similar to those based on numerical analysis as the overturning moments progressed. The measured load-strain and strain-stroke relationships of the structural components of the precast beamcolumn joints were presented in Figs. 3.3.22–3.3.25. Fig. 3.3.22B shows that the concrete strain reached in Specimens B3 and B4 were the lowest—less than 0.003—whereas those in Specimens B2 and B6 reached strains of 0.008 and 0.0045, respectively. A significant difference between them was noticed. The large deformation on the thin beam endplates for Specimen B4 resulted in the mode similar to the rigid body rotation of the concrete section with the insignificant slip-bond effects between concrete, steels, and rebars, activating the least strains in the concrete section attached to beam plates.

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Load-strain curve (concrete)

Strain-strain curve (concrete) 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0

140 120

Strain

Load (kN)

180 160

100

B2

80

B3

60 40 20 0

B4 (malfunction) B6

0

0.002

0.004

0.008

0.006

B2 B3 B4 B6 0

20

0.01

40

60

80

Stroke (mm)

Strain

(A)

(B)

Load strain curve

Strain stroke curve

FIG. 3.3.22 Measured load-strain and strain-stroke relationships for concrete [7, Chapter 2]. Strain-stroke curve (rebar) 0.004 0.0035 0.003 B2 B3

Strain

Load (kN)

Load-strain curve (rebar) 180 160 140 120 100 80 60 40 20 0

B4

0.001

0.002

0.003

B2 B3

0.0015

B4

0.001

B6 0

0.0025 0.002

0.0005 0

0.004

B6 0

50

Strain

(A)

100

150

200

Stroke (mm)

(B)

Load strain curve

Strain stroke curve

FIG. 3.3.23 Measured load-strain and strain-stroke relationships for rebar [7, Chapter 2].

Strain-stroke curve (steel) 0.0025 0.002 B2 B3

Strain

Load (kN)

Load-strain curve (steel) 180 160 140 120 100 80 60 40 20 0

0.0015

0

0.0005

0.001

0.0015

0.002

B3

0.001

B4 B6

B2

B4

0.0005 0

0.0025

B6

0

50

Strain

(A)

Load-strain curve

(B)

100 150 Stroke (mm)

200

250

Strain-stroke curve

FIG. 3.3.24 Measured load-strain and strain-stroke relationships for steel section [7, Chapter 2].

Influence of the stiffness of metal and concrete plates on the rates of the strain increase of rebar The rebar strains observed in Specimens B3 and B4 were smaller than those of Specimens B2 and B6, as shown in Fig. 3.3.23A and B, showing that the measured rebar strains of Specimens B4 and B3 reached 0.0025 and 0.0018, respectively, while the rebar strain of the monolithic specimen reached 0.0035. During the strain evolutions, the maximum load capacity of 83.4 kN for Specimen B3 was reached at a stroke of 105 mm (83.4 kN, 105 mm) with a positive load direction followed by a rapid load reduction. All specimens demonstrated the similar initial rate of strain increase, as shown in both the rebar and beam endplates of Specimens B3 and B4. These structural elements contributed to the resistance of the loads when the loads were small in the beginning of the loading application until the rates of the strain increase of Specimens B3 and B4 (Fig. 3.3.23B) rapidly decreased from a strain of 0.001 at a 35–40 mm stroke and 0.0017 at a 60–70 mm stoke, respectively. In Fig. 3.3.23A and B, the contribution of the rebar to the flexural capacity of Specimens B3 and B4 was limited owing to the deformation concentrated on the beam endplates as the loads exerted on the plats.

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0.001

0.002 0.003 Strain

Load strain curve

0.001

0.005

Strain

Load (kN)

(A)

B2 B3 B4

0

171

Strain-strain curve (plate)

Load-strain curve (plate) 160 140 120 100 80 60 40 20 0

3

0.005 0.0045 0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0

B2 B3 B4

0

50

100

150

Stroke (mm)

(B)

Strain stroke curve

FIG. 3.3.25 Measured load-strain and strain-stroke relationships for metal plate [7, Chapter 2].

Influence of the stiffness of metal and concrete plates on the rate of strain increase of the steel sections For the rate of strain increase of the steel flanges shown in Fig. 3.3.24A and B, trends similar to those of the rebars were followed. Fig. 3.3.24B demonstrates the maximum flange strains (0.0023) reached by Specimens B2 and B6, which were larger than those (0.0019) of Specimens B3 and B4. The contribution of the steel flanges to the resistance against loads in Specimens B3 and B4 was, thus, limited; whereas strains of 0.0025–0.0023, reached by the rebar and steel flanges for Specimen B2, respectively, implied that the metal plates offered sufficient stiffness, activating structural elements of the steel-concrete composite frames more effectively. Strength of extended endplate and concrete filler plates The plates without sufficient stiffness shown in Fig. 3.3.25A and B are more vulnerable to deformation. In Fig. 3.3.25B, the strains of endplates of Specimen B2 reached only 0.0013, driving the full stress activation of the other structural elements, concrete, rebar, and steel sections, attached to endplates, as shown in Figs. 3.3.22B, 3.3.23B, and 3.3.24B, whereas the metal beam endplates of B4 with 16-mm thickness demonstrated a greater rate of strain increase than those of B3 (20-mm thick endplate). Influence of the stiffness of the metal plates on the load paths validated by numerical and experimental microscopic strains Contribution of the metal plates to the flexural capacity of the beams: The strains and stresses of Specimen B3 up to a concrete strain of 0.003 obtained by Abaqus [12, Chapter 2] are presented in Fig. 3.3.26A for the selected structural components. It was numerically shown in Fig. 3.3.26B that 20-mm thick endplates (Specimen B3) with insufficient stiffness lost substantial strength with noticeable plate deformation, forming a partially restrained connection, which led to less activation of the rebars and steel sections than that of Specimen B2, where loads with 45-mm thick beam end-plates were successfully transferred at the beam-to-column joint. In Fig. 3.3.26B, substantial deformation of Specimen B3 was observed as the stroke increases. The discrepancy of the deflection of the endplates between Specimen B5 with metal filler plate and Specimen B3 with concrete filler plate was shown to be insignificant, implying that no significant structural degradations were caused by concrete filler plate. The structural behavior of the proposed beam-column joints were, subsequently, retrieved in Figs. 3.3.28–3.3.30. Strains obtained by test and numerical investigation were compared at the locations shown in Fig. 3.3.27, which exhibited that the beam endplates for Specimens B2 and B3 yielded at the strokes of 30 and 9 mm (Fig. 3.3.30C), respectively. The high-cost experimental investigations can be replaced by a numerical alternative for the design of complex composite structural systems. Strain-stroke relationships: Fig. 3.3.28A and B exhibited that strains of the concrete filler plate increased rapidly from the stroke of 17 mm as shown in the relationships of strain-stress and strain-stroke. In Figs. 3.1.17C and 3.3.26B, the deformation of the beam endplates of B3 having concrete filler plate also increased rapidly at this stroke. Similar deformations of the plates between the two Specimens B3 and B5 prior to 15–17 mm stroke were noticed, whereas a less rapid increase in the strain of the metal filler plate (B5) was identified, leading to less deformed endplates than the one with a concrete filler plate (B3) after the stroke of 17 mm. The strains of the rebar, steel section, and bolts connecting plates for Specimen B2 were activated enough to offer strength similar to that in a monolithic beam-column joint (Specimen B6), as shown in Fig. 3.3.29A–C. In Fig. 3.3.29D and E, the lower strains of Specimen B2 than those in B3 were illustrated for the beam endplates and the connecting bolts. Rates of the strain increase of the rebar of Specimens B2 versus stroke similar to those of Specimens B3 and B5 prior to the stroke of 12 mm were obtained in Fig. 3.3.30A. However, the rebar in Specimen B2 is more rapidly activated than in Specimens B3 and B5 after the stroke of 12 mm. For Specimens B2 and B3/B5, activation of

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FIG. 3.3.26 Contribution of the metal plates to the flexural capacity of the beams, numerical [7, Chapter 2].

Stress-strain curve

800

Stress (MPa)

700 600

H-steel section: tensile strain

500

Endplate: tensile strain

400 Rebar: tensile strain

300 200

Bolt: tensile strain

100

Concrete: compressive strain

0

0

0.001

0.002 0.003 Strain

0.004

0.005

Strains and stresses of selected structural components up to a concrete strain of 0.003 for B3

Plate deformation (mm)

(A) 20 18 16 14 12 10 8 6 4 2 0

B3 (concrete filler plate) B5 (metal filler plate) B2 (thick plates without filler plate)

0

20

40

60

80

100

120

140

Stroke (mm)

(B)

Plate deformation vs. stroke

FIG. 3.3.27 Locations of the microscopic strains for the comparison of test and numerical investigation for B2 and B3 [7, Chapter 2].

160

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FIG. 3.3.28 Relationships of strainstress and strain-stroke for concrete filler plate for B3, numerical analysis [7, Chapter 2].

FIG. 3.3.29 Stress-strain relationships, numerical analysis [7, Chapter 2].

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Hybrid composite precast systems

FIG. 3.3.30 Strain-stroke relationships; test data versus numerical analysis [7, Chapter 2].

the steel section similar to the rebars was found, as shown in Fig 3.3.30B, indicating the rebars and steel sections were activated similarly with small loads at the initial phase of the load application. The rates of the strain increase of the endplates for Specimens B2 and B3/B5 was opposite as illustrated in Fig. 3.3.30C, in which Specimens B3 and B5 underwent severe deformation with high rates of the strain increase, failing to provide a rigid joint. In Fig. 3.3.30C, the structural behavior of the endplates and the rates of the strain increase based on the numerical analysis were well correlated with that obtained by the experimental investigation for Specimen B2 up to the stroke of 18 mm. Strain evolution of the structural elements of the hybrid joints Influence of metal plate on strain-stress relationships of structural components The strain activation of the endplates of Specimen B3, shown in Figs. 3.3.29D and 3.3.30C, are larger than that of Specimen B5. The deflection of the endplates of Specimen B3 with concrete filler plate was a little lager than that of Specimen B5 with metal filler plate, as shown in Fig. 3.3.26B. The influence of the bearing strength of the concrete filler plates on the flexural capacity of the column-beam joints was similar to that of the metal filler plates when the damage variables were implemented in the concrete filler plate. Points A and B corresponding to the compressive concrete strain of 0.003 and 0.008 were indicated on the load-displacement relationship. In Fig. 3.3.31, the strains and stresses for the H-steel section, beam endplates and bolts for Specimen B3 were displayed at their design and ultimate limit states corresponding to concrete strains of 0.003 and 0.008. A strain of 2ey was reached at bolts when the beam endplates deformed 1.2 mm, whereas the steel section remained elastic at the design limit state. Fracture mode of concrete filler plate In Fig. 3.3.32, structural performance of the mechanical joints and deformation of the concrete filler plates was evaluated with the damages and failure modes of the concrete filler plate based on the parameters used to construct Fig. 3.3.21. The damage of the concrete filler plate with bearing failure was most severe in the area

FIG. 3.3.31 Strain-stress evolution of the joint [7, Chapter 2].

FIG. 3.3.32 Failure [7, Chapter 2].

mode

of

concrete

filler

plate

176

Hybrid composite precast systems

where compression was concentrated by the rebar. The deformation of the concrete plates and the cracks propagated through the plates were also predicted by the FE analysis in Fig. 3.3.31. In Fig. 3.3.32, the failure modes and the damage evolution of the concrete filler plate at concrete strains of 0.003 (Point A), 0.008 (Point B), and the end of the test were uncovered, both numerically and experimentally. The compressive crushing observed at concrete filler plate during testing did not affect the overall flexural strength of the joint as indicated by the flexural strength represented by Legends 3–5 of Fig. 3.3.21. The influence of the joint loadings on the stress concentration, and bearing capacity of the concrete filler plates was well predicted based on nonlinear numerical analysis with concrete damaged plasticity. Reliable and practical design of hybrid composite concrete frames with concrete and metal plates was attained. Conclusions The mechanical joint implemented in precast concrete based moment-resisting connections with concrete filler plates provided assembly speed similar to that of a steel frame. The flexural capacity similar to that of mechanical joints with steel filler plates was also offered. The behavior of hybrid composite precast frame joints with metal beam endplates and concrete filler plates was validated by the experimental and computational investigation. The continuum damage modeling approach for successive initiation of cracks was introduced to track the failure modes with deformation of the metal, concrete plates, and flexural capacity of the bolted frame joint. Surface-to-surface contact elements especially suitable for the metal and concrete filler plates in contact with bolts and the nuts threaded on the rebar ends were developed. The computed structural behavior in terms of the microscopic strains and rates of strain increase of the structural elements including laminated metal and concrete plates were well matched with the test data, elucidating how the stiffness of the concrete filler plates influenced the strains of structural components, the metal plates, rebar, steel flanges, and concrete attached to the endplates. The tensile strains of the rebar and steel sections in Specimen B3 were higher than those of Specimen B4. The rates of strain increase in the concrete, rebar, and steel flanges of the precast beam-to-column frame fabricated with 16 mm beam endplates were also smaller than those of the precast beam-to-column frame fabricated with 20 mm beam endplates. The structural behavior of the mechanical connections was not influenced by the types of the filler plates, but mostly by the stiffness of the mechanical joints.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

J. Lee, G.L. Fenves, Plastic-damage model for cyclic loading of concrete structures, J. Eng. Mech. 124 (8) (1998). J.B. Mander, M.J.N. Priestly, R. Park, Theoretical stress-strain model for confined concrete, J. Struct. Eng. 114 (8) (1988). J. Lubliner, J. Oliver, S. Oller, E. Onate, A plastic-damage model for concrete, Int. J. Solids Struct. 25 (3) (1989) 299–326. H. Kupfer, Das Verhalten des Betons unter mehrachsiger Kurzzeitbelastung unter besonderen Ber€ucksichtigung der zweiachsigen Beanspruchung, Verlag von Wilhelm Ernst und Sohn, 1973. R. Malm, Shear Cracks in Concrete Structures Subjected to In-Plane Stress, Licentiate Thesis, School of Architecture and the Built Environment, 2006. M. Khatibinia, et al., Shape optimization of concrete gravity dams considering dam-water-foundation interaction and nonlinear effects, Int. J. Optim. Civil Eng. 6 (1) (2016) 115–134. B.V.S. Viswanadham, Advanced Geotechnical Engineering, Lecture No-55, Dilatancy Angle of the Soil, NPTEL, MHRD, Government of India, 2015, p.25. https://www.finesoftware.eu/help/geo5/en/angle-of-dilation-01/. J.C. Galvez, J. Cervenka, D.A. Cendon, V. Saouma, A discrete crack approach to normal/shear cracking of concrete, Cement Concrete Res 32 (2002) 1567–1585. W. Chen, D. Han, Plasticity for Structural Engineers, Gau Lih Book Co. Ltd, Taiwan, 1995. J.D. Nzabonimpa, W.-K. Hong, J. Kim, Strength and post-yield behavior of T-section steel encased by structural concrete, Struct. Des. Tall and Spec. Build. 27 (5) (2017), https://doi.org/10.1002/tal.1447. G. Duvaut, J.L. Lions, Les inequations en mechanique et en physique (The inequations in mechanics and physics), Dunod, Paris, p. 197. J.D. Nzabonimpa, W.-K. Hong, Use of artificial damping factors to enhance numerical stability for irregular joints, J. Construct. Steel Res. 148 (2018) 295–303. Tresca Yield Criterion (Wikipedia: https://en.wikipedia.org/wiki/Yield_surface). R.S. Rani, K.N. Prasad, T.S. Krishna, Applicability of Mohr-Coulomb & Drucker-Prager models for assessment of undrained shear behaviour of clayey soils, Int. J. Civil Eng. Technol 5 (10) (2014) 104–123. J.D. Nzabonimpa, W.K. Hong, J. Kim, Nonlinear finite element model for the novel mechanical beam-column joints of precast concrete-based frames, Comput. Struct. 189 (2017) 31–48. J.D. Nzabonimpa, W.K. Hong, D.H. Nguyen, Post-yield behavior of fixed steel beams encased in concrete with plastic rotation capability under monotonic loads, Mater. Struct. 51 (2018) 70, https://doi.org/10.1617/s11527-018-1201-4.

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[18] J. Murcia-Delso, A. Stavridis, B. Shing, Modeling the Bond-Slip Behavior of Confined Large Diameter Reinforcing Bars, University of California San Diego, Department of Structural Engineerin, 2011. [19] X. Li, Z. Wu, J. Zheng, H. Liu, W. Dong, Hysteretic bond stress-slip response of deformed bars in concrete under uniaxial lateral pressure, J. Struct. Eng. 144 (6) (2018). [20] S. Wan, C.H. Loh, S.Y. Peng, Experimental and theoretical study on softening and pinching effects of bridge column, Soil Dyn. Earthq. Eng. 21 (1) (2001) 75–81. [21] A. Ali, D. Kim, S.G. Cho, Modeling of nonlinear cyclic load behavior of I-shaped composite steel-concrete shear walls of nuclear power plants, Nucl. Eng. Technol. 45 (1) (2013) 89–98. [22] D.C. Kent, R. Park, Flexural members with confined concrete, J. Struct. Div. 97 (7) (1971) 1969–1990. [23] P. Grassl, K. Lundgren, K. Gylltoft, Concrete in compression: a plasticity theory with a novel hardening law, Int. J. Solids Struct. 39 (2002) 5205–5223. [24] S.C. Roy, S. Goyal, R. Sandhya, S.K. Ray, Low cycle fatigue life prediction of 316 L (N) stainless steel based on cyclic elasto-plastic response, Nucl. Eng. Des. 253 (2012) 219–225. [25] F.C. Campbell (Ed.), Elements of Metallurgy and Engineering Alloys, ASM International, 2008.

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Chapter 4

L-type hybrid precast frames with mechanical joints using laminated metal plates 4.1 Experimental investigation of the L-type hybrid precast frames using mechanical joints with laminated metal plates 4.1.1 Why L-type precast frames? In conventional precast joints using grouted sleeve connections, the quality of the grouted joints depends on tensile strength of the grouted sleeves (refer to Fig. 1.2.1B-(2)). In this type of connection, the tensile strength of the grouted sleeves is needed for quality grouted joints. The hybrid mechanical joint with metal plates for irregular shaped columns was presented to replace conventional grouted sleeve connections. The time required to cure concrete for conventional grouted sleeve connections can be eliminated by the proposed joints containing bolted metal plates. In this chapter, irregular precast concrete columns with L-shaped sections which fit inside the corners of the walls in residential buildings were proposed, replacing rectangular columns that do not fit at the corners. L-shaped sections are preferred by architects because of their architectural flexibility, fitting inside at the corners and replacing walls in residential buildings. The objectives were to implement these irregular columns into the construction of residential buildings, with the aim of replacing rectangular columns. Studies of the influence of interior bolts on the flexural capacity of the joint connections were overlooked. The use of thicker plates was avoided to create the structural capacity similar to the monolithically designed specimen by using interior bolts in the metal plates. The numerical and experimental investigations were performed to verify the influence of interior bolts on the stiffness of the mechanical joint with metal plates [1]–[3]. The structural behavior of the mechanical joints was explored numerically based on the concrete plasticity. Parameters affecting the activation of the rebar and steel sections which contributed to the flexural capacity of the metal plates were explored.

4.1.2 Specimen details and test preparation of Specimens LC1–LC3 The structural performance and failure modes at the mechanical joint of L-type concrete columns, depicted in Fig. 4.1.1A, were investigated. The joint details for Specimens LC1 and LC2 were identical, except eight interior bolts, shown in Fig. 4.1.1A and B, were added to Specimen LC2 to verify the increase in the structural strength of the stiffened column plates. Structural details of the tested specimens are shown via finite element meshes in Fig. 4.1.1C. Bolted metal plates consisting of an upper plate, a filler plate, and a lower plate are shown in Fig. 4.1.1D and E. Specimen LC3, shown in Fig. 4.1.1F, was a control monolithic (cast-in-place column) steel-concrete hybrid composite column without plates. The three specimens were loaded to failure under the same cyclic loads. The results indicated that the specimen strengthened with interior bolts (LC2) demonstrated structural performance similar to that of the monolithic specimen (LC3), indicating that use of interior bolts enhanced the stiffness of the proposed joint. Material properties and the dimensions of rebars, metal plates, bolts, and L-shaped steel are specified in Table 4.1.1. Fig. 4.1.2A and B depict column plates without/with holes for interior bolts. The threaded ends of the vertical rebars splicing vertical column rebars were anchored in the counterbores prepared on the rear side of the column plates, as exhibited in Fig. 4.1.2A. Column plates with a thickness of 35 mm and filler plates with a thickness of 15 mm were manufactured. The filler plate was to accommodate the nuts connecting the column rebars to the lower and upper column plates, not as a structural element. The L-shaped steel sections groove welded to the upper and lower plates are shown in Fig. 4.1.2C. In Fig. 4.1.2D, the interior bolts are placed in the holes prepared inside the column plate of the upper column unit. Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00004-2 © 2020 Elsevier Ltd. All rights reserved.

179

180 Hybrid composite precast systems

FIG. 4.1.1 L-type precast frame [1].

4.1.3 Preparation of the test Extensive strain gauges are used for the test specimens (LC1, LC2, and LC3) as shown in Fig. 4.1.3. Strains in response to the application of cyclic loads were collected to capture the complete structural behavior and failure modes at the mechanical joint. Not only the contribution of each structural element to the flexural capacity of the proposed joint, but also the load path during the application of loads at each structural element of the mechanical joint was explored. Table 4.1.2 summarizes a total of 163 gauges attached on rebars, steel, and concrete, shown in Fig. 4.1.3. Fig. 4.1.3A

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181

(C) Structural details of the tested specimens; L-type composite columns [1]

(D)

Details mechanical joint; Specimen LC1 (without interior bolts) [1]

FIG. 4.1.1, Cont’d

illustrates a total of 48 strain gauges for Specimen LC1, which included concrete gauges (from Gauge LC1 to Gauge LC16), rebar strain gauges (from Gauge 9 to Gauge 24), upper column plate gauges (from Gauge 1 to Gauge 4), lower column plate gauges (from Gauge 5 to Gauge 8), and strain gauges for the L-shaped embedded steel (from Gauge 25 to Gauge 32). Alternatively, Fig. 4.1.3B shows a total of 52 strain gauges attached to Specimen LC2. In Fig. 4.1.3C, 40 strain gauges were equipped with the control specimen (LC3) with no metal plates. Fig. 4.1.3D depicts gauges attached to metal plates and steel columns. Strain gauges were attached to polished surfaces of column rebars, metal plates, and L-shaped steel. They were protected with waterproof tape before casting concrete, as indicated in Fig. 4.1.3D. Fig. 4.1.3D shows gauges attached to metal plates and steel columns, and the locations of strain gauges relative to the height of the specimen are shown in Fig. 4.1.3E.

182 Hybrid composite precast systems

(E)

Details mechanical joint; Specimen LC2 (with interior bolts) [1]

(F)

Details for monolithic Specimen LC3 [1]

FIG. 4.1.1, Cont’d

In Fig. 4.1.4A and B, column rebars and L-shaped steel sections were cut, bent, and assembled to Specimens LC1, LC2, and LC3. Specimen LC3 did not have a mechanical joint connection, with no amputated rebars and L-shaped steel. The instrumented monolithic test specimen and specimens with laminated metal plates with/without interior bolts are shown in Fig. 4.1.4B. In Table 4.1.3, the material properties of the structural elements including concrete, rebars, and steels were determined by sample test. Samples were loaded to failure to find the maximum compressive strength of the concrete and yield strengths of steel sections and rebars. The average yield strengths of 646.7 MPa and 387.1 MPa were found for steel sections and rebars, respectively, whereas the average compressive strength of concrete of 29.1 MPa was obtained from five concrete test samples. Full-scale specimens (LC1, LC2, and LC3) ready for load application are shown in Fig. 4.1.5A, where the same boundary and loading conditions were implemented in all three specimens. The height of each specimen measured 3.5 m from foundation level to the top of the wall column. The estimated weight of each specimen was approximately 9.4 tons. In Fig. 4.1.1C, the foundation was 2.5 m
2.5 m wide and 0.5 m high, whereas the L-shaped wall column was 800 mm
800 mm with a thickness of 200 mm. The foundation manufactured with substantial steel sections and

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183

TABLE 4.1.1 Summary of the material properties of the structural elements for the tested specimens [1]. Category

Size (mm)

Material

Concrete column (all specimens)

L shape: 800
800 (width: 200)

Concrete compressive strength: 40 MPa

Upper plate for column (Specimens LC1 and LC2)

L shape: 1000
1000 (width: 400, thickness: 35)

Lower plate for column (Specimens LC1 and LC2)

L shape: 1000
1000 (width: 400, thickness: 35)

Material (Steel, SM490), tensile yield stress (Fy ¼ 325 MPa) Ultimate strength (Fu ¼ 490 MPa)

Filler plate for column (Specimens LC1 and LC2)

L shape: 1000
1000 (width: 400, thickness: 15)

Bolts (Specimens LC1 and LC2)

M22 (diameter: 22)

Tensile yield stress (Fy ¼ 900 MPa) Ultimate strength (Fu ¼ 1000 MPa)

Nuts (Specimens LC1 and LC2)

M25 (diameter: 25)

Tensile yield stress (Fy ¼ 900 MPa) Ultimate strength (Fu ¼ 1000 MPa)

Column rebar (all specimens)

HD25 (diameter: 25)

Tensile yield stress (Fy ¼ 600 MPa)

Hoops for column (all specimens)

HD10 (diameter: 10)

Tensile yield stress (Fy ¼ 400 MPa)

rebars (refer to Figs. 4.1.1C and 4.1.4A) was wrapped and reinforced with two layers of carbon sheets along directions perpendicular to each other to prevent base rotation, as illustrated in Fig. 4.1.5A. The cyclic loading protocol to explore the hysteretic behavior of the specimens is presented in Fig. 4.1.5A and B. The displacements of the columns were measured by LVDTs (linear variable differential transformers). Cyclic loads (shown in Fig. 4.1.5B) were controlled by displacements using an actuator with a capacity of 2000 kN, located at 1.7 and 2.785 m from the joint level and top of the foundation, respectively. The structural performance of the proposed mechanical joint for precast composite frames and the hysteretic behavior was captured by quasistatic testing. The main failures with ductility and energy dissipation capability were observed at the column, not on the foundation.

4.1.4 Experimental investigations The structural behavior with the associated failure modes of the mechanical joints of the three specimens (LC1, LC2, and LC3) was exhibited during the test. The flexural capacity of the monolithic specimen (LC3) was compared with that of the hybrid precast wall columns having metal plates at the joints (LC1 and LC2). The strains and stresses observed during the test identified how each structural element, including metal plates, column rebars, high-strength bolts, and L-shaped steel were activated to contribute to the flexural capacity of the mechanical joint.

4.1.4.1 Structural behavior and associated failure modes for Specimen LC3 (monolithic specimen) In Figs. 4.1.6 and 4.1.7A and B, concrete damage and cracks occurred at a stroke of 81 mm, and severe crush of the concrete was concentrated at the column near foundation around a lateral displacement of 135 mm when the major compressive failures were observed. Points C and F indicated in load-displacement relationships of the specimens in Fig. 4.1.6, reaching maximum loads, which was followed by a buckling of embedded rebars and L-shaped steel when the concrete was completely damaged in compression. The deformed shape and buckling of both rebars and L-shaped steel at a stroke of 135 mm are illustrated in Fig. 4.1.7B. The load began to decrease from points C and F. Thereafter, the specimen was further pushed and pulled until it reached the end of the specimen test at a stroke of 158 mm when the applied loads were removed, as shown in Fig. 4.1.7C. The design limit state of the Specimens LC1, LC2, and LC3 were found by dots when concrete strain reached 0.003 as shown in Fig. 4.1.6. In Fig. 4.1.8, the hysteresis behavior of Specimen LC3 with asymmetric structural responses were demonstrated in both the push and pull regions due to an irregular L-shaped section. As much as 800 kN of nominal flexural load capacity was reached at a stroke of 102 mm in the push region (positive region), whereas the load capacity of 938 kN at a stroke of 107 mm was reached as the peak in the pull region (negative region). The test was terminated with loads of 800 and 732 kN in the pull and push region, respectively, as the specimen reached a stroke of 158 mm.

184 Hybrid composite precast systems

FIG. 4.1.2 Joint details for the proposed mechanical joint [1].

4.1.4.2 Structural behavior and associated failure modes for Specimen LC1 Metal plates consisting of the upper plate (35 mm thick), lower plate (35 mm thick), and filler plate (15 mm thick) were fabricated at 1 m above the foundation. The metal plates were interconnected by high strength bolts, having a yield strength of 900 MPa. At a stroke of 54 mm, depicted in Fig. 4.1.9A, the large compressive forces acting on the metal plates caused concrete cracks to begin above and below the metal plates of Specimen LC1. Deformation of the metal plates initiated the creation of a gap between the laminated plates when the specimen was loaded continuously until it reached a stroke of 81 mm. This gap increased as the specimen was pushed further. In Fig. 4.1.9B, metal plates were observed to separate when the specimen was pushed at 108 mm. The metal plates kept on deforming and separating due to the tensions exerted by both the column rebar and L-shaped steel section. At a stroke of 108 mm, the first bolt fractured during the first cycle,

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

FIG. 4.1.2, Cont’d

4

185

186 Hybrid composite precast systems

FIG. 4.1.2, Cont’d

followed by the fracture of another bolt when the specimen was pulled at 108 mm. A total of four bolts fractured after two cycles at strokes of 108 and 108 mm. In Fig. 4.1.9C, severe damages accompanying large plate deformations at a stroke of 135 mm were observed with failure of nine bolts in tension—depicted from Specimen LC1—before the end of the test. Fig. 4.1.9D illustrates the disassembled metal plate showing deformations. The deformations of 2 and 3 mm for the upper and lower column plates were observed, respectively, indicating that a rigid joint was not able to be created, which suggests that these metal plates were not stiff enough as a rigid joint when interior bolts were not present. The two major failures that dissipated a large amount of energy at mechanical joints were associated with the lack of plate stiffness and fracture of highstrength bolts, limiting the structural performance of the mechanical joint. Concrete crushing did not cause a major failure mode for Specimen LC1. The nominal flexural load capacity of Specimen LC1 reached 520 kN-m and 606 kN when the specimen was pushed at a stroke of 106 mm (in the push region and positive region) and at a stroke of 80 mm (in the pull region and negative region), respectively. Failure modes are shown on the load-displacement relationships for Specimen LC1, shown in Fig. 4.1.9E. Fracture of bolts, shown in Fig. 4.1.9E, caused the sudden decrease indicated in the load at points A and D (refer to Fig. 4.1.6).

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

(A)

Strain gauges attached to Specimen LC1

(B)

Strain gauges attached to Specimen LC2

4

187

FIG. 4.1.3 Strain gauges for the test specimens [1].

4.1.4.3 Structural behavior and associated failure modes for Specimen LC2 Eight interior bolts were added in Specimen LC2 (refer to Fig. 4.1.1B and E) to realize a fully restrained moment connection. The stiffness of the joint plate increased by adding interior bolts, so that structural performance of the mechanical joint similar to that of the monolithic steel-concrete composite column (Specimen LC3) was demonstrated. Fig. 4.1.10A identifies the concrete cracks, which initiated at a lateral displacement of 81 mm. Significant plate deformation at a stroke of 108 mm (Fig. 4.1.10B) was not noticed in Specimen LC2 with interior bolts, whereas the plate at a similar stroke started deforming when interior bolts were absent (Fig. 4.1.9B). Fractures of the joint and exterior bolts were delayed compared with those of Specimen LC1 without interior bolts (Fig. 4.1.9B, at a stroke of 108 mm). Fig. 4.1.10C shows the separation between metal plates at around a stroke of 135 mm, whereas most of the exterior bolts for Specimen LC1 without interior bolt were fractured, terminating the test, as can be seen in Fig. 4.1.9C. The large stiffness of the mechanical joint with interior bolts in Specimen LC2 delayed degradation of the joint, not being deformed as much as in Specimen LC1 until the interior bolts failed. Fig. 4.1.10D shows Specimen LC2 was loaded until six exterior bolts failed at a stroke of 165 mm. Severe damage of the concrete was not exhibited until the specimen was loaded further to a lateral displacement of 183 mm, in which concrete was severely degraded in both the negative and positive regions, as shown in Fig. 4.1.10E, followed by deteriorated mechanical joint, as shown in Fig. 4.1.10F. The test was terminated upon completion of the cycle at 183 mm. Large tensile forces acting on the metal plates caused two interior bolts to fracture at a stroke of 91 mm for Specimen LC2, accompanying a loud sound when the interior bolts

188 Hybrid composite precast systems

(C)

Strain gauges attached to Specimen LC3

(D)

Gauges attached to metal plates and steel columns Load

1.7 m Plate gauges were attached on the plate

Upper column Line for concrete gauges, rebar gauges, steel gauges (upper column): Located at 50 mm above the upper plate

85 mm 85 mm Plate gauges were attached on the plate 1.0 m Lower column 0.5 m

(E)

Plate level Line for concrete gauges, rebar gauges, steel gauges (lower column): Located at 950 mm above the foundation level Foundation Location of gauges

FIG. 4.1.3, Cont’d

were fractured (refer to (Fig. 4.1.10G). Fracture of the remaining six high-strength interior bolts originated the substantial drop of loads at a stroke of 91 mm (push region). Failure modes at the end of the test, shown in Fig. 4.1.10F, for Specimen LC2 having both interior and exterior bolts, indicated that large energy was dissipated during the hysteresis behavior of Specimen LC2. However, in the negative region (pull region), the load continued to increase at a stroke of 91 mm. No severe fractures of the structural elements, including fracture of bolts or deformation of metal plates, did not occur.

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TABLE 4.1.2 Summary of the strain gauges attached to the tested specimens [1]. Specimen

Strain gauges for metal plates

Strain gauges for rebars

Strain gauges for L-shaped steel

Strain gauges for concrete

LC1 (without interior bolts)

Upper plate: 1–4 Lower plate : 5–8

9–24

25–32

C1–C16

48 gauges

LC2 (with interior bolts)

Upper plate: 1–6 Lower plate : 7–12

13–28

29–36

C1–C16

52 gauges

LC3 (control specimen)

N/A

1–16

17–24

C1–C16

40 gauges

Total

In positive (at a stroke of 91 mm) and negative direction (at a stroke of 130 mm), the specimen reached its nominal lateral load capacity of 699 kN (push region), and 846 kN (pull region), respectively. Point B of the negative region in Fig. 4.1.6 represents a stroke of 158 mm where the load started dropping due to concrete failure in the compression zone.

4.1.4.4 Comparisons of the structural performance of the three specimens (LC1, LC2, and LC3) The structural behavior and failure modes of the L-shaped precast steel-concrete composite columns were explored by loading the three specimens, LC1, LC2, and LC3, to failure. In general, it was demonstrated that structural behavior and failure modes from Specimen LC1 were similar to those of Specimen LC2, however, the failure modes associated with fracture of bolts in tension and the crushing of concrete were substantially different. The interior bolts played an important role in obtaining a better structural response with Specimen LC2 than with Specimen LC1. Due to the stiffness of the metal plates for Specimen LC2 having interior bolts larger than that of Specimen LC1, the structural deterioration in Specimen LC2 was delayed compared with Specimen LC1. Insufficient plate stiffness for Specimen LC1 initiated the separation of the two metal plates whereas the stiffness of the metal plates for Specimen LC2 created a joint similar to fully restrained moment connection. For specimen LC2, reinforced by interior bolts, strength similar to that of the monolithic steel-concrete composite column (Specimen LC3) was achieved. In Fig. 4.1.6 (Fig. 4.2.4), initial stiffness of Specimen LC2 similar to that of Specimen LC3 was obtained until the load reached 564 kN at a stroke of 38 mm (see push region). Nominal capacity of 699 kN (1188.3 kN-m) was measured for Specimen LC2, whereas a nominal lateral load capacity of 800 kN (1360 kN-m) was reached in the monolithic Specimen LC3. The metal plates Specimen LC1 deformed, reaching a load of 400 kN at 38 mm with the dissipation of the most of the energy via inelastic deformation, leading to the lowest flexural moment capacity for Specimen LC1. The strengths at the design limit state for the mechanical joints (shown by dots in Fig. 4.1.6) obtained when concrete strain reached 0.003, were greater than moment demand (Mu) of 350 kN-m identified from seismic analysis. Specimens LC1 and LC2 were eligible to meet design requirements, indicating that a mechanical joint with and without interior bolts can replace the conventional steel-concrete hybrid composite precast columns at moment demand (Mu). The mechanical joint with interior bolts in Specimen LC2 dissipated the hysteretic energy (1.50
106 kN-mm) similar to that of monolithic Specimen LC3 (1.62
106 kN-mm). The ductility of the mechanical joint for columns with irregular shapes was also effectively enhanced to a level similar to a monolithic column by the use of interior bolts. However, Specimen LC1 dissipated significantly less energy (6.57
105 kN-mm) with inelastic deformation than any other specimens including Specimen LC2 having a mechanical joint with interior bolts, allowing the lowest flexural moment capacity. The lowest flexural moment capacity was caused by the ductility of the mechanical joint which was degraded by the absence of interior bolts. The energy dissipation was defined as the area under the hysteresis curve. The inelastic energy dissipation was evaluated at the reduction of 20% load with respect to the loads at the maximum load limit state.

4.1.4.5 Activation of the structural elements contributing to the flexural capacity of the hybrid precast column-column joint Figs. 4.1.11–4.1.14 elucidate the contribution of the structural elements, including the concrete, column rebars, and L-shaped steel members to the flexural capacity of the tested specimens. Fig. 4.1.11 presents load-strain relationships for Specimen LC3. Maximum concrete compressive strains as high as 0.0022 (push region, Legend 1) and 0.0013 (pull region, Legend 2) were observed in Specimen LC3, in which concrete compressive strain did not reach a strain of

190 Hybrid composite precast systems

FIG. 4.1.4 Fabrication of test specimens.

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TABLE 4.1.3 Summary of the material properties obtained from the test samples [1]. Category

Average value

Concrete samples [five samples]

Compressive strength: 29.1 MPa

Rebar [three samples]

Yield strength: 646.7 MPa Ultimate strength: 831.3 MPa

Steel [three samples]

Yield strength: 387.1 MPa Ultimate strength: 520.6 MPa

0.003 (design limit) due to gauge malfunctioned. For column rebars with yield stress and strain of, 600 MPa and 0.0029, maximum strains with 2.4 times the yield strain in tension (2.4ey, 0.0068) were reached when pushed at Gauge 9, shown by Legend 5 as measured in Fig. 4.1.11. Strains in column rebars (Gauge 9) indicated that column rebars contributed significantly to the flexural capacity of Specimen LC3. Alternatively, maximum strains observed in the embedded L-shaped steel were three times larger (as much as 0.005) when pushed than the yield strain (refer to the load-strain relationship indicated by Legend 3 of Fig. 4.1.11). The contribution of the column rebar, L-shaped steel, concrete, and metal plates to the flexural capacity of Specimen LC1 was identified in Fig. 4.1.12A and B. The definition of push and pull is shown in Fig. 4.1.10G. As shown in the loadstrain relationships indicated by Legend 1 of Fig. 4.1.12A, concrete compressive strain reached the design limit corresponding to a strain of 0.003 when the load attained a value of 500 kN. When the specimen was pushed, the load-strain relationship by Legend 3 of Fig. 4.1.12A indicated that the L-shaped steel almost yielded with a tensile strain of 0.0014 while the rebar did not yield with a tensile strain of 0.0018 as shown in the load-strain relationship by Legend 5. In Fig. 4.1.12B, the deformations of the metal plates were accompanied by large strains which were measured as 0.00214 at the upper plate (push by Legend 1) and as 0.0068 at the lower plate (push by Legend 2) at the concrete strain of 0.003. The strain gauge attached to the upper plate malfunctioned after recording a strain of 0.00214. The plate strains resulted in the steel section and rebars that were activated with small tensile strains which were 0.0014 and 0.0018, respectively, as shown in the load-strain relationship by Legends 3 and 5 of Fig. 4.1.12A when the specimen was pushed. The maximum strains of steel section and rebars were 0.0008 and 0.0021, respectively, as shown the in load-strain relationship by Legends 4 and 6 of Fig. 4.1.12A when the specimen was pulled. In Fig. 4.1.13A and B, the contribution of the structural elements to the flexural capacity of Specimen LC2 is explored. The concrete strain reaching a compressive strain of 0.003 in both the positive and negative regions are shown in the loadstrain relationship by Legends 1 and 2 of Fig. 4.1.13A. It was found that the L-shaped steel and column rebars reached almost their yield points at tensile strains of 0.0015 and 0.0029 indicated by Legends 4 (pull direction with steel in tension, the negative region) and 5 (push direction with rebars in tension, the positive region) in Fig. 4.1.13A. The gauge strain for the L-shaped steel did not function properly in the push region (Legend 3 of Fig. 4.1.13A). The tensile strains of 0.0014 (steel) and 0.0021 (rebars) at Gauges 35 and 26, respectively, are shown by Legends 4 and 6 of the load-strain relationships in the negative pull region. The tensile strain in the upper column plate reached 0.0069, and the tensile strain reached 0.0071 in the lower column plate, as indicated by the load-strain relationship shown as Legends 1 and 2 of Fig. 4.1.13B, respectively, when concrete compressive strain reached the design limit (ec ¼ 0.003), demonstrating that strains in the metal plates were as much as five times larger than the yield strain. Fig. 4.1.13B also illustrates that the specimen reached its nominal flexural load capacity of 699 kN (push region), leading to the yielding of the upper plate. Fig. 4.1.14 compares the contribution of the structural elements to the flexural capacity between Specimens LC1, LC2, and LC3. The concrete compressive strains in Specimens LC1 and LC2 reached their design limits; however, the strain gauges for the concrete in Specimen LC3 did not function properly, as illustrated in Fig. 4.1.14A. As indicated by the load-strain relationships shown as Legends 1, 2, 4, and 5 of Fig. 4.1.14A, the specimens fabricated with metal plates demonstrate less brittle concrete behavior than the monolithic column (Legends 3 and 6 in Fig. 4.1.14A). The higher flexural capacity of the specimen with interior bolts was demonstrated due to the confining effects provided by the interior bolts for concrete columns. Fig. 4.1.14B and C summarize the tensile strains in the L-shaped steel and rebars for the three specimens. The monolithic Specimen LC3 offered the largest magnitudes of strains in both the L-shaped steel and rebars, as shown in the load-strain relationships with Legends 3 and 6. The strains were followed in magnitude by Specimen LC2 (refer to the load-strain relationships shown by Legend 5 in Figs. 4.1.14 B and C) and Specimen LC1 (refer to the load-strain relationships shown by Legends 1 and 4 in Fig. 4.1.14B and C).

192 Hybrid composite precast systems

14.6% 11.3% 8.0%

Drift ratio (%)

6.0%

1.0% 0.75%

4.0% 2.0% 1.5% 0.0%

N Number of cycles

0.25% 3

0.37%

0.50%

0.75%

1.0%

Cycles

3

3

3

3

Displacement (mm)

(6.75)

(10.2)

(13.5)

(20.3)

(27.0)

1.5% 2.0%

2

2

(40.5) (54)

2

2

2

2

Loading step

Interstory drift angle (rad)

Number of cycles

Lateral displacement (mm)

1

0.00250

3

6.75

2

0.00375

3

10.2

3

0.00500

3

13.5

4

0.00750

3

20.3

5

0.01000

3

27.0

6

0.01500

2

40.5

7

0.02000

2

54.0

8

0.03000

2

81.0

9

0.04000

2

108.0

10

0.05000

2

135.0

11

0.06000

2

162.0

12

0.07000

2

189.0

Loading protocol used during the experiment [1]

FIG. 4.1.5 Specimens being subjected to the loading protocol.

2

(81) (108) (135) (162) (189)

Drift angle × column height (loading point: 27,000 mm)

(B)

14.6%

6.0% 8.0% 11.3%

4.0%

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FIG. 4.1.6 Load-displacement relationships for LC1, LC2, and LC3 [1].

The least joint stiffness of Specimen LC1 was responsible for the least tensile strain activation for the rebar and steel section, owing to the largest plate deformation. The interior bolts provided column plates with extra stiffness, contributing to higher flexural capacity. In Fig. 4.1.14C, the deformation of the metal plates of Specimen LC1 prevented the rebars from full activation, resulting in a limited contribution to the flexural capacity compared with a specimen having sufficient stiffness of column plate. A maximum tensile rebar strain of 0.0028 for Specimen LC2 was observed in the load-strain relationship by Legend 2 of Fig. 4.1.14C, while maximum tensile rebar strain reached as much as 0.0068 in Specimen LC3 (refer to the load-strain relationship shown as Legend 3 in Fig. 4.1.14C). The largest maximum tensile rebar strains were found from Specimen LC3 among all three specimens, whereas large deformations of the metal plates for Specimen LC1 activated rebar with the smallest tensile strain (0.0018), as shown in the load-strain relationship by Legend 1 of Fig. 4.1.14C. Fig. 4.1.14D also demonstrated the reduced activation for the steel section (refer to strain of 0.0014, shown in the load-strain relationship by Legend 1 of Fig. 4.1.14B) caused by the lower metal plates for Specimen LC1 which yielded large tensile strains of 0.0118 (refer to data by Gauge 8, Legend 2 of Fig. 4.1.14D), while the tensile strains of 0.0085 and 0.007 [refer to data by Legends 3(Gauge 3) and 4(Gauge 7) of Fig. 4.1.14D] were yielded for top and bottom plates, respectively, in Specimen LC2. Better activation of tensile strains of rebars and steel sections was attained by increasing the stiffness of the mechanical joint via the addition of interior bolts.

4.1.5 Conclusion Factors influencing the structural performance and failure modes of the mechanical joints for “L”-shaped hybrid precast concrete-based composite columns were explored by identifying microscopic strains of the joint components. The influence of stiffness for the mechanical connection on the activations of structural components attached to column plates was uncovered throughout the experimental investigations. Hysteretic energy dissipation capacities were compared for all three specimens, demonstrating similar initial stiffness among all specimens before the metal plates started deforming. At the factored moment demand (Mu ¼ 350 kN-m), Specimen LC2 (with eight-interior bolts) reached the flexural moment capacity similar to the strength of Specimen LC3 (monolithic column). Both specimens reached the flexural moment capacity of 350 kN-m at a stroke of 9 mm, demonstrating that the mechanical joint has increased the stiffness of the joint plates, resulting in the structural capability similar to the strength provided by conventional monolithic columns. However, it was worth noting that the same flexural strength (350 kN-m) was reached by Specimen LC1 (without interior bolts) at a stroke of 13 mm even if the mechanical connection used in Specimen LC1 did not create a rigid joint similar to the joint observed from the monolithic column. However, the maximum load capacity with Specimen LC2 increased by 37.5% compared with the load capacity measured in Specimen LC1. For the mechanical joint fabricated with interior bolts, hysteretic energy was dissipated in a similar manner to the energy dissipated by the conventional monolithic column. However, the metal plates in Specimen LC1 demonstrated the lowest inelastic energy dissipation capability when interior bolts were absent. The hysteretic energy dissipation in Specimen LC2

(A)

Concrete crushed at a stroke of 81 mm [1]

Buckling of the embedded elements (rebars and L-shaped steel) at a stroke of 135 mm, corresponding to points C and F (Fig. 4.1.6) [1]

(B)

(C)

End of the test at a stroke of 158 mm [1]

FIG. 4.1.7 Failure modes of Specimen LC3 (monolithic specimen).

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FIG. 4.1.8 Load-displacement relationships for Specimen LC3 [1].

(with interior bolts) was measured 128.3% higher than that of Specimen LC1 (without interior bolts), indicating that the interior bolts significantly contributed to the ductility and the flexural strength of the mechanical joints. The ductility and flexural strength of columns fabricated with the mechanical joint for irregular shapes can effectively be enhanced to a level similar to the monolithic steel-concrete column by the increased plate stiffness via interior bolts. A significant contribution was made to the flexural strength by the increased tensile strains of the joint components attached to column plates with interior bolts, while the large deformations caused at the metal plates retarded the activation of the tensile strains of the structural components attached to the plates when interior bolts were not used. Seeking flexural capacity similar to that of the monolithic columns without using interior bolts was not a practical option. Tensile rebar strains of between 0.001 and 0.002 in the specimen having metal plates without interior bolts were reached, while rebar tensile strains reached as much as 0.0068 in the monolithic specimen. Using interior bolts can contribute to an efficient way to obtain a flexural capacity as large as possible. Tensile strains of the plate were 0.007 in specimens with interior bolts, while the lower metal plates for specimens without interior bolts demonstrated tensile strains as large as 0.0118. The use of interior bolts with metal plates was verified to increase the stiffness of the mechanical joint, leading to the increased activation of the structural components attached to the plates. The use of thicker plates to increase the stiffness of the mechanical joint can be avoided by recommending the use of a sufficient number of interior bolts, rather than thicker plates, in achieving a structural strength similar to that of the monolithic columns. This chapter was devoted to the experimental investigations of the precast concrete-based frames with irregular column shapes whereas, in Section 4, the use of these frames was shown to contribute to rapid erection with a significant shortening of the construction period. As benefits of this chapter, the conventional use of grouted sleeve for the traditional precast connections can be replaced. Rectangular columns that do not fit at the corners can be also replaced by the L-shaped precast columns capable of efficient and effortless assembly.

4.2 Nonlinear finite element analyses of the L-type columns with mechanical joints 4.2.1 Selection of the elements and discretization The finite element (FE) models introduced in this section were developed based on continuum elements (8-node linear brick) of type C3D8R, as indicated in Fig. 4.2.1A and B [1]–[3]. These elements were suitable for modeling the nonlinear material properties to capture the complex behavior, accommodating contacts, plasticity, and large deformations subjected to loads. Beside, they were characterized by a constant volume change within the elements, preventing mesh locking when the material response was incompressible. Both normal and shears stresses under bending were zero at the integration points. However, full integration elements (C3D8) considered shear deformation, and they were very stiff in bending applications. The use of C3D8 (full integration elements) may generate false results since these elements were exposed to shear locking problems. Full integration elements (C3D8) were not used in this chapter, instead, reduced C3D8R integration elements with lower-order integrations were selected to create the element stiffness matrix by discretizing the structural elements including rebars, bolts, metal plates, upper and lower columns, and nuts. These elements significantly reduced the computation time since the integration was performed at one single integration point per element. Alternatively, the rigid body on which a lateral force (controlled by displacements) was exerted was modeled by linear quadrilateral elements R3D4. Specimen LC1 with 35-mm-thick plates having no interior bolts was modeled with 736,268 solid elements. A large

196 Hybrid composite precast systems

FIG. 4.1.9 Structural performance and failure modes for Specimen LC1 [1].

number of elements were observed in Specimen LC2 in which interior bolts were used to increase the flexural capacity of the connections. Local and global seeds of 10 and 30 mm were used, respectively, to discretize these specimens. Fine meshes were created by assigning local seeds at the joint (area of importance) whereas global seeds were applied to generate coarse mesh elsewhere. Specimen LC2 was constructed with a total mesh of 756,860 solid elements, whereas a total mesh of 251,761 solid elements was created to model Specimen LC3, fabricated as the monolithic column having no plates. A lower number of elements compared with Specimens LC1 and LC2 was used to model monolithic Specimen LC3. A fine mesh of 10 mm was assigned at the area of importance (metal joint) to ensure the accuracy of FE results, while the remaining part of the specimen was discretized with a coarse mesh. The geometric configurations of the full-scale finite element models are illustrated in Fig. 4.2.1A and B, whereas Fig. 4.2.1C depicts the test specimens.

4.2.2 Defining interactions; surface-to-surface contact The contact interactions introduced in Section 3.1.5 of Chapter 3 between deformable and rigid surfaces including concrete beam, metal plates, bolts, plates, and nuts were established to prevent elements from penetrating each other during the

FIG. 4.1.9, Cont’d

198 Hybrid composite precast systems

analysis. A contact pair was selected to define contact interactions between two surfaces during the analysis, as shown in Fig. 4.2.2. The contact formulation used to define contact interaction was based on a surface-to-surface approach. The selection of these two surfaces must comply with the guidelines available in Abaqus library. The following guidelines for selecting master and slave surfaces must always be checked: (1) the master should be the surface with a coarse mesh and (2) in case the mesh sizes are comparable, the mesh with higher stiffness should be assigned as a master surface. Fig. 4.2.2 depicts the master and slave surfaces used to study the nonlinear behaviors of the proposed columns. Surface-to-surface contact properties based on tangential and normal behavior was assigned; normal behavior was established based on the penalty method with hard contact for the pressure-overclosure relationship whereas tangential behavior was defined as frictionless. Constraint enforcement, referred to as the penalty method, was used at surface-to-surface contacts to enhance the solver efficiency. The penalty method allowed some minor penetrations to occur between master and slave surfaces; the contact force was proportional to the penetration distance. A nonlinear variation of contact stiffness in terms of contact pressureoverclosure relationship is illustrated in Fig. 3.1.20 of Chapter 3. With this regard, FE models accounting for the nonlinear penalty method were provided, in which the penalty stiffness increased linearly between areas of low initial stiffness and high final stiffness, resulting in the nonlinear pressure-overclosure relationship. Abaqus users prefer this method due to the following advantages (although this method allows some degree of penetration). By the penalty method, over-constraints were mitigated by reducing the number of iterations required in analysis, and Lagrange multipliers were also eliminated. The contact surfaces (master and slave surfaces) are defined for the proposed column-to-column mechanical joint in Fig. 4.2.2. It was recommended to avoid surfaces and nodes that did not experience contact during the analysis. This was because the addition of unnecessary contact surfaces and nodes may result in extra computational time unless the penalty contact enforcement was applied. The linear variations based penalty method was not used in the present FE models because the mechanical joints demonstrated high contact pressures between metal plates.

4.2.3 Definition of the host, embedded elements, and constraints The constraints between concrete and reinforcing bars/steel sections were defined for modeling steel-concrete hybrid composite members. This method allows Abaqus [12, Chapter 2] users to place the embedded elements (reinforcing bars and steel sections) into the host elements (concrete). Abaqus tracked the embedded elements, which were constrained by the response of the host elements, and eliminated the translational DOFs of the nodes in the case of embedded elements lying within the host region. These nodes are referred to as embedded nodes. The translational movement of embedded elements was controlled by the host elements. The host elements (upper and lower concrete columns) embedded L-shaped steels, rebars, and hoops in the present FE model, as shown in Fig. 4.2.3. Movements of the specimen during the application of loading were restricted at a fixed boundary. The material properties for embedded and host elements were defined based on the tested samples. The average tested concrete strength was 29.1 MPa. The yield strengths of 387.1 and 646.7 MPa were used for the embedded L-shaped steels and rebars, respectively. The elasto-hardening behavior of steel materials was used for the constitutive relationships of embedded elements (L-shaped steels, rebars) whereas the damaged plasticity was considered based on the stress-strain curve for the unconfined concrete suggested by Kent et al. [22, Chapter 3].

4.2.4 FE models with a foundation; load application at a test center The nonlinear finite element analyses under static load were undertaken to verify the structural performance of the monolithic irregular L-shaped column. A constant monotonic load controlled by displacement was applied for all specimens (LC1, LC2, and LC3) at a height of 2.7 m above the foundation under the same load condition. Numerical and test results of Specimen LC3 (monolithic column) demonstrated a good agreement until a stroke of 100 mm, as shown in Fig. 4.2.4. A decrease of the load was observed in the load-displacement relationship by Legend 1 of Fig. 4.2.4, caused by the buckling of rebars and L-shaped steels, as shown in Fig. 4.1.7B and C. However, a load reduction was not observed in FE model (refer to the load-displacement relationship shown by Legend 4 of Fig. 4.2.4); instead, the load slightly increased between a stroke ranging from 100 to 160 mm. This was because the present FE model was modeled using “embedded region” technique. This technique did not simulate the buckling behavior of embedded elements (rebars and L-shaped steels). Buckling of embedded elements, such as reinforcing bars and L-shaped steels, was restrained and prevented by the response of the host element. However, the overall numerical load-displacement relationship of monotonic L-shaped column matched well the experimental behavior.

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FIG. 4.1.10 Structural performance and failure modes of Specimen LC2 [1].

The load-displacement relationship of Specimen LC1, having only exterior bolts (refer to Legend 6 of Fig. 4.2.4), exhibited a load 528 kN with a stroke of 62.5 mm, leading to fracture due to large tensile forces at metal plates. As shown in Fig. 4.2.5, a sudden load drop of Specimen LC1, fabricated without interior bolts, was observed when two exterior bolts fractured during the numerical analysis, by which stresses and strains of the fractured Specimen LC1 were also calculated. This fracture was also found in experimental investigation, shown in Fig. 4.1.9E. The numerical analysis stopped due to the numerical instability when the necking of exterior bolts occurred, as shown in Fig. 4.2.5A and B, where a deformed shape of the proposed mechanical joint is also demonstrated. In Specimen LC1 (without interior bolts), strains in bolts were found as much as 0.11, that is, 22 times the yield strain of the bolt. As shown in Fig. 4.2.5, the plates of Specimen LC1 were detached from each other by 3 mm at the end of the analysis. Interior bolts of Specimen LC2 were more activated compared to

200 Hybrid composite precast systems

FIG. 4.1.10, Cont’d

exterior bolts, as can be seen in Fig. 4.2.6A and B. Strains of interior bolts seven times larger than those of exterior bolts at a stroke of 54 mm were found in the load-displacement relationship, shown by Legend 5 of Fig. 4.2.4, verifying that interior bolts significantly contributed to the flexural capacity of the joint. It is worth noting that the flexural capacity (refer to Legend 5 of Fig. 4.2.4) was well predicted when elastic-softening constitutive relationship for headed studs was used to represent the low cycle fatigue [16, Chapter 3], whereas flexural capacity (refer to Legend 7 of Fig. 4.2.4) was overestimated when elastic-plastic material property of headed studs was implemented in the numerical analysis. As shown in Fig. 4.2.7, finite element meshes of Specimen LC2 were created to identify the load path of the column-tocolumn connections, evaluating the response of the mechanical joints in the microscopic analysis. FE models were calibrated against test data, and their results were compared with the test data. The numerical and test results of Specimen LC3-WF are compared at the concrete strain of 0.0022 and 0.01 in Table 4.2.1, whereas comparisons of Specimens LC2WF and LC1-WF at the concrete strains of 0.003 and 0.01 are presented in Tables 4.2.2 and 4.2.3, respectively. The concrete strain of 0.003 was taken as a design limit while the concrete strain of 0.01 was considered as the ultimate strain value of the concrete, as specified by ACI code. The experimental and numerical results for the monolithic column with foundation (Specimen LC3-WF) are compared in Table 4.2.1, presenting the contribution of each structural element including rebars and L-shaped steel to the flexural capacity of the mechanical joint. Numerical analysis based on FE models predicted strains in rebars and steels accurately, matching test data at the concrete strain of 0.0022.

FIG. 4.1.10, Cont’d

FIG. 4.1.11 Load-strain relationships for the monolithic Specimen LC3 [1].

FIG. 4.1.12 Load-strain relationships for Specimen LC1 [1].

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

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FIG. 4.1.13 Load-strain relationships for Specimen LC2 [1].

The upper column plate of Specimen LC1-WF (without interior bolts, Table 4.2.3) underwent the tensile strain of 0.006, which is larger than the tensile strain of 0.0014 of the upper column plate for Specimen LC2-WF (with interior bolts, Table 4.2.2). The plates without interior bolts, thus, underwent large deformations during the analysis. Tables 4.2.2 (Specimen LC2-WF) and 4.2.3 (Specimen LC1-WF) also show the activation of structural elements attached to the joint plate. The much higher tensile strain was exerted on the exterior bolts of Specimen LC1-WF without the interior bolts than on those of Specimen LC2-WF, because interior bolts of the Specimen LC2-WF contributed to resist tension forces exerted by the rebars and L-shaped steel sections attached to the plates.

4.2.5 Structural behavior of laminated metal plates The structural performance of the metal plates for Specimen LC1 (without interior bolts) and Specimen LC2 (with interior bolts) were compared at the concrete compressive strain of 0.003 (design limit), as shown in Fig. 4.2.8. Tensile strains were observed at metal plates used for Specimens LC1 and LC2 during the application of lateral load. In Fig. 4.2.8A and B, the metal plate stiffened with interior bolts exhibited a smaller deformation of 0.4 mm compared with the deformation of 1.5 mm observed from the metal plate without interior bolts. As verified in the experimental investigation described in the previous section, the structural performance of the mechanical joint was greatly enhanced by the interior bolts. In

204 Hybrid composite precast systems

Fig. 4.2.8A and B, strains in the upper and lower column plates were large when interior bolts were absent. Steel section attached to the plates in Specimen LC2 was more activated than in Specimen LC1. Specimen LC2, having interior bolts, exhibited greater flexural capacity than Specimen LC1, having no interior bolts. Fig. 4.2.8A and B show the stroke (36.4 mm) of Specimen LC1 (without interior bolts), which was larger than that (26 mm) of Specimen LC2 (with interior bolts) when the concrete compressive strain reached 0.003 (design limit). For the concrete compressive strain of 0.003

FIG. 4.1.14 Comparison of strain-load relationships for all specimens (LC1, LC2, and LC3) [1].

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205

FIG. 4.1.14, Cont’d

(design limit), the strains in the upper and lower column plates were large (0.006 (3ey) and 0.007 (5ey), respectively) while they were smaller (0.0014 (0.7ey) and 0.0013 (0.7ey), respectively) when interior bolts were used. The structural performance of the proposed mechanical joint was significantly enhanced by the use of the interior bolts (0.009, 2ey), helping the steel sections attached to the plates in Specimen LC2 with interior bolts to highly activate with strains (0.002, 1.0ey) compared to those (0.0016, 0.8ey) in Specimen LC1 with no interior bolts. The structural behavior became more stable by reducing tensile strain to 0.002 (0.4ey) in the exterior bolts of LC2 from that (0.028, 6ey) in the exterior bolts of LC1, indicating that the interior bolts were well activated for Specimen LC2. The interior bolts reached strain of 0.009 (2ey) at the concrete strain of 0.003 (refer to Fig. 4.2.8B), and strain of 0.03 (7ey) was reached at a stroke of 54 mm (refer to Fig. 4.2.6A) where strains in the interior bolts were seven times higher than those in the exterior bolts at a stroke of 54 mm (refer to the load-displacement relationship in Legend 5 of Fig. 4.2.4). This indicated that the interior bolts significantly contributed to the flexural capacity of the joint. Fig. 4.2.8C compares the observed failure mode of LC3 to that

206 Hybrid composite precast systems

obtained by numerical investigation for a stroke of around 108 mm. Failure of the lower part of the column found from the experiments similar to that obtained by the numerical investigation was shown.

4.2.6 FE models without foundations 4.2.6.1 Load applied at a test center, not a shear center Three FE models (LC1-NF, LC2-NF, and LC3-NF, *NF ¼ no foundation) were constructed without foundation to remove the influence of the boundary condition on the flexural capacity of the mechanical joints [2]. The geometric configurations were kept the same relative to the previous models except for the lack of foundation, as indicated in Fig. 4.2.9A. After removing the foundation, the three specimens (LC1-NF, LC2-NF, and LC3-NF, *NF ¼ No foundation) were loaded under monotonic load, and their load-displacement relationships were compared, as shown in Fig. 4.2.9B, when the load was applied at the test center. In Fig. 4.2.10, the influence of the foundation on the structural performance of the proposed column-to-column connections was explored based on nonlinear finite element analysis. All six FE models (three models with foundations (LC1-WF, LC2-WF, and LC3-WF), three models without foundations (LC1-NF, LC2-NF, and LC3-NF)) were subjected to identical monotonic loads controlled by displacement at the test center. Their numerical results are compared in Fig. 4.2.10, where the monolithic specimen demonstrated the largest discrepancy between models with/without foundations (refer to Legends 1 and 4 of Fig. 4.2.10). The foundation rotation of the monolithic column (Specimen LC3) was represented by discrepancy 1 (Legends 1 and 4 of Fig. 4.2.10). However, discrepancy 3 (Legends 3 and 6 of Fig. 4.2.10), caused by the foundation rotation of the Specimen LC1 with mechanical joints without interior bolts, was not as significant as that with Specimen LC3. The metal plates in Specimen LC1 without interior bolts deformed, not taking part in causing the rotation of foundation. Specimen LC2 stiffened with interior bolts demonstrated discrepancy 2 (Legends 2 and 5 of Fig. 4.2.10), which was larger than discrepancy 3 of specimens without interior bolts, but smaller than that of the monolithic specimen. Creating a rigid joint to prevent the metal plates with interior bolts from deforming contributed to the enhanced flexural capacity of the mechanical joint up to the level of the monolithic column. The rotation of foundation with LC2 became more prominent than that of foundation with LC1. The structural performance of these specimens without foundations was evaluated and documented in Tables 4.2.4–4.2.6, which summarize the activation of each structural element and its contribution to the flexural capacity of the proposed mechanical joint. The presence of interior bolts in Specimen LC2-NF substantially reduced the deformation of metal plates, resulting in the full activation of column rebars and steel attached to the column plate. The rebar strain of 0.0076 was recorded in Specimen LC2-NF at the concrete strain of 0.003, whereas the rebar strain of 0.004 was found in Specimen LC1-NF (specimen without interior bolts). The numerical findings indicated that the rebars in the specimen having interior bolts were more activated than in the specimen without interior bolts. Similarly, L-shaped steel sections attached to the plates in Specimen LC2-NF, having interior bolts, were more activated than in Specimen LC1NF, having no interior bolts.

4.2.6.2 Load applied at shear center In Fig. 4.2.11A, the foundation was removed for three FE models (LC1-NF, LC2-NF, and LC3-NF) in which the lateral load was applied at the shear center to investigate the influence of where the load is applied on the flexural capacity of the proposed mechanical joint. Greater flexural capacity (refer to Fig. 4.2.11B) was observed than when loads were applied at the shear center (refer to Figs. 4.2.11B and 4.2.4), where the greater flexural capacity was resulted in by torsional modes. Points corresponding to the concrete strain of 0.003 are indicated on the load-displacement relationship, shown in Fig. 4.2.11B.

4.2.7 Strain evolution of L-type columns (monolithic and mechanical joints with no axial force) with/without foundation The activation of structural members (rebars, steels, and metal plates) in columns was explored with FE models having no foundations. The strain evolution of rebars in the proposed FE models (LC1-NF, LC2-NF, and LC3-NF) was plotted in Fig. 4.2.12A. Rebars in the specimen with interior bolts were more activated compared to that in specimen modeled without interior bolts. This was because metal plates in specimen stiffened with interior bolts did not deform, leading to the full activation of rebars attached to metal plates. However, less activation of rebars was observed due to the large deformation of metal plates in the specimen without interior bolts (LC1-NF). It should be noted that the activation of rebars in the mechanical joint reinforced with interior bolts was similar to that in the monolithically designed specimen. Similarly, steel sections in the specimen with interior bolts were more activated than that in the specimen without interior bolts, as can be

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

FIG. 4.2.1 Three-dimensional FE models for the proposed specimens [1].

4

207

208 Hybrid composite precast systems

FIG. 4.2.2 Definition of interactions between surfaces in contact; master and slave surfaces [1].

FIG. 4.2.3 Host and embedded elements [1].

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

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209

FIG. 4.2.4 Numerical and test results of the tested specimens (LC1–LC3).

seen in Fig. 4.2.12B. The structural activation of metal plates is summarized in Fig. 4.2.13C and D, in which large deformations were concentrated at metal plates in the specimen without interior bolts, causing a rapid increase in the rate of strain increase. Both the upper and lower plates were more activated when the interior bolts were absent (Specimen LC1-NF), indicating that interior bolts played an important rule to diminish the deformations in metal plates. The structural performance of the proposed mechanical joints for hybrid precast concrete columns was enhanced by the use of interior bolts. The measured activation of rebars, steels, and metal plates for specimens with foundations (LC1-WF to LC3-WF) was also plotted in Fig. 4.2.13. The activation of rebars and steels was higher in the monolithically designed specimen, as indicated in Fig. 4.2.13A and B. Similarly, the specimen stiffened with interior bolts showed a rapid increase in strains in both steels and rebars compared with the specimen without interior bolts. Rebars and steels were not fully activated in the specimen without interior bolts. The metal plates in the specimen without interior bolts experienced large deformations, hindering the activation of column rebars. The deformation of metal plates in the specimen without interior bolts was initiated at the stroke of 81 mm (refer to Fig. 4.1.9B). The activation of metal plates was observed during the experimental test, and it was verified via numerical analyses, as shown in Fig. 4.2.13C and D. Both numerical and experimental results demonstrated that metal plates were activated higher in the specimen without interior bolts due to large deformations of the column plates. However, metal plates reinforced with interior bolts did not demonstrate severe deteriorations during the application of cyclic loadings. At the design level, both monolithic specimen (LC3) and mechanical joint with interior bolts (Specimen LC2) exhibited similar flexural strength, indicating that the mechanical joint offered structural performance similar to that of the conventional monolithic column. It was noteworthy that nonlinear finite element analysis considering damaged concrete plasticity offered the strain evolution relative to the stroke of the columns as plotted in Fig. 4.2.13C and D. They demonstrated discrepancy to some extent; however, a tendency similar to that obtained by the experimental investigation was elicited.

4.2.8 Conclusions Conventional grouted sleeve connections for irregular shape of columns can be replaced by hybrid mechanical joints with laminated metal plates. The L-shaped precast columns with the capability for efficient and effortless assembly of precast columns were preferred over the conventional rectangular columns due to their architectural flexibility at the corners of the walls in residential buildings. This chapter was devoted to experimentally verifying the structural performance and failure modes of the mechanical joints for L-shaped hybrid precast concrete-based columns [1]. The factors influencing the stiffness of the mechanical joint were identified by the test of three specimens in which two specimens were designed with metal plates at the joints, while the remaining specimen was designed as a conventional monolithic steel-concrete column. The structural performance and failure modes of the mechanical joints for L-shaped precast steel-concrete composite

210 Hybrid composite precast systems

FIG. 4.2.5 Failure mode of Specimen LC1 (without interior bolts) [1].

columns were explored experimentally, and microscopic strains of the elements influencing the structural behavior of the joint were identified numerically as well. The three specimens demonstrated identical initial stiffness before the metal plates started deforming, which was followed by different hysteretic energy dissipation capacities among the three specimens. The mechanical joint reinforced with interior bolts was able to dissipate energy similarly to the energy dissipated by the conventional monolithic column, whereas the inelastically dissipated energy of the specimen with metal plates was the lowest when interior bolts were absent. A flexural capacity similar to that of the monolithic steel-concrete column was delivered when mechanical joints with sufficient stiffness were provided by interior bolts. The ductility of the mechanical joint for columns with irregular shapes was also brought up to a level similar to the monolithic steel-concrete column by the use of interior bolts providing additional plate stiffness. The use of thicker plates to increase the stiffness of the proposed mechanical joint can be less

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

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211

FIG. 4.2.6 Activation of interior bolts in Specimen LC2 [1].

economic. The use of a sufficient number of interior bolts rather than thicker plates was recommended based on the experimental and numerical investigation of L-shaped precast concrete column joints with fully and partially restrained moment connections. The following recommendations were suggested for the design of the proposed mechanical joints to splice precast columns. (1) Rapid erection of precast concrete-based frames has been achieved. A significant shortening of the construction period required by conventional concrete frames can be obtained by implementing the novel erection method based on mechanical joints, contributing to the rapid erection of precast concrete-based frames with irregular shapes. The conventional grouted sleeves for splicing precast columns can also be replaced. (2) Effective column splicing of L-type irregular precast columns has been achieved. Structural performance with efficient and effortless assembly capability of hybrid precast columns with irregular sections was demonstrated using mechanical joints. The hybrid precast wall columns with L shape can be used to replace rectangular columns that do not fit at the corners. The architectural flexibility at the corners of the walls in residential buildings over the conventional rectangular columns is noteworthy.

212 Hybrid composite precast systems

FIG. 4.2.7 Selected meshes for the microscopic analysis of the proposed mechanical joint of Specimen LC2 [1].

TABLE 4.2.1 Strains of proposed column connection identified from Legends 1 and 4 of Fig. 4.2.4; monolithic specimen (LC3-WF) [1]. FEA results (Legend 4)

Test results (Legend 1)

Legends 1 and 4 of Fig. 4.2.4

Concrete strain of 0.0022 / 0.003

Concrete strain of 0.01

Concrete strain of 0.0022

Concrete strain of 0.01

Load

569 kN/637 kN

743 kN

760 kN

Strain gauge malfunctioned

Displacement

33 mm/41 mm

62.1 mm

90.6 mm

Strain gauge malfunctioned

Strain

0.0022/0.003

0.01

0.0022

Strain gauge malfunctioned

Stress

26 MPa/29MPa

13 MPa

Not measured

Not measured

Strain

0.0029/0.0035 (0.9ey)/(1.2ey)

0.0056 (1.8ey)

0.0023 (0.7ey)

Strain gauge malfunctioned

Stress

607 MPa/660 MPa

660 MPa

Not measured

Not measured

Strain

0.0025/0.0028 (1.3ey)/(1.6ey)

0.005 (2.6ey)

0.00251 (1.3ey)

Strain gauge malfunctioned

Stress

430 MPa/431 MPa

450 MPa

Not measured

Not measured

Concrete

Rebar (average)

Steel (average)

(3) Fractures and strength degradations were identified based on extensive nonlinear finite element models, accounting for decreasing trends in the load-displacement relationships. Extensive strain data were obtained to explore the structural elements’ influence on the flexural capacity of the test specimens. (4) The ductility and flexural strength were improved to levels similar to the monolithic steel-concrete column through the use of interior bolts, which provided additional plate stiffness and effectively activated the rebar and steel sections attached to the metal plate. Using a sufficient number of interior bolts rather than thicker plates is recommended to effectively enhance the stiffness of the irregular mechanical metal plates. Both experiments [1, 2] and the numerical investigation of L-shaped hybrid precast concrete column joints were described in detail, with fully and partially restrained moment connections. The contribution of each structural element attached to the mechanical joint to the flexural capacity of the test specimens was investigated based on microscopic strains of the elements. Tensile strains of lower plates were substantially reduced to 0.007 (5ey) in specimens without interior bolts, while tensile strains as large as 0.0013 (0.7ey) were found in the lower metal plates for specimens with interior bolts. The stiffness of the

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

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TABLE 4.2.2 Strains of proposed column connection identified from Legends 2 and 5 of Fig. 4.2.4; specimen with interior bolts (LC2-WF) [1]. FEA results (Legend 5)

Test results (Legend 2)

Legends 2 and 5 of Fig. 4.2.4

Concrete strain of 0.003

Concrete strain of 0.01

Concrete strain of 0.003

Concrete strain of 0.01

Load

435 kN

596 kN

500 kN

Strain gauge malfunctioned

Displacement

26 mm

54 mm

100 mm

Strain gauge malfunctioned

Strain

0.003

0.012

0.003

Strain gauge malfunctioned

Stress

26 MPa

7 MPa

Not measured

Not measured

Strain

0.0017 (0.5ey)

0.006 (3ey)

0.0013 (0.4ey)

Strain gauge malfunctioned

Stress

440 MPa

530 MPa

Not measured

Not measured

Steel (average)

Strain

0.002 (1ey)

0.006 (1.6ey)

0.0012 (0.4ey)

Strain gauge malfunctioned

Stress

490 MPa

550 MPa

Not measured

Not measured

Upper plate

Strain

0.00141 (0.4ey)

0.0033 (1.7ey)

0.0069 (3.6ey)

Strain gauge malfunctioned

Stress

318 MPa

452 MPa

Not measured

Not measured

Deformation

0.31 mm

0.67 mm

Not measured

Not measured

Strain

0.00138 (0.7ey)

0.0031 (1.7ey)

0.0072 (3.8ey)

Strain gauge malfunctioned

Stress

317 MPa

447 MPa

Not measured

Not measured

Deformation

0.4 mm

0.7 mm

Not measured

Not measured

Strain

0.002 (0.4ey)

0.005 (0.4ey)

Not measured

Strain gauge malfunctioned

Stress

478 MPa

1005 MPa

Not measured

Not measured

Strain

0.009 (2ey)

0.027 (5ey)

Not measured

Strain gauge malfunctioned

Stress

1015 MPa

1005 MPa

Not measured

Not measured

Concrete

Rebar (average)

Lower plate

Exterior bolt Interior bolts

mechanical joint increased by the use of interior bolts activated the rebars and steels attached to plates, enhancing the design of the joint metal plate. (5) Effective activation of structural components has been achieved by increased plate stiffness. Tensile strains of the specimen with interior bolts significantly contributed to the flexural capacity, while the large deformations occurring at the irregular metal plates without interior bolts prevented tensile strains of the column from activating. Rebar tensile strains attached to metal plates without interior bolts were as low as between 0.001 and 0.0024 (0.8ey), while the maximum rebar tensile strains of the monolithic specimen showed values as high as 0.0068. Providing interior bolts to create a rigid joint is one of the most effective ways to obtain a flexural capacity that is as large as possible. All three specimens demonstrated identical initial stiffness until the moment demand at Mu. The columns with mechanical joints provided moment strengths similar to those of monolithic columns at Mu, demonstrating that a significant contribution of mechanical joints to the spliced irregular precast columns was achieved. The stiffness of laminated metal plates was sufficiently high to transfer loads for a given load demand. However, the stiffness of the joint plates sufficient to provide flexural capacity similar to that of the monolithic columns must be sought at larger loads. The stiffness

214 Hybrid composite precast systems

TABLE 4.2.3 Strains of proposed column connection identified from Legends 3 and 6 of Fig. 4.2.4; specimen without interior bolts (LC1-WF) [1]. FEA results (Legend 6)

Test results (Legend 3)

Legends 3 and 6 of Fig. 4.2.4

Concrete strain of 0.003

Concrete strain of 0.01

Concrete strain of 0.003

Concrete strain of 0.01

Load

440 kN

527 kN

500 kN

Strain gauge malfunctioned

Displacement

36.4 mm

60 mm

77 mm

Strain gauge malfunctioned

Strain

0.003

0.013

0.003

Strain gauge malfunctioned

Stress

28.4 MPa

8 MPa

Not measured

Not measured

Strain

0.0024 (0.8ey)

0.0041 (1.3ey)

0.0021 (0.7ey)

Strain gauge malfunctioned

Stress

346 MPa

630 MPa

Not measured

Not measured

Steel (average)

Strain

0.0016 (0.8ey)

0.0038 (2ey)

0.0014 (0.7ey)

Strain gauge malfunctioned

Stress

416 MPa

506 MPa

Not measured

Not measured

Upper plate

Strain

0.006 (3ey)

0.013 (7ey)

0.0022 (1ey)

Strain gauge malfunctioned

Stress

463 MPa

470 MPa

Not measured

Not measured

Deformation

1.4 mm

4.4 mm

Not measured

Not measured

Strain

0.007 (5ey)

0.015 (5ey)

0.0068 (5ey)

Strain gauge malfunctioned

Stress

464 MPa

472 MPa

Not measured

Not measured

Deformation

1.5 mm

4.7 mm

Not measured

Not measured

Strain

0.028 (6ey)

0.09 (18ey)

Not measured

Not measured

Stress

1037 MPa

827 MPa

Not measured

Not measured

Concrete

Rebar (average)

Lower plate

Exterior bolt

and ductility of the mechanical joint for columns having irregular shapes to a level similar to the monolithic steel-concrete column were achieved by the use of interior bolts, sufficing to create rigid joints resisting tensioncompression couples exerted on the plates.

4.3

Design verification of the beam-column frames

4.3.1 Nonlinear numerical model The finite element parameters were based on the parameters defining the Drucker-Prager hyperbolic plastic potential function, which was described in Section 3.1.3 of Chapter 3. Material properties implemented in the nonlinear numerical analysis considering the concrete plasticity for the verification of the proposed frames are presented in Tables 4.3.1 and 4.3.2.

4.3.1.1 Description of the numerical model Abaqus has a wide range of elements, providing a powerful set of tools for solving a variety of problems. Three types of elements, shown in Table 4.3.3, were selected to discretize the proposed mechanical joints. Figs. 4.3.1 and 4.3.2 illustrate FEA mesh modeling column-to-column joints and beam-to-column, respectively. Element types used to model the

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

FIG. 4.2.8 Structural behavior of Specimens LC1, LC2, and LC3 at a stroke of 108 mm.

4

215

216 Hybrid composite precast systems

FIG. 4.2.9 FE models without foundations for Specimens LC1, LC2, and LC3 (load applied at test center) [2].

FIG. 4.2.10 Flexural strength of FE models with/without foundations [2].

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217

TABLE 4.2.4 Strains of proposed column connection identified from Legends 1 of Fig. 4.2.9; monolithic specimen (LC3-NF, with no rotations of foundation) [2]. FEA results Legends 1 of Fig. 4.2.9

Concrete strain of 0.003

Concrete strain of 0.01

Load

958 kN

1277 kN

Displacement

31 mm

81 mm

Strain

0.003

0.011

Stress

33 MPa

7.0 MPa

Strain

0.0086 (2.7ey)

0.027 (8ey)

Stress

647 MPa

583 MPa

Strain

0.0096 (2.7ey)

0.03 (9ey)

Stress

413 MPa

582 MPa

Concrete

Rebar (average)

Steel (average)

TABLE 4.2.5 Strains of proposed column connection identified from Legends 2 of Fig. 4.2.9; specimen with interior bolts (LC2-NF, with no rotations of foundation) [2]. FEA results Legends 2 of Fig. 4.2.9

Concrete strain of 0.003

Concrete strain of 0.01

Load

697 kN

626 kN

Displacement

32.4 mm

50 mm

Strain

0.003

0.010

Stress

32 MPa

6.7 MPa

Strain

0.0076 (2.4ey)

0.014 (4.7ey)

Stress

670 MPa

682 MPa

Strain

0.0029 (1.5ey)

0.0052 (2.7ey)

Stress

440 MPa

518 MPa

Strain

0.0042 (2.2ey)

0.0071 (3.7ey)

Stress

439 MPa

430 MPa

Deformation

0.8 mm

3.5 mm

Strain

0.0044 (2.2ey)

0.0076 (4ey)

Stress

440 MPa

430 MPa

Deformation

0.9 mm

3.8 mm

Strain

0.019 (4ey)

0.068 (14ey)

Stress

1033 MPa

811 MPa

Strain

0.14 (28ey)

0.37 (74ey)

Stress

531 MPa

355 MPa

Concrete

Rebar (average)

Steel (average)

Upper plate

Lower plate

Exterior bolt

Interior bolts

218 Hybrid composite precast systems

TABLE 4.2.6 Strains of proposed column connection identified from Legends 3 and 6 of Fig. 4.2.9; specimen without interior bolts (LC1-NF, with no rotations of foundation) [2]. FEA results Legends 3 Fig. 4.2.9

Concrete strain of 0.003

Concrete strain of 0.01

Load

480 kN

532 kN

Displacement

30 mm

42 mm

Strain

0.003

0.010

Stress

31 MPa

9 MPa

Strain

0.004 (1.3ey)

0.006 (2ey)

Stress

670 MPa

671 MPa

Strain

0.0024 (1.3ey)

0.0043 (2.3ey)

Stress

358 MPa

388 MPa

Strain

0.011 (6ey)

0.018 (9ey)

Stress

453 MPa

461 MPa

Deformation

1.8 mm

4.8 mm

Strain

0.012 (6ey)

0.019 (9ey)

Stress

455 MPa

464 MPa

Deformation

2 mm

4.9 mm

Strain

0.035 (7ey)

0.077 (15ey)

Stress

1051 MPa

888 MPa

Concrete

Rebar (average)

Steel (average)

Upper plate

Lower plate

Exterior bolt

proposed mechanical joints including C3D8R element known as the reduced integration element were also presented. Elements of type B31 representing a first-order three-dimensional beam element were implemented for column rebars to reduce the number of degrees of freedom in the FE model. Three-dimensional elements of type R3D4 were used to model the rigid body. A reference point where a monotonic load was applied was located by a rigid body. The R3D4 elements each having four nodes with three DOFs were characterized with a positive normal that was defined by the right-hand rule going around the nodes of elements in order to maintain the element’s connectivity. Figs. 4.3.1A and 4.3.2A show totals of 201,632 and 113,432 elements established in this FE model, each having four nodes with three DOFs.

4.3.1.2 Modeling column-girder joints The proposed beam-column mechanical joint shown in Fig. 4.3.2 was modeled using elements of types C3D8R and R3D4. The concrete beam, concrete column, rebars, bolts, embedded H-steels, hoops, stirrups, and extended endplates were established by C3D8R elements. A rigid body was discretized by elements of type R3D4 for the application of a monotonic force.

4.3.1.3 Modeling the surface element In Fig. 4.3.3, various contact surfaces, including surfaces between plates, plates and bolts, and concrete and plates were established in the numerical model for the verification of the proposed connection for precast frames. Contacts shown in Fig. 4.3.3 were formulated for the column-to-column and beam-to-column mechanical joints based on a total of seven interactions (Int-1 to Int-7), where each formulation depended on the choice of contact discretization, tracking approach, and assignment of master and slave roles to the contact surfaces. Nodes of the steel section were shared with those of the metal plates at their contacts in the FE model, generating complete composite actions by these two materials.

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

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FIG. 4.2.11 FE models without foundations (load applied at shear center) [2].

4.3.2 Design verification 4.3.2.1 Dynamic analysis of high-rise buildings with multibay L-type composite precast frames Fig. 4.3.4A [1] describes a multibay frame with proposed L-type hybrid composite precast frames having mechanical joints, for a selected 20-story apartment building. In Fig. 4.3.4B, wall frames of the 20-story apartment building were replaced by the proposed frames. Dead (2 kN/m2) and live (4 kN/m2) loads were calculated from the plans shown in Fig. 4.3.4A, resulting in a total axial load of 11,680 kN on the columns. The L-shaped columns shown in Fig. 4.3.4A provided the architectural flexibility at the corners similar to that of the wall frames, replacing structural walls with dry partitions, and saving substantial amounts of concrete and construction time. Table 4.3.4 presents the dynamic behaviors of the two structural frames shown in Fig. 4.3.4, including the periods and mode shapes of all modes. The fundamental period of the proposed frame was 2.1 s, while that of the conventional wall frame, found from the fundamental translational mode (2nd mode), was 2.2 s. showing that the fundamental periods of a 20story apartment building with the proposed L-type composite precast frames with mechanical joints were slightly less than those calculated from a 20-story apartment building with conventional wall frames. In Fig. 4.3.5, the 1st, 3rd, and 5th modes of the two structural frames are caused by the torsional modes whereas the 2nd, 4th and 6th are translational modes. The load demands for the design, in terms of the moment (Mu), shear (Vu), and axial forces (Pu), are presented in Table 4.3.5; these must be resisted by the proposed mechanical joints.

220 Hybrid composite precast systems

4.3.2.2 Determination of the nominal strength at a concrete strain of 0.003 based on the concrete mesh under the average compression A numerical investigation was conducted to verify the design of the proposed precast frame. The distribution of the strains in the hybrid composite column section is explored in Fig. 4.3.6A and B to obtain the nominal strength based on a concrete strain of 0.003. The neutral axis was determined based on the meshes with average compression and maximum compression, respectively, as shown in Fig. 4.3.6A and B. In Figs. 4.3.6A-(1) and 4.3.8A, the nominal flexural and shear capacities were calculated to be 1175.3 kN-m and 691 kN, respectively, based on a concrete strain of 0.003. This strain value was identified based on the concrete meshes under average compression in the columns without interior bolts when an axial force of 5000 kN was exerted. The nominal flexural strength of 208 kN-m for girders with 200 mm width and 400 mm depth, based on the neutral axis with average compression, was also found, as shown in Figs. 4.3.6A-(2) and 4.3.8C. Conservative value with the nominal flexural strength of 239.4 kN-m is obtained from Fig. 4.3.6B, as identified by the concrete meshes under maximum compression. The strain distributions of the mechanical joints, which were identified based on the concrete meshes under average compression, are exhibited in Figs. 4.3.7–4.3.9. The moment demand (Mu) of the column (refer to Figs. 4.3.7A and 4.3.8A) and beams (refer to Figs. 4.3.7C, 4.3.8C, and 4.3.9A, B) with the proposed joint was calculated to be 355 and 238 kN-m (refer to Table 4.3.5). The strains at the mechanical joints of the L-shaped column and girder 200 mm wide
400 mm deep are identified in Fig. 4.3.7A and B. Punching shear stresses built around the neck of the counterbores at Mu are compared with the shear strength in Fig. 4.3.7B, indicating that the thickness (13 mm) of the neck of the counterbores provided sufficient shear strength. However, in Fig. 4.3.8C, a girder with a width of 200 mm and a depth of 400 mm provided 208 kN-m at a concrete strain of 0.003, failing to meet flexural strength equal to Mu (238 kN-m, refer to Table 4.3.5 and Fig. 4.3.7C); these data were of special interest when the mechanical joints were designed, suggesting the girder be re-sized. In Fig. 4.3.8A, the nominal strength of the column with the proposed joint was calculated as 1175 kN-m at the concrete strain corresponding to 0.003. Fig. 4.3.8A and B also illustrate strains at the mechanical joints of the L-shaped column. A shear strength greater than the punching shear stresses at Mu was offered by the 13-mm thick neck of the counterbores, as shown in Fig. 4.3.7B. At a concrete strain of 0.003, the design shear strength of the counterbores calculated to be 322.4 kN was sufficient to resist punching shear stresses of 255 kN, 318.7 MPa, as shown in Fig. 4.3.8B, ensuring structural safety at the joints. However, as shown in Fig. 4.3.8C, it was found that the mechanical joints of the column-girder joint with 200 mm wide
400 mm deep girder provided flexural strength (208 kN-m) at a concrete strain of girder corresponding to 0.003, which was not sufficient to resist Mu, 238 kN-m, as shown in Table 4.3.5. The flexural strength at a concrete strain of girder corresponding to 0.003 increased to 311 kN-m when the 200 mm wide
500 mm deep girder was used, as shown in Fig. 4.3.9B. The concrete column strain at Mu (355 kN-m) was 0.00048, as shown in Fig. 4.3.7A. In Figs. 4.3.8D and 4.3.9C, strains (0.0006–0.0009) on the face of the concrete column at a concrete strain of girder corresponding to 0.003 for the 200 mm wide
400 mm deep girder increased to 0.001–0.002 when 200 mm wide
500 mm deep girder was implemented, contributing the increase of flexural strength from 208 to 311 kN-m, as described above. The structural behavior at joints was ensured by the strain analysis based on the numerical investigation.

4.3.2.3 Strain evolutions of the mechanical joints The moment-displacement relationship of the columns with an axial force of 5000 kN is presented in Fig. 4.3.10. The flexural moment capacity corresponding to a concrete strain of 0.003, marked by a red dot, showed that the monolithic columns (moment-displacement relationship by Legend 1) delivered the greatest moment strength. The use of interior bolts increased the moment strength (moment-displacement relationship by Legend 2) compared to the moment strength without interior bolts (moment-displacement relationship by Legend 3). However, these three columns provided similar moment strengths at Mu, indicating that the mechanical joint with a laminated metal plate offered sufficient flexural capacity for a given load demand. The proposed joint can replace columns with monolithic joints for the load demand. The influence of the joint details on the flexural capacity of the proposed connection is explored in the following section. The vertical rebars were connected directly onto the 30-mm-thick metal plates. Figs. 4.3.7 and 4.3.8 summarize the entire evolutions of strains of the mechanical joints. The average strains in the upper and lower plates were negligible: et ¼ 0.000025 (average, 0.016ey) at Mu (350 kN-m), as shown in Fig. 4.3.7A and et ¼ 0.0015 (average, 0.94ey) at the moment corresponding to a concrete strain of 0.003 (1175.3 kN-m) as shown in Fig. 4.3.8A. In Fig. 4.3.7A, the strain of the concrete column at Mu was identified to be 0.00048. The strains of the vertical rebars are 0.00006 (0.02ey, refer to Fig. 4.3.7A) and 0.0026 (0.89ey, refer to Fig. 4.3.8A) at Mu and at the moment corresponding to a concrete strain of 0.003, respectively. The strains exerted on

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FIG. 4.2.12 Activation of structural components without foundation [2].

the joints for columns are identified in Fig. 4.3.10; here, the moment-displacement relationships of the concrete, rebars, and column plates at Mu, as well as the moment corresponding to a concrete strain of 0.003, are displayed. The moment-displacement relationship of girders (200 mm wide
400 mm deep) is presented in Fig. 4.3.11, where the moment corresponding to a given moment demand (Mu, 238 kN-m as marked by Point (4) on the moment-displacement relationship by Legend 4 of Fig. 4.3.11, and referring to Fig. 4.3.7C). The given moment demand was greater than the moment strength (208 kN-m as marked by Point (3) on the moment-displacement relationship by Legend 4 of Fig. 4.3.11, and referring to Fig. 4.3.8C), corresponding to a concrete strain of 0.003 due to the insufficient girder size. In Fig. 4.3.12, a moment strength (311 kN-m as marked by Point (2) on the moment-displacement relationship by Legend 2 of Fig. 4.3.12, and referring to Fig. 4.3.9B) greater than Mu (238 kN-m), at the concrete strain of 0.003 based on the

222 Hybrid composite precast systems

FIG. 4.2.12, Cont’d

average meshes in the compression side, was achieved by resizing girder to 200 mm width
500 mm depth. The concrete strain of 200 mm wide
500 mm deep girder reached only 0.00099 at Mu (238 kN-m) as shown in the momentdisplacement relationship by Legend 2 of Fig. 4.3.12 (Fig. 4.3.9A and Table 4.3.6). Table 4.3.6 summarizes the strains identified from the mechanical beam-column joint including metal plates and bolts. The girder resized to a width of 200 mm and a depth of 500 mm showed that the new design strength of the proposed girder section is sufficient to resist the demand, Mu. The strains of metal plates (upper and lower) were found below the yield level, as shown in Figs. 4.3.8A and 4.3.13C and D. The use of interior bolts can limit strains in the upper and lower plates to 0.00176 and 0.00124, respectively, at a concrete strain of 0.003. Fig. 4.3.13E and F demonstrate large strains (0.0076) in the interior bolts, which were twice that of the exterior bolts, which reached small strains (0.0034). However, strains (0.00022) in the interior bolts smaller than those of strains (0.00024) at the exterior bolts were found at Mu (refer to Fig. 4.3.7A), indicating interior bolts were activated rapidly when loads increased. The interior bolt located near the embedded L-shaped steel section contributed to the direct transfer of substantial tension loads exerted on the metal plate at mechanical joints. In Fig. 4.3.13G, maximum compressive

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FIG. 4.2.13 Activation of structural components with foundation [2].

strength of concrete reaching 37 MPa was also observed at a corresponding strain of 0.002. The strain data found at a concrete strain of 0.003 verified the performance of structural elements of the proposed joint, demonstrating flexural strength similar to that of monolithic frames at the design load limit state.

4.3.2.4 Strain evolution of the structural components attached to plates For the selected elements of the mechanical joint splicing precast columns shown in Fig. 4.3.13, the red dots identify the stresses and strains at the concrete compressive strain of its design limit with 0.003. At a concrete compressive strain of 0.003, the rebar (which has a yield strain of 0.0029) was close to yielding, only reaching 0.0026, while the strains in the L-shaped steel section were 1.5 times reaching 0.0024 larger than its yield strain (ey ¼ 0.0015). This demonstrated that the flexural capacity of the proposed mechanical joint was well contributed by embedded L-shaped steel section. Fig. 4.3.14 shows rates of strain increase relative to the deflection (strain-stroke relationships of the beam). As shown by Legend 3 Fig. 4.3.14A, sufficient design strengths for the monolithic beam-column joint at a concrete strain of 0.003 were provided to resist the required moment (Mu). Table 4.3.6 identifies the contributions to the flexural strength from the structural component attached to the plates based on microscopic strains. As shown in Fig. 4.3.14, the rate of strain increase of concrete,

224 Hybrid composite precast systems

FIG. 4.2.13, Cont’d

rebars, and steel flanges attached to plates relative to the deflection indicates that considerable strains were developed at the structural elements attached to the plates, whereas no structural degradations of the plates or the degradations of joints were observed. The strain of a concrete beam section with a depth of 400 mm increases slowly compared to that with a depth of 500 mm, as shown in Fig. 4.3.14 A. Insufficient design strength with a depth of 400 mm was found to resist required moment (Mu) in which a concrete beam strain greater than 0.006 was reached at a concrete strain of 0.003 (refer to Legend 4 Fig. 4.3.14A). Mu is reached fast with a concrete beam strain of 0.0024 when the beam depth was 400 mm. However, as shown by Legends 1 and 2 in Fig. 4.3.14A, sufficient design strengths of both the monolithic beam-column joint and beam-column joint with a mechanical plate were identified to resist the required moment (Mu) at a concrete strain of 0.003 when the beam depth was increased to 500 mm. The strains of beams (0.006) (refer to Fig. 4.3.7C) concentrated by the endplates of 400 mm beam depth were relieved to a concrete beam strain of 0.00099 at Mu (refer to Fig. 4.3.9A and Table 4.3.6), when the beam depth was increased to 500 mm, reaching a design strength greater than the required moment (Mu) at a concrete strain of 0.003. Fig. 4.3.14B and C show that rates of strain increase of rebars and steel flanges (represented by the slopes) relative to

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TABLE 4.3.1 Summary of the FEA parameters for the nonlinear numerical analysis. Parameter

Concrete

Steel

Young’s modulus

30,008 MPa

205,000 MPa

Poisson’s ratio

0.167

0.3

Dilation angle (degree)

30° (default value)

N/A

Eccentricity

0.1 (default value)

Fbo/fco

1.16 (default value)

K value

0.6667 (default value)

Viscosity parameter

0.003

TABLE 4.3.2 Summary of material properties, including the rebars, metal plates, and concrete [2]. Category

Size (mm)

Material

Concrete column

L shape: 800
800 (width: 200)

Concrete compressive strength: 40 MPa

Concrete girder

B
H: 400
200

Upper plate for the columns

L shape:1000
1000 (width: 400, thickness: 35)

Lower plate for the columns

L shape:1000
1000 (width: 400, thickness: 35)

Extended end plate for the girders

480
200
30

Filler plate for the girders

480
200
5

Bolts for all specimens

M22 (diameter: 22)

Tensile yield stress (Fy ¼ 900 MPa) Ultimate strength (Fu ¼ 1000 MPa)

Rebar for all specimens

HD25 (diameter: 25)

Tensile yield stress (Fy ¼ 600 MPa)

Hoops for the columns and stirrups for the girders

HD10 (diameter: 10)

Tensile yield stress (Fy ¼ 400 MPa)

Material (steel, SM490), tensile yield stress (Fy ¼ 325 MPa) Ultimate strength (Fu ¼ 490 MPa)

TABLE 4.3.3 Description of FEA elements. Element

Type

Description

C3D8R

3D solid element

Eight-node linear brick, reduced integration with hourglass control

B31

Beam element

Two-node linear beam

R3D4

Rigid element

Four-node, bilinear quadrilateral

the deflection were similar to those of concrete, indicating how fast the strains developed as deflections progressed. Strains in the rebars of mechanical beam-column joints for the 500 mm-deep beam increased fastest, whereas rates of strain increase in the steel flanges of the 500 mm-deep beam were similar among all beam-column joints. The moment capacity of the beams can also be increased by confining the concrete beam using carbon polymers to sustain higher strains to yield higher strength.

226 Hybrid composite precast systems

FIG. 4.3.1 Description of the finite element model for the column joints [3].

4.3.3 Conclusion Fractures and strength degradations of the structural elements in the mechanical joint including rebar and steel sections attached to plates were identified by numerical models to avoid brittle failure modes in joints. Design recommendations and collateral benefits were verified for the high-rise building design below. (1) Resizing based on strains. Fig. 4.3.7C shows stress concentrations with a strain of 0.006 in beam exerted by extended beam endplates when the beam was subjected to Mu. Stress concentrations on beam were relieved down with the strain of 0.00099 by providing sufficient beam depth with 500 mm, resulting in a sufficient flexural strength to resist Mu as shown in Fig. 4.3.9A. A moment strength of 311 kN-m corresponding to a concrete strain of 0.003 was achieved, as shown in the design of the proposed building (refer to Fig. 4.3.9B), resulting in reduced concrete strain when the girder was resized to 200 mm width
500 mm depth. This moment strength was greater than the Mu of 238 kN-m. (2) Joint plate. The laminated metal plate resisted tensions exerted by rebars and steel sections more effectively by embedding steel sections near the interior bolts. As shown in Fig. 4.3.8A, use of interior bolts limited strains in the upper and lower plates to 0.00176 and 0.00124, respectively, which was not yielding at a concrete strain of

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FIG. 4.3.2 Description of the finite element model for column-girder joints [3].

0.003. Strains (0.00022) in the interior bolts smaller than those (0.00024, refer to Fig. 4.3.7A) at the exterior bolts were found at Mu for the girder is 200 mm wide
400 mm deep. However, strains (0.0076) in the interior bolts became twice those of the exterior bolts, while the strains in exterior bolts at a concrete strain of 0.003 (refer to Fig. 4.3.8A) were small. The use of the bolts increased the stiffness of the mechanical joint, activating high tensile strains of rebar and steel sections attached to the plates. These results suggest an efficient way to obtain a flexural capacity that is as large as possible. (3) Application to high-rise buildings. For the design of the 20-story apartment building shown in Fig. 4.3.4 [1] using mechanical joint splicing L-shaped precast steel-concrete composite columns, an extensive strain analysis was performed considering the concrete damaged plasticity and elastic-softening properties of the headed studs, which reflected low cycle fatigue. Microscopic strains of the structural components attached to laminated plates were investigated based on nonlinear finite element models. The architectural flexibility at the corners was similar to that of the wall frames. This was achieved using L-shaped columns while accounting for axial loads.

228 Hybrid composite precast systems

FIG. 4.3.3 Description of the contact surfaces and surface elements [3].

4.4

Test erection

4.4.1 Erection of irregular L-shaped frames 4.4.1.1 Significance of the test erection The rapid and effortless erection of a full-scale irregular L-shaped precast frame assembled using bolted metal plates was demonstrated with reduced construction time. There was a corresponding reduction in construction costs compared with conventional monolithic assemblies because pour forms and curing times, which are required for conventional concrete frames, were eliminated. Joint details were introduced, and a full-scale erection test was performed for the verification of the proposed joints in terms of constructability and design with affordable cost. The erection efficiency was demonstrated through mechanical connection involving splicing steel-concrete hybrid composite precast columns and reinforced concrete precast columns. The spliced precast concrete column delivered moment strength similar to that offered by a conventional cast-in-place steel-concrete composite column. The nonlinear structural behavior of the mechanical joints was also investigated based on the concrete plasticity in Sections 4.2 and 4.3 of this chapter.

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FIG. 4.3.3, Cont’d

4.4.1.2 Column-to-column connection Connection mechanism The mechanical joint with the L-shaped columns was implemented in both precast steel-concrete composite frames and precast concrete frames. The proposed connections are similar to those used in the rectangular columns and consist of two endplates (lower and upper column plates) interconnected by high-strength bolts. The 35-mm-thick plates for the upper and lower columns were fabricated with a metal filler plate for being between them. Nuts encased in the counterbores of the column plates (and in the filler plates) were incorporated to anchor the vertical reinforcing bars to the endplates. Anchorage using nuts was offered in the column plates thick enough to accommodate the nuts completely. Three columns, having vertical rebars of 25 mm diameter, were prepared for the erection test; two columns with the mechanical joints; and one monolithically cured column. The L-shaped steel sections encased in the precast concrete columns are shown in Fig. 4.4.1. The full-scale assembly test demonstrated the assembly efficiency of the precast frames compared to the conventional precast construction. The structural behavior of the proposed joint was explored via the extensive numerical and experimental studies in Sections 4.2 and 4.3, identifying the parameters that influence the structural performance of the joints.

230 Hybrid composite precast systems

FIG. 4.3.3, Cont’d

Erection test for column-to-column assembly The test erection of the full-scale precast columns was conducted based on the sequence outlined in Figs. 4.4.1– 4.4.3, being assembled with the bolted metal plates, which demonstrated the easy and rapid erection. In the numerical and experimental investigations described in earlier sections, the test frames showed that the steel connections can act as either fully rigid or semirigid connections, depending on the endplate stiffness, bolt diameter, number of bolt rows and columns, bolt spacing, bolt grade, interior stiffeners, column and beam sizes, and yield strength of the steel. For the full-scale erection test, the

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FIG. 4.3.4 A 20-story apartment building with wall frames replaced by the proposed L-type composite precast frames [1].

TABLE 4.3.4 Fundamental periods and mode shapes. Node no.

Wall frame

Irregular composite precast frame

Period

TRAN-X

TRAN-Y

TRAN-Z

(s)

MASS (%)

SUM (%)

MASS (%)

SUM (%)

MASS (%)

SUM (%)

1

4.12

5.43

5.43

20.07

20.07

53.34

53.34

2

2.21

39.79

45.22

24.08

44.15

1.09

54.43

3

1.34

0.44

45.66

2.17

46.32

6.85

61.29

4

1.11

21.21

66.87

24.60

70.93

19.63

80.92

5

0.76

0.26

67.13

0.85

71.78

2.57

83.49

6

0.51

0.14

67.30

0.56

72.33

1.37

84.86

1

3.72

5.35

5.35

19.98

19.98

52.37

52.37

2

2.14

40.11

45.46

23.95

43.94

1.08

53.46

3

1.18

0.49

45.95

2.27

46.21

6.95

60.41

4

1.08

20.98

66.93

24.64

70.85

19.90

80.32

5

0.66

0.30

67.23

0.95

71.80

2.68

83.00

6

0.43

11.42

78.65

7.09

78.89

0.21

83.21

mechanical joints with fully restrained moment connections were developed to provide rapid and facile connections for the composite precast columns. Columns are lifted and placed in position as shown in Fig. 4.4.1. In Fig. 4.4.1B and C, the plates are ready to be bolted after they are placed in the position within a few minutes. The column joints consist of both the upper and lower metal plates with the interior and exterior bolt holes. The interior bolts to be locked at the upper plate were preinstalled in the lower plate, providing additional flexural strength to the mechanical joint during the application of overturning moments. Fig. 4.4.1A and C shows the interior bolts used to interconnect two plates through the preinstalled bolt holes in the recessed area prepared inside the upper column, creating moment connections and making the plate connection more ductile. Fig. 4.4.3C also shows the exterior bolts interconnecting the two plates. The holes for accommodating and protecting the interior bolts were grouted with nonshrinking concrete mortar after the erection was completed. These bolts were embedded with the concrete mortar. Loud sounds were heard when these bolts were fractured during the structural testing, as described in Figs. 4.1.9 and 4.1.10.

232 Hybrid composite precast systems

FIG. 4.3.5 Comparison of dynamic modes [1].

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TABLE 4.3.5 Load demands for the design [1]. Mux

Muy

Pu

Columns

355 kN-m

349 kN-m

11,680 kN

Girders

Mu

Vu

238.2 kN-m

216.6 kN

FIG. 4.3.6 Neutral axis with an axial force of 5000 kN [1].

4.4.1.3 Girder-to-column connections Connection mechanism As shown in Figs. 4.4.2 and 4.4.3, the rigid mechanical joints modified from the conventional steel joints were implemented in both steel-concrete composite precast frames and reinforced concrete precast frames. The modified extended endplates were introduced for the girder-to-column joint assembly shown in Figs. 4.4.2 and 4.4.3. AISC 358 introduced the girder-tocolumn connections using bolted extended endplates for transferring moments between steel frames. The behavior of the extended endplate connections for the steel erections that were subjected to monotonic, cyclic, and seismic loads has been explored in a significant number of experimental and numerical studies over the past decades. The flexural strength of the connection of the composite frames is determined by the stiffness of the endplates, shown in Fig. 4.4.2, the number of bolts, and their positions. The rigidity of the mechanical joints was determined based on the stiffness interacted between the metal plates and the concrete. In the proposed connections for the steel-concrete composite precast frames, the girder steels were groove-welded to the extended endplates, enabling the moment of the steel sections to be transferred by the stiffness of the

FIG. 4.3.7 Nominal strength at Mu (238 kN-m), refer to Table 4.3.5 (load demands for the design), and Fig. 4.3.6 (based on average strains); girder with 200 mm wide
400 mm deep [3].

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FIG. 4.3.8 Nominal strength at a concrete strain of 0.003 (refer to Fig. 4.3.6 based on average strains); girder with 200 mm wide
400 mm deep.

endplates. The girder rebars were directly anchored to the couplers embedded in a column unit permitting the moment to be transferred directly between the girder rebars and column units, not by the stiffness of the extended endplates. In Fig. 4.4.2A, the couplers embedded in the column face were used to anchor the horizontal rebars to transfer the loads at the joints. The vertical and horizontal couplers should be placed in an accurate position for the fast assembly. Erection test for column-to-beam assembly The full-scale erection test based on the proposed erection procedures is shown in Fig. 4.4.3A and B, where the girder is lifted and placed between the columns (for the girder-to-column connection) with filler plates. The extended endplates were bolted to the couplers embedded in the column, connecting the girder to the column, as shown in 4.4.3B. For the beam-to-

236 Hybrid composite precast systems

FIG. 4.3.8, Cont’d

girder connection, the beam endplates were bolted to wide plates preinstalled on the column (preinstalled on girders in actual construction). The steel sections for the beams and girders were welded to the endplates. The column plates and girder endplates were connected via high-strength bolts. The torque in the bolts should be measured to ensure that the required pretension force in the bolt shank be successfully introduced.

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FIG. 4.3.9 Nominal strength at a concrete strain of 0.003 (refer to Fig. 4.3.6 based on average strains); girder with 200 mm wide
500 mm deep [3].

238 Hybrid composite precast systems

FIG. 4.3.9, Cont’d

FIG. 4.3.10 Moment-displacement relationship of columns with an axial force of 5000 kN [1].

Verification of the erection test The frame assembly with two bays was completed in Fig. 4.4.4A. Metal deck plates or pour forms for the construction of the slabs were then graphically placed, as shown in Fig. 4.4.4B, where the connection details between the girder-to-column and the column-to-column are demonstrated in detail. The efficiency of the mechanical joints used in the two-bay frames that were designed to resist gravity and lateral loads was demonstrated. Fig. 4.4.4C depicts graphically how effectively the frames with multibays and multifloors are erected. The fast assembly of the precast columns with the irregular sections was demonstrated. The assembly of the diverse structural shapes was demonstrated, showing the flexibility of the architectural expressions. In the design of the connections in this precast erection test, the dimensional variations between the precast members were accounted for by providing erection tolerances between the precast concrete components. The test erection showed that the dimensional variations caused by the thicknesses of plates and the lengths of the precast members were well addressed using the metal filler plates. The clearance for the tolerance between the precast units and structures was adjusted by modifying the metal filler plates. An accurate and rapid erection was possible based on both filler plates and grouted clearance.

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

FIG. 4.3.11 Moment-displacement relationship of girders (200 mm wide
400 mm deep) [3].

FIG. 4.3.12 Moment-displacement relationship of girders (200 mm wide
500 mm deep) [3].

4

239

240 Hybrid composite precast systems

TABLE 4.3.6 Summary of strains identified from mechanical beam-column joint including metal plates and bolts [3]. 200 × 500 (mm × mm) Mechanical

200 × 400 (mm × mm) Control

Mechanical

Mu

Concrete strain 0.003

Mu

Concrete strain 0.003

Concrete strain 0.003

Mu

Moment (kN-m)

239

311.4

240.4

304

208

238

Load (kN)

141

183

141.4

179

122.3

140

Stroke (mm)

11.3

18

12

18

25

35

Concrete

Strain

0.00099

0.0029

0.0015

0.003

0.003

0.0062

Rebar

Strain

0.0021

0.003

0.00163

0.0028

0.0028

0.00611

Stress (MPa)

418

598

472

563

587

587

Strain

0.00098

0.00109

–

–

0.00109

0.00140

Stress (MPa)

200

224

–

–

269

291

Steel flange

Strain

0.00113

0.00163

0.00114

0.00158

0.0027

0.0046

Stress (MPa)

235

221.4

237

327

335

349

Steel web

Strain

0.0008

0.00106

0.00104

0.0014

0.0022

0.0043

Stress (MPa)

167

225

217

293

339.5

363

Strain

0.00023

0.0003

–

–

0.00025

0.0003

Stress (MPa)

80

105

–

–

145

154

Deformation

0.6

0.8

–

–

1.0

1.4

Strain

0.00054

0.0008

–

–

0.00098

0.00131

Stress (MPa)

111

156

–

–

213

286

Interior bolt

Beam plate

Headed stud

4.4.2 Conclusion A novel erection of the irregular L-shaped precast frames was demonstrated by utilizing the mechanical joints with a fully restrained moment [1–3]. The fast and effortless assembly of the precast columns with the irregular L-shaped sections was introduced to replace the rectangular columns, which do not fit at the corners. The columns and beams were assembled into frames using the extended endplates. The column rebars were spliced through metal plates, which were subsequently assembled with the precast beams. A numerical investigation of the proposed frames conducted in Sections 4.2 and 4.3 verified the structural performance. The predictable and stable nonlinear structural behavior of the mechanical joints was demonstrated. The metal plates that were of prescribed thickness provided a flexural capacity that was similar to that of the monolithic column connections. The proposed joints had sufficient strength and were able to deliver adequate flexural strength and resistance for the construction and service loads. The conventional buildings with wall frames can be replaced by the proposed L-type composite precast frames using the provided mechanical connection details. The L-shaped bolted mechanical plates also presented a cost-saving alternative to the conventional monolithic cast-in-place joints. The full-scale test erection using the precast columns of the irregular sections interconnected by the mechanical plates demonstrated that the construction time relative to a conventional monolithic assembly could be reduced substantially, leading to a corresponding reduction in construction costs. This erection time was similar to that needed to assemble the steel frames. In Chapter 8, a rapid erection was introduced using the mechanical joints that can be employed as an alternative for the modular offsite construction for the high-rise buildings and heavy industrial plants. The economics can be improved when using the precast-based concrete or composite frames than when using the steel structures for the similar modular construction.

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

4

FIG. 4.3.13 Stress-strain relationships of the selected structural elements identified from Legend 2 of Fig. 4.3.10 with axial loads of 5000 kN.

241

FIG. 4.3.14 Strain evolution of the structural components attached to plates [3].

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

FIG. 4.4.1 Assembly of the precast columns via dry mechanical joint.

4

243

244 Hybrid composite precast systems

FIG. 4.4.2 Manufacturing girders.

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

4

245

FIG. 4.4.3 Assembly of the girder-to-column and girder-to-beam connections via mechanical joints; full-scale erection test (with metal column plates and extended beam/girder endplates).

246 Hybrid composite precast systems

FIG. 4.4.4 Precast frames of multiple bays with the proposed joints. Continued

L-type hybrid precast frames with mechanical joints using laminated metal plates Chapter

4

247

FIG. 4.4.4, Cont’d

References [1] J.D. Nzabonimpa, W.-K. Hong, Experimental investigation of hybrid mechanical joints for L-shaped columns replacing conventional grouted sleeve connections, Eng. Struct. 185 (2019) 243–277. [2] J.D. Nzabonimpa, Development of Lego-Type Column-to-Column Connections (Ph.D. Thesis), SECT (Structural Engineering/Construction Technology) Lab of Kyung Hee University, 2018. [3] J. Kim, Bolted Assembly of the Precast Structural Frames with Mechanical Joints (Master’s Thesis), SECT (Structural Engineering/Construction Technology) Lab of Kyung Hee University, 2017.

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Chapter 5

Novel erection of the precast frames using interlocking mechanical couplers 5.1 Significance of the precast erection using interlocking mechanical joints The conventional precast members required concrete pour forms at the joints, which, despite many advantages, are lacking in the treatment of the construction waste. As an alternative to these problems, couplers are interlocked by the weight of the upper column heavy enough to push the vertical rebars into the couplers prepared at the lower part of the upper column. Sufficient verticality of the rebars is demonstrated when the upper columns are spliced to the lower columns. A nonlinear finite element analysis (FEA) considering concrete plasticity proved stresses and strains were within allowable limits during the assembly of the precast frames subjected to heavy loads. Throughout the erection test, the proposed erection using interlocking type couplers contributed to the replacement of the traditional concrete frames, including cast-in-place and precast frames with conventional joints, offering a rapid and dependable erection. This chapter aimed to introduce the interlocking couplers for the connections of rectangular precast column shapes, presenting a full-scale erection test to demonstrate an efficient and effortless assembly of the precast frames [1]. The erection test showed the substantial construction time was reduced compared with the conventional monolithic construction along with the corresponding cost. The assembly time of the precast column decreased to approximately 20 min, resulting in the elimination of the pour forms and curing times required for the conventional concrete frames, successfully replacing conventional monolithic cast-in-place joints.

5.2 Assembly of the full-scale precast frame by interlocking couplers 5.2.1 Column-to-column connections 5.2.1.1 Using interlocking one-touch interlocking couplers to splice precast columns Interlocking one-touch interlocking couplers, shown in Fig. 5.2.1, are used to directly splice the upper and lower rebars [1]. In Fig. 5.2.1A and B, the vertical rebars are spliced through the metal plates attached to the upper and lower columns. The column-to-column connection entirely depends on the column rebars spliced by the couplers. The assembly of multiple joints between modules is illustrated in Fig. 5.2.1C and D, in which the upper module was released slowly enough to avoid any possible mismatch between the rebars and the couplers from occurring. The assembly of the modules is completed when the lower rebars were completely interlocked into the couplers, as depicted in Fig. 5.2.1C and D. The joint interlocking details of the test specimens for the column connections using one-touch interlocking couplers are shown in Fig. 5.2.2 [1]. In Figs. 5.2.3–5.2.5, the frames are assembled with a proposed novel joint, in which each plate was installed at the bottom of the upper columns and on the top of the lower columns. The one-touch interlocking couplers served as connectors to enable an assembly in which the rebars were locked automatically at the joint with the groove of the coupler, shown in Fig. 5.2.3A, when the rebar was pushed into the coupler (CK intersteel, 2016) [2]. The inner shell (20) strongly grabs not only the joint, but also the body with the rebar rib via sharp teeth (21) when the center of the plastic holder breaks through, resulting in a flexural capacity (provided by the vertical column rebars that pass through the metal plates) similar to that of conventional monolithic column connections. Fig. 5.2.3B illustrates the exposed recessed area and the connection details between the couplers and the plates for the upper columns before the concrete was cast through. The couplers welded to the metal plate that was attached at the bottom of the upper column in the exposed recessed area are shown in Fig. 5.2.3C. Fig. 5.2.3D and E depict a fabrication of the girder with extended endplates and the couplers embedded on the column face, into which the horizontal girder rebars were installed. Fast and effortless splices of the vertical rebars for the connection of the precast frames were possible when rebars were pushed into the couplers prepared on the upper columns by the weight of the upper precast columns [1]. Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00005-4 © 2020 Elsevier Ltd. All rights reserved.

249

250 Hybrid composite precast systems

FIG. 5.2.1 See figure legend on opposite page. (Continued)

Novel erection of the precast frames Chapter

5

251

FIG. 5.2.1, cont’d Assembly details for modules using interlocking one touch couplers.

FIG. 5.2.2 Column-to-column and beam-to-column connection details using one-touch couplers [1].

5.2.1.2 Test erection Fig. 5.2.4A and B exhibit the connection mechanism of the full-scale erection test specimens, details of the splicing couplers, and the minimum protruded length of the rebars [1]. The upper columns with couplers and lower columns with vertical rebars are shown in Fig. 5.2.4C and D. In Fig. 5.2.4A, the verticality was carefully ensured to accurately insert rebars into couplers when the upper column descended to the lower column. The plate size installed with an upper column is reduced, as shown in Fig. 5.2.4A-(2) and (3). The column plates can be completely omitted because the loads are directly transferred by the rebars and the couplers across the joints, not by the stiffness of the metal column plates, resulting in a flexural capacity of the proposed joint that is not dependent on the stiffness of the metal plates. The easy fit of the rebars into the couplers was further ensured without the column plates, leading to the fast assembly of the two precast concrete components. The column plates were, thereby, used as only erection elements, not as structural elements. The spliced column rebars using interlocking couplers highlighted the assembly of the full-scale precast columns, offering the flexural capacity similar to that of the conventional monolithic column connections [1].

252 Hybrid composite precast systems

(A)

Interlocking coupler splicing vertical rebars [2]

(C)

Couplers welded to the metal plate attached at the bottom of the upper column

(D) Fabrication of the girder with extended end plates FIG. 5.2.3 Manufacturing frames [1].

(E) Embedded couplers to install horizontal girder rebars

Novel erection of the precast frames Chapter

5

253

FIG. 5.2.4 See figure legend on next page. (Continued)

FIG. 5.2.4, cont’d Summarized assembly method.

Novel erection of the precast frames Chapter

5

255

FIG. 5.2.5 Assembly of the precast columns via interlocking mechanical joints.

In Fig. 5.2.4B [1], the rebar (32-mm diameter) length of 115–123 mm was inserted into the couplers to anchor the rebars. The vertical rebars, therefore, protruded 115–120 mm from the plate of the lower column. The assembly, shown in Fig. 5.2.5A and B, was completed when the rebars were locked automatically by the groove of the mechanical joints, taking less than half an hour for this assembly. The weight of the upper column exerts gravity loads so that the rebars are interlocked into the couplers rapidly, as shown in Fig. 5.2.5A-(4). The axial loads of 13,443 kN loads were exerted on columns during the full-scale assembly tests, anchoring vertical rebars into the couplers to form monolithic columns [1]. The advantages of the proposed method capable of assembling and disassembling were verified for the use with practical applications. The erection method using precast-based concrete frames was also proved as an alternative for offsite modular constructions for buildings and industrial plants subjected to heavy loads. The cost of the modular construction is expected to decrease compared with the steel structures used for the similar modular construction.

5.2.1.3 Replacing couplers Couplers can be replaced at any time through the exposed recessed area prepared for grouting, shown in Fig. 5.2.5B in case a mismatch between rebars and couplers occurs due to a bad rebar verticality. A similar assembly of the precast columns without a recessed area in the upper column is shown in Fig. 5.2.6. However, disassembly of the columns without a recessed

256 Hybrid composite precast systems

FIG. 5.2.6 Assembly of the precast columns (without exposed recessed area) via interlocking mechanical joints [1].

area is not possible for the correction of the column assembly. The couplers with minor mismatches caused by verticality issues can be replaced by other couplers easily. However, the exchange of entire columns may be required when considerable rebar dislocations arise [1].

5.2.2 Girder-to-column connections and the test erection The entire assemblage of the precast concrete frame is completed with a girder as shown in Fig. 5.2.7. It was demonstrated that the assembly method using couplers embedded in columns significantly reduced the time required to assemble girder-to-column connections [1]. In Fig. 5.2.7, the metal girder endplates at the ends of the girders and plates embedded on the face of columns are inter-connected, being assembled to girder-to-column joints. In Fig. 5.2.7A and B, the girder is lifted and placed between the column plates. The girder-to-column connection was then assembled by interconnecting the girder and column plates using bolts, as shown in Fig. 5.2.7C. The required pretension force in the bolt shank was ensured by torque gage, as shown in Fig. 5.2.7D. The girder-to-column frame assembly by interconnecting extended girder endplates and column plates is completed in Fig. 5.2.8A and B. The horizontal rebars at the top of girders, shown in Fig. 5.2.8C, were directly anchored to the couplers embedded on the column face, enabling the creation of the moment connections for the girder-to-column joint. The plates for girders and columns were only used as erection plates. The vertical and horizontal

FIG. 5.2.7 See figure legend on page 258. (Continued)

(Continued)

FIG. 5.2.7, cont’d Assembly of the girder-to-column connection via extended beam endplates.

FIG. 5.2.8 Assembly of the girder-to-column connection via interlocking mechanical joint.

Novel erection of the precast frames Chapter

5

259

FIG. 5.2.9 Precast frame completed with interlocking mechanical joint assembly (refer to Fig. 5.2.11 for assembly details).

couplers with anchor rebars should be placed accurately during a fabrication. Column joints with and without exposed recessed areas are apparent in Fig. 5.2.9, where the connection details between the girder-to-column and column-to-column are illustrated. The erection test demonstrated that the frame shown in Fig. 5.2.9 was assembled within one hour, and can be even faster when the preparation for the erection is well planned [1]. The design and structural performance of the proposed joints were verified by the numerical investigation shown in Section 5.3 of this chapter. The metal deck plates or pour forms for floor framing are installed, as shown in Fig. 5.2.10, where details with the girders from multi directions and the corrugated metal decks are depicted. In Fig. 5.2.11, the assembly procedure with the specific time spent for the assembly of one bay frame

FIG. 5.2.10 Assembly of the precast frame completed with construction of slabs.

260 Hybrid composite precast systems

FIG. 5.2.11 Observed time for the frame assembly with interlocking mechanical joints [1].

with heavyweight is observed when the interlocking couplers were implemented in the assembly of the precast frames subjected to heavy loads [1]. Total assembly time of around 20 min was observed. The time required for the erection shown in this chapter may differ from the real frame construction, because much more sophisticated preparations may be required. The connection details utilizing interlocking couplers for the test erection are depicted in Fig. 5.2.12, illustrating inter-locking couplers and rebars spliced by couplers. In Fig. 5.2.12A-(1) and (2) (refer to Section C-C of

FIG. 5.2.12 See figure legend on page 263. (Continued)

Novel erection of the precast frames Chapter

5

261

1200 214

105

214 156

105 203

214

156

1200

214

203

105

203

105

203

Tie D10@300 20 - HD32 Rebar

Section A-A (B)

Rebar detail of column (Continued)

262 Hybrid composite precast systems

Novel erection of the precast frames Chapter

FIG. 5.2.12, cont’d Connection details utilizing interlocking couplers for the test erection.

5

263

264 Hybrid composite precast systems

Fig. 5.2.12D), joint the details of the column-to-girder are shown, where interlocking couplers splice vertical rebars, and couplers embedded in column are shown to anchor horizontal girder rebars. The rebar details of the column and girder are presented in Fig. 5.2.12B and C. The girder endplate attached to the face of the column concrete and the locations of the girder rebars anchored into the column by the embedded couplers are also illustrated in Fig. 5.2.12A-(2) and D. Bolts top and below the girder section interconnecting the girder plate with the column concrete face are also shown. Any misalignments of the vertical rebars with the couplers interlocked with rebars can be revised through an exposed recessed area, shown in Fig. 5.2.12E. The exposed recessed area was grouted with high-strength nonshrinking concrete mortar. The locations of the interlocking couplers and the rebars were indicated in the upper and lower plates. Fig. 5.2.12 presents the structural frame and the connection details implemented in a full-scale erection test [1]. Engineers may refer to these details for their design of the precast assembly subjected to heavy loads.

5.3

Numerical investigation

This section presents a numerical investigation of the precast connections using interlocking mechanical connections, exploring the strains and stresses exerted on the joints. The flexural strength was calculated to design mechanical connections based on the nonlinear FEA with modeling techniques and numerical parameters [1] considering damaged concrete plasticity.

5.3.1 Description of the mechanical connections for design verification The design of composite precast frames subjected to heavy loads with the use of interlocking couplers and metal plates is verified based on a numerical investigation in this section. In Fig. 5.3.1, the precast columns having laminated metal plates and one-touch interlocking couplers were implemented in the design of warehouses, supporting heavy gravity loads with an

FIG. 5.3.1 See figure legend on opposite page. (Continued)

Novel erection of the precast frames Chapter

FIG. 5.3.1, cont’d Warehouse with heavy loads.

5

265

266 Hybrid composite precast systems

TABLE 5.3.1 Summary of the FEA parameters for the nonlinear numerical analysis. Parameter

Concrete

Steel

Young’s modulus

30,008 MPa

205,000 MPa

Poisson’s ratio

0.167

0.3

Dilation angle (degree)

30° (default value)

N/A

Eccentricity

0.1 (default value)

Fbo/fco

1.16 (default value)

K value

0.6667 (default value)

Viscosity parameter

0.001

11 m floor height and an 11 m long spanned girder. A typical plan and elevation view for the building were presented. The steel-concrete composite girders, weighing over 200 kN, were selected to provide structural resistance to the floor loading up to 20 kN/m2. In this section, the hybrid precast columns were adopted to design a warehouse of seven floors, supporting gravity loads as heavy as 20 kN/m2 on the 11 m
11 m tributary area. Numerical investigation exploring the microscopic strains of the column joints with an axial load of 13,443 kN was performed [1]. The nonlinear numerical analysis considering the damaged concrete plasticity was conducted based on FEA parameters, presented in Table 5.3.1, where the proposed parameters defined Drucker-Prager hyperbolic plastic potential function. In Table 5.3.2 [1], the material properties, including the rebars, metal plates, and concrete are also presented. The structural behavior of column plates, shown in Fig. 5.3.2A, is represented by the moment-displacement relationship indicated by Legend 3 (15-mm thick plate) of Fig. 5.3.5. The mechanical joint was inter-connected by four exterior bolts, but, without interior bolts to transfer axial forces and moments, whereas the column rebars were spliced by interlocking couplers. In the

TABLE 5.3.2 Material properties [1]. Category

Size

Material

Concrete columns

1000
1000 (mm
mm)

Concrete compressive strength: 40 MPa

Upper plates for Legends 2, 3, 4, and 5, respectively (Fig. 5.3.5)

1000
1000 (mm
1000
1000 (mm
1200
1200 (mm
Thickness: 30 mm 1200
1200 (mm
Thickness: 20 mm

mm) Thickness: 10 mm mm) Thickness: 15 mm mm)

Material (Steel, SM490), tensile yield stress (Fy ¼ 325 MPa) Ultimate strength (Fu ¼ 490 MPa)

1000
1000 (mm
Thickness: 10 mm 1000
1000 (mm
Thickness: 15 mm 1200
1200 (mm
Thickness: 30 mm 1200
1200 (mm
Thickness: 20mm

mm)

Lower plates for Legends 2, 3, 4, and 5, respectively (Fig. 5.3.5)

mm)

mm)

Material (Steel, SM490), tensile yield stress (Fy ¼ 325 MPa) Ultimate strength (Fu ¼ 490 MPa)

mm) mm)

Bolts

M22

Tensile yield stress (fy ¼ 900 MPa) Ultimate strength (Fu ¼ 1000 MPa)

Rebar

HD32

Tensile yield stress (fy ¼ 600 MPa)

Hoops

HD10

Tensile yield stress (Fy ¼ 400 MPa) Ultimate strength (Fu ¼ 490 MPa)

Novel erection of the precast frames Chapter

5

267

FIG. 5.3.2 See figure legend on next page. (Continued)

268 Hybrid composite precast systems

FIG. 5.3.2, cont’d Connections details for numerical analysis.

joints shown in Fig. 5.3.2B, rebars were spliced by interlocking couplers only to transfer loads without exterior/interior bolts. The moment-displacement relationship of this joint is represented by Legend 2 (10-mm thick plate) of Fig. 5.3.5. Six interior bolts (4 + 2, not shown) with 30 mm plates and eight interior bolts (6 + 2, Fig. 5.3.2C) with 20 mm plates were used to inter-connect the metal column plates, whereas the couplers anchoring vertical rebars were welded on the metal plates, contributing to loads at the joint. Fourteen exterior bolts were installed for both column connections. The moment-displacement relationships of the column plates connected by six and eight interior bolts are represented by the moment-displacement relationships indicated by Legends 4 and 5 of Fig. 5.3.5, respectively.

5.3.2 Finite element model of the proposed joint Readers are referred to Chapter 3 for the numerical investigation implementing numerical parameters calibrated by test data. In Fig 5.3.3A [1], the proposed joints of precast frames, including vertical rebars, metal plates, stirrups, and concrete were modeled for a nonlinear FEA. In Fig. 5.3.3B, a symmetric model was established with respect to the y-axis, assigning constrained areas that restrained column movements when the lateral load is applied. The interactions based on surface-tosurface contact formulation, including the stiffer master surface and the weaker slave surface, were also established. In Fig. 5.3.3C, the pair of master and slave surfaces, as well as the interactions, was assigned to prevent any penetrations between contacts of the joint. The tangential and normal contact behaviors were implemented in surface-to-surface contact properties to prevent surfaces in contact from penetrating each other. The normal behavior was assigned based on the standard penalty method and hard contact for the pressure-overclosure provided in Abaqus software, whereas the tangential behavior was applied to be frictionless in all three interactions [12, Chapter 2].

5.3.3 Verification of the numerical analysis In Fig. 5.3.4, the axial force-moment interaction diagram of the columns with monolithic joints used in the design of warehouse frames shown in Fig. 5.3.1 is obtained based on the strain compatibility of the structural components of the column section at a concrete strain of 0.003. The nominal flexural moment capacity of 5600 kN m was found corresponding to the axial load of 13,446 kN in the P-M diagram, shown in Fig. 5.3.4. The flexural capacity of the column (5465 kN m) for monolithic concrete joints was calculated at the concrete strain of 0.003 based on the nonlinear FEA considering concrete plasticity, as indicated by Legend 1 of Fig. 5.3.5. A good correlation between the two flexural moment capacities was

FIG. 5.3.3 Finite element model of the proposed connection (Legend 2, Fig. 5.3.5).

270 Hybrid composite precast systems

P (kN) 42,500

q = 0.08 N.A. = 0.10

Pn, Mn

37,500

Legend 1 of Fig. 5.3.5

32,500

(Mn = 5465 kN-m)

27,500

jPn, jMn

22,500 20,952 (13,443, 2170)

12,500

ABAQUS moment corresponding to Mu

7500

Mn = 5600 kN-m

2500 0 –2500

Legend 1 of Fig. 5.3.5

M(kN-m)

6000

5400

4800

4200

3600

3000

2400

1800

1200

600

jMn = 3552.3 kN-m 0

–7500

At concrete strain of 0.003

– Stroke: 44.8 mm – Moment: 4259 kN-m – Rebar strain: 0.0028 (1*ey), Stress:584 MPa – Plate strain: 0.00021 (0.13*ey), Stress: 32 MPa – Plate slippage: 1.3 mm eb = 465.77 mm

17,718, 2824)

17,500

ABAQUS results [Legend 2 of Fig. 5.3.5]

– Stroke: 29.3 mm – Moment: 3338 kN-m – Concrete strain: 0.00204 – Rebar strain: 0.0013 (0.8*ey), Stress:283 MPa – Plate strain: 0.00012 (0.07*ey) – Plate slippage: 0.7 mm

Legend 2 of Fig. 5.3.5 Capacity, jMn = 2769 kN-m [ABAQUS] ∗ Strength reduction factor: j = 0.65 Demand, Mu = 2170 kN-m [Midas Gen]

FIG. 5.3.4 Calibration of the nonlinear numerical results with the axial force-moment interaction diagram of the columns with monolithic joints at a concrete strain of 0.003 [1].

FIG. 5.3.5 Moment-displacement relationship [1].

exhibited, verifying the accuracy of the nonlinear FEA model with parameters proposed in Table 5.3.1. The factored moment demand (Mu) of 2170 kN m for the frame shown in Fig. 5.3.1 was obtained based on the three-dimensional dynamic frame analysis. The factored moment demand (Mu¼2170 kN m) is indicated in the P-M diagram shown Fig. 5.3.4 [1]. The nominal moment strength corresponding to the factored moment demand of 3338 kN m (Mu/f), obtained

Novel erection of the precast frames Chapter

5

271

TABLE 5.3.3 Nominal flexural and design strengths of the columns shown in Fig. 5.3.5; factored moment demand (Mu 5 2170 kN m). Nominal (Mu/f)

Design (Mu)

3338 kN m

2170.0 kN m

Legend 1

5465.0 kN m

3552.3 kN m

Legend 2

4259.0 kN m

2768.4 kN m

Legend 3

4818.4 kN m

3132.0 kN m

Legend 4

4715.0 kN m

3064.8 kN m

Legend 5

4542.8 kN m

2952.8 kN m

Design criteria ABAQUS models

by dividing the factored moment demand (Mu¼2170 kN m) by a strength reduction factor of 0.65, is indicated in Fig. 5.3.5. The design moment strengths estimated numerically for all of the columns with mechanical joints, including the column represented by Legend 2, were greater than the required factored moment (2170 kN m). Nominal flexural and design strengths of the columns shown in Fig. 5.3.5 are summarized in Table 5.3.3 when strength reduction factor of 0.65 was used.

5.3.4 Flexural capacity of the connection The structural behavior of the mechanical joint is explored in this section, identifying the influence of the stiffness of the column plates, described in Fig. 5.3.5 [1], on the flexural capacity of the connections. In a moment-displacement relationship, shown by Legend 2 in Fig. 5.3.5, the flexural nominal capacity of the joint (4259 kN m) corresponding to a concrete strain of 0.003 was greater than the nominal moment strength corresponding to the factored moment demand (Mu/f) of 3338 kN m when no interior and exterior bolts were used; all of the vertical rebars were spliced directly by the interlocking couplers, whereas the 10-mm thick metal plates were not structurally connected. In the numerical results indicated by Legend 2 of Fig. 5.3.6, the concrete strain of 0.00204 was calculated at 3338 kN m (nominal moment strength corresponding to the factored moment demand, Mu/f). The tensile strains of 0.0013 (0.8 ey) and 0.00274 (1.0 ey) for the vertical rebar were also reached at the nominal moment strength corresponding to the factored moment demand (Mu/f¼3338 kN m) and the moment corresponding to a concrete strain of 0.003, respectively. However, the tensile strains in the plates were found negligible, demonstrating et ¼ 0.00012 (0.07ey) at the nominal moment strength corresponding to the factored moment demand (Mu/f¼3338 kN m) and et ¼ 0.00021 (0.13 ey) at the moment (4259 kN m) corresponding to a concrete strain of 0.003. This indicates that the structural components such as rebars and concrete were activated, contributing to the flexural strength of the spliced column, while the column plate did not show any noticeable strains because the column plates used to calculate the moment-displacement relationship denoted by Legend 2 were not subjected to any loads. Similar increases in the moment capacity for all joints having varied joint stiffnesses based on the different bolt designs were demonstrated, presenting the moment strength curve indicated Legends 1–6 of Fig. 5.3.5. The column with monolithic connections demonstrated the largest capacity and stroke. The rest of the moment strengths were shown in magnitude by order of Legends 3, 4, 5, and 2 in Fig. 5.3.5. It was elucidated that the strengths were influenced by the plate stiffness (except for the case with Legend 2) and the numbers and positioning of interior bolts. The moment strength indicated by Legend 3 of Fig. 5.3.5 provided a moment strength similar to that of the monotonic column, enabling the replacement of the columns with monolithic joints. The smallest moment strength was elicited with the mechanical joint having 10-mm thick column plate (refer to Legend 2 of Fig. 5.3.5). However, columns with all mechanical connections provided the nominal moment strengths greater than the nominal moment strength corresponding to the factored moment demand of 3338 kN m. The direct splicing of column rebars without using the interior, or exterior bolts provides the flexural strength large enough to resist the moment demand. Fig. 5.3.6 [1] demonstrates strain evolutions at the nominal moment strength corresponding to the factored moment demand (Mu/ f¼3338 kN m) and the moment corresponding to a concrete strain of 0.003. From the moment-displacement relationship represented by Legends 2 and 3 of Fig. 5.3.5, strains and stress exerted on the joints and stress-strain relationships of concrete, rebars, and column plates were identified at the nominal moment strength corresponding to the factored moment demand (Mu/ f¼3338 kN m) and the moment corresponding to a concrete strain of 0.003 in Fig. 5.3.6. The stresses in the concrete, rebar, and column plate less than a yield strength at the nominal moment strength corresponding to the factored moment demand

272 Hybrid composite precast systems

45

Moment: 4259 kN-m

700 600

Moment: 4259 kN-m

35

500

30

400 Stress (MPa)

Compressive stress (MPa)

40

25 20 15

300 Moment: 3338 kN-m (moment corresponding to Mu)

200 100

10

Moment: 3338 kN-m (moment corresponding to Mu)

5

0 –0.002

0 0

0.002 0.004 0.006 0.008

0.01

0.012

–100

0

Concrete

0.004

0.006

–200

Compressive strain

(A)

0.002

Strain

(B)

Rebar

0 –0.0005

–0.0004

–0.0003

–0.0002

–0.0001

0 –5

Compressive stress (MPa)

–10 Moment: 3338 kN-m (moment corresponding to Mu)

–15 –20 –25

Moment: 4259 kN-m –30 –35 –40 –45 Compressive strain

(C)

Column plate

FIG. 5.3.6 Stress-strain relationships of the concrete, rebars, and column plates; retrieved from Legend 2 of Fig. 5.3.5 [1].

(Mu/f¼3338 kN m) were exhibited. In Fig. 5.3.6A, the compressive concrete stress, and the corresponding concrete strain approached as high as 27 MPa and 0.00204, respectively, at the nominal moment strength corresponding to the factored moment demand (Mu/f¼3338 kN m). At the design load limit state corresponding to a concrete strain of 0.003, the concrete compressive stress reached 38 MPa. Alternatively, in Fig. 5.3.6B, the strain, and stress observed in the rebars at the nominal moment strength corresponding to the factored moment demand (Mu/f¼3338 kN m) were 0.0013 and 283 MPa, respectively, whereas the stress and strain in the rebars increased to as high as 582 MPa and 0.00274 at the design load limit state corresponding to a concrete strain of 0.003. Fig. 5.3.6C indicates the compressive stresses and strains acting on the metal plates were not significant because there was no tensile force transferred onto the metal plates. A compressive force was exerted from the concrete columns on the upper and lower plates when the column was pushed laterally. The compressive stress of 21 MPa with a strain of 0.00012 was exerted on the plate at the nominal moment strength corresponding to the factored moment demand (Mu/ f¼3338 kN m), whereas the compressive stress of 32 MPa with a strain of 0.00021 was found in the metal plate at the design load limit state corresponding to the concrete strain of 0.003. The deformed and undeformed meshes of the proposed joints are illustrated in Figs. 5.3.7–5.3.9 for the column connections represented by Legend 2 of Fig. 5.3.5 at the nominal moment strength corresponding to the factored moment demand (Mu/f ¼ 3338 kN m), design limit state, and ultimate limit states, respectively. The deformations of 29, 45, and 56 mm were exhibited at these limit states, respectively. The story drift of 1/380 was found at the nominal moment strength corresponding to the factored moment (Mu/f¼3338 kN m), which is considered to be acceptable for the design of the frames subjected to the heavy loads at the service limit state.

FIG. 5.3.7 Deformed and undeformed shape at the nominal moment strength corresponding to the factored moment demand (Mu/f ¼ 3338 kN m) level [1].

FIG. 5.3.8 Deformed and undeformed shape at a concrete strain of 0.003 (4259 kN m).

FIG. 5.3.9 Deformed and undeformed shape at the end of the analysis.

274 Hybrid composite precast systems

5.3.5 Conclusions The use of the interlocking couplers and the laminated plates was ensured by the test erection of the full-scale precast frames subjected to heavy loads after all. The efficient and effortless assembly method implementing interlocking couplers and with a 5- to 10-mm thick guiding plate was demonstrated. The stiffness of the metal column plates did not contribute to the structural behavior of the proposed connections when the plates were not connected structurally, while the spliced vertical rebars via interlocking couplers transferred axial loads and the moments at the joint directly. A numerical investigation exploring the microscopic strains and stress exerted on the joints was verified by the PM diagram at a concrete strain of 0.003 for the use in the design. The stresses and strains numerically calculated based on the nonlinear FEA model demonstrated sufficient ductility and resistance for loads. The use of the layered metal plates and the interlocking couplers as mechanical joints was also numerically verified to ensure the present applicability to the industrial frames subjected to heavy loads. The time observed for assembling the precast frames was similar to that of the steel frames, proving the assembly method safe and useful. The assembly of the precast concrete frames utilizing the inter-locking couplers splicing vertical rebars and laminated plates is expected to provide benefits as cost-saving alternatives to the conventional concrete for the construction industry subjected to heavy loads [1].

References [1] J.D. Nzabonimpa, W.K. Hong, Novel precast erection method of interlocking mechanical joints using couplers, J. Construct. Eng. Manage. (ASCE) 144 (6) (2018). [2] C.K. Intersteel, One Touch Coupler, Korean Patent No. 10-164-3846-0000, 2016.

Chapter 6

Novel precast frame for facile construction of low-rise buildings using mechanically assembled joint to replace conventional monolithic concrete frame 6.1 Introduction The erection test of L type columns was introduced in Chapter 4, ensuring that the mechanical connections expedited assembly speed of the precast frame components. In this chapter, laminated mechanical plates interconnected by both interior and exterior high-strength bolts are implemented in low-rise building design based on the extensive and numerical investigations described in Chapter 3. Well-designed mechanical joints for precast frames close to the monolithic joint were provided for column-to-column, column-to-girder, and girder-to-beam connections of the four-story building. The mechanical joints constituted by the endplates demonstrated a wide range of structural responses depending on the stiffness of the connections. The novel and innovative application of mechanically assembled precast joints used in the connections, including column-to-column, column-to-girder, and girder-to-beam strongly influenced the global response of the precast frames. This topic is of high scientific interest since it could be widely recognized as a reference for the considered connections that offer a competitive frame assemble pointing out good performance relative to the conventional cast-in-place constructions. An attractive alternative based on mechanical assembly method can provide quick residences for people who are suffering from housing shortages.

6.1.1 Advantages and challenges Alternative connections for precast columns based on the mechanical joints to the conventional sleeve connections were offered in Chapters 2 and 3. The conventional bolted steel connections commonly used in steelwork were modified to assemble the precast components, completely removing the use of the temporary pour forms at joints required for conventional cast-in-place concrete construction. In Chapter 4, the efficient and simple erection of full-scale precast frames was demonstrated using the mechanical joints with bolted metal plates. Fig. 6.1.1C shows the observed time of around 20 min for the assembly of full-scale precast frames with two bays.

6.1.2 Methodology of joint details for low-rise frames; connections for column-to-column, column-to-girder, and girder-to-beam The joint details of precast frame connections for columns, columns-girders, and girders-beams are illustrated in Fig 6.1.1. These joints were created as fully restrained moment connections for the use with reinforced concrete precast frames to replace the design of a four-story building. The mechanical connections for columns (Fig. 6.1.1A and C-(1)), column-togirder/girder-to-beam joints (Fig. 6.1.1B and C-(2) and (3)) for precast frame assembly introduced in previous erection test were proposed to replace the conventional monolithic, cast-in-place concrete frames for low-rise buildings. Nuts were anchored to rebars at both ends of beam/girder endplates, shown in Fig. 6.1.1C-(4). Three types of column-to-column connections are summarized in Section 2.7.3 of Chapter 2. In Fig. 6.1.1C-(4); nuts are threaded with straight re-bars in the counterbores of the column plates, thick enough to accommodate the nuts completely. Nuts were encased in the column plates, not in a filler plate. As illustrated in Fig. 6.1.1C-(3) and (5), the endplates of beams/girders were placed between the Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00006-6 © 2020 Elsevier Ltd. All rights reserved.

275

(1) Connection details

(2) Bolted beam-column connection

(B)

(3) Bolted beam-column connection Beam-to-column assembly with mechanical joints

FIG. 6.1.1 See figure legend on next page (Continued)

Novel precast frame for facile construction of low-rise buildings Chapter

6

277

FIG. 6.1.1, cont’d Novel mechanical joint details for precast frames.

column plates, eliminating the use of conventional pour forms that were required in cast-in-place concrete construction. Fully restrained moment connections were implemented for the design of a four-story building. Similar construction speed and accuracy to that offered by steel frames was demonstrated for the low-rise buildings. A numerical model based on damaged concrete plasticity was developed to verify joint behavior. The connection details which influenced the global response strongly were explored both experimentally and analytically to understand the strain evolution, the deformation of the metal plates, and their influence on the flexural capacity of the proposed joints. The details of these experimental studies, shown in Fig. 6.1.2, can be found in Sections 2.5.1 and 2.5.2 of Chapter 2.

6.2 Design of the building with the mechanical joints 6.2.1 Design load combination and conventional design detail Frames having mechanical joints, shown in Fig. 6.2.1, were proposed to replace conventional cast-in-place monolithic concrete frames (refer to Fig. 6.2.2) of a four-story building. The frame with mechanical joints was designed with an intermediate moment frame against the ground motions of 0.2 g. The R factor of 5 defined as response modification

278 Hybrid composite precast systems

FIG. 6.1.2 Test for precast frames with mechanical connections.

FIG. 6.2.1 Cast-in-place monolithic building frame to be replaced by a frame having the proposed mechanical joints.

coefficient recommended by local building code of the city was used to reduce elastic seismic forces. Plans of the original design of four story-reinforced concrete building are shown in Fig. 6.2.2A. Fig. 6.2.2B presents the conventional monolithic column. The moment and axial force demands with a design load combination caused by wind and seismic loadings expected at the building site were identified by three-dimensional dynamic analysis and summarized in Table 6.2.1. These calculations were omitted in this chapter because it was a straightforward procedure.

6.2.2 Design of mechanically layered plates based on nonlinear finite element analysis Two prototypes of columns, including mechanical joints for column connections; one without and one with a steel section, are available in Fig. 6.2.3. The exterior and interior bolts inter-connecting column plates and nuts anchored to the rebars in counterbores are shown in Fig. 6.2.3A and B. It is also recommended that the holes in which the nuts are installed should be 5 mm larger in diameter so that the nuts can be freely displaced, preventing collisions with column plates. Interior bolts were added in the column plates, shown in Fig. 6.2.3B-(1) and (2), to provide additional stiffness to the column plates; heads of interior bolts were buried in the lower concrete column. The upper column plate is then placed on the interior bolts before the access to the interior bolts is grouted with nonshrinkage high strength mortar, as illustrated in Fig. 6.2.3B-(1). The steel column welded to metal plates was encased in the structural concrete, as presented in Fig. 6.2.3B. The structural behavior of the column plates experimentally observed was verified by nonlinear inelastic finite element analysis (FEA). Fig. 6.2.3

Novel precast frame for facile construction of low-rise buildings Chapter

Name Story

6

279

C1A, C3A 500 mm

Y

500 mm

X 2–4F

Design load combination: -Axial force: 1092 kN -Mux: 124 kN-m -Muy: 124 kN-m Main bar: 12-HD22 Tie bar: HD10@200

(B)

Conventional monolithic column

FIG. 6.2.2 Plan of the reinforced concrete building with conventional design.

presents a design summary of the mechanical joints, including metal plate and bolt connections; this figure includes the thicknesses of metal plates, grades, and the numbers and positions of the bolts. In the proposed mechanical joints, loads from upper rebars must be transferred to the column plate via nuts, to the lower column plate, and back to the lower rebars, as shown in Fig. 6.2.3C-(1). As illustrated in Fig. 6.2.3C-(2), double nuts were installed to ensure the transfer of

280 Hybrid composite precast systems

TABLE 6.2.1 Moment and axial force demands for the joint design. Column

Girder

Mux

Muy

Pu

124 kN-m

124 kN-m

1,092 kN

Negative Mu

Positive Mu

Vu

299 kN-m Beam

258 kN

Negative Mu

Positive Mu

Vu

223.2 kN-m

84 kN-m

167.9 kN

compression force to the column plates. The experimental investigation confirmed the load path. Washers were also used to distribute compression force on the column plates.

6.2.3 Numerical model and nonlinear finite element analysis parameters Modeling techniques developed to represent the complexity of the geometric configuration of the connections for precast frames in the previous study [4, Chapter 2] and [16, Chapter 3] were implemented in the design of the building. The contact stiffness between surfaces in contact, modeling of concrete (host element), modeling of the discretized reinforcing bars and H-steels embedded in the concrete were defined in the FE models. The details of FEA considering damaged concrete plasticity are found in Chapter 3.

6.2.3.1 Defining contact properties The proposed joints consisted of laminated metal plates, which were bolted together to create a rigid connection, as shown in Fig. 6.2.4A. Throughout experimental observations [2, Chapter 2], [3, Chapter 2] and [2], it was found that metal plates experienced large contact pressures when lateral forces were exerted on the test specimens. FE models were carefully modeled in a way that prevented metal plates from penetrating each other due to large compressive forces. The contact properties were defined between the upper and lower metal plates, bolts and plates, and nuts and endplates to avoid possible penetrations from occurring among these elements. The interactions shown in Fig. 6.2.4B were assigned based on surfaceto-surface contact method. The interaction properties based on penalty method were defined, which considered the nonlinear stiffness for the interface between the master and slave surfaces. The penalty method was suitable for the proposed joints since it deals with hard contact surfaces. Additionally, the penalty method demonstrated a good treatment of overconstraints caused by overlapping contact definitions. Each surface in contact was assigned with normal and tangential behaviors.

6.2.3.2 Modeling of embedded elements (reinforcing bars and H-steels) Reinforcing bars and H-steels were modeled as embedded elements; this technique assumed a perfect bond between the concrete and the embedded elements. The translational DOFs were eliminated, and the movement of embedded nodes was controlled by the DOFs of the host elements. A geometric tolerance of 0.15 was issued to keep track of embedded nodes lying outside the regions of the host elements. The default value of the geometric tolerance is defined as 0.05 [12, Chapter 2]. The material properties for embedded elements (re-bars and H-steels) are summarized in Table 6.2.2.

6.2.3.3 Discretization A fine mesh was assigned at the area of importance, as shown in Fig. 6.2.4A. Structural elements located at the joint level were discretized with a fine mesh having a size of 10 mm while a coarse mesh was assigned to other locations. The average number of nodes and elements recorded in each FE model was estimated as 190,552 and 149,490, respectively.

6.2.4 Design of connection plates Fig. 6.2.4 describes the finite element model for the nonlinear numerical evaluations of the structural performance of the metal plates for column connections with and without interior bolts. Moment-displacement relationships are presented in

Novel precast frame for facile construction of low-rise buildings Chapter

6

281

FIG. 6.2.3 See figure legend on next page (Continued)

282 Hybrid composite precast systems

FIG. 6.2.3, cont’d Design of metal plates for columns.

Fig. 6.2.5, which were obtained from the varied design parameters, including one with internal bolts. Concrete damage was considered for moment-displacement relationships, indicated by Legends 4–6, whereas the others, indicated by Legends 1–3, were obtained without considering concrete damage. Moment-displacement relationships of reinforced concrete (RC) and steel-reinforced concrete (SRC) composite columns were represented by Legends 2 and 5, and 3 and 6, respectively.

Novel precast frame for facile construction of low-rise buildings Chapter

FIG. 6.2.4 Nonlinear numerical model.

TABLE 6.2.2 Material properties for embedded elements (rebars and H-steels). Embedded elements

Tensile yield strength

Poisson’s ratio and Young’s modulus

Rebar size

fy ¼ 550 MPa

0.3 and 206,000 MPa

H-steels

fy ¼ 325 MPa

0.3 and 205,000 MPa

6

283

284 Hybrid composite precast systems

FIG. 6.2.5 Conventional frame versus frame having mechanical joints (overturning moments at column joints) with the axial force of 1092 kN (data shown in Table 6.2.3).

Flexural moment capacity similar to those of the conventional monolithic frame at the design loads (Mu of 124 kN-m) and axial load of 1092 kN was demonstrated for all specimens. However, in Fig. 6.2.5, the difference was noticed between flexural strength of moment-displacement relationships (refer to Legends 1 (monolithic specimen) and 3 (mechanical joint with internal bolts)) at the concrete strain of 0.003. Additional stiffness should be added to the mechanical joint of the column represented by Legend 3 to yield strength equivalent to that of the monolithic column at concrete strain reaching 0.003. Table 6.2.3 presents the strains identified at the factored design loads (Mu) and the loads corresponding to the concrete strain of 0.003 in the column joints for both concrete column (Figs. 6.2.3A and 6.2.5) and SRC column (Figs. 6.2.3B

TABLE 6.2.3 Strains identified at the factored design loads (Mu) and the loads corresponding to the concrete strain of 0.003 for each column joints (Figs. 6.2.3 and 6.2.5). With concrete damage Mechanical joint (RC) (Legend #2)

Control (Legend #1)

Mechanical joint (SRC) (Legend #3)

With axial loads of 1092 kN and lateral loads

Design load (Mu)

Concrete strain 0.003

Factored design load (Mu)

Concrete strain 0.003

Factored design load (Mu)

Concrete strain 0.003

Moment (kN-m)

128

458

133

395

134.8

362.4

Lateral load (kN)

64

229

66.5

197.7

67.4

181

Stroke (mm)

5

30

5.3

32

5.3

28

0.00049

0.0029

0.00059

0.003

0.00056

0.0029

6.9

21.8

Concrete

Strain Stress (MPa)

Rebar

Steel (flange)

Strain

0.00008

0.002

0.00006

0.0024

0.00024

0.0022

Stress (MPa)

11.8

412

15

515

48

449

Strain

0.00013

0.0013

Stress (MPa)

25

252

Novel precast frame for facile construction of low-rise buildings Chapter

6

285

TABLE 6.2.3 Strains identified at the factored design loads (Mu) and the loads corresponding to the concrete strain of 0.003 for each column joints (Figs. 6.2.3 and 6.2.5).—cont’d With concrete damage Mechanical joint (RC) (Legend #2)

Control (Legend #1)

Factored design load (Mu)

Concrete strain 0.003

Strain

0.00001

0.0003

Stress (MPa)

6

67

Interior bolt

Strain

0.000094

0.0032

Stress (MPa)

16.4

660

Exterior bolt

Strain

0.00007

0.0045

0.000089

0.00134

Stress (MPa)

11

932

19.4

277.4

Upper plate

Strain

0.00006

0.0035

0.00015

0.00255

Stress (MPa)

4

356

31

347

Deformation (mm)

0.03

0.42

0.081

0.46

Strain

0.00016

0.0036

0.00002

0.0044

Stress (MPa)

34

349

55

362

Deformation (mm)

0.06

0.6

0.085

0.65

With axial loads of 1092 kN and lateral loads Steel (web)

Lower plate

Design load (Mu)

Concrete strain 0.003

Factored design load (Mu)

Concrete strain 0.003

Mechanical joint (SRC) (Legend #3)

and 6.2.5). In this table, strains from specimens represented by Legends 1–3 of Fig. 6.2.5 (without application of damage parameters) were identified at the factored design loads (Mu) and the loads corresponding to the concrete strain of 0.003. The damage index did not affect the flexural strength up to the strain of 0.003, as shown in Fig. 6.2.5. The strains of the lower metal plate and the interior bolts corresponding to Mu were 0.00002 and 0.000094 below yielding, respectively, for the SRC column (refer to Table 6.2.3 and Legend 3 of Fig. 6.2.5). The strains of exterior bolts decreased significantly from 0.0045 (refer to Legend 2, without interior bolts) to 0.00134 (refer to Legend 3, with interior bolts) when the interior bolts were responsible for the strain of 0.0032 (refer to Legend 3). Fig. 6.2.6 presents verification of structural behavior of the mechanical plates of the precast concrete column based on nonlinear inelastic FEA with a design summary of the mechanical joints, including metal plate and bolt connections. It was also noticed that the strains of upper plates decreased from 0.0035 identified at specimen by Legend 2 to 0.00255 at Legend 3 when the interior bolts were installed. Shear design details of the mechanical metal plates for the SRC columns to replace the conventional monolithic columns are presented in Fig. 6.2.6; four interior bolts were provided for additional strength against overturning moments. Fig. 6.2.6 also illustrates the deformed finite element meshes of column joints for the four-story building for loads corresponding to the concrete strain of 0.003. In this case, the axial load of 1092 kN and the moment of 362.4 kN-m were exerted, as shown in Fig. 6.2.6A and B. The strains of plates interconnected by high-strength bolts are depicted in Fig. 6.2.6C and D, where the von Mises stresses of bolts corresponding to the concrete strain of 0.003 are presented, indicating that the structural integrity of the bolted connection was ensured. The punching shear demand of 113 kN inside the counterbores shown in FEA meshes of Fig. 6.2.6D obtained from the numerical analysis at a concrete strain of 0.003 was less than the design shear strength (FVu) of 220.4 kN around the neck of the counterbore of the column plates with steel section at the loads corresponding to the concrete strain of 0.003. The stresses of structural components attached to the mechanical joints were also below the allowable. For tall buildings, however, lateral overturning loads increase tension forces on columns, requiring greater flexural stiffness of the plates or the use of more interior bolts/increased rib stiffness to size practical thicknesses for the plates.

286 Hybrid composite precast systems

FIG. 6.2.6 Deformed column connection at the loads corresponding to the concrete strain of 0.003 for the column with a steel section (Fig. 6.2.3B, Legend 3 Fig. 6.2.5).

6.2.5 Implementation of the extended endplates in girder-to-beam 6.2.5.1 Design of mechanical connections In Fig. 6.2.7A, nuts anchoring rebars are installed in two ways. Rebars were anchored on the opposite face of the beam endplates in Fig. 6.2.7A and nuts anchoring threaded ends of the rebars were encased in counterbores of the opposite side of the beam endplates in Fig. 6.2.7B. All of the numerical analysis shown in Fig. 6.2.7C, except the analysis with Legend 2, was based on the 20-mm thick beam endplates and 10-mm thick girder plate. The moment-displacement relationship

FIG. 6.2.7 Design of the novel mechanical joint of girder-to-beam connection.

288 Hybrid composite precast systems

FIG. 6.2.8 Strains at mechanical joint of girder-to-beam connection at factored design loads (Mu).

calculated by the model having headed studs with Legend 2 of Fig. 6.2.7C was based on the 30-mm thick beam endplates with 5-mm thick girder plate. The moment-displacement relationship of the girder-to-beam connections was obtained by FEA for the use without headed studs (Figs. 6.2.7A and 6.2.8A) indicated by Legends 3–5 of Fig. 6.2.7C and with headed studs (Figs. 6.2.7B and 6.2.8B) indicated by Legend 2 of Fig. 6.2.7C. The combination of FEA parameters for the predictions of the composite precast column-to-girder connections with mechanical endplates was proposed in Section 3.1.3.3 of Chapter 3; dilation angle of 30° without consideration of damage variable or higher dilation angle with the consideration of damage variable were suggested. The mechanical girder-to-beam joints consist of a pair of plates between the end faces of the girder and the beam section. Figs. 6.2.7D and 6.2.11A and B show one of the beam-to-girder connections with metal plates that were used in the building design. In these models, the rebars were subjected to the tensions. Fig. 6.2.7C compares the flexural capacity of the conventional frame to that of the frames with mechanical joints based on nonlinear analysis when moments were applied at lower joints due to the lateral loads. The flexural capacity of the mechanical beam joint without headed studs (refer to Legends 3 and 4 in Fig. 6.2.7C) was 36% less than that of the monolithic control specimen (refer to Legend 1 in Fig. 6.2.7C) for the strain corresponding to the concrete strain of 0.003. The interior bolts were positioned above the lower

Novel precast frame for facile construction of low-rise buildings Chapter

6

289

rebars by 65 mm in the plate (refer to Fig. 6.2.8A to reduce the unsupported distance of the plates; this change did not influence the flexural capacity of the metal plates (refer to the moment-displacement relationship by Legend 3 of Fig. 6.2.7C). In Fig. 6.2.8B, the interior bolts in the plate were lowered to the same level between rebars when headed studs were added to the girder-to-beam plate; flexural capacities similar to that of the monolithic control beam were obtained at the factored design load (Mu) (refer to the moment-displacement relationship by Legend 2 of Fig. 6.2.7C). The flexural stability of the plates was validated by deformed joint meshes of girder-to-beam connections for the two mechanical joints, as shown in Fig. 6.2.8A without headed studs (refer to Legend 3, Fig. 6.2.7C), and Fig. 6.2.8B with headed studs (refer to Legend 2, Fig. 6.2.7C), for the factored design moments of 79 kN-m. The selected construction document for the novel mechanical joint of the girder-to-beam connection is presented in Figs. 6.2.7D and 6.2.11A and B. Fig. 6.2.8A-③ and B-③ demonstrate that the strains of the beam end-plate were 0.000593 and 0.00035, respectively, with negligible deformation. However, greater strains, of 0.00204 and 0.0016, for interior bolts interconnecting beam and girder plates were found as depicted in Fig. 6.2.8A-③ and B-③, respectively. The separations of concrete girder from the beam endplates were negligible, and they were 0.15 and 0.12 mm, as shown in Fig. 6.2.8A-③ and B-③, respectively, verifying concrete was well bonded to the metal plates regardless of the use of headed studs. The column connection shown in Fig. 6.2.8B contributed to the flexural capacity most effectively and significantly at the concrete strain of 0.003.

6.2.5.2 Design of headed studs In Fig. 6.2.9, the strain of almost 0.005 was reached by headed studs installed in the plate. Considerable reduction of the strain of the lower rebars from 0.08 (refer to Fig. 6.2.9B) to 0.009 (refer to Fig. 6.2.9A) was found, resulting in necking of the rebars which was removed in the specimen with headed studs. The moment–displacement relationship shown by Legend 2 of Fig. 6.2.7C demonstrated the increase of the flexural strength of the mechanical joint when headed studs were implemented to the column joint, replacing conventional monolithic concrete frames. Nuts were located in counterbores in the beam endplates, so the 20-mm-thick beam plates also contributed to creating fully restrained moment connections at girder-to-beam joints, as shown in Figs. 6.2.8 and 6.2.9. Stresses and strains of the structural components comprising mechanical joints corresponding to Fig. 6.2.7C are summarized in Table 6.2.4; the strain of the connecting bolts and metal plate without headed studs (the moment-displacement relationship indicated by Legend 3 of Fig. 6.2.7C) were 0.00277 and 0.00083, respectively, when the concrete strain reached 0.003. The strains of 0.003 and 0.0008 at the connecting bolts and metal plate with headed studs (the moment-displacement relationship indicated by Legend 2 of Fig. 6.2.7C) were also obtained. In Fig. 6.2.7C, the flexural strengths similar to the conventional monolithic specimen were exhibited for all specimens with mechanical connections represented by Legends 2–5 at the factored design loads (Mu of 79 kN-m). A conventional cast-in-place monolithic connection can be replaced by girder-to-beam joints with endplates (Legends 2 to 5), shown in Fig. 6.2.7C, at the factored design loads. However, in Fig. 6.2.7C, quite a little difference among the moment-displacement

FIG. 6.2.9 Influence of headed studs on strains of rebars and beam endplates.

Control, Legend 1

Legend 2

Legend 3

Legend 4

Legend 5

Beam

Design load

Concrete strain 0.003

Design load

Concrete strain 0.003

Design load

Concrete strain 0.003

Design load

Concrete strain 0.003

Design load

Concrete strain 0.003

Moment (kN-m)

79

133.7

79

172

79

114.6.

79

114.4

79

98.5

Lateral load (kN)

46.5

78.6

46.5

101.4

46.5

67.4

46.5

67.3

46.5

57.9

Stroke (mm)

3.78

14

4.4

16.2

5

13.2

4.4

12.3

7.2

14

Strain

0.00095

0.003

0.00085

0.003

0.00122

0.003

0.00114

0.003

0.00174

0.003

Stress (MPa)

11.8

21

9.5

20

12.1

15.1

12

21

20

21

Strain

0.00126

0.005

0.0013

0.009

0.00140

0.08

0.0017

0.082

0.00103

0.0674

Concrete

Rebar

Stress (MPa)

259.2

323.1

292.5

385

301.7

401.2

365

384

196.8

372

Upper bolts

Strain

–

–

0.0016

0.003

0.00204

0.00277

0.0017

0.0023

0.00268

0.00328

Stress (MPa)

–

–

330.7

632

411

557.9

347

466

565.5

693.3

Side bolts

Strain

–

–

0.0013

0.0029

0.00167

0.00232

0.0012

0.00167

0.00195

0.00239

Stress (MPa)

–

–

267.3

595.4

347.8

483

245

343

397.7

487.5

Strain

–

–

0.00035

0.0008

0.000593

0.000839

0.0004

0.0006

0.00143

0.00169

Stress (MPa)

–

–

82

192

140.4

172.8

96

123

303.4

333.6

Deformation (mm)

–

–

0.2

0.5

0.7

1

0.2

0.37

1.3

1.7

Strain

–

–

0.0009

0.0048

–

–

–

–

–

Stress(MPa)

–

–

197

458

–

–

–

–

–

Beamplate

Headed studs

290 Hybrid composite precast systems

TABLE 6.2.4 Strain identified at the factored design loads and the loads corresponding to concrete strain of 0.003 (rebar «y: 0.002, plate «y: 0.0016, bolt «y: 0.0045, headed stud «y: 0.002) (Fig. 6.2.7C).

Novel precast frame for facile construction of low-rise buildings Chapter

6

291

FIG. 6.2.10 Shear rigidity of plate with headed studs and interior bolts positioned between the lower rebars at factored design loads (momentdisplacement relationship by Legend 2).

relationships was noticed when a concrete strain reached 0.003. The headed studs reduced the strains of plates, concrete, and nuts in the neighborhood. The shear strength (232 kN) of the counterbores was greater than the punching shear stress obtained numerically as 58 kN with the stress of 44 MPa at the counterbore neck, as shown in the stress contour of Fig. 6.2.10A and B. Mechanical joint details for girder-to-beam connection meeting the requirements for both design and constructability are provided in Fig. 6.2.11. The seven top rebars of 22 mm diameter in the concrete beam shown in Fig. 6.2.11A can be replaced by two rebars and T section steel (T-75  150  7  10), groove-welded at the top of the beam endplates (refer to Fig. 6.2.11B), enhancing the constructability of the girder-to-beam connections by reducing rebars in a congested joint area. Four interior bolts were used to add stiffness to the beam endplates, in addition to the six exterior bolts that interconnected beam and girder plate. In Table 6.2.5, strains for the conventional frame and the frame with mechanical joints with moments applied at lower joints were evaluated at the factored design loads and the loads corresponding to a concrete strain of 0.003. Influence of headed studs upon the strains of plates, concrete, and nuts in their neighborhood (refer to moment-displacement relationships indicated by Legends 2 and 3 in Fig. 6.2.7C) was explored. Concrete, which was bonded to the metal plates via headed studs, contributed to the flexural capacity of the joints significantly, as represented by moment-displacement relationship, Legend 2 of Fig. 6.2.7C.

6.2.6 Implementation of the extended endplates in column-to-girder connections Fig. 6.2.12 illustrates details of girder endplates that were proposed for the joint of the low rise frames. Two types of mechanical joints for column-to-girder connection were also proposed to replace the conventional monolithic frame; herein, the mechanical joint with precast concrete (RC) and steel-concrete (SRC) hybrid girder were suggested in Fig. 6.2.12, with three girder rebars anchored to columns via embedded couplers. T section steel (T-75  100  6  9) was groove welded at the top of the girder endplates, as shown in Fig. 6.2.12A. No moment was acting through the bottom rebars of the girders. Thicknesses of 5 and 30 mm for column and girder endplates were determined at columnto-girder joints, as shown in Fig. 6.2.12. The same plate thicknesses of 5 and 30 mm for girder and beam endplates at girder-to-beam joints were assigned, as shown in Figs. 6.2.7B and 6.2.11. In this design, girder and column plates were connected by two bolts at the top of the endplates, resisting tensile forces exerted by the rebars and T section steel. Fig. 6.2.12B demonstrates moment-displacement relationships of the mechanical joint when the damage variable in the finite element model was not considered; the structural behavior of the mechanical connection was compared with that of the monolithic joint at the factored design loads (Mu of 299 kN-m) and the loads corresponding to the concrete strain of 0.003 (349.5 kN-m). Strains of the column-to-girder connection obtained based on the finite element meshes are identified in Fig. 6.2.12C and D at the loads corresponding to the concrete strain of 0.003, indicating that the joint provided greater flexural load capacity (349.5 kN-m) than the moment demand of 299 kN, which was determined by seismic analysis. In Fig. 6.2.12D, design parameters such as the stiffness of the joints, including plates, and the numbers and positions of bolts for column-girder connections were verified by the nonlinear FEA considering damaged concrete plasticity. Stable structural behavior of the joints was demonstrated by exhibiting strain of girder plate being 0.0038 with separation of 1.2 mm of girder plate from column face. The efficient contribution to the flexural strength of the joint by both rebars and steel sections was observed. However, the tensile strain of rebars (0.00425, 2.125 ey) was activated greater than that of steel sections (0.0022, 1.375ey). Construction plan for the precast building frames showing mechanical joints with plates is presented in Fig. 6.2.13. Precast columns of 2 stories were proposed to be erected.

292 Hybrid composite precast systems

FIG. 6.2.11 Design detail of girder-to-beam connections for concrete and composite section based on R factor of 5.

6.3

Design verification

6.3.1 Rates of strain increase and strain activation of the structural components at connection As shown in Figs. 6.3.1 and 6.3.2, the stress-strain relationship and the rates of strain increase of the structural components at connection were identified based on the load-displacement relationships (mechanical joint of SRC column with interior bolts) indicated by Legend 6 in Fig. 6.2.5; herein, the influence of the flexural strength of the metal plates upon the deformability of bolts, rebars, and concrete for the column connection was observed. The design limit state and the limit state corresponding to the concrete strain of 0.003 were indicated in the figures. In Fig. 6.3.1, stress-strain relationships identified from the load-displacement relationships of SRC column with interior bolts indicated by Legend 6 of Fig. 6.2.5,

Novel precast frame for facile construction of low-rise buildings Chapter

6

293

TABLE 6.2.5 Influence of headed studs upon the strains of plates, concrete, and nuts in their neighborhood (curves indicated by Legends 2 and 3 in Fig. 6.2.7C). Legend 2

Legend 3

Beam

Concrete strain 0.003

Rebar necking

Concrete strain 0.003

Rebar necking

Moment (kN-m)

172

205.9

114.6.

114.6

Lateral load (kN)

101.4

121.1

67.4

67.4

Stroke (mm)

16.2

33

13.2

13.2

Concrete (compression)

Strain

0.003

–

0.003

–

Stress (MPa)

20

–

15.1

–

Concrete (tension)

Strain

0.0041

–

0.0015

–

Stress (MPa)

0.4

–

0.6

–

Strain

0.009

–

0.08

–

Stress (MPa)

385

–

401.2

–

Strain

0.0048

–

–

–

Stress (MPa)

452

–

–

–

Strain

0.0018

–

0.0024

–

Stress (MPa)

380

–

507

–

Strain

0.00085

–

0.000839

–

Stress (MPa)

192

–

172.8

–

Deformation (mm)

0.5

–

1

–

Rebar

Stud bolt

Nut

Plate

FIG. 6.2.12 See figure legend on next page (Continued)

294 Hybrid composite precast systems

FIG. 6.2.12, cont’d Numerical evaluation of the mechanical joint for the column-girder connection.

Novel precast frame for facile construction of low-rise buildings Chapter

Y7

Y6

Y5

Y4

Y3

Y2

6

295

Y1

30,800

5,000

3,600

RG12

RG11

5,800

5,000

RG11

RG11

4,700

5,450

RG11

1,250

RG11

4G11

4G12

4G11B

4G11B

(500*500)

4G11

4G11

(300*500)

(500*500)

(300*500)

(500*500)

(300*500)

(500*500)

(300*500)

(500*500)

(300*500)

3,000

(300*500)

RCG11 (500*500)

C1

(500*500)

2G11

2G11

(300*500)

3G11

(300*500)

3G11

3G11

(300*500)

(500*500)

(500*500)

(300*500)

(300*500) (300*500)

(300*500)

2G11B

(500*500)

2G11

C1

C1

(500*500)

C1

(400*500)

(500*500)

(400*500)

(500*500)

(400*500)

(400*500)

C3A

(500*500)

3G11B

2G11B (500*500)

(500*500)

(400*500)

(500*500)

3,800

(500*500)

(500*500)

3G11B

(500*500)

(300*500)

2G12

(500*500)

(400*500)

(300*500)

(500*500)

(300*500)

2G11

3G12

(300*500)

2,900

(500*500)

2,900

9600

12600

3G11

(500*500)

(300*500)

4CG11 (500*500)

C1

C3

Mechanical joints (lower and upper plates)

FIG. 6.2.13 Erection of precast columns of 2 stories implementing mechanical plates.

(A)

(B) 400

Strain-stress curve (steel flange)

350 Stress (MPa)

300 250 200 6. Mechanical joint (SRC, with damage)

150 100

Concrete strain: 0.003

50 0 –0.002 –50 0

0.002

0.004

0.006

0.008

0.01

–100 Strain

(C)

Steel flange

FIG. 6.3.1 See figure legend on next page (Continued)

296 Hybrid composite precast systems

Strain-stress curve (upper plate) 400 300 250 200 6. Mechanical joint (SRC, with damage)

150 100

Concrete strain: 0.003

50 0

Stress (MPa)

Stress (MPa)

350

0

0.002

0.004

0.006

0.008

0.01

450 400 350 300 250 200 150 100 50 0

Strain-stress curve (lower plate)

6. Mechanical joint (SRC, with damage) Concrete strain: 0.003 0

0.005

0.01

Strain

(D)

0.015

0.02

0.025

Strain

(E)

Upper plate

Lower plate

Strain-stress curve (interior bolts) 1200

Strain-stress curve (exterior bolts) 700 600

800 600 6. Mechanical joint (SRC, with damage) 400

Concrete strain: 0.003

200 0

Stress (MPa)

Stress (MPa)

1000

500 400 300

6. Mechanical joint (SRC, with damage)

200

Concrete strain: 0.003

100 0

0.005

0.01

0

0.015

0

0.005

Strain

(F)

0.01

0.015

Strain

(G)

Interior bolt

Exterior bolt

FIG. 6.3.1, cont’d Stress-strain relationships, Legend 6 of Fig. 6.2.5.

(A)

(B) Strain-stroke curve (steel flange) 0.009 0.008

6. Mechanical joint (SRC, with damage)

0.007 Concrete strain: 0.003

Strain

0.006 0.005 0.004 0.003 0.002 0.001 0 –0.001

0

10

20

30

40

50

60

70

Stroke (mm)

(C)

Steel flange

FIG. 6.3.2 See figure legend on opposite page (Continued)

Novel precast frame for facile construction of low-rise buildings Chapter

Strain–stroke curve (upper plate)

6

297

Strain–stroke curve (lower plate)

0.012

0.025

0.01

0.02 Strain

Strain

0.008 0.006 0.004

6. Mechanical joint (SRC, with damage)

0.002 0

0.01

6. Mechanical joint (SRC, with damage)

0.005

Concrete strain: 0.003

Concrete strain: 0.003 0

10

20

(D)

30 40 50 Stroke (mm)

60

0

70

Strain–stroke curve (interior bolts)

0.014

Strain

0.006

0.001 0.0005

(F)

20

30 40 Stroke (mm)

Interior bolt

50

60

60

70

6. Mechanical joint (SRC, with damage) Concrete strain: 0.003

0.0015

0.002 10

50

0.002

0.004

0

30 40 Stroke (mm)

Strain–stroke curve (exterior bolt)

0.0025

0.008

0

20

Lower plate

0.003

Concrete strain: 0.003

0.01

10

0.0035

6. Mechanical joint (SRC, with damage)

0.012

0

(E)

Upper plate

0.016

Strain

0.015

0

70

0

10

20

(G)

30 40 Stroke (mm)

50

60

70

Exterior bolt

FIG. 6.3.2, cont’d Rates of strain increase of plates; Legend 6 of Fig. 6.2.5.

demonstrated both the lower and upper column plates for mechanical connection yielded, as shown in Fig. 6.3.1D and E, while structural elements other than plates (Fig. 6.3.1A–C, F, and G), were under yield limit. This consideration may suggest that more interior bolts be implemented to effectively reduce strain and deformation of column plates, which then let structural elements other than plates yield, providing structural performance similar to that of the monolithic frame. As illustrated in Fig. 6.3.2, the rates of strain increase of plates, the concrete/steel section, and the rebars/nuts with varying strokes were explored, allowing identification of how the mechanical connections contributed to the flexural capacity of the columns. The strains of the interior and exterior bolts corresponding to the concrete strain of 0.003 reached 0.0032 and 0.00134, respectively, as shown in Fig. 6.3.2F and G, suggesting that interior bolts contributed more significantly to the structural integration of the mechanical joints than the exterior bolts did. Strain activation of the structural components at connection increased rapidly after the concrete strain of 0.003, as can be seen in Fig. 6.3.2A–C for concrete, rebars, and steel flanges. The structural details suggested in this design were capable of providing sufficient strength (flexural capacity) for plates to transfer tension and compression couples induced by the loads, enabling to replace the conventional joints of cast-in-place monolithic concrete buildings. The structural performances of the proposed frame shown in Fig. 2.5.5 of Chapter 2 showed the structural behavior similar to that of monolithic behavior of concrete frames. The strength reduction factors were used in obtaining design moment and shear strength.

6.3.2 Construction quantities The alternative design utilizing precast frames with the proposed mechanical joints replaced 42 columns and 234 beams designed with conventional monolithic, cast-in-place frames. Table 6.3.1 provides the structural tonnages, including the plates and bolts used in the proposed mechanical joints; construction quantities of the volume of concrete were also given to help estimate the construction cost.

6.3.3 Reduction of construction period by mechanical connection As shown in the erection test of the multi-bay frames with mechanical connections described in Section 4.4 of Chapter 4, the proposed assembly of precast columns was quick and easy, proving constructability and outstanding construction energy efficiencies. Bolt holes were accurately aligned for bolt installations, improving the assembly efficiency. The proposed

298 Hybrid composite precast systems

TABLE 6.3.1 Design summary of the frame, including structural quantities based on the proposed mechanical connections. Concrete (m3)

PC concrete (m3)

Rebar (tonf)

Steel (tonf)

Plate (tonf)

Bolt (EA)

Nut (EA)

Coupler (EA)

Headed stud (EA)

Quantity

193.63

135.54

22.53

0.39

22.65

1374

1142

2268

831

Quantity/ m2

0.1241

0.0869

0.0144

0.0002

0.0145

0.88

0.73

1.45

0.53

Quantity

45.44

45.44

6.56

1.24

5.63

236

1420

0

1012

Quantity/ m2

0.0291

0.0291

0.0042

0.0008

0.0036

0.15

0.91

0.00

0.65

Total quantity

239.070

181.35

29.15

1.62

28.29

1610

2562

2268

1843

Quantity/ m2

0.1532

0.1160

0.0186

0.0010

0.0181

1.03

1.64

1.45

1.18

Quantity Girder

Column

Total

TABLE 6.3.2 Comparison of construction periods: proposed precast method versus conventional cast-in-place construction. Precast method

Conventional cast-in-place method

Member type

Column (two stories each)

Beam

Number of precast members

42

234

Installation time per 1 member

30 min

1h

Total member installation time

255 h (25 work days)

Prefabrication

14 days

Total construction period

39 days

Construction period per story

15 days

Stories

4

Total construction period

60 days

erection method can be implemented in the construction of low-rise buildings. Table 6.3.2 compares the construction schedule of the building using the proposed method to that which would be required when using the conventional castin-place monolithic method. Each column-to-column connection was expected to take half an hour, and the observed time for each column-to-beam connection was about an hour. Table 6.3.2 also lists an estimate of the total assembly time for erecting one floor following the conventional erection method, showing that 10–15 days would be required to erect one floor, which results in approximately 60 days for entire frame erection when workers were on the job site for 10 h per day. The whole frame could be erected within only 25 days by means of the proposed method, under the same work conditions. Precast frames with joints assembled using mechanically laminated plates can be erected as quickly as steel frames, significantly reducing both time and cost. Another 14 days will be required to prefabricate the 268 precast members (42 columns with two stories, 234 beams); the total construction period of 39 days will demonstrate a schedule reduction of 35%, which would accordingly save labor and operational costs at the construction site.

6.3.4 Reduction of energy consumption and CO2 emissions with the new precast frame Besides reducing the construction schedule, using the construction method yielded both reduced CO2 emissions and increased energy efficiency. Tables 6.3.3 [1] and 6.3.4 [2] list the estimated CO2 emissions for conventional bearingwall-type buildings by components, including pour form, precast concrete, and cast-in-place concrete. Table 6.3.5 summarizes the improved total CO2 emission and energy consumption when the frame with mechanical connections was implemented in the construction of the four-story building. In Table 6.3.5, the conventional use of pour forms was

Novel precast frame for facile construction of low-rise buildings Chapter

6

299

TABLE 6.3.3 CO2 emissions due to the use of concrete and concrete products in bearing-wall and precast buildings [1]. Bearing wall

Precast composite frame (three columns)

6742.0

3916.0

–

905.0

8685.4

8685.4

0.776

0.451

167.7

167.7

CO2 emission per unit area from concrete use (kg-CO2/m )

130.2

75.6

Total CO2 emission from concrete use (kg-CO2)

1,130,839.1

656,616.2

–

0.104

–

82.7

CO2 emission per unit area from concrete product (kg-CO2/m )

–

8.6

Total CO2 emission from concrete product (kg-CO2)

–

74,694.4

Total CO2 emission (kg-CO2)

1,130,839.1

731,310.7

CO2 emission due to concrete and concrete product use as a fraction of total bearing wall type apartment

19.6%

12.7%

Item Total concrete use (m3) 3

Total concrete product (m ) 2

Gross coverage (m ) 3

2

Concrete use per unit area (m /m ) 3

CO2 emission per concrete use (kg-CO2/m ) 2

3

2

Concrete product per unit area (m /m ) 3

CO2 emission per concrete product (kg-CO2/m ) 2

Note: CO2 emission from concrete use was estimated based on the concrete used in a bearing wall apartment and the total concrete amount used in each module of the precast composite frame.

TABLE 6.3.4 CO2 emissions due to the use of formwork in bearing-wall and precast buildings [1]. Bearing wall

Precast composite frame (three columns)

41,834.0

9213.0

8685.4

8685.4

4.817

1.061

4.6

4.6

CO2 emission per unit area from formwork use (kg-CO2/m )

22.2

4.9

Total CO2 emission from formwork use (kg-CO2)

192,815.9

42,558.5

CO2 emission due to formwork as a fraction of total bearing wall type apartment

3.4%

0.7%

Item Total formwork use (m2) 2

Gross coverage (m ) 2

2

Formwork use per unit area (m /m ) 2

CO2 emission per formwork use (kg-CO2/m ) 2

eliminated completely by the method, along with the corresponding CO2 emissions (34,500 kg-CO2). Eliminating the use of pour forms was also estimated to yield construction energy savings of 1802.1 GJ, based on Table 6.3.5. The erection of building frame with precast concrete members also reduced 50% of the total CO2 emission (14,965 kg-CO2) that would be emitted by the use of monolithic, cast-in-place concrete.

6.4 Results and conclusions The implementation of precast joints carried many advantages allowing quick and effortless construction without any corresponding compromises in building performance. The required construction energy was expected to be significantly reduced by eliminating the use of pour forms entirely. The method contributed to the reduction of the construction periods and cost substantially by completely removing the needs of pour forms and concrete casting that were involved in forming monolithic joints. The results of the design offered direct industrial relevance with reliable seismic guidelines for the

300 Hybrid composite precast systems

TABLE 6.3.5 Summary of total CO2 emissions and energy consumption with the proposed frame and mechanical connection (total building area: 1560 m2). Formwork 2

Cast in place concrete

2

3

2

Precast concrete

Use per unit area

4.8 (m /m )

0.116 (m /m )

0.116 (m3/m2)

CO2 emission per application

4.6 (kg-CO2/m2)

167.7 (kg-CO2/m3)

82.7 (kg-CO2/m3)

Total CO2 emission

34,445 (kg-CO2)

30,347 (kg-CO2)

14,965 (kg-CO2)

Energy consumption per application

2

240.67 (MJ/m )

–

–

Total energy consumption

1,802,137 (MJ)

–

–

240.67 MJ/m2

Form-work

1178.57 MJ/m2

Gypsum board

Steel section

4065.78 MJ/kN

Reinforcing steel

3522.22 MJ/kN

2406.39 MJ/m3

Concrete 0

500

1000

1500

2000

2500

3000

3500

4000

4500

construction of precast concrete structures. Design recommendations were presented based on experimental evidence and numerical analyses. Extensive FEAs for the low-rise columns were performed to explore the structural behavior of the frame with mechanical metal plates. Nonlinear finite element models describing the three types of metal mechanical joints for column-to-column, columnto-girder, and beam-to-girder connections were developed to design a low-rise building with multibay precast frames. The structural behaviors of the joints consisting of high-strength bolts, rebars, and steel sections were also evaluated to ensure that they functioned properly, contributing to the flexural capacity. In the design process of the low-rise building, the conventional monolithic, cast-in-place frames of a total of 42 columns and 234 beams were replaced by precast frames with the mechanical joints. The structural behavior of the conventional monolithic frame and that of the frame with mechanical metal plates were similar when the sufficient stiffness of the laminated joint plates was appropriately determined and provided. It was recommended that mechanical joints providing structural performance similar to that of the monolithic frame be implemented with the use of internal bolts, by which strain and deformation of column plates can be effectively reduced. The mechanical joints of this chapter can be used in design with both intermediate moment frames and building frames, however, the proposed frame can be extended to be used with special moment frames when the mechanical joints are deliberately designed. The design of the four-story building adopted intermediate moment frame, providing resistance to the ground motions up to 0.2 g, based on the inelastic design response spectrum, with an R factor of 5 to reduce elastic seismic forces. This chapter demonstrated that significant tension forces that would degrade mechanical joints were not expected for low-rise buildings. The joints with mechanical metal plates should also be suitable for tall buildings when the significant forces at mechanical joints are dealt with carefully. The cast-in-place monolithic concrete was replaced in design with many advantages, including a significant reduction of both CO2 emissions and construction energy use. CO2 emission can be reduced by up to 50% with the mechanical connection for precast frames. The rapid and facile construction of shelters with the dependable budget may be possible to relieve the problems of housing shortages.

References [1] W.K. Hong, J.M. Kim, S.C. Park, S.G. Lee, S.I. Kim, K.J. Yoon, et al., A new apartment construction technology with effective CO2 emission reduction capabilities, Energy 35 (6) (2010) 2639–2646. [2] J.Y. Hu, W.K. Hong, Steel beam-column joint with discontinuous vertical reinforcing bars, J. Civil Eng. Manage. 23 (4) (2017) 440–445.

Chapter 7

Novel pipe rack frames with rigid joints 7.1 Overview of the pipe rack frames introduced in this chapter 7.1.1 The innovated pipe rack frames Pipe racks are well-known prefabricated open-frame structures with braces that are adopted for the modular construction. The modules are preconstructed units that can be easily connected in order to make a larger pipe rack structure. Pipe racks support various types of supplies including pipe-lines, equipment, air coolers, cable tray (electrical cables), walkways, stairs, ladders, and platforms for controlling and maintaining. Steel pipe rack frames with pinned connections require braces that resist both gravity and lateral loads. In some applications, the steel pipe racks are encased in concrete for fire protection, which is not, however, designed to offer structural support since no rebars are placed to perform composite actions with the surrounding concrete. This chapter proposes innovated types of novel frames having rigid joints for pipe racks, and explores their structural performance. In the first type, steel-concrete hybrid frames with monolithic rigid beam-column connections were implemented in which wide flange or T shaped steel sections are encased in structural concrete to save steel tonnages. Beam-column connections may not be cast with concrete to contribute to rapid constructions when proper fire-proof were provided to protect the steel joints. The second type of precast concrete frames with detachable laminated joint plates contributed to both flexural strength and fireproof. The detachable mechanical joints were designed based on a nonlinear inelastic finite element analysis. In Chapters 2 and 3, significant experimental and numerical investigations were conducted to verify the structural performance of the mechanical connections. Tertiary frame proposed to replace the conventional pipe racks is prestressed precast frames. In Fig. 7.1.2D, the pipes are placed in a saddle in which frictions between the pipes and a saddle occur whereas the pipes are clamped in anchor type where the movements are constrained.

7.1.2 Overall historical development, advantages and challenges of existing pipe rack frames A significant number of studies by various groups have discussed the overall historical development, advantages and challenges, trends, healthy monitoring process, and implications of steel pipe racks. Annan et al. [1] studied the strength, stiffness, inelastic force, deformation, and energy dissipation of modular steel-braced frames. In their research, test specimens were calibrated in order to verify the reliability of the results obtained from the analytical investigation. They found that steel-braced frames demonstrated good ductile behavior when cyclic loadings were applied to the test specimens. In previous studies, the same group conducted an analytical investigation of semirigid floor beam connections in modular steel structures [2]. Several other studies including Tremblay et al. [3] were conducted to examine various parameters including the buckling strength of the bracing members, the inelastic response of braced structures, and the lateral deformations of the braces upon buckling. Later, Yoo et al. [4] conducted an experimental and numerical investigation (FE model) to determine the frame ductility and concentration of plastic strains at various locations on a member and the welds. Significant studies were carried out to predict the behavior of bolted beam-to-column extended endplates. Vahid et al. [5] calculated the performance of bolted connections as a function of the thicknesses of the endplates and T-stub flange using a numerical method. They concluded that the performance of bolted T-stub connections was more sensitive to component thickness than endplate connections. Jingfeng et al. [6] investigated the effect of endplate thickness and the column section type on the static behavior and failure modes of connections. They pointed out that the strength and stiffness of the connections can be improved by providing anchorage extensions on the blind bolts. They also showed that the use of moderately thick endplates led to extended endplates connections that provided almost full strength. Bedair et al. [7] introduced some industrial guidelines for designing steel pipe racks. These guidelines included a recommendation for optimizing a design for structural applications by refraining from the use of excessive member size. To understand better the structural performance of pipe rack modules, Wong et al. [8] compared design wind load calculations for pipe rack structures based on Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00007-8 © 2020 Elsevier Ltd. All rights reserved.

301

302 Hybrid composite precast systems

FIG. 7.1.1 Conventional and hybrid composite steel pipe rack.

seven international codes and standards. They provided several recommendations for using the standard to calculate wind loads on pipe rack modules. Richard et al. [9] summarized the building codes and design criteria for industrial practice, design loads, and other design aspects for pipe racks. Conventional design guidelines of the steel pipe rack have been developed to modernize structural steel design and construction systems. Joint connections, including bolted extended endplates were generally designed as pinned joint in the pipe rack industry, which were not able to transfer the moment through interconnected steel components. Steel pipe rack frames can be assembled with pinned connections to rapidly cope with design changes. The conventional steel (Fig. 7.1.1A), concrete (Fig. 7.1.1B), and hybrid pipe rack (Fig. 7.1.1C) frames are shown in Fig. 7.1.1 where the steel pipe racks are the most conventionally used, whereas precast pipe racks started being constructed recently. In some cases, hybrid precast pipe racks were used to replace the steel frames, providing a robust frame system again harsh environment. Nonprestressed precast stanchions supported pipe-lines in Uzbekistan as shown in Fig. 7.1.1D), whereas Fig. 9.2.38 of Section 9.2.4 illustrates prestressed precast frames which can span longer supporting heavy loads.

7.1.3 Significance of the pipe rack frames with rigid joints; motivations and objectives In Fig. 7.1.2A, how the pipe rack frames can be innovated is presented when the steel pipe rack frames are fabricated with pinned connections to cope rapidly with design changes, such as unexpected alterations of equipment including air coolers, cable tray (electrical cables), and pipe-lines. As shown in Fig. 7.1.2B, the conventional practices of using concrete or FRP cover for fireproof of steel pipe racks require pour forms. However, structural strength is not contributed by the concrete in

Novel pipe rack frames with rigid joints Chapter

FIG. 7.1.2 Conventional and composite steel pipe rack with concrete cover.

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304 Hybrid composite precast systems

conventional pipe rack frames because no proper reinforcements are placed to interact with the surrounding concrete, only providing fireproof for conventional steel pipe rack frames. The pinned joints require braces to resist gravity and lateral loads, causing large moment demand at the mid-span of the beams. Innovative novel frames for pipe racks are suggested in this chapter. In Fig. 7.1.2C, the first type of pipe rack frame uses steel-concrete hybrid composite frames with monolithic rigid beam-column connections, which are discussed in Section 7.2. The steel frames encased in concrete with rigid joint are similar to steel pipe racks shown in Fig. 7.1.2B, except that the precast concrete section provides load-resisting capacity because reinforcements are placed in the concrete. In Fig. 7.1.2C hybrid composite precast frames contributed to both load resisting structural capacity and fireproof. The second type of frame implements mechanical joints having detachable laminated joint with assembly and disassembly capability to cope with sudden design changes. Traditional steel joints using endplates were modified for the use in steel-concrete composite precast frames and reinforced concrete precast frames with rigid joints. Joint details for the proposed rigid mechanical connection were designed based on AISC 358 (2005) [1, Chapter 2]. The mechanical joints with laminated plates would transfer the moment with unnoticeable plate deformations when joint plates with sufficient stiffness and strength were provided, demonstrating structural behavior similar to those of rigid monolithic joints. Additional explanation of the mechanical joints can be found in Chapters 2 and 3. The third type of pipe rack structure implements prestressed precast frames. These rigid frames for pipe rack structures highlighted the contributions to the structural strength, fireproofing, and a significant reduction in the amount of steel (over 70%), as compared to the steel pipe rack frames with pinned joints.

7.2

Novel pipe rack frames with rigid joints

7.2.1 Precast concrete-based pipe rack frames with rigid monolithic beam-column connections Fig. 7.1.2 compares steel frames having conventional concrete covers with the proposed composite steel pipe racks. The concrete cover in the steel pipe rack depicted in Fig. 7.1.2B provides only fire protection. The concrete covers do not offer load resisting strength because no proper reinforcements are included to interact with the surrounding concrete. Concrete is used for fireproof only in most conventional steel pipe rack applications. However, pipe rack frames encased in concrete in Fig. 7.1.2C are similar to pipe racks in Fig. 7.1.2B except the precast concrete section, utilizes the structural strength of the concrete. In the pipe rack shown in Fig. 7.1.2C, reinforcements are placed in the precast concrete to provide both load resisting structural capacity and fireproof. The rigid monolithic joints with steel-concrete composite joints are implemented to replace steel pipe rack frames. In Fig. 7.2.1, four types of steel pipes rack frames encased in structural concrete with rigid monolithic beam-column connections are illustrated. T shaped steel sections are shown in Fig. 7.2.1A and B, whereas wide flange steel frames are introduced in Fig. 7.2.1C and D. Steel sections shown in Fig. 7.2.1A and C are used at the entire span of the beams; however, in Fig. 7.2.1B and D, steel sections are placed at each end of the beams. The assembly methods shown in Fig. 9.4.3 of Chapter 9 and Fig. 7.2.6A of this chapter using L type guide angles can also be implemented for rapid and facile assembly of the beams. This type of connection can be disassembled to meet sudden design changes as quickly as possible. Fig. 7.2.1A-(4) illustrates moment connection for transverse direction, along which heavy pipe loads are supported. For longitudinal direction, pipe loads are not as heavy as the loads on a transverse direction. Longitudinal braces shown in Fig. 7.2.1A-(3) are inevitable when shear beam-column joint connections are implemented. Concrete can be cast at beam-column joints to form steel-concrete composite monolithic connections. However, the steel sections of the pipe rack frames at the joint can be exposed without concrete being cast when proper fireproof are provided to protect the steel joints. This option may offer rapid construction at the cost of increased steel at joints. The selection of the structural type should be made based on the considerations, including the overall steel tonnages and construction schedule. In Section 7.3.4, the structural quantities, including steel tonnages, were compared to identify the frame system that required the lowest steel quantities.

7.2.2 Precast concrete-based pipe rack frames with rigid mechanical joints This chapter proposes precast concrete-based pipe rack frames with detachable laminated joint plates, which can provide structural strength, contributing to flexural capacity and fireproof as well. Extensive experimental and numerical investigations were conducted in Chapters 2 and 3 to verify the structural performance of the proposed composite pipe rack frames having rigid mechanical joints with detachable endplates. Structural behavior of the novel mechanical connections was also examined by nonlinear finite element analysis considering damaged concrete plasticity.

FIG. 7.2.1 See figure legend on page 307.

FIG. 7.2.1, Cont’d

Novel pipe rack frames with rigid joints Chapter

FIG. 7.2.1, Cont’d Composite pipe rack frames with rigid monolithic joints.

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308 Hybrid composite precast systems

7.2.2.1 Frame module for easy assembly by the use of mechanical joints In Fig. 2.2.1B of Chapter 2 and Fig. 7.2.5A of this chapter, precast concrete-based frames with endplates are shown with or without steel sections encased in concrete. Steel-concrete composite frames shown in Fig. 7.2.5 also highlight the advantages of the suggested novel method, which utilized the structural strength of the concrete with fireproof capability, eliminating pour forms for concrete cast on site by introducing precast concrete. Implementing rigid moment connections also removes braces from steel pipe racks, reducing steel tonnage, and distributing large mid moments demand to both fixed ends with reduction of additional steels. Loads acting on the endplates, the design of joint components including plate thickness, and positions of bolts are identified in Figs. 2.2.6 and 2.3.1 of Chapter 2, for beam-column and column-column joints, respectively.

7.2.2.2 Assembly sequence Assembly sequence proposed for the entire pipe rack frames are illustrated in Fig. 7.2.2 in which -shaped basic monolithic beam-column modules were assembled vertically and horizontally to form an entire multifloor pipe rack frame. The

FIG. 7.2.2 Assembly sequence of the monolithic module for pipe-rack frame; entire pipe rack frames.

Novel pipe rack frames with rigid joints Chapter

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309

beam-column joints of the basic frame modules are monolithically manufactured with fully restrained moment connection. Test erection of monolithic frame modules, which are spliced vertically by interlocking couplers or bolted plates, are shown in Fig. 7.2.3 [1, Chapter 5] and Fig. 7.2.4 [2, Chapter 1], respectively. The test assembly and disassembly of columns are conducted in Fig. 7.2.4, where the rapid and facile erection of the precast concrete-based columns are demonstrated by bolting laminated base and cap plates in the preinstalled holes. Fig. 7.2.4C demonstrates that the bolted connection required only 20 s to unfasten 20 high strength bolts in disassembling the specimens after structural tests. This allows for timely management of unexpected design changes frequently seen in the pipe rack assembly. Monolithic basic frame modules, shown in Fig. 7.2.2, were also assembled horizontally by interconnecting extended beam endplates with plates embedded in columns by high strength bolts, as shown in Fig. 7.2.5. Beam endplates are guided by slots in Fig. 7.2.5C and D. Installation tests of full-scale composite precast frames with mechanical column-to-beam connections are illustrated in Fig. 7.2.5E. Automated construction procedures were introduced with endplates and 5-mm thick filler plates for the assembly of column-to-beam connections. These joint bolts had to be disassembled easily and rapidly to accommodate sudden design changes that may occur during the fabrication of pipe racks. Another type of horizontal connection of the modules is illustrated in Fig. 7.2.6, in which difficult horizontal fits are prevented as much as possible (see Section 9.4 of Chapter 9). Basic frame modules can also be connected horizontally by the steels with skew web, shown in Figs. 7.2.6A and B, in which beam steels with skew web are placed and connected in L-type guide pockets preinstalled to column brackets, as shown in Fig. 7.2.6B. In Fig. 7.2.6C, the beam was placed in L-type guide pocket while not supported by the crane, allowing bolting off the critical path. Figs. 7.2.7A and B display stacked modules, which utilize mechanical joints for reinforced concrete precast and hybrid frames, respectively. The simplified connections can be implemented in the precast frames for both pipe rack construction and in the construction of buildings. Further description of the erection test for precast-based frames with mechanical joints and L-type guide pockets for steel-concrete composite beams can be found in Chapters 4 and 9, respectively.

7.2.2.3 Numerical investigation The experimental investigations to explore the structural performance of the mechanical joints using laminated metal and concrete plates were described in Chapter 2. Readers can consult this chapter for the test details to find the load-carrying capability of the precast based pipe rack frames. In Chapter 3, the finite element model of the mechanical joint details, including column-to-beam and column-to-column connections was presented, where the structural performance of extended beam endplates, column plates, couplers, rebars anchored in the column plates, and high strength bolts was explored. Fig. 3.3.12 of Chapter 3 (refer to Fig. 7.2.4 of this chapter) and Fig. 3.2.6 of Chapter 3 (refer to Fig. 7.2.4 of this chapter) present the precast concrete-based frames with their numerical investigations and test erections. The joint plates assembled by high strength bolts were shown. Stresses in high strength bolts and beam endplates provided important data for the design of precast concrete-based mechanical joints. The structural behavior in the microscopic level of bolts and endplates were explored. The strains of bolts were 0.0029 and 0.0036 at a concrete strain of 0.003 for the Specimen B5

FIG. 7.2.3 Vertical connections by interlocking coupler [1, Chapter 5].

310 Hybrid composite precast systems

Plate connection

(A)

Erection for laminated column-to-column connection [2, Chapter 1]

(B)

Nuts in couterbores anchoring rebars Detached plate Detached bolt holes

(C)

Quick disassembly after structural test

FIG. 7.2.4 Vertical connections using laminated plates.

(beam-to-column joint using 20-mm thick beam plate) and C5 (column-to-column joint using 20-mm thick column plate), respectively, as shown in Figs. 3.3.13A and 3.2.7A of Chapter 3, respectively. The strains of plates were also computed as 0.0015 and 0.0024 at a concrete strain of 0.003 for Specimens B5 and C5, respectively, as shown in Figs. 3.3.13B and 3.2.7B of Chapter 3, respectively. The strains found in plates and bolts are considered suitable for the use in pipe rack frames. Deformation of beam endplate due to the tension was numerically calculated to be 16.2 mm (refer to Fig. 3.3.12B) at a stroke of 115 mm for Specimen B5, which compared well with the test results, as shown in Fig. 3.3.12C of Chapter 3. In Fig. 3.2.6B of Chapter 3, deformations of the column plates above and below were also calculated as 5.3 and 16.7 mm, well correlated with the test results. The failure patterns of the proposed mechanical joints were also elicited. In Chapters 2 and 3, the detailed experimental and numerical investigation based on

Novel pipe rack frames with rigid joints Chapter

Concrete

End plate Steel

Stirrup

[Beam unit]

Concrete

End plate

Stirrup

(A)

Rebar

Rebar

[Beam unit]

Precast concrete and composite precast beams with extended end plates; SRC and RC

Bolt holes interconnecting plates

Nuts anchoring rebars

Plate mechanical joint

(B)

Detail of the mechanical joint using extended end plates and nuts anchoring rebars; rebar end threaded with nuts on the beam end plates

FIG. 7.2.5 See figure legend on next page.

7

311

FIG. 7.2.5, Cont’d Erection of beams using extended beam end plates.

Novel pipe rack frames with rigid joints Chapter

(A)

(B)

Lifted for installation and guided/placed into the pre-installed L-type angles; web preparation (refer to Fig. 9.4.3B-(2), Fig. 9.4.4A-(2) of Chapter 9)

(C) FIG. 7.2.6 Erection of beam steels with L-type pockets; horizontal connections.

7

313

314 Hybrid composite precast systems

FIG. 7.2.7 Module connections for stacked modules.

nonlinear finite element analysis considering damaged concrete plasticity can be found for further understanding of the performance of frames assembled by mechanical connecting plates for the use in pipe rack frames.

7.2.3 Pipe-racks with prestressed frames The third type of pipe rack structure implements prestressed precast frames, as shown in Fig. 7.2.8 (refer to Fig. 9.2.38 of Section 2.5 of Chapter 9). The 400 mm deep and 350 wide precast beams span 9 m long, with deflection of L/270 while supporting a load of 45 kN m when they are pretensioned.

7.2.4 Rigid steel frames Figs. 9.4.2 and 9.4.3 of Chapter 9 demonstrate web preparation and rigid steel joints having L type guide angles. The column brackets were welded or bolted to column steels. The fast assembly of the beam-column connection was demonstrated in the erection test (refer to Section 9.4.2 of Chapter 9). In Fig. 7.2.9, the rigid steel frames removed entire braces required by the pinned steel frames, substantially reducing structural steel tonnages and corresponding construction schedule. The pipe rack engineers may verify the advantages of having rigid joints leading to the reduction of the construction quantities.

7.3

Case study

7.3.1 Steel-concrete hybrid composite precast frames with moment connections Fig. 7.3.1A and B present typical steel pipe rack frames with a nonstructural concrete cover used only for fireproof. Extensive braces were required to support both lateral and vertical loadings since steel joints were assembled having pinned

Novel pipe rack frames with rigid joints Chapter

FIG. 7.2.8 Prestressed precast beam monolithically integrated with columns.

FIG. 7.2.9 Steel frames with moment connections.

7

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316 Hybrid composite precast systems

FIG. 7.3.1 Pinned steel pipe rack frame with braces and nonstructural concrete cover.

Novel pipe rack frames with rigid joints Chapter

7

317

TABLE 7.3.1 Material data. Material data 0

Concrete fc , light weight 1.4 tonf/m3

Reinforcement (yield strength, fy)

Steel (yield strength, fy)

300  300

21 MPa

500 MPa

325 MPa

350  450

21 MPa

500 MPa

325 MPa

500  500

21 MPa

500 MPa

325 MPa

Size Beam

Column

joints in order to quickly respond to design changes that may arise during the assembly of the pipe racks. Table 7.3.1 presents material data for the new composite precast pipe rack frames introduced in the case study. Vertical and lateral braces were not used in the pipe rack with composite precast frames, shown in Fig. 7.3.2A, owing to the joints being capable of the resisting moment. Gravity loads (18 kN m) by pipes with seismic loads are exerted on transverse beams. In Fig. 7.3.2B-(1) and (2), the moment demands required by a pinned frame are compared with those obtained by moment frame, indicating that larger moments at the mid-span found from pinned frames led to large structural members. At mid-span, the composite frames, having fully restrained moment connections, showed only 33% of moment demand required by a pinned frame. The moment of 172.9 kN m at mid-span of the steel beams with pinned joints was distributed to both beam ends of rigid composite beams, reducing it to a moment of 122.2 kN m, which resulted in 57.4 kN m at the mid-span. This reduction in moment demand, subsequently, made the composite frames economical with structural stability. In Figs. 7.3.3 and 7.3.4, the beam and column dimensions of the steel pipe rack frames with pinned joint in both directions are compared with those of the precast composite pipe rack frames having rigid joints. Steel members with H and T sections used for composite precast beams without braces are shown in Figs. 7.3.3 and 7.3.4, respectively. The concrete encasing steel sections used to protect frames from the fire also interacted with the steel frames in the new frames, contributing to providing structural capacity and lateral stability. Rebars, steel, and concrete dimensions of hybrid frames were determined when steel beams are used over the entire span or at each end of the beam. Column section designed to resist loads is also illustrated in Fig. 7.3.3B, which was compared with the dimensions of the column used with frames having pinned joints in both directions. In Fig. 7.3.3A-(1), moment ratios defined as the factored moment demand divided by the design moment strength were 99.4% and 89.2% at end and mid-span for transverse direction, respectively when steel section was used in the entire span of the beam. These ratios were 99.4% and 91.2% when steel section was used at each end of the beam. Moment ratios of longitudinal beam presented in Fig. 7.3.3A-(2) were small because beams along with longitudinal direction were not primarily responsible for supporting vertical loads. A similar comparison for column steel was presented in Fig. 7.3.3B with moment ratio of 45.3%. The steel frame sizes implemented in composite beams and columns shown in Fig. 7.3.3 for H steel section and in Fig. 7.3.4 for T steel section were significantly reduced when they are compared with steel frames with pinned joints. In Figs. 7.3.5–7.3.7, the deflections of the pinned pipe racks resulted from gravity, and lateral loadings were compared with those of composite precast frames having rigid connections with steel beams installed in the entire beam span. In Fig. 7.3.5A, in which composite beams with steel beams in entire span are used, the vertical deflections of 6.354 mm (L/944) for transverse direction were acceptable by the code for pipe racks. The lateral deflections of the frames due to seismic loads were 1.813 mm (L/3201) and 1.806 mm (L/3214) for longitudinal and transverse directions, respectively, as can be seen, in Fig. 7.3.5B and C. The deflections of the rigid steel frames and pinned frames were also demonstrated in Figs. 7.3.6 and 7.3.7, respectively. It was noticed that the proposed rigid pipe rack frames without braces exhibited lateral deflections similar to those observed by the pinned steel frames with braces. However, it was noted that the vertical deflection of the pinned frame reached 27 mm (refer to Fig. 7.3.7A), which was greater than 6.354 mm (refer to Fig. 7.3.5A) reached by hybrid composite frames with H-shaped steel section and 4.3 mm (refer to Fig. 7.3.6A) reached by rigid steel section without concrete section, as summarized in Table 7.3.2, indicating that braces on horizontal plane shown in Fig. 7.3.1B did not provide enough stiffness due to gravity loads. For composite frames, the concrete covers integrated with rebars, which were placed in the concrete, contributed to the decrease of beam deflections. The mid-moment of the beam, which was distributed to the ends, also decreased beam deflection. In both directions, the deflections were efficiently reduced by the composite actions. The piperacks with precast frames without integrated steel sections reached

318 Hybrid composite precast systems

FIG. 7.3.2 Moment demand.

Novel pipe rack frames with rigid joints Chapter

FIG. 7.3.3 See figure legend on page 321.

7

319

320 Hybrid composite precast systems

FIG. 7.3.3, Cont’d

Novel pipe rack frames with rigid joints Chapter

7

321

FIG. 7.3.3, Cont’d Frame sizes with steel (H section)-concrete composite precast frames without braces.

6.7 mm (L/891) vertically, and 1.810 mm (H/3207), 1.857 mm (H/3126) along with transverse and longitudinal directions, respectively. The seismically induced vertical and lateral deflections of the precast concrete pipe rack are summarized in Table 7.3.2.

7.3.2 Dynamic characteristics The periods and mode shapes of all types of frames proposed for pipe racks in this chapter were explored. In Table 7.3.3, the first three modes are presented where the lowest fundamental period was found as 0.14 s from the rigid steel frames. The fundamental period of the pinned steel structure and those of the other frames were around 0.18 s. All modes were well separated in three directions (two translational modes and one rotational mode). It was noticed that the proposed rigid pipe rack frames without braces exhibited dynamic characteristics similar to those observed by the pinned steel frames with braces.

7.3.3 Suggestion for rapid construction based on the fast track using the proposed frames Frames can be over-sized intentionally to cope with design changes as fast and easy as possible, avoiding needs for disassembling and re-construction which are caused by the unexpected alterations of the superimposed loads on the frames. The ranges of load changes (increases) need to be estimated with reliability based on occurrences of such occasions. In Fig. 7.3.8, the fast track assembly is illustrated, in which reduced schedule was obtained despite the design changes indicated in the scheduling chart. The design changes do not influence overall construction schedule which would have significantly been delayed in conventional steel frames. The structural construction quantities may increase; however, the saving of the construction quantity by having rigid frames will make surplus construction eventually.

7.3.4 Structural savings In Figs. 7.3.3 and 7.3.4, the new pipe racks with composite frames having rigid joints were verified efficient in reducing construction material quantities. The concrete encasing steel frame in the new pipe rack frames provided more than just fireproof, resulting in a significant reduction of the construction materials. In Table 7.3.4, it is shown that the quantities of

322 Hybrid composite precast systems

FIG. 7.3.4 See figure legend on opposite page.

Novel pipe rack frames with rigid joints Chapter

FIG. 7.3.4, Cont’d Frame sizes with steel (T section)-concrete composite precast frames without braces.

7

323

324 Hybrid composite precast systems

FIG. 7.3.5 Displacement by gravity and seismic loads; composite beams with steel beams in entire span.

Novel pipe rack frames with rigid joints Chapter

FIG. 7.3.6 Displacement by gravity and seismic loads; rigid steel frames.

7

325

326 Hybrid composite precast systems

FIG. 7.3.7 Displacement by gravity and seismic loads; conventional steel frames with braces.

Novel pipe rack frames with rigid joints Chapter

7

327

TABLE 7.3.2 Seismic deflection summary. Vertical

Lateral (transverse)

Lateral (longitudinal)

1. Composite frame; Rigid monotonic joints (mechanical joints) (1) Steels in all span H-shaped steels

6.354 mm (L/944)

1.806 mm (H/3214)

1.813 mm (H/3201)

T-shaped steels

N/A

N/A

N/A

H-shaped steels

N/A

N/A

N/A

T-shaped steels

N/A

N/A

N/A

(1) Rigid joints

4.262 mm (H/1408)

2.393 mm (H/2426)

1.158 mm (H/5013)

(2) Pinned joints

27.26 mm (L/220)

2.091 mm (H/2776)

0.572 mm (H/10148)

3. Concrete frame (transverse direction)

6.729 mm (L/891)

1.810 mm (H/3207)

1.857 mm (H/3126)

(2) Steels at each end

2. Steel frame (transverse direction)

TABLE 7.3.3 Dynamic characteristics. 1st mode

2nd mode

3rd mode

1. Composite frame; Rigid monotonic joints (mechanical joints) (1) Steels in all span H-shaped steels

0.1804

0.1773

0.1628

T-shaped steels

N/A

N/A

N/A

H-shaped steels

N/A

N/A

N/A

T-shaped steels

N/A

N/A

N/A

(1) Rigid joints

0.1449

0.0741

0.0738

(2) Pinned joints

0.1820

0.1154

0.0994

3. Concrete frame (transverse direction)

0.1821

0.1775

0.1630

(2) Steels at each end

2. Steel frame (transverse direction)

structural material were significantly saved compared with those of steel pipe racks when the pipe racks with hybrid composite frames having rigid steel joints were used. The steel sections with wide flange and T shaped steel sections were implemented with concrete to replace the steel pipe rack frames. Significant material savings were realized when the interaction of rebars with surrounding concrete was introduced to contribute to the structural capacity for pipe racks. Table 7.3.4 also elicits reduced structural quantity obtained by precast concrete pipe racks with rigid connections using concrete of 40 MPa without steel sections. A significant amount of steel reduction was observed with all precast composite frames at the cost of the use of the additional materials, such as concrete and rebars. Extensive braces removed by rigid precast composite frames also contributed to these reductions. The series of case studies shown in Table 7.3.4 demonstrates a reduction in the amount of steel of over 20% compared to that of steel pipe rack when rigid precast composite frames were employed.

328 Hybrid composite precast systems

FIG. 7.3.8 Fast track construction based on the proposed frames.

TABLE 7.3.4 Reduction of material quantity of pipe racks with rigid composite frame and precast concrete versus a pinned steel pipe rack frame. Pipe rack frame with fire-proofing (total) H-shaped steel

Frame type

T-shaped steel

End H-shaped steel

End T-shaped steel

fc ¼ 21 MPa, fy ¼ 500 MPa, Fy ¼ 325 MPa

3

Rigid steel frame (both directions)

fc0 ¼ 40 MPa, fy ¼ 500 MPa

0

Components

Precast frame

Concrete (m )

21.1

21.1

21.1

21.1

21.1

0

Rebar (kgf)

2026.2

2531.6

2159.4

2119.6

2292.9

0

Steel (kgf)

8998.1

8062.1

7477.1

7504.1

–

14,161.5

Rebar + Steel (kgf)

11,024.2

10,593.7

9636.4

9623.6

2292.9

14,161.5

Comparison with rigid steel pipe rack (% reduction)

Concrete

57.2% reduction

–

–

Rebar

–

–

–

Steel

36.5% reduction

43.1% reduction

47.2% reduction

47.0% reduction

–

–

Rebar + Steel

22.2% reduction

25.2% reduction

32.0% reduction

32.0% reduction

–

–

7.3.5 Offsite modular construction with base template A base template was suggested to provide efficient offsite modular construction, as depicted in Fig. 7.3.9. The precast composite pipe rack frames can be assembled on the template, which eliminated conventional foundations used for construction. A damper can also be inserted in the template to reduce vibrations experienced during transportation, thus stabilizing pipe rack modules against unexpected damage to frames. Templates adjusted to the size of the pipe racks can be reused for repeated trips, making the template economical in the long run. In Fig. 7.3.9, the pipe racks are disassembled from the template for the stacks of the modules.

Novel pipe rack frames with rigid joints Chapter

7

329

FIG. 7.3.9 Offsite modular construction using base template.

7.4 Conclusions Innovated frames for pipe racks having rigid joints were suggested in this chapter; the proposed hybrid rigid frames may replace steel frames for the offsite modular construction with facile assembly/disassembly capability. The proposed frames for pipe racks are steel-concrete hybrid composite frames with monolithic rigid beam-column connections, hybrid frames implementing mechanical joints having a detachable laminated plated, prestressed precast frames and steel frames with moment connection. The fully restrained steel moment connections can be assembled without concrete cover at the joint, allowing quick response to design changes that may arise during construction. Entire braces required by the pinned steel frames were removed. Beams of a long span with shallow depth supporting heavy loads can be realized by the prestressed precast pipe rack modules having monolithic beam-column joints. The proposed fast track method can even remove the necessity for correcting frames when the needs for design changes occur. Structural steel tonnages and corresponding construction schedule were able to be saved by implementing the rigid joints. The advantages leading to multiple merits may be verified by the piperack engineers who will use them.

References [1] C.D. Annan, M.A. Youssef, M.H. El Naggar, Experimental evaluation of the seismic performance of modular steel-braced frames, Eng. Struct. 31 (7) (2009) 1435–1446. [2] C.D. Annan, M.A. Youssef, M.H. El-Naggar, Analytical investigation of semi-rigid floor beams connection in modular steel structures, in: 33rd Annual General Conference of the Canadian Society for Civil Engineering, 2005. [3] R. Tremblay, Inelastic seismic response of steel bracing members, J. Constr. Steel Res. 58 (5) (2002) 665–701. [4] J.H. Yoo, C.W. Roeder, D.E. Lehman, Analytical performance simulation of special concentrically braced frames, J. Struct. Eng. 134 (6) (2008) 881–889.

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[5] S.Z. Vahid, S.A. Osman, A.R. Khalim, Monotonic and cyclic loading simulation of structural steelwork beam to column bolted connections with castellated beam, J. Eng. Sci. Technol. 8 (4) (2013) 416–427. [6] J. Wang, X. Chen, J. Shen, Performance of CFTST column to steel beam joints with blind bolts under cyclic loading, Thin Wall. Struct. 60 (2012) 69–84. [7] O. Bedair, Modern steel design and construction in Canada’s oil sands industry, Steel Construct. 7 (1) (2014) 32–40. [8] S. Wong, E. Wey, C. Letchford, K. Kernaghan, A. Yesare, A comparative study of international wind load standards for pipe rack modules, in: Structures Congress 2015, ASCE, 2015, pp. 1975–1986. [9] R.M. Drake, R.J. Walter, Design of structural steel pipe racks, AISC Eng. J. 47 (4) (2010) 241–252.

Chapter 8

Application to the modular construction 8.1 Overview of the modular construction for low-rise buildings Modular construction refers to a process in which building components are constructed off-site. These components are then transported as a completed component to a building site. The modular construction institute reported that modular construction allowed projects to be completed in a half the time of the conventional construction, with the conclusion that the modular construction eliminated weather delays because 60%–90% of the construction work was achieved inside the factory. Modular construction institute [1] showed modular structures of being lifted and assembled. Easier construction management, improvement of safety and security, sustainable designs, and substantial reduction in the construction period can be offered by the modular construction. Schoenborn [2] suggested the use of modular construction to save construction time compared with that of the site-built construction schedule. Although the conventional modular construction shortens the construction period, the modules were not suitable for high-rise building systems. In general, these conventional modular constructions were limited to low-rise residential buildings, implying that they may lack proper moment connections to resist wind and seismic forces for the high-rise structures. The design of the high-rise buildings requires special treatments against moments caused by the combination of wind and seismic loads. The adequate connections for modular high-rise construction are introduced in Section 8.2.4 and 8.4.

8.2 Conventional modular construction 8.2.1 Structural and connection systems Lacey et al. [3] classified connections into three types: inter-module, intra-module, and module to the foundation. Lacey et al. [3] also summarized the structural systems and materials used in recent modular buildings. The most frequently used structural material for modular buildings [4–8] is light steel. The modular building design [9] were also introduced for high-rise building applications [10, 11]. Table 8.2.1 provides a summary of the connections for steel, showing that an inter-module connection can also be assembled by a skeletal structure with concrete-steel composite frames [7, 10, 11]. For modular construction, a primary steel or concrete structure was combined as a podium, skeletal structure, or a concrete core around which modules were arranged.

8.2.2 Cellular-type modules and intra-module connection (Fig. 8.2.1) [3] The term modular construction refers to a construction process in which individual “modules” are manufactured off-site within a well-controlled plant environment. Steel modules are prefabricated in the construction factory to form one unified structure (cellular-type modules), as shown in Fig. 8.2.1 [3]. Endplates or deep fin plates for lateral stiffness are commonly utilized to create the moment-resisting connections of the modules for the use in low rise buildings (refer to the design in modular construction by Lawson et al. [12]). The details of the intra-module connection used in low rise buildings shown in Fig. 8.2.1 are not suitable for high-rise building systems because they may lack proper moment connections against lateral loads.

8.2.3 Inter-module connection [1] Park et al. [13] emphasized the importance of the connection between modules, which is critical to the structural stability of the modular buildings. However, the investigations on these connection systems were limited. Lacey et al. [3] reported that horizontal connections (HC) between adjacent modules next to each other, and vertical connection (VC) between stacked modules, were assembled at the site by bolted connection, preferred over site welding. Modules fixed to braced steel cores Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00008-X © 2020 Elsevier Ltd. All rights reserved.

331

332 Hybrid composite precast systems

TABLE 8.2.1 Module classification [3]. Category

Applications

Advantages

Disadvantages

Steel-MSB module

Hotel, residential apartments

Suited to high-rise buildings, high strength

Corrosion, lack of design guidance

Steel-Light steel framed module

Max. 10-story, 25-story with additional core

Lightweight

Suited to low rise buildings

SteelContainer module

Postdisaster housing, military operations, and residential developments

Recycle shipping containers, easy transport

Additional reinforcing required to strengthen container when openings are cut in wall

Precast concrete module

Hotel, prison, secure accommodation

Fire resistance, acoustic insulation, thermal performance, high mass helps meet vibration criteria, high capacity

Heavy, potential cracking at corners

Timber frame module

1- to 2-story, education buildings, housing

Sustainable material, easy to fabricate

Poor fire resistance, durability

FIG. 8.2.1 Application of modular construction to low-rise buildings; intramodule connection [3].

(inter-module connections) to resist lateral loads were illustrated in [1]. Vertical gaps between the floor and ceiling beams were usually provided to allow external access to inter-module connections. Sufficient rooms should be provided to accommodate the bolted connection of the modules stacked in all directions, ensuring access to fasteners. Gunawardena et al. [14] suggested that the tolerance accumulation over the multiple levels, and the vulnerability to slip failure in the event of large horizontal forces, can be treated by long slotted holes. Friction-grip or pretensioned bolts can be used to control the connection slip. Concrete or grout was used to lock the joint in place, creating a composite concrete-steel connection. Readers are referred to Table 4 of the study by Lacey et al. [3] which summarized inter-module connections for the steel modules of the literature, and identified the numerical and experimental investigation of the structural behavior of these connections.

8.2.4 Application of the modular construction to high-rise buildings Lawson et al. [9, 10] presented a review of the modular constructions that were widely used in Europe for high-rise residential buildings. They pointed out that the existing modular construction of the cellular-type buildings demonstrated

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(1) Modules clustered around a core [10]

(2) Use of concrete cores to resist lateral forces; lateral stability for modular buildings [10]

(A)

Cluster arrangement

FIG. 8.2.2, Cont’d

primary advantages, including construction speed, quality control, and reduction of construction waste. In most applications, the cellular-type buildings were reinforced with concrete or steel cores to ensure their resistance to horizontal forces. Modules were fastened at their corners to assure that they acted together to transfer lateral forces, and to offer an alternative load path in the case when one module experienced severe damage. Lawson et al. [9, 10] reported that the structural performance of the conventional modules was complex due to many reasons including tolerances used during the installation process, the existence of many connections between modules, and unclear loading path. They concluded that proper connections capable of resisting both gravity and lateral loads were required for the structural safety of tall buildings. The importance of the inter-module connection was also emphasized by Park et al. [13]. For tall buildings, the concrete cores were commonly used to offer the lateral stability of the modules. Lawson et al. [9, 10] presented two types of the module arrangements that were commonly used in high-rise buildings. In the first module arrangement (cluster arrangement), the modules clustered around the concrete cores, as shown in Fig. 8.2.2A-(1) [10]. The lateral resisting connection between modules and the concrete cores was established by tying them via cast-in plates in the core, as shown in Fig. 8.2.2A-(2) [10], which depicts a 25-story building of the cluster type. In the second module arrangement (corridor arrangement), lateral forces were transmitted through in-plane bracing located in the corridors, as shown in Fig. 8.2.2B [10]. These modules were then connected to the concrete cores. Fig. 8.2.2C [10] illustrates the plan form of modules in which lateral loads were resisted by four braced steel cores. Lawson et al. [9, 10] also stated that the distance of the outer module from the concrete core was restrained by the two important factors including the shear force that could be transferred via the corridor, and the travel distance that was reserved for fire evacuation purposes.

334 Hybrid composite precast systems

(B)

(C)

Corridor arrangement of modules [10]

Plan of modular building using Irregular-shaped core positions [10]

FIG. 8.2.2 Cellular-type high-rise buildings with concrete cores.

Lawson et al. [9, 10] conducted case studies with the three different multistory residential buildings having 12, 17, and 25 stories. The application of the modular construction to the high-rise buildings is shown in [15], which demonstrates a modular construction for high-rise buildings with 24 floors.

8.3 Implementation of the mechanical joints in precast connections for modular construction The present chapter is devoted to the application of the hybrid composite precast frames with mechanical joints for the off-site modular construction of buildings and industrial plants subjected to heavy loads including frames for pipe racks. The hybrid composite precast frames can provide an effortless erection via mechanical connections.

8.3.1 High-rise building application A novel modular construction for the high-rise buildings using the precast concrete-based frames with mechanical joints is introduced to offer not only fast construction but also a fully restrained moment connection for both concrete and steelconcrete composite frames. Fig. 8.3.1 (refer to Fig. 5.2.1 of Chapter 5) demonstrates how frame modules capable of

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FIG. 8.3.1 Connection details for frame modules; bolted metal plates and one-touch interlocking couplers.

transferring moments across the interconnected plate joints are assembled. The modular construction was proposed by implementing mechanical joints for beam-to-column and column-to-column connections, ensuring the structural safety during construction. The frame modules are vertically connected via laminated metal endplates or interlocking couplers, shown in Fig. 8.3.1A and B, respectively. The column plates installed with the upper, and the lower frame modules are layered and connected with bolts, as illustrated in Fig. 8.3.1A, whereas the upper and the lower frame modules become monolithic joints via interlocking couplers, as shown in Fig. 8.3.1B. The details of these column connections were elucidated in Chapters 2 and 3 with experimental and numerical investigations. The extended beam plates were also implemented in the connections for the precast concrete frames. The traditional cellular-type modules shown in [1] can be replaced by the frame modules using mechanical plate joints, as shown in Fig. 8.3.2A, where the three types of the modular constructions implementing the hybrid composite precast frames with the rigid mechanical joints are illustrated in Fig. 8.3.2B. Two bay frames are the basic module in Fig. 8.3.2B-(1), followed by the installation of the beams between the basic modules. In Fig. 8.3.2B-(2) and (3), the extended frame modules are used for a faster assembly. The cellular modules are inserted between the frame modules prior to the installation of the beams. The modular constructions utilizing the composite precast frames with the rigid mechanical joints, introduced in Fig. 8.3.2B, can also be used in the construction of the frames for high-rise buildings without installing cellular modules. The designs and the related structural behaviors of the L-shaped composite precast frames with the rigid mechanical joints are presented in Section 4.3 of Chapter 4. The test erection of the multibay frames with the mechanical joints using endplates for the connection of the column-to-column and column-to-beam joints was performed in Section 4.4 of Chapter 4. The test erection demonstrated that the proposed precast concrete-based frames with the mechanical joints

336 Hybrid composite precast systems

FIG. 8.3.2, Cont’d

provided lateral resistance, enabling to replace concrete cores. In Chapter 9, the bolted steel connections with wide flange and T-shaped steel sections were also used for the connections of the precast composite frames.

8.3.2 Application to special structures Precast concrete-based frames having mechanical joints can be used in diverse structures, such as pipe-rack frames and parking structures. Chapter 7 was devoted to the application of the composite frames with mechanical joints to pipe rack frames. As shown in Fig. 8.3.3A, parking structures are often built with skewed slabs having shear walls to resist lateral loads. Parking structures implemented with hybrid precast frames were proposed in this chapter to remove shear walls, as shown in Fig. 8.3.3B, where the prefabricated concrete-based frames are implemented for the assembly of parking structures with inclined slabs. The mechanical joints are implemented to assemble the column-to-beam connections, as shown in Fig. 8.3.3C, where the horizontal and skewed beams with extended endplates are connected to the column plates by bolting,

Application to the modular construction Chapter

FIG. 8.3.2 Proposed frame modules having mechanical joints.

8

337

338 Hybrid composite precast systems

FIG. 8.3.3, Cont’d

simultaneously. Each column has dual plate joints (refer to Fig. 8.3.3C-(1)) to be connected to the two precast composite beams. The horizontal and skewed beams with extended endplates are connected to the column plates, as shown in Fig. 8.3.3C-(2) and (3), respectively. The conventional bolted steel connections can also be utilized to assemble the skew frames, as shown in Fig. 8.3.3D, in which the dual precast beams having the conventional steel sections are bolted to columns. The steel sections are placed at the ends of the beams where the moments due to gravity loads are concentrated. The assembly procedures of the beam-to-column joints using the bolted steel sections were elucidated in Section 9.4 of Chapter 9, in which the skewed shape made to both column brackets and beam steel webs were guided into the preinstalled L shaped pockets (refer to Figs. 9.4.3 and 9.4.4 of Chapter 9). In Fig. 8.3.3E, the precast slabs with double tees are used to expedite the construction speed with a facile and rapid assembly. Modularization of this type of the parking structure with skewed slabs will substantially influence the construction schedule and corresponding costs. The original design with massive shear walls (Fig. 8.3.3A) resisting lateral loads, can be replaced by the precast frames, with the mechanical joints or the bolted conventional steel connections.

8.4 Lateral stability of the hybrid composite precast frames with rigid mechanical joints Extensive numerical and experimental investigations were performed to explore the structural performance of the proposed joints implemented in the modular construction, identifying the failure modes, strength, ductility, and energy dissipation capacity of the mechanical joint.

8.4.1 Seismic responses and fundamental period of the modular building Annan et al. [16] conducted studies of the seismic responses for braced modular structures. They performed experimental studies on the hysteretic behaviors of an MSB (modular steel building)-braced frame and a regular concentrically braced

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FIG. 8.3.3, Cont’d

frame. It was reported that both specimens showed stable and ductile behavior up to a very high drift ratio (3.5%). The MSB frame was more vulnerable to the column bending deformation, whereas the traditional frame was vulnerable to the out of plane buckling of the bracing. Annan et al. [17] further conducted an incremental dynamic analysis (IDA) for 2, 4, and 6 story MSB-braced frames. It was reported that the selected MSB-braced frames predominantly exhibited a first-mode response; the mass participation factors for the 2 story frame were 94% for the first mode and 5% for the second mode; similarly, for the 4 story frame, the percentages were 81% and 15% respectively, and for the 6 story frame, the mass participation factors were 77% and 17%. Fathieh and Mercan [18] conducted nonlinear static pushover and IDA analyses for both 2D and 3D MSB-braced 4 story frames. It verified the concentration of inelasticity at the first level due to the limited redistribution of internal forces. They found the 2D model overestimated the structural capacity against an incipient collapse because the torsional response was not accounted for in the 2D model. Gunawardena et al. [14] conducted a nonlinear time history analysis for a freestanding 10 story modular building subject to six selected ground motions. Column hinge formation was found unavoidable in severe ground motions, and the column ductility was important to redistribute post-yield loads. It was indicated that further studies were needed to investigate the dynamic behaviors for the mid- to highrise modular buildings.

340 Hybrid composite precast systems

FIG. 8.3.3 Connection details for a slanted parking structure implementing hybrid precast frames, removing shear walls.

8.4.2 Modular steel building with braced frames Numerous standards, including Standards Australia [19] provided an empirical formula for the fundamental period (T1 [s]) of the traditional building structures. AS 1170.4 [19] provided T1 ¼ 1.25kth0.75 n , where hn is the height from the base to the uppermost seismic mass in meters, and kt is a constant depending on the structural type with a value ranging between 0.11 (for moment-resisting steel frames) and 0.05 (for all other structures). Studies have been extended to modular buildings, recently. Fig. 8.4.1, reproduced from Fig. 6 of the study by Lacey et al. [3], summarizes the fundamental periods for the rectangular modular buildings with the upper and lower bounds defined in AS 1170.4. C.D. Annan et al. [17] proposed the fundamental periods by the numerical analyses of the 2D modular steel building with braced frames. Gunawardena et al. [14] and Fathieh et al. [18] also presented the fundamental periods of the 3D modular steel building with braced frames. The fundamental periods for the steel moment-resisting frame (SMRF) modules were provided by Choi et al. [20] and Shirokov et al. [21]. Many variations in the fundamental period for the SMRF modules were demonstrated due to the inter-module connection type, and stiffness [20, 21]. Reasonable estimates for the 2D and 3D modular steel building with braced frames were based on kt ¼ 0.05 and kt ¼ 0.075, respectively, whereas the most accurate estimation of the fundamental period for the SMRF modules was obtained by implementing kt ¼ 0.11 when they had a rigid inter-module connection. A significant influence on the fundamental period would be expected when masses with cladding and other nonstructural components were included. The experimental analysis of stacked timber frame modules was performed by Malo [22].

8.4.3 Precast concrete-based frames having mechanical joints In Fig. 8.4.2, a three-dimensional frame analysis was conducted to evaluate the structural performance of the cores (refer to Fig. 8.2.2A) for the modules clustered around the concrete core subjected to lateral forces (wind and seismic forces). The fundamental period of the composite precast frames with the rigid mechanical joints (refer to Fig. 8.3.2 A and B) was also estimated. Fig. 8.4.2A and B illustrate the three-dimensional modeling of the concrete cores and the composite precast frames with the rigid mechanical joints. The concrete cores provided resistance to both seismic and wind loads for the stacked modules. Fig. 8.4.3A and B depict the structural response of the two types of the frames due to seismic lateral forces. The partitions and claddings shown in Fig. 8.4.3A were not considered as structural elements. The floor loads (dead load of 5.0 kN/m2 and live load of 2.5 kN/m2 including the weights of the partitions per floor) were used for the three-dimensional

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FIG. 8.4.1 Variations of fundamental period with height for modular buildings [3].

35 30

Height (m)

25 20 15 10 5 0

0

0.5

1

1.5

2

2.5

T1 (s) AS 1170.4 kt = 0.05

AS 1170.4 kt = 0.11

2D MSB-braced (21)

Timber frame (93)

3D MSB-braced (17)

SMRF (49)

3D MSB-braced (22)

SMRF (92)

FIG. 8.4.2 Three-dimensional modeling of concrete cores and the composite precast frames with rigid mechanical joints; refer to Figs. 8.2.2A and 8.3.2A and B.

models for the composite precast frames with the rigid mechanical joints (shown in Fig. 8.4.3A) and the concrete core (shown in Fig. 8.4.3B). The two types of structural systems (the composite precast frames with the rigid mechanical joints and the concrete core, shown in Fig. 8.4.3A and B, respectively) were subjected to the same gravity and lateral forces. The wall thickness was taken as 200 mm for the concrete cores whereas the frames supporting the cell modules were not included in the dynamic analysis. The hybrid composite steel-concrete precast frames with the rigid mechanical joints were modeled in which the beams (500 mm  700 mm encasing a steel section: H-300  150  6.5  9), and columns (700 mm  700 mm encasing a steel section: 400  400  13  21) were used. A fixed moment condition was assigned at the joints between beams and columns. The size of the hybrid precast frames can be reduced further when the precast frames are prestressed as shown in Section 9.2.3 of Chapter 9. The concrete core walls and the composite precast frames with the rigid mechanical joints were then subjected to lateral forces defined based on IBC. In previous work [3–5, 7, 9, Chapter 2] and [16, Chapter 3], the author, experimentally and numerically, verified that the mechanical joints consisting of the laminated metal plates were capable of creating rigid

342 Hybrid composite precast systems

FIG. 8.4.3 Structural response due to lateral forces; seismic loads.

Application to the modular construction Chapter

FIG. 8.4.4 Structural response due to lateral forces; wind loads.

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344 Hybrid composite precast systems

TABLE 8.4.1 Lateral stability of the concrete cores and composite precast frames with rigid mechanical joints. Category

Concrete core wall

Composite precast frames

Fundamental period

1.64 s

1.74 s

X-direction

24 mm (H/2500)

20 mm (H/3000)

Y-direction

6.0 mm (H/10,000)

20 mm (H/3000)

X-direction

88 mm (H/680)

82 mm (H/740)

Y-direction

22 mm (H/3000)

82 mm (H/740)

Lateral displacement due to wind forces

Lateral displacement due to seismic forces

TABLE 8.4.2 Estimated construction period of a 20 story precast building (composite precast frames with rigid mechanical joints vs. conventional modular buildings). Frames with mechanical joints

Modular construction with core wall

Activity

Estimated time

Activity

Estimated time

Lifting and installation of one column module

2h

Cast-in-place of the core walls

7 days/floor

Erection and installation of one beam module

2h

1 day/floor

Assembly of one frame module (four beams and four columns)

16 h

Jacking modules, connecting modules to the concrete core

Assembly of frame modules of one floor

2.7 days

Connecting modules

1 day/ floor

Estimated time to complete a 20-story building 74 days

160 days

joints. Figs. 8.4.3 and 8.4.4 compare the lateral stability of the two structural systems under earthquake and wind loads. Under seismic forces, a lateral deformation of 88 mm was observed at the concrete cores, while the composite precast frames with the rigid mechanical joints deformed as much as 82 mm. Alternately, wind loads caused the concrete cores to deform as much as 24 mm, while a lateral deformation of 20 mm by the composite precast frames with the rigid mechanical joints was exhibited. The lateral stability of the two structural systems (concrete cores and composite precast frames with rigid mechanical joints) subjected to both wind and seismic forces are summarized in Table 8.4.1, demonstrating that the overall structural stability similar to each other was observed from the composite precast frames with the rigid mechanical joints and that obtained from the concrete cores. The concrete core walls and the composite precast frames with the rigid mechanical joints demonstrated fundamental periods of 1.64 and 1.74 s, respectively. In addition to the structural performance, the construction periods of these two structural systems are compared in Table 8.4.2, which assumes the concrete cores shown in Fig. 8.4.2A are constructed based on the conventional cast-in-place method, which may lengthen the construction period. The time required to complete one floor was estimated as 8 days. However, the proposed modules using the composite precast frames, shown in Fig. 8.4.2B, required approximately 3.7 days, including an erecting and assembling the frame modules, providing a fast erection compared with the cast-in-place methods. A total of 70 days was estimated to complete a 20-story building implementing the composite precast frames with the rigid mechanical joints, while casting the concrete cores, despite without considering the time for the construction of the supporting frames for the cell modules, requires 160 days to complete. The entire construction time for the precast frames may take longer when the lead time for the manufacture of the precast frame members are included.

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8.5 Conclusions The mechanical joints were proposed for the modular construction of the composite precast frames. The assembly of the joints for the modules was designed not only to ease the erection process but also to create a moment connection of the frames. The upper modules can be stacked on the top of the preinstalled modules via one-touch interlocking couples (refer to Chapter 5) or bolted layered plates (see Chapters 2 and 3). The erection using mechanical joints was simple and straightforward. The advantages of the proposed modular construction demonstrating a fast constructions speed with an assembly safety similar to those obtained by the steel frame were proved through the test erection. The highlights of the proposed modular construction with the mechanical joints can be summarized into the three categories: (1) Structural: The composite precast frames with the rigid mechanical joints exhibited a lateral stability similar to that of the modules with the cast-in-place cores. The lateral deflection of the composite precast frames with the mechanical joints similar to that of the concrete cores was observed under both seismic and wind forces, indicating that proposed frames with the mechanical joints were suitable for seismic regions. (2) Economy: The use of the composite precast frames eliminated extensive concrete cores and steel frames which are tied to the individual cellular modules for lateral stability. (3) Constructability: The time required to complete one floor was estimated as 8 days when the conventional concrete core wall had to be cast-in-place. However, the proposed frame modules with the mechanical joints (Table 8.4.2) required approximately 3.7 days for erecting and assembling one floor on the top of another, providing a fast erection compared to the cast-in-place cores. Only 74 days were projected to complete a 20-story building using the novel modular construction, while casting the concrete core walls may require 160 days even if the time for the installations of the frames supporting the cell modules was not considered.

References [1] Modular Construction, Source, https://www.linkedin.com/pulse/different-construction-process-modular-wave-future-grant-smereczynsky-1, 2019. [2] Schoenborn, J., 2012. A Case Study Approach to Identifying the Constraints and Barriers to Design Innovation for Modular Construction. Doctoral Dissertation, Virginia Tech. [3] A.W. Lacey, et al., Structural response of modular buildings—an overview, J. Build. Eng. 16 (2018) 45–56. [4] M.T. Gorgolewski, P.J. Grubb, R.M. Lawson, Modular Construction Using Light Steel Framing: Design of Residential Buildings, The Steel Construction Institute, Ascot, Berkshire, England, 2001. [5] R.M. Lawson, R.G. Ogden, R. Pedreschi, P.J. Grubb, S.O. Popo-Ola, Developments in pre-fabricated systems in light steel and modular construction, Struct. Eng. 83 (2005) 28–35. [6] R.M. Lawson, P.J. Grubb, J. Prewer, P.J. Trebilcock, Modular Construction Using Light Steel Framing: An Architect’s Guide, The Steel Construction Institute, Ascot, Berkshire, England, 1999. [7] R.M. Lawson, R.G. Ogden, ‘Hybrid’ light steel panel and modular systems, Thin Wall Struct. 46 (2008) 720–730, https://doi.org/10.1016/ j.tws.2008.01.042. [8] R.M. Lawson, M.P. Byfield, S.O. Popo-Ola, P.J. Grubb, Robustness of light steel frames and modular construction, Proc. Inst. Civ. Eng. Struct. Build. 161 (2008) 3–16, https://doi.org/10.1680/stbu.2008.161.1.3. [9] R.M. Lawson, Building Design Using Modules, The Steel Construction Institute, Ascot, Berkshire, England, 2007. [10] R.M. Lawson, R.G. Ogden, R. Bergin, Application of modular construction in high-rise, Build. J. Arch. Eng. 18 (2012) 148–154, https://doi.org/ 10.1061/(asce)ae.1943-5568.0000057. [11] R.M. Lawson, J. Richards, Modular design for high-rise buildings, Proc. Inst. Civ. Eng. Struct. Build. 163 (2010) 151–164, https://doi.org/10.1680/ stbu.2010.163.3.151. [12] R.M. Lawson, R.G. Ogden, C. Goodier, Design in Modular Construction, CRC Press, Boca Raton, FL, USA, 2014. [13] K.S. Park, J. Moon, S.S. Lee, K.W. Bae, C.W. Roeder, Embedded steel column-to-foundation connection for a modular structural system, Eng. Struct. 110 (2016) 244–257, https://doi.org/10.1016/j.engstruct.2015.11.034. [14] T. Gunawardena, et al., Behaviour of Prefabricated Modular Buildings Subjected to Lateral Loads, Ph.D. Thesis, The University of Melbourne, Melbourne, Australia, 2016. [15] Modular Building Institute, http://www.modular.org/htmlPage.aspx?name¼24_story_modular, 2019. [16] C.D. Annan, M.A. Youssef, M.H. El Naggar, Experimental evaluation of the seismic performance of modular steel-braced frames, Eng. Struct. 31 (2009) 1435–1446, https://doi.org/10.1016/j.engstruct.2009.02.024. [17] C.D. Annan, M.A. Youssef, M.H. El Naggar, Seismic vulnerability assessment of modular steel buildings, J. Earthq. Eng. 13 (2009) 1065–1088, https://doi.org/10.1080/13632460902933881. [18] A. Fathieh, O. Mercan, Seismic evaluation of modular steel buildings, Eng. Struct. 122 (2016) 83–92, https://doi.org/10.1016/j.engstruct. 2016.04.054.

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[19] AS 1170.4, Standards Australia, AS 1170.4-2007(+A1) Australian Standard—Structural Design Actions. Part 4. Earthquake Actions in Australia, SAI Global Limited, Sydney, Australia, 2007, p. 64. [20] K.-S. Choi, H.-C. Lee, H.-J. Kim, Influence of analytical models on the seismic response of modular structures, J. Korea Inst. Struct. Maint. Insp. 20 (2016) 74–85, https://doi.org/10.11112/jksmi.2016.20.2.074. [21] V.S. Shirokov, I.S. Kholopov, A.V. Solovejv, Determination of the frequency of natural vibrations of a modular building, Procedia Eng. 153 (2016) 655–661, https://doi.org/10.1016/j.proeng.2016.08.218. [22] K.A. Malo, R.B. Abrahamsen, M.A. Bjertnæs, Some structural design issues of the 14-storey timber framed building “Treet” in Norway, Eur. J. Wood Wood Prod. 74 (2016) 407–424, https://doi.org/10.1007/s00107-016-1022-5.

Chapter 9

Precast steel-concrete hybrid composite structural frames with monolithic joints Nomenclature Αri Αsi B Bi ci c11, c12 c21, c22 Cci C0 ci Cc11, Cc12 C0 c11, C0 c12 D di dc ds dsi Es Er Fri Fsi Faxial FRtension FRcompression Fsteeltension Fsteelcompression «cmi «yR «yS «ri «si fyR fyS f 0c f 0 cc fc1 fc2 f«cm1 f«cm2 h Kh Kp tf1

area of rebar layer i (i ¼ 1–2), mm2 area of part i of H-steel section, mm2 width of the concrete section width of unconfined, confined, partially, highly confined concrete area (i ¼ 1–4), mm height of concrete compression zone of unconfined, confined, partially, highly confined concrete area (i ¼ 1–4), mm height of components of unconfined area, mm height of components of unconfined area inside, mm compressive force given by unconfined, confined, partially, highly confined concrete area (i ¼ 1–4), kN compressive force given by unconfined, confined, partially confined concrete area inside (i ¼ 1–3), kN components of compressive force given by unconfined area, kN components of compressive force given by unconfined area inside, kN height of the concrete section distance from rebar layer i (i ¼ 1–2) to top of concrete section, mm distance from centroid to top of the concrete section, mm distance from top flange of H-steel to top of the concrete section, mm distance from the force given by the part i of H-steel to top of the concrete section, mm Young’s modulus of steel, MPa Young’s modulus of rebar, MPa force given by rebar layer i (i ¼ 1– 2), kN force given by part i of H-steel section (i ¼ 1–5), kN the external axial forces, kN the internal forces contributed by rebar in tension, kN the internal forces contributed by rebar in compression, kN the internal forces contributed by steel in tension, kN the internal forces contributed by steel in compression, kN strain at fiber of unconfined, confined, partially, highly confined concrete area (i ¼ 1–4) yield strain of rebar yield strain of steel strain of rebar layer i (i ¼ 1–2) strain respect to part i of H-steel section yield strength of rebar, MPa yield strength of steel, MPa compressive strength of unconfined concrete, MPa compressive strength of equivalent confined concrete, MPa concrete compressive stress in term of concrete strain of unconfined area, MPa concrete compressive stress in term of concrete strain of equivalent confined area, MPa concrete compressive strength at the extreme fiber of unconfined region, MPa concrete compressive strength at the extreme fiber of confined region, MPa depth of H-steel section, mm confinement factors for highly confined concrete Confinement factors for partially confined concrete top flange thickness of H-steel section, mm

Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00009-1 © 2020 Elsevier Ltd. All rights reserved.

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tf2 tw xi w ai a0 i st0 gi g0 i e fb0 fc0 Kc G(s) p, q c

bottom flange thickness of H-steel section, mm web thickness of H-steel section, mm distance from the edge of the concrete confined areas to the extreme compressive fiber of the concrete section, mm width of H-steel section, mm stress factors for the concrete areas i (i ¼ 1–4) Stress factors for the concrete areas inside i uniaxial tensile stress, MPa centroid factor for the concrete areas i (i ¼ 1,2) centroid factor for the concrete areas inside eccentricity initial equibiaxial compressive yield stress of concrete, MPa initial uniaxial compressive yield stress of concrete, MPa the ratio of the second stress invariant on the tensile meridian nonassociated plastic flow potential, Druker-Prager formulation the plane in which plastic potential function is defined dilation angle

9.1

Why the precast steel-concrete hybrid composite with monolithic joints?

Construction of the conventional cast-in-place steel-concrete composite frames (Fig. 9.1.1) traditionally required the use of the concrete pour forms and the use of temporary supports for the wet concretes before the joint concretes were cured and erected, lengthening the construction period, thus, losing the traditional merits offered by the steel members. The traditional construction also demanded significant labor on the construction site. In this chapter, the fast erection of the steel-concrete hybrid composite frames similar to that of the erection of the steel frames was sought by implementing the precast technique. Steel frames offer an advantage of rapid construction, but suffer from high cost and lower fire resistance than concrete. The sustainability and resiliency of the hybrid frame were demonstrated contributing to facing the climate change issues. In this chapter, the hybrid composite precast frames with the conventional steel connections offers the construction speed as fast as that of the steel erection to overcome shortcomings of the traditional construction materials used alone

FIG. 9.1.1 Traditional concrete pour forms for the construction of steel-concrete hybrid composite frames.

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as the steel or the concrete. The composite precast frames have proven to improve productivity and quality, while reducing the cost by shortening the construction period, construction resources, CO2 emissions, and construction wastes. The bearing-wall system in the high-rise apartment constructions can also be replaced by the composite precast frames to reduce construction material quantities and CO2 emissions, eventually leading to the higher productivity and cost savings. The hybrid composite precast frames maintain the advantages of both precast concrete structures and the steel frames; they combine the steel and the concrete to offer advantages, not only in structural stability, but also in the constructability, cost-effectiveness, and environmental friendliness. The method has also been shown to reduce construction waste in addition to many other benefits. The composite precast frame-related technologies developed to date present considerable progress towards a novel building structural system and construction technology. Efforts are being made to further enhance the composite precast frame technology with considerable success. In the composite precast frames introduced in this chapter, The floor depth reduction capability of the hybrid beams are introduced, enabling to add one additional floor for every 20 floors without altering the overall height of the building. The slabs were constructed on the top of the edges of the precast concrete instead of on the top of the steel flanges, reducing the depth of the slab and beam by up to 220 mm per floor, as can be seen Fig. 9.1.2. Successful reduction of the floor depth led to a significant reduction in the floor height. The effective interaction between the two materials can also reduce the required size of the steel beams. The steel sections were either placed throughout the entire length of the beam or installed at each end of the beam (refer to Fig. 9.1.3A and B). Diverse steel modules can be integrated with the precast concrete to cope with loads on the hybrid beams as shown in Fig. 9.1.3A-(1), whereas the beam-to-column joints are shown in Fig. 9.1.3A-(2) and B. In Fig. 9.1.3C, the three types of the precast concrete were preintegrated with the steel sections to reduce the weight of the

FIG. 9.1.2 Floor depth reduction of the composite beams compared with the steel beams.

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FIG. 9.1.3 Modular constructions of the composite precast frames.

composite beams [1, 2]. The bottom flange of the wide-flange steel beams was fabricated encased in the concrete at a manufacturing plant as a replacement for the conventional cast-in-place composite beams, eliminating the use of temporary pour forms on site. The lower steel reinforcements and the flanges of steel beams were preintegrated with the concrete of rectangular, U, and flat shapes at the manufacturing plant (refer to Fig. 9.1.3C). The concrete was cast to cover up the top steel reinforcement and upper flange at the construction site with slabs. The weight of the composite beams and fabrication cost were affected by the shape of precast concrete. The application of the hybrid precast beams to building frames with a long span can be seen in Fig. 9.1.3D, where the hybrid beams with flat shapes are combined with the U-shaped precast beams (refer to Fig. 9.1.3D-(3)).

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

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351

FIG. 9.1.3, cont’d

Four full-scale composite beams composed of wide steel flanges (shown in Fig. 9.2.1) [1,3], where the bottom flange was encased in precast concrete, were tested to determine the load-carrying capabilities of the beams at both the yield load and the maximum load limit state. It is obviously possible, without sacrificing building schedules and construction quality, to save the construction cost with the steel-concrete composite precast frames compared with that by only steel frames. The 68-m tall, 18-story steel building was redesigned to a 19-story building using the steel sections encased in structural

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Hybrid composite precast systems

FIG. 9.1.3, cont’d

concrete (refer to Tables 9.5.6 and 9.5.7, and Figs. 9.5.6–9.5.13). Application of the precast steel-concrete composite structural system to high-rise buildings made it possible to add one additional floor while the overall building height was maintained, as shown in Table 9.5.7. The steel sections were placed throughout the entire length of the beam, which combines the merits of ductile steel and concrete components to withstand external loading while reducing floor height. The erection process of the composite beams was identical to that of traditional steel construction. This chapter also describes more than 30 potential applications of high-rise composite construction using the precast steel-concrete composite beams.

9.2

Structural behavior of the hybrid composite beams with monolithic joints

9.2.1 Wide steel flanges encased in concrete; the interaction between steel and concrete Wide flange steel beams with the bottom flange encased in the precast concrete are shown in Fig. 9.2.1, where the effective interaction between the two materials reduced the dimension of the steel beams. The manufacturer of the composite beams was able to maintain a quality control program with specifications for material properties, steam, and natural concrete curing, transport, storing, and erection.

9.2.1.1 Experimental investigation; flexural strength of the composite beam Four full-scale composite beams with a slab, demonstrating the effective interaction between the steel and concrete (shown in Fig. 9.2.1) were tested as shown in Fig. 9.2.2. The experimental investigation examined the hysteretic behavior, moment capacity, and energy dissipation capacity of the composite beams under cyclic loading. The deflected shapes both in the upward and downward directions are attained, as shown in Fig. 9.2.3A, and failure modes observed from the tested specimens are shown in Fig. 9.2.3B. Fig. 9.2.3C illustrates the load-displacement relationships of the test specimens shown in Figs. 9.2.1 and 9.2.2. The flexural strength sufficient to resist loads exerted on the composite frame was attained with ductile failure modes. The analytical investigations based on a strain compatibility and plastic stress distribution are introduced in Section 9.3 of this chapter. The detailed description of the test results can be found in Ref. [2].

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FIG. 9.1.3, cont’d

9.2.1.2 Flexural moment capacity at the deflection of 1/360 Similar failure modes were observed among all four specimens, particularly demonstrating that all specimens displayed crack widths less than 0.1 mm at the deflection corresponding to L/360 (28 mm). Test results verified that the proposed composite beams were capable of providing the moment and shear capacity at the deflection corresponding to L/360 when beams of 8 m length placed at every 5 m were subjected to the dead load of 4 kN/m2 and live load of 2 kN/m2, which resulted in the moments with 213 and 107 kN-m at ends and mid-span, respectively. The flexural moment capacities of all

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Hybrid composite precast systems

FIG. 9.2.1 Specimen details [6].

400

400

3,000

FIG. 9.2.2 Full-scale test of the composite beam with a slab [2].

specimens corresponding to deflection of L/360 (28 mm) are presented in Table 9.2.1, where the flexural moment capacities of 250 and 125 kN-m were measured at the ends and mid-span, respectively, for Specimen #1.

9.2.1.3 Load bearing strength of the precast wings against construction loads A 1.6 m specimen was manufactured and tested to observe the failure modes during the concrete cast for slabs. The loading that caused the failure of the precast concrete encasing lower steel flanges was symmetrically distributed on the edges of the precast concrete, as depicted in Fig. 9.2.4A and B, which show the test set-up with the reaction frame designed to apply vertical loads on the top of the precast wings, simulating the construction loads including uncured concrete weight. The weight of the concrete slabs and other construction loads must be supported by the precast concrete wings attached to the lower steel flange, when concrete was cast on the metal deck plate located on the edges of the precast concrete. The test result is presented in Fig. 9.2.5. The precast wings when loaded must not exhibit shear failures and bearing failures caused by the torsion due to the construction loads as shown in Fig. 9.2.5. When the contact area between the concrete and the bottom flange of the steel sections was small, the bearing failure of the concrete could occur, but must be prevented. During the test, these types of failure of the concrete encasing the steel sections were avoided, safely resisting vertical loads. At the ultimate load, the

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

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FIG. 9.2.3 Load-displacement relationships of the composite beam [6].

bearing failure of the concrete on the bottom flanges (shown in Fig. 9.2.5B) was observed at 199.6 kN, as shown in the load– displacement relationship at the mid-point of the tested composite beam (refer to Fig. 9.2.6). Longitudinal bearing cracks (Fig. 9.2.5B) in the bottom surface of the precast concrete were caused by the compression at the end of the test. These bearing cracks were caused by the torsion along with the longitudinal directions initiated by the symmetrically distributed loads on the edges of the precast concrete. The U-shaped precast composite beams can support loads 4.7 and 3.1 times the weight exerted by the concrete slabs with thicknesses of 150 and 250 mm, respectively.

9.2.2 T-shaped steel section encased in concrete 9.2.2.1 Experimental investigation of the composite precast beams with T-shaped steel sections In Fig. 9.2.7A, the structural capacity of the unsymmetrical steel-concrete composite precast beams with T-shaped steel sections (shown in Figs. 9.1.2B-(2) and 9.1.3D-(2)) was experimentally investigated [4, 6]. The postyield behavior obtained

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Hybrid composite precast systems

Load-displacement curve 1200 1000 210.1 mm, 511.0 kN 800

277.0 mm, 460.9 kN

64.0 mm, 359.0 kN 600 28.3 mm, 190.6 kN

Load (kN)

400 200 0 -250

-200

-150

-100

-50

-200

0

50

100

150

200

250

300

350

-400 -600 -29.4 mm, -248.9 kN -800 -216.0 mm, -791.7 kN

-1000

-55.9 mm, -425.8 kN -1200 Midspan displacement (mm)

(1) Composite beam #1

FIG. 9.2.3, cont’d

experimentally was then validated by the nonlinear finite element analysis in Sections 9.2.2.3 and 9.2.2.5. The beamcolumn joint was designed based on the strain compatibility, described in Section 9.2.2.6. Specimens PS1 and PS2 were assembled using sleeves (refer to Fig. 9.2.7B) while columns were fabricated by pressure welding (refer to Fig. 9.2.7C) for Specimen PS3. In Figs. 9.2.7 and 9.2.8, the three T-shaped steel sections with the dimension of 150  150  6.5  9 and the yield strength of 330 MPa were encased in the concrete beams of 300 mm wide with a depth of 350 mm, having the reinforcing steel bars, 2-HD13 and 4-HD22, at the bottom and top reinforcement, respectively. The composite actions between the steel and concrete sections, contributing to the structural performance, were investigated. Material properties were obtained from the tensile tests. The average tested tensile strength of the rebars was 437.5 MPa. The average compressive strength of 33.1 MPa was measured from the three specimens. In Figs. 9.2.7 and 9.2.8 and Table 9.2.2, slippages between the embedded elements and concrete during the test were prevented by providing two headed studs of 22 mm diameter spaced at 95 mm on the web and one spaced at 450 mm on the flange. The material properties of composite beams are described in Table 9.2.3.

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Load-displacement curve 1200

65.8 mm, 654.4 kN

262.2 mm, 899.0 kN

1000 800 27.6 mm, 352.3 kN 600

Load (kN)

400 200 0 -250

-200

-150

-137.2 mm, -1090.7 kN

-100

-50

-200

0

50

100

150

200

250

300

350

-400 -600 -28.4 mm, -361.0 kN -800 -1000

-63.9 mm, -742.3 kN

-1200 Midspan displacement (mm)

(3) Composite beam #3

FIG. 9.2.3, cont’d

9.2.2.2 Instrumentation and the test set-up In Fig. 9.2.9, a load of 2000 kN was applied by an actuator located at 1.78 m from the foundation surface. The length of the beam and the height of the column component were 2 and 1 m, respectively. The cyclic loading protocol is depicted in Fig. 9.2.10; 2 or 3 cycles were applied for each stroke length consisting of first and stabilized cycles. The applied lateral displacements were estimated by calculating the product between the inter-story drift angle (rad) and the height of the specimen measured from the slab surface. Fig. 9.2.10 also illustrates the drift angles (radian) with the associated lateral displacements and the number of cycles applied for each displacement [5]. As many as 80 strain gauges were installed on each test specimen; the gauges were attached to the top/bottom/web of flanges, and to the reinforcement. The influence of the unsymmetrical steel on the concrete section was explored based on the measured strains, comparing it with that of nonlinear-inelastic finite element analysis.

TABLE 9.2.1 Moment capacity at the deflection corresponding to L/360 [1]. Steel (d × bf × tw × tf)

Rebars

Specimen Composite beam #1

Top: 6 Bottom: 2 (diameter: 25 mm) o

Composite beam #2 Composite beam #3 Composite beam #4

Top: 4 Bottom:5 (diameter: 25 mm)

o

340 × 250 × 9 × 14

400 × 300 × 11 × 18

Beam depth (mm)

500

600

Load (kN)

Pull

Push

o

o

250

191

o

o

221

238

o o

FIG. 9.2.4 Test of the U-shaped precast wing and reaction frame [2].

o

o

361

352

o

o

365

364

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

FIG. 9.2.5 Failure modes of the precast wings [2].

FIG. 9.2.6 Load-displacement relationship of the U-shaped MHS specimen [2].

9

359

360

Hybrid composite precast systems

FIG. 9.2.7 Section properties and geometry of the specimens used for the experimental investigation [3].

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FIG. 9.2.8 T-section steel encased in the precast concrete [4].

TABLE 9.2.2 Description of the three identical test specimens [3]. Headed stud bolt (l 5 65 mm)

Stirrup Web

Bottom flange

Category

Spacing (mm)

Diameter (mm)

Spacing (mm)

Diameter (mm)

Spacing (mm)

Diameter (mm)

Specimen PS1

500

10

95

13

450

13

Specimen PS2

500

10

95

13

450

13

Specimen PS3

500

10

95

13

450

13

TABLE 9.2.3 Material property used in the finite element analysis [4]. Size

Material properties

Concrete beam

300  350 (mm )

f0 c ¼ 33.1 MPa

Concrete column

550  550 (mm2)

f0 c ¼ 33.1 MPa

T-Steel (SM490)

150  150  6.5  9 (mm3)

Fy ¼ 325 MPa; ey ¼ 0.0016

Bolt

M22-F10T

Fu ¼ 1000 MPa; ey ¼ 0.0045

Stud bolt

D13 (height: 53 mm)

fy ¼ 400 MPa; ey ¼ 0.0019

Rebar

D22, D13

fy ¼ 400 MPa; ey ¼ 0.0019

2

9.2.2.3 Numerical investigation 3D mesh for finite element analysis The structural performance of the test specimen shown in Fig. 9.2.9 was explored by a numerical analysis [4]. The analysis results agreed with the experimental results when the concrete-damaged plasticity model and the von Mises yield criterion of metal sections were implemented in the FEA model. The influence of the concrete confinement provided by the T-shaped steel section on the concrete degradations and damage evolution was also investigated to determine the flexural strength and ductility. The material properties used in the experimental and numerical investigation are presented in Table 9.2.3. Figs. 9.2.11 and 9.2.12 depict the 3D meshes for the finite element analysis; these were not symmetrical, yielding different flexural capacity and damage characteristics in each load direction.

FIG. 9.2.9 Test set-up and the load application of the specimen [4].

FIG. 9.2.10 Cyclic loading protocol [4,5].

FIG. 9.2.11 Finite element model; modeling headed studs [4].

FIG. 9.2.12 Finite element model; 3D model of the test specimen and 3D mesh of the test specimen [4].

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TABLE 9.2.4 FEA parameters identified for an unsymmetrical composite beam [4]. Damage variables

Eccentricity

fbo/fco

Kc

Viscosity parameter

30 (Legend 6)

D100%

0.1

1.16

2/3

0.001

35 (Legend 7)

D100%

0.1

1.16

2/3

0.001

30 (Legend 8)

D100%

0.1

1.16

2/3

0.004

30 (Legend 9)

D100%

0.1

1.16

2/3

0.007

35 (Legend 4)

D10%

0.1

1.16

2/3

0.001

40 (Legend 5)

D10%

0.1

1.16

2/3

0.001

Dilation angle First quadrant

Third quadrant

Parameters for the nonlinear numerical model The damaged plasticity model for concrete with the constitutive relationship, described in Section 3.1.1 of Chapter 3, was implemented in the evaluation of the structural performance of the unsymmetrical steel-concrete composite precast beams with T-section steel. Plastic flow potential function and concrete-damaged plasticity in the nonlinear finite element model were governed by parameters presented in Section 3.1.3 of Chapter 3. The damage variable as a function of plastic strain was implemented in the constitutive relationship for the concrete; it was also suggested to explore the degradation of concrete both in compression and tension. The parameters for the precast composite beam consisting of T-section steel are listed in Table 9.2.4.

9.2.2.4 Test results Fig. 9.2.13 displays the major failure modes of the composite beams [4]. The deflected shape of the steel-concrete composite beams is numerically obtained based on the damage-plastic model of concrete in Fig. 9.2.14. In Table 9.2.4 and Fig. 9.2.15 (refer to Section 3.1.3.3 of Chapter 3), the average flexural moment capacity of the beam section at the maximum load limit state was measured as 178 kN-m (99.8 kN) in the direction along which the major concrete was unbonded with a steel flange in the compression zone. No steel flange was available in compression. However, 221 kN-m (124.1 kN) was reached when the major concrete was bonded with a steel flange in the compression zone; the steel flange was available in compression. The precast composite beams with a T-section steel showed a significant increase in the flexural moment capacity with good ductility in addition to providing the steel connection for the column-to beam joint, which would enhance the erection

FIG. 9.2.13 Failure modes of specimens [4].

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FIG. 9.2.14 Unsymmetrical deflected shapes for the tested specimen [4].

FIG. 9.2.15 Sensitivity of dilation angles and damage parameter to the flexural capacity of the composite beam; Legends 4, 5, 6, and 7 [4].

capacity similar to that of the steel frames. At the drift angle of 0.03°, cracks were observed along with the height of the beams (3–4 mm wide cracks in the bottom of specimens and 0.1–0.2 mm wide cracks at the top). When the major concrete section in the compression zone (in the third quadrant) was confined by the steel flanges, the composite action of the steel flanges with concrete was demonstrated, contributing to the greater flexural strength of the composite section, rather than contributing to the flexural strength in the first quadrant, where concrete section was not confined by the steel flange. In the third quadrant, shown in Fig. 9.2.16, the compressive steel flange strains reached 0.0014 and 0.0029, corresponding to the compressive concrete strains of 0.0056 and 0.008, respectively. However, more tensile cracks were observed in the concrete of the tension zone (in the first quadrant), which was not confined by the steel sections, when loads were applied in a negative direction. Fewer tensile cracks were observed in the concrete of the tension zone (in the third quadrant), which was confined by the steel sections when loads were applied in a positive direction. Both the predicted flexural capacity and the crack patterns were in agreement with the experiment results. Table 9.2.5 summarizes the results of the test and numerical investigations for all specimens. More hysteretic energy was also dissipated when the concrete was confined by the steel flanges in the compression zone, as shown in the observed test of Table 9.2.5. Readers are referred to the in-depth description of the test results found in Ref. [4].

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FIG. 9.2.16 Test data versus nonlinear numerical results (Specimen PS2); Legends 4, 5, 6, and 7 [4].

TABLE 9.2.5 Summary of the test and numerical data for all specimens [3]. Yield limit state Specimens Specimen #1 (PS1)

Specimen #2 (PS2)

Specimen #3 (PS3)

Average

Maximum load limit state

Test

Numerical

Error

Test

Numerical

Error

Positive moment

Load (kN)

80.4

83.1

3.2%

98.3

95.2

+3.3%

Rebar strain

0.00216

0.00219

1.4%

0.00786

0.00786

0%

Negative moment

Load (kN)

115.2

111.5

+3.3%

124.3

120.4

+3.2%

Rebar strain

0.00220

0.00219

+0.5%

0.00517

0.00482

+7.2%

Positive moment

Load (kN)

83.9

83.1

+1.0%

103.2

95.2

+8.4%

Rebar strain

0.00219

0.00219

0%

0.00898

0.00786

+14.2%

Negative moment

Load (kN)

112.3

111.5

+0.7%

121.7

120.4

+1.1%

Rebar strain

0.00217

0.00219

0.9%

0.00500

0.00482

+3.7%

Positive moment

Load (kN)

83.3

83.1

+0.2%

98.0

95.2

+2.9%

Rebar strain

0.00214

0.00219

2.3%

0.00760

0.00786

3.3%

Negative moment

Load (kN)

109.7

111.5

1.6%

126.4

120.4

+5.0%

Rebar strain

0.00216

0.00219

1.4%

0.00490

0.00482

+1.7%

Positive moment

Load (kN)

82.5

83.1

0.7%

99.8

95.2

+4.9%

Rebar strain

0.00216

0.00219

1.2%

0.00815

0.00786

+3.6%

Negative moment

Load (kN)

112.4

111.5

0.8%

124.1

120.4

+3.1%

Rebar strain

0.00218

0.00219

0.5%

0.00502

0.00482

+4.2%

9.2.2.5 Structural behavior of the unsymmetrical precast composite beams The structural characteristics varied across the load direction, since the specimens were not symmetrical (refer to Section 3.1.3.3 of Chapter 3). The evaluated structural response of the specimens is presented in Fig. 9.2.15, where a good correlation between the numerical estimation and test observation was found. The strains of concrete, rebars, and steel section were presented on the load-displacement relationship. A lateral load capacity of 83.4 and 96.0 kN for the

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load reversals corresponding to a concrete strain of 0.003 were identified in Fig. 9.2.15. The numerical estimation without damaged plasticity demonstrated a significant inconsistency with the observed performance of the specimens. The magnitude of the damaged plasticity variable should be calibrated differently along the direction for the estimation of the flexural capacity of the steel-concrete composite beams, especially when the composite beams were fabricated with unsymmetrical steel sections. The selection of a constitutive relationship for a concrete based on damage variables with appropriate magnitude should reflect how the concrete was bonded with the steel sections in the compression zone, since the nonlinear parameters were influenced by the ductility of the composite sections. Results from the numerical estimation of the test specimens represented by the load-displacement relationship of Legend 6 in the first quadrant (Fig. 9.2.15), where no steel flange was available for bonding to the major concrete section in the compression zone, were in agreement with test data when the full damaged plasticity was used with a dilation angle of 30° and viscosity of 0.001. It was demonstrated that the flexural capacity with a dilation angle of 35°, represented by Legend 7 in Fig. 9.2.15, is greater by 3.7% than the computed capacity with a dilation angle of 30°, as shown in Fig. 9.2.15. However, the loaddisplacement relationship represented by Legend 6 was small relative to the test data in the third quadrant, where a steel flange was available for bonding with the major concrete section in the compression zone (refer to Fig. 9.2.15). The loaddisplacement relationship represented by Legend 4 (damage variable of 10%) was in agreement with the test data in the third quadrant, which displays the composite action with the concrete, allowing the compressive steel flange strains to reach 0.0014 and 0.0029 for a compressive concrete strains of 0.0056 and 0.008, respectively, in all specimens shown in Figs. 9.2.15–9.2.18. This result indicated that a smaller damage variable and large dilation angle were preferable for the composite beam sections where major concrete sections were bonded and confined by steel flanges; however, the numerical analysis indicated by Legend 4 yielded values greater than the experimentally observed data, with a large discrepancy in the first quadrant when small damaged plasticity model (10%) with a dilation angle of 35° was implemented in the first quadrant (refer to Fig. 9.2.15). Sections 9.3.1 and 9.3.2 of this chapter present the analytical prediction of the postyield behavior of the composite beams and columns based on the concrete confinements provided by not only stirrups, but the steel cores encased in structural concrete. In Fig. 9.2.18, the postyield behavior of Specimen PS1 based on von Mises and Tresca yield criterion for the steel section was compared indicating that load with von Mises criterion was less conservative than that of Tresca, because the von Mises criterion overestimated yield criterion more than Tresca. The von Mises model predicted lower effective stress (lower actual comparison to the yield strength) with a slightly lower load-displacement relationship than Tresca’s model for a given status of stress, as shown in Fig. 9.2.18. A good correlation with cyclic test data was demonstrated based on the implemented FE model up to the maximum loads even if the cyclic degradation of the materials and mechanical properties occurred during testing were not fully reflected in the descending region of the load-displacement relationship in the numerical analysis.

FIG. 9.2.17 Test data vs. nonlinear numerical results (Specimen PS3); Legends 4, 5, 6, and 7 [4].

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

367

FIG. 9.2.18 Test data vs. nonlinear numerical results (Specimen PS1); Legends 4, 5, 6, and 7 [4].

9.2.2.6 Load-strain relationship using strain compatibility based method The load-strain (rebars) relationship represented by Legend 10 of Fig. 9.2.19A was obtained based on the strain compatibility, which allowed for the precise prediction of the nominal moments at all limit states including the yield and maximum load limit state; the flexural moment capacities were calculated based on the neutral axes determined from the equilibrium equations at each limit state. Fig. 9.2.19B and C shows the strain and the stress of the composite beam section at the yield and maximum load limit state, showing the neutral axis and corresponding stress, and equilibrium of internal forces of the composite sections. From the equilibrium conditions when the loads were applied in a negative direction, the location of the neutral axis c from the top of the section can be calculated by Eq. (9.2.1) at the yield limit state. Solving the quadratic equation for c, the location of the neutral axis from the compressive extreme side of the beam was obtained as 122 mm at the yield limit state. The concrete strain (ec ¼ 0.00160) at the yield limit state corresponding to the rebar strain (et ¼ ey ¼ 0.00219) was calculated through the iteration. The corresponding nominal moment capacity (Eq. 9.2.2) of the composite beam was calculated to be 182 kN-m. The nominal moment capacity of the composite beam was calculated as 198.8 kN-m at the maximum load limit state. The simplified method based on the strain compatibility was in agreement with the full-scale test data indicated by Legend 1. The results were well compared with those obtained by the nonlinear finite element analysis represented by Legends 4 for the third quadrant and 6 for the first quadrant, as shown in Fig. 9.2.19A. 9 8
2 > > = < e sy 1 1 0 afc b + tw ec Es + tw Es + t w Fy c 2 > > 2 2 ec ; : n o
00 0  + A0s ec Es + A0f ec Es  tw ec Es d + tf  As fy  tw Fy ðd  d0 Þ c (9.2.1) (  
0 00 2 tf 1 00 00 0 +  A0s ec Es d  A0f ec Es d + + t w e c Es d + t f ¼ 0 2 2 C ¼ 122:0 mm

 e
00 2 Mn ¼ afc0 bcðc  gcÞ + A0s Es c c  d c       tf tf tf ec
000 0 00 000 0 c  d  tf c  d  cd  + Af Es + c 2 2 3 !
 2 esy 1 0 ec 1 0 00 0 c  d  tf + As fy ðd  cÞ + Awp Fy d  c  d + c + Aw E s 3 2 c ec
2 esy 1 + Awny Es c 3 ec ¼ 182:4 kNm-m  
 esy esy 000 0 0 where Aw ¼ tw c  d  tf , Awp ¼ tw d  c  d  , Awnp ¼ tw c: ec ec

(9.2.2)

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Hybrid composite precast systems

et = ey = 0.00219 est = 0.00168(1.16 esy)

437.5 MPa 330 MPa

esy = 0.00165

T C

122.0 mm

est¢ = 0.000288 et¢ = 0.000858

et¢Es = 171.6 MPa

ec = 0.00160

(B)

fc¢

At yield limit state

et = 0.00501(2.29 ey)

437.5 MPa 330 MPa

est = 0.00393(2.38 esy) esy = 0.00165

T C

est¢ = 0.000227 108.2 mm

et¢ = 0.00143

et¢Es = 286.6 MPa ec = 0.003

(C)

fc¢

At maximum load limit state

FIG. 9.2.19 Test data vs. numerical data (based on FE analysis and strain compatibility) [4].

9.2.2.7 Sensitivity of the dilation angles and damage variable to the nonlinear numerical behavior of the composite beams A dilation angle of 30° and the full damage application were successfully implemented to predict the structural behavior of the specimens where no steel sections were available for the confining concrete sections in the compression zone, resulting in less ductility than in the region where the concrete was confined by the steel flanges in the compression zone. Large

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

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concrete-damaged plasticity and smaller dilation angles were recommended to consider the decreased concrete ductility for the numerical investigation of the steel-concrete composite beams when the concrete was less confined with the steel sections in the compression zone. Large dilation angles and small damage variables reflecting an increased concrete ductility were implemented in regions where the concrete was confined strongly with the steel sections in the compression zone, preventing concrete damage. The load-displacement relationship of the specimens correlated well with test data.

9.2.2.8 Viscosity The use of the viscosity enhanced the convergence of the solution by decreasing the rate of the plastic flow and fracture with plastic degradation. The sensitivity of the viscosity to the execution time is compared in Table 9.2.6, where the strokes were calculated further with faster computing speed. In Fig. 9.2.20 and Table 9.2.6, the computing speed was substantially enhanced from 1.43 to 4.8 mm/h when a viscosity of 0.007 was implemented instead of 0.001. The numerical analysis results with increase in viscosity also increased the flexural capacity slightly, by 8.6%, even if some studies stated that changes in viscosity do not compromise the analysis results. The solution accuracy and convergence for the finite element solutions were influenced by the viscosity parameters and rate of plastic strains, showing that the rate of convergence and computation efficiency were significantly improved as a viscosity increased. However, the increase in viscosity can lead to the over-estimation of the structural capacities of the proposed hybrid steel-concrete beams, as shown in flexural capacities represented by Legends 9 and 6 in Table 9.2.6 and Fig. 9.2.20. This indicated that the viscosity should be carefully selected, since the large viscosity values can influence the numerical results. Good agreement with the test data was obtained when a value of 0.001 was used for the viscosity parameter, as illustrated by the load-displacement relationship in Legend 6 in the first quadrant of Fig. 9.2.15.

TABLE 9.2.6 Run efficiency vs. viscosity parameter [4]. Viscosity parameter

CPU/Run efficiency

Legend 6 (reached stroke: 89.0 mm, reached force: 104.2 kN)

0.001

62.2 h (2.6 days)/ 1.43 (mm/h)

Legend 8 (reached stroke: 89.0 mm, reached force: 109.2 kN, force increased by 4.8%)

0.004

26.9 h (1.1 days)/ 3.3 (mm/h)

Legend 9 (reached stroke: 106.9 mm, reached force: 113.2 kN; force increased by 8.6%)

0.007

22.5 h (0.9 days)/ 4.8 (mm/h)

ABAQUS model

FIG. 9.2.20 Influence of the viscosity on the flexural capacity of the unsymmetrical composite beams; Legends 1 (PS2, Fig. 9.2.16), 6, 8, and 9 [4].

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Hybrid composite precast systems

9.2.2.9 Influence of the steel section on the activation of the rebars and concrete in compression for the damage assessment The compressive strains of the concrete (refer to Fig. 9.2.21A), which increased similarly to those of rebars (refer to Fig. 9.2.21B), up to a concrete strain of 0.003 were retrieved from Legends 4 and 6 of Fig. 9.2.15 in both directions of the loading application [4]. The strain rates of the concrete (refer to Fig. 9.2.21A), and rebar (refer to Fig. 9.2.21B) in the compression zone increased more significantly in the third quadrant than in the first quadrant after undergoing strains of 0.006 for the concrete and 0.002 for the rebars. A steel flange was integrated with the concrete in the third quadrant while the concrete was not confined by the steel sections in the first quadrant. In Fig. 9.2.21A, the compressive concrete strain remained constant in the region where the concrete was not confined by the steel sections (in the first quadrant), while those in the region (in the third quadrant) where the steel sections were strongly confining the concrete were constantly increasing; the use of the increased concrete ductility with greater dilation angle and less damage variable were reflected in the numerical parameters. Fig. 9.2.21D illustrates the compressive strain rates of the steel flange, which increased linearly from the stroke of 18 and 94.4 mm; herein, the larger concrete strains were also sustained. However, in Fig. 9.2.21C, the compressive strain rates of the steel web in the third quadrant were smaller than those of the steel web in the first quadrant where the steel flange was not available. In Fig. 9.2.22A, it is shown that the use of the rebars with the steel section contributed to the flexural capacity effectively. The greater activation of the steel web section than that of the rebars in the compression zone, retrieved from Legend 6 of Fig. 9.2.15, maximizes the interaction of the steel section with the rebars and the reinforced concrete when the first quadrant is in compression. In Fig. 9.2.22B, where the third quadrant was in the compression zone, faster rates of the strain increase of the compressive strain were found for the rebars than those of the steel flange, headed studs, and steel web after the strains corresponding to a concrete strain of 0.003 (strains retrieved from Legend 4 of Fig. 9.2.15). The use of the rebars, which were activated quickly in the compression zone, can save the use of the steel sections, providing an effective contribution to the flexural capacity. The rates of the tensile strain increase for all structural components were illustrated in Fig. 9.2.22C and D which are retrieved from Legend 6 of Fig. 9.2.15 and Legend 4 of Fig. 9.2.15, respectively. In Fig. 9.2.22, the strain evolution of the hybrid composite beam was numerically evaluated at the concrete compressive strains of 0.003 and 0.008 (refer to Fig. 9.2.23A and B), demonstrating that the tensile rebar strain was well compared with the test data at the concrete compressive strains of 0.003. In Fig. 9.2.23A-(1) and 9.2.22C, the tensile strains of the rebar and steel flange reached 0.002 and 0.0015 (retrieved from the third quadrant; Legend 4 of Fig. 9.2.15), respectively, at the concrete compressive strain of 0.003 when the first quadrant was in compression (retrieved from the first quadrant; Legend 6 of Figs. 9.2.15 and 9.2.22A). Figs. 9.2.23B-(1) and 9.2.22D illustrate the tensile strains of the rebar and steel web reaching

FIG. 9.2.21 Influence of the steel flange on the strain rates of concrete and rebars (compression) [4].

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

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371

FIG. 9.2.22 Strain-stroke of the selected structural components; activation of the structural members (data extracted from Legends 4 and 6 of Fig. 9.2.15); refer to Fig. 9.2.23 [4].

0.0018 and 0.0011 retrieved from the first quandrant; Legend 6 of Fig. 9.2.15, respectively, at the concrete compressive strain of 0.003 when the third quadrant was in compression (retrieved from the third quadrant; Legend 4 of Figs. 9.2.15 and 9.2.22B). The compressive concrete strains increased to 0.006 and 0.0061 in the first quadrant (refer to Legend 6 of Fig. 9.2.18) and to 0.0056 and 0.008 in the third quadrant (refer to Legend 4 of Fig. 9.2.16) when rebar tensile strain reached 2ey and 5ey, respectively. The greater flexural capacity along with the direction with the steel flange being in compression was obtained because the concrete sections were confined by a steel section, allowing the concrete strains to reach 0.008 or greater. A maximized structural capacity with greater seismic capacity and ductility of the composite precast beams can be achieved by the effective use of the two materials, steel and concrete.

9.2.2.10 Prediction of the propagation for the tensile cracks and compressive crushing; an evaluation of damage evolution In Fig. 9.2.24, the estimation of the crack propagation and the concrete spalling with the failure modes was numerically estimated based on the concrete plasticity, resulting in an agreement with photos taken during testing. In Fig. 9.2.25, the influence of the interactive behavior between the steel and concrete materials on the flexural capacity of the precast composite beams was explored based on the concrete damage in compression with the identified strains and failure modes of the concrete, rebars, and steel sections. The concrete-damaged plasticity model representing the nonlinear, inelastic failure mechanisms of a concrete with the tensile cracking and compressive crushing was implemented to evaluate concrete cracks, as shown in Fig. 9.2.24, for the compression in both quadrants. The concrete spalling numerically evaluated in both compression and tension was validated via the experimental observations. Readers are referred to Section 3.1.1.1 of Chapter 3 for the description of cracks and their treatment.

FIG. 9.2.23 Stress evolution in the hybrid composite beam at a concrete compressive strains of 0.003 and 0.008 [4].

FIG. 9.2.24 Degradation of the steel-concrete composite beam based on damaged plasticity [4].

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

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373

FIG. 9.2.25 Concrete damage in the compression zone with identified strains [4].

9.2.3 Seismic capacity of the hybrid precast beams 9.2.3.1 Strong column-weak beam frame The ultimate strengths of the precast beam and column specimens with plastic hinges were assumed to occur at the concrete strain of 0.01. Tables 9.2.7 and 9.2.8 present the strains of the rebars and steel sections that yielded at a concrete strain of 0.01 while they were about to yield at a concrete strain of 0.003. Finite element analysis was implemented to determine the ultimate flexural capacities of the precast beam specimens at a concrete strain of 0.008–0.01. The calculated ultimate strengths were also compared with that of the tested results, as shown in Fig. 9.2.27B. All calculated ultimate flexural capacities of the precast beam specimens (refer to Fig. 9.2.26A and B) at the concrete strains of 0.01 are compared with the axial load-moment interaction diagram at a concrete strain of 0.01, which was defined as fracture criteria (refer to Fig. 9.2.27A and B). The ultimate strength of the column specimens with plastic hinges is greater than that of beam specimens, ensuring the seismic details as a strong column-weak beam system.

9.2.3.2 Story drift angle qualified as a special moment frame The beam-column joint having a T-shaped steel section (Fig. 9.2.28A) achieved a story drift ratio (inner-story drift angle) of 0.0045 radians before experiencing a 20% strength degradation when subjected to a quasistatic cyclic loading protocol, as shown in Fig. 9.2.28B. The tested beam-column joints achieved story drift ratios (inner-story drift angle) of 0.071 (120 mm at 315 kN) and 0.075 (120 + 105)/2 mm at 150 kN) radians for the test specimen shown in Fig. 2.5.5(A)-(2) of Chapter 2 (Specimen C6) and Fig. 2.6.13 of Chapter 2 (Specimen B6), respectively, before reaching 20% strength degradation. This

374

Hybrid composite precast systems

TABLE 9.2.7 Strains of the rebars and steel flanges of the column at a concrete strain of 0.003.

TABLE 9.2.8 Strains of the rebars and steel flanges of the column at a concrete strain of 0.008.

44 mm 44 mm 44 mm

Cast-in-place concrete d≤ = 61 mm

T–150¥150¥6.5¥9 (SM490)

A¢s(Atop) = 1548.4 mm2 (4-HD22) d¢¢¢ = 100 mm Headed stud (d = 13 mm)

d¢ = 43.5 mm

h = 350 mm

d¢ = 293.5 mm

As(Abottom) = 253.4 mm2 (2-HD13)

100 mm

h = 350 mm, d = 289 mm, b = 300 mm Es = 200,000 MPa fy = 400 MPa f ¢c = 27 MPa

Precast concrete

(A)

56.5 mm

b = 300 mm

Fy = 330 MPa

Beam section

h = 550 mm

25 mm

134.5 mm

50 mm b = 550 mm h = 550 mm f ¢c = 30 MPa Hoop HD10@200 As = 3096.8 mm2 (8-HD22) H–194¥150¥6¥9 (SM490) b = 550 mm

(B) FIG. 9.2.26 Tested beam-column joint.

Column section

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

FIG. 9.2.27 Strong column-weak beam verification of the tested joint.

9

375

376

Hybrid composite precast systems

D = 80 mm 44 mm 44 mm 44 mm

Cast-in-place concrete d≤ = 61 mm T–150¥150¥6.5¥9 (SM490)

h = 350 mm

d¢ = 293.5 mm

As(Abottom) = 253.4 mm2 (2-HD13) A¢s(Atop) = 1548.4 mm2 (4-HD22) d¢¢¢ = 100 mm Headed stud (d = 13 mm)

d¢ = 43.5 mm

100 mm

h = 350 mm, d = 289 mm, b = 300 mm Es = 200,000 MPa fy = 400 MPa f ¢c = 27 MPa

L = 1780 mm Precast concrete

b = 300 mm

56.5 mm

Fy = 330 MPa

q : inner-story drift angle Tanq = Δ / L = 80/1780 = 0.045 → q ≈ 0.045 rad

q

(B)

q

Rotation capacity of the joint

FIG. 9.2.28 Story drift angle qualified as a special moment frame (T-shaped steel section).

indicated that these precast beam-column frames, can be used as either a special moment frame or intermediate moment frame. The details of the test specimens can be found in Chapter 2.

9.2.4 Prestressed precast beam monolithically integrated with columns Figs. 9.2.29 and 9.2.30 show a prestressed precast beam that was monolithically integrated with the columns having the laminated plates, introduced in Chapter 2. The erection procedure using the integrated beam-column frame module for pipe-rack frames is demonstrated in Fig. 7.2.2 of Chapter 7. The locations of the mechanical joints are shown in Figs. 9.2.29 and 9.2.30A-(1) where the upper, lower, and filler plates are laminated, such that the rebars are anchored by the nuts in the filler plates (refer to Fig. 9.2.30A-(2) and (3)). Details of the laminated mechanical plates showing holes for the rebars and bolts are also presented. Fig. 9.2.30B also shows the locations of the anchorages for straight tendons. However, a parabolic tendon profile can be implemented for a more efficient introduction of the prestressing forces.

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

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377

FIG. 9.2.29 Reinforcement of the frame with locations of the mechanical joints.

Anchorages are installed as shown in Fig. 9.2.30B-(1) and (2), where the straight tendons provide initial cambering, as shown in Fig. 9.2.30D-(1). As shown in Fig. 9.2.30C, a finite element model was developed for the numerical investigation of the frame module, where a total of 579,834 elements with C3D8R and R3D4 element types was used, as shown in Fig. 9.2.30C-(1). Eight types of the interactions for all surfaces in contact are defined as the master or slave surfaces (refer to Section 3.2.1 of Chapter 3) to avoid the penetrations between the interface as shown in Fig. 9.2.30C-(2) and (3) in which the penetration between the tendon anchorages and the concrete was avoided by assigning the master and slave surfaces to the tendon anchorage and concrete, respectively. The strain contour with the deflection at the final stage is shown in Fig. 9.2.30D-(2), elucidating that the prestressed precast pipe-rack module performed well to support loads with 45 kN/m including equipment and pipe-lines. Readers are referred to the assembly and installations of the pipe-racks using a prestressed precast pipe-rack module as introduced in Section 7.2.2 of Chapter 7.

9.2.5 Discussions and conclusions 9.2.5.1 Composite precast beam with T section steel The use of steel structures was beneficial for an assembly of building frames, offering good structural performance when replacing conventional cast-in-place composite beams. The proposed structural solution combines the steel and concrete, offering the advantages not only in terms of the structural stability but also the constructability, cost-effectiveness, and environmental friendliness. The hybrid composite structural system exhibited the advantages that both precast concrete and steel frames have; that is, the hybrid composite precast concrete frames were assembled with the steel joints, combining the economy of concrete construction with the speed of steel construction. This section provided the numerical parameters and design recommendations by examining the influence of the precast composite beams encasing the unsymmetrical steel sections on the concrete degradation and damage evolution. In this chapter, the influence of the stiffness degradation variables and dilation angles on the nonlinear plastic deformation of the steel-concrete precast hybrid composite beams was investigated, and verified by the tests to evaluate the seismic capacity of the steel-concrete hybrid composite precast beams. Parameters including stiffness degradation variables and dilation angles were calibrated to provide an accurate estimation of the nonlinear structural behavior of the steel-concrete precast composite beams. Ductility, confining pressures for calculating dilation angles and stiffness degradation, were important nonlinear numerical parameters to determine the DCA between the steel and concrete when numerically estimating the flexural capacity of the composite beams. The application of the numerical method led to the understanding of the structural behavior of the precast composite beams encasing the wide flange and T-shaped steel section in the concrete. In the past, engineers had limited access to such sophisticated numerical analyses and the use of the complex nonlinear FEA parameters for the analysis and design of the steel-concrete composite members. In the following section, the simplified but highly accurate analysis and design methodology for the steel-concrete composite members based on a strain compatibility are introduced.

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Hybrid composite precast systems

FIG. 9.2.30 Prestressed precast beam monolithically integrated with columns.

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

FIG. 9.2.30, cont’d

9

379

380

Hybrid composite precast systems

FIG. 9.2.30, cont’d

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

FIG. 9.2.30, cont’d

9

381

382

Hybrid composite precast systems

9.3 Analytical prediction of the nonlinear structural behavior of the steel-concrete hybrid composite structures 9.3.1 Conventional strain compatibility approach AISC specification Section I.3.3 (AISC 2010, AISC. 2010. Specification for structural steel buildings. ANSI/AISC 360-10, Chicago [8]) prescribes methods to determine the nominal flexural strength of SRC members for two cases with/without shear anchors. The Fig. 9.3.1, cited from the study of Chen [9], distinguished new analytical aspects of the present chapter compared to those AISC methods. The AISC method proposed analytical expressions for the following two cases. (A) For members without shear anchors between the steel section and concrete, the nominal flexural strength shall be determined using (1) or (2) below: (1) Superposition of elastic stresses on the composite section (refer to Fig. 9.3.1A); the equilibrium of the section is based on the elastic stress distribution considering the effects of shoring. (2) Plastic stress distribution on the steel section alone (refer to Fig. 9.3.1B); the equilibrium is based on the plastic stress distribution of the steel section only. (B) When shear anchors are provided between the steel section and concrete, the nominal flexural strength shall be determined based on the PSD method (refer to Fig. 9.3.1C), or the strain compatibility (refer to Fig. 9.3.1D and E): (1) Plastic stress distribution on the composite section method; a plastic design for rebars and steel section (refer to Fig. 9.3.1C) is used with the concrete rectangular stress block based on the neural axis. (2) Strain compatibility method; a design based on the strain compatibility for the rebars and steel section (refer to Fig. 9.3.1D) with the concrete rectangular stress block is used. The equilibrium based on the concrete rectangular stress can be refined better based on a nonlinear stress-strain relationship. (3) Modified strain compatibility method; a plastic design for the rebars and steel section (refer to Fig. 9.3.1E) is used. The concrete rectangular stress block for both the concrete and the plastic stress distribution for the steel sections is used in which the strain compatibility for the steel sections was not considered. 0.85fc¢

Ecec

Eses¢ £ (Fy)r

(Fy)r (Fy)r

Eses Concrete

EseS1 £ (Fy)r Concrete

(A)

EseS2 £ (Fy)r Fy Reinforcing bars Steel

(C)

c

Reinforcing bars

Steel

0.85fc¢

a = b1c

Eses¢ £ (Fy)r

EseS1 £ (Fy)r Fy (Fy)r Concrete Reinforcing bars Steel

Fy

(D)

Stress distribution based on strain compatibility method εc = 0.003

Fy

(B)

Fy

Plastic stress distribution on the composite section ε c = 0.003

Stress distribution based on superposition of elastic stresses

Steel

Fy

(Fy)r

c

c

0.85fc¢

a = b1c

Plastic stress distribution on the steel section

(Fy)r (Fy)r Strain profile Concrete

Fy

(Fy)r

Fy

Reinforcing bars Steel

(E) Modified plastic stress distribution on the composite section FIG. 9.3.1 Conventional strain compatibility approach [9].

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

383

However, the strain compatibility method of the present chapter is distinguished in mainly two aspects to improve the assumptions introduced in AISC methods: (1) A rectangular concrete stress block was not used. Instead, the nonlinear constitutive relationships of the concrete were implemented to calculate the mean stress factor a and the centroid factor g for any given concrete strains at the extreme compression as shown in Eqs. (9.3.5)–(9.3.12) [10], and followed by the determination of the neutral axes. The neutral axes are not as accurate as the ones calculated in this chapter [10] when using the traditional approaches of calculating neutral axes based on elastic distributions (Fig. 9.3.1A) or the plastic stress distribution of steel sections (Fig. 9.3.1B, C, and E). (2) A computation algorithm [10], shown in Fig. 9.3.2F, based on the strain compatibility was developed to estimate the neutral axis and the corresponding nominal moment capacity of a steel-concrete composite section. This algorithm automatically analyzed entire sections from the top to the bottom to locate the neutral axis of the section based on the accurate stress factor a and the centroid factor g via the iterations indicated in the flow chart.

9.3.2 Steel-concrete hybrid composite beams without axial loads 9.3.2.1 Analytical models of the concrete confined by transverse rebars and wide-flange steel sections based on an iterated strain compatibility The accurate prediction of the postyield behavior of the composite beams requires an understanding of the constitutive relationships of the concrete with the confinements provided by the surrounding structural elements including stirrups and wide flange steel sections encased in a concrete. However, the estimation of the postyield structural behavior of the composite beams composed of the structural steel and concrete is quite a complicated issue. In this section, the neutral axis was estimated using equations based on an iterated strain compatibility. The postyield behavior and the flexural moment strength reflecting the buckling of the reinforcing rebars in the compression zone were evaluated, considering the concrete section confined by the transverse shear reinforcement and the steel flange. The parabolic arching (refer to Fig. 9.3.2A) for the concrete confined by the steel beam section and the reinforcing bars was proposed by Chen and Lin [11] in which the confinement of the concrete encasing steel section were divided into three regions: (1) an unconfined concrete region outside the parabolic arch formed by the longitudinal bars, (2) a highly confined region inside the arch formed by the steel section, and (3) a partially confined region outside the highly confined concrete region and inside the parabolic arch formed by the longitudinal bars. Concrete stress-strain distributions at the yield limit state and the maximum limit state are established based on the confined concrete by the four zones simplified by straight lines, as shown in Fig. 9.3.2B and C [10]. The steel beam encased in the structural concrete and the nomenclature describing the section is shown in Fig. 9.3.2. The steel flanges yield at the yield limit state. The maximum load limit state is the state when the nominal flexural strength was at the maximum value, while the ultimate flexural strength was obtained when the substantial contribution of the concrete was lost. In Fig. 9.3.2B

Concrete confined by stirrups and a steel section (Parabolic arching formed by the

(A)

longitudinal bars and structural steel section (Chen and Lin, 2006)) [11] FIG. 9.3.2 Four simplified zones with concrete stress-strain profiles.

384

Hybrid composite precast systems

FIG. 9.3.2, cont’d

and C, the neutral axes satisfying the equilibrium for these three limit states are calculated using the analytical expressions derived based on the concrete stress-strain profiles with the four simplified zones. This section presents an iterated strain compatibility based analytical model to predict the postyield behavior of the composite beams. The neutral axis and the corresponding nominal moment capacity of the steel-concrete composite beam section were calculated based on a

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

385

FIG. 9.3.2, cont’d

computing algorithm, which used analytical equations with a strain compatibility, shown in Fig. 9.3.2F [10], when the axial loads were not applied. The computing algorithm was proposed to estimate the neutral axis and the corresponding nominal moment capacity of the steel-concrete composite beam section. In Fig. 9.3.2G, an algorithm automatically performed 1,440,000 iterations to locate the neutral axis of the entire cross section of the composite beams from top to bottom [10]. A total of 1200 strains at the extreme fiber of the upper section corresponded to the same numbers of strains at the lower extreme fiber for the iteration. The neutral axes of the composite sections were fast and accurately identified by finding locations satisfying equilibrium equations. The algorithm also

386

Hybrid composite precast systems

[10]

(E)

Rebars buckled during beam testing

FIG. 9.3.2, cont’d

calculated parameters required to design composite beams, including the nominal moment capacity considering concrete confinement provided by both transverse reinforcements and wide flange steel sections. The prediction of the precast composite beams based on the iterated strain compatibility was verified by the test and the nonlinear finite element analysis considering concrete damaged plasticity.

9.3.2.2 Prediction of the nonlinear structural behavior of the steel-concrete composite beams Equivalent confining factors The influence of the wide flange steel sections on the concrete confinement was investigated to establish the confinement factors for the composite beams. The concrete zone confined by the steel flange and transverse rebars was formulated in terms of the confinement factors, Kh and Kp. In this model, rebars lost their strength when the concrete cover reached the peak strength, initiating the buckling of rebars in the compression zone. The formation of a hinge length and its influence on the postyield behavior were also influenced by the buckling of rebar in the compression zone. The automated evaluation of the postyield behavior and the flexural strength of the composite beams were performed by implementing Matlab. For the composite beams, the confining factors did not significantly influence the flexural load resisting capacity at both the yield

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

387

FIG. 9.3.2, cont’d

limit and the maximum load limit state. The highly confined zones with the concrete stress-strain profiles, shown in Fig. 9.3.2B and C, were small at the yield and maximum load limit state. However, the rebar buckling caused a decrease in the moment strength. The buckling in the compression zone was not normally considered in the flexural analysis of beams. The proposed analysis results were validated by the test data and the numerical results using nonlinear finite element analyses considering concrete plasticity. Idealization of the concrete confined by the structural steel sections Sheikh and Uzumeri [18] and Mander et al. [2, Chapter 3] modeled the area of effectively confined concrete core that occurred between the reinforcing bars of a composite beam section as parabolic arching. The concrete region confined by the structural steel section was formed with the arching similar to that suggested by Mirza and Skrabek [12] and ElTawil and Deierlein [13]. In Equations (9.3.1a) and (9.3.1b), the confined concrete strengths were defined by fc ¼ Kp fco and fcc ¼ Kh fco, according to Chen and Lin [11], where Kp and Kh were confinement factors for partially and highly confined concrete, respectively. In Fig. 9.3.2B and C, the confined concretes, and the stress-strain relationships are represented by the four zones shown, in Fig. 9.3.2A and D. fcc ¼ Kp fco

(9.3.1a)

fcc ¼ Kh fco

(9.3.1b)

388

Hybrid composite precast systems

De is assigned to determine neutral axis De = 0.0000125 1200 steps

Total = 1200 x 1200 = 1400,000

1200 steps

(G)

Computation algorithm based on strain compatibility, iteration scheme

[11] FIG. 9.3.2, cont’d

Influence of the buckling of the longitudinal bars and the structural steel A constitutive model of the longitudinal reinforcing rebars in the compression zone suggested by Bayrak and Sheikh [14] was slightly modified to consider the confined concrete effect (Fig. 9.3.2H). The rebar buckling in compression zone is represented by the postbuckling strength of the rebar, which maintained constant (20% of its yield strength from the maximum concrete strain (ec,max) corresponding to the maximum confined concrete compressive strength (fcc)) after the longitudinal rebars under the compression reached the ultimate concrete strain (ecu). Rebars buckled and lost their strength when concrete covers spalled, as observed in the experimental investigation shown in Fig. 9.3.2E. The local buckling of the longitudinal reinforcing rebars occurred after the partially confined concrete was crushed, while the steel section encased in the concrete did not buckle. The constitutive relationship considering buckling was used for the reinforcing steels (Fig. 9.3.2H). In the tension zone, the longitudinal reinforcing steels of the composite members subjected to a flexural bending moment were modeled based on the elasto-plastic constitutive relationship. For the steel sections, the elasto-plastic constitutive relationship was used for both the compression and tension zones.

9.3.2.3 Formulation of the equilibrium at the yield and maximum load limit states based on an iterated strain compatibility In Fig. 9.3.2B and C, the neutral axes satisfying the equilibrium are calculated using equations derived at the limit state including the yield limit, maximum load, and ultimate load limit state based on the four simplified zones with the concrete

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

389

stress-strain profiles. The equilibrium at the yield and maximum load limit states based on an iterated strain compatibility shown in Section 9.3.2 was formulated and validated by Nguyen and Hong [10].

At the yield limit state The equilibrium equations are given in Eqs. (9.3.2), (9.3.3), where the neutral axis, c1, is calculated. In Eq. (9.3.4), the four zones, including the unconfined concrete (green region), confined concrete (cyan region), partially confined concrete (yellow region), and highly confined concrete (orange region) were formulated for the concrete compressive forces. Here, c1 is the neutral axis of the section at the yield limit state. The mean stress factors a and centroid factors g are derived in Eqs. (9.3.5)–(9.3.8), (9.3.9)–(9.3.12), respectively. In Fig. 9.3.2B, the depths of the compressive concrete blocks indicated by c2, c3, and c4, represent the zones confined by the steel section. Eq. (9.3.4) calculates relationships between the compressive concrete blocks and the neutral axis (c1). The Mander confining curve was used in these equations. Faxial ðzero when there is no axial loadsÞ + Cc + FRcompression + Fsteelcompression ¼ FRtension + Fsteeltenstion

(9.3.2)

Faxial ¼ FRtension + Fsteeltenstion  Cc  FRcompressioon  Fsteelcompression

(9.3.3)

or

where the compressive concrete components were calculated using, Cc ¼ a1  c1  B1  f 0 c  a0 1  c2  B2  f 0 c + a2  c2  B2  f 0 cc  a0 2  c3 B3  f 0 cc + a3  c3  B3  Kp  f 0 cc  a0 3  c4  B4  Kp  f 0 cc + a4  c4  B4  Kh  f 0 cc

(9.3.4)

The concrete components in Eq. (9.3.4) were replaced for the green region based on the unconfining curve of Fig. 9.3.2B as follows: Cc1 ¼ a1  c1  B1  f 0 c 0

C’c1 ¼ a 1  c2  B2  f

(9.3.4a) 0

c

(9.3.4b)

For the confined concrete based on the Mander curves (refer to cyan region of Fig. 9.3.2B): Cc2 ¼ a2  c2  B2  f 0 cc

(9.3.4c)

C0 c2 ¼ a0 2  c3  B3  f 0 cc

(9.3.4d)

For the partially confined concrete based on the Mander curves (refer to yellow region of Fig. 9.3.2B): Cc3 ¼ a3  c3  B3  Kp  f 0 cc

(9.3.4e)

For the highly confined concrete, based on the Mander approach (refer to orange region of Fig. 9.3.2B): C0 c4 ¼ a0 4  c4  B4  Kh  f 0 cc

(9.3.4f)

where the depths of each compressive concrete block were obtained based on the knowledge of the neutral axis, c1, as follows: c2 ¼ c1  x1; x1 (40 mm) c3 ¼ c1  x2; x2 (93.75 mm) c4 ¼ c1  x3; x3 (139 mm) and the mean stress factors a for the four zones are obtained by: ð ecm1 fc1 dec c1 0 a1 ¼ 0 ;ecm1 ¼ eyS  f c ecm1 ds + h  c1 ð ecm2 fc1 dec 0 0 a1¼ 0 f c ecm2

(9.3.5)

(9.3.5a)

390

Hybrid composite precast systems

ð ecm2 a2 ¼

fc2 dec

0

f0

cc ecm2

;ecm2 ¼ eyS  ð ecm3

a0 2 ¼ ð ecm3 a3 ¼

0

Kp f 0 cc ecm3

¼

ð ecm4

0

a3¼

0

(9.3.6a)

f 0 cc ecm3

fc2 dec

f 0 cc ecm3

;ecm3 ¼ eyS  ð ecm4

Kp fc2 dec

c3 ds + h  c1

0

(9.3.7)

fc2 dec

¼ 0 Kp f 0 cc ecm4 f cc ecm4 ð ecm4 ð ecm4 Kh fc2 dec fc2 dec c4 ¼ 00 ;ecm4 ¼ eyS  a4 ¼ 0 0 Kh f cc ecm4 f cc ecm4 ds + h  c1 0

(9.3.6)

fc2 dec

0

ð ecm3 Kp fc2 dec

c2 ds + h  c 1

(9.3.7a)

(9.3.8)

Here, the centroid factors g are given as: ð ecm1 g1 ¼ 1 

0

ecm1

ec fc1 dec

ð ecm1 0

(9.3.9) fc1 dec

ð ecm2

g0 1 ¼ 1 

ec fc1 dec ð ecm2 ecm2 fc1 dec 0

0

ð ecm2

g2 ¼ 1 

(9.3.9a)

ec fc2 dec ð ecm2 ecm2 fc2 dec 0

(9.3.10)

0

ð ecm3

g0 2 ¼ 1 

0

ð ecm3 g3 ¼ 1 

0

ecm3

ec ðKp fc2 Þdec

ð ecm3 0

ð ecm4

g0 3 ¼ 1 

(9.3.10a)

ð ecm3

ec fc2 dec ð ¼1 ecm3 ðKp fc2 Þdec ecm3 fc2 dec 0

ð ecm4

ec ðKp fc2 Þdec ec fc2 dec ð ecm4 ¼ 1  0 ð ecm4 ecm4 ðKp fc2 Þdec ecm4 fc2 dec 0

ð ecm4

ec ðKh fc2 Þdec ec fc2 dec ð ecm4 ¼ 1  0 ð ecm4 ecm4 ðKh fc2 Þdec ecm4 fc2 dec

where As1 ¼ bf  tf1, As2 ¼ (ds + h  c1  tf1)  tw.

(9.3.11a)

0

0

0

(9.3.11)

0

0

ð ecm4

g4 ¼ 1 

ec fc2 dec ð ecm3 ecm3 fc2 dec 0

0

(9.3.12)

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

391

The internal forces contributed by the structural components of the section are shown as follows: FRcompression 5Ar2  Er  eyS  Fsteelcompression ¼ 0:5  As3  fyS 


 c 1  ds + t f 2 d s + h  c1

c 1  d2 ds + h  c 1

+ As4  fyS 

(9.3.13a)
 c1  ds + 0:5tf 2 ds + h  c 1

(9.3.13b)

where As3 ¼ [c1  (ds + tf2)]  tw, As4 ¼ bf  tf2. FRtenssion ¼ Ar1  Er  eyR  Fsteeltenstion 5As1  fyS 

d1  c 1 d s + h  c1

ds + h  c1  0:5tf 1 ds + h  c1  tf 1 + 0:5  As2  fyS  ds + h  c1 ds + h  c 1

(9.3.14a) (9.3.14b)

The nominal moment strength at the yield limit state was then obtained using Eq. (9.3.15): Mnominal ¼ MR=centroid + Msteel=centroid  MConc=centroid

(9.3.15)

where the flexural moment capacities provided by the structural components (with respect to the centroid) are shown as follows: MR=centroid 5Ar1  Er  eyS  

d1  c 1  ðd1  dc Þ  Ar2  Er  eyS ds + h  c 1

c 1  d2  ðd2  dc Þ ds + h  c 1

(9.3.15a)

ds + h  c1  0:5tf 1   ds1  dc + 0:5  As2  fyS ds + h  c 1
 c1  ds + tf 2 ds + h  c1  tf 1    ds2  dc  0:5  As3  fyS  ds + h  c1 ds + h  c 1

Msteel=centroid 5As1  fyS 


 c1  ds + 0:5tf 2    ds3  dc  As4  fyS   ds4  dc ds + h  c 1

(9.3.15b)

where the lever arms for the moment calculations are given as follows: ds1 ¼ ds + h  0:5tf 1  2
ds2 ¼ ds + h  tf 1 + 0:5c1 3  1
ds3 ¼ c1 + 2ds + 2tf 2 3 ds4 ¼ ds + 0:5tf 2 MConc=centroid 5a1  c1  B1  f 0 c  ðg1  c1  dc Þ  a0 1  c2  B2  f 0 c ðg0 1  c2 + x1  dc Þ + a2  c2  B2  f 0 cc  ðg2  c2 + x1  dc Þ a0 2  c3  B3  f 0 cc  ðg0 2  c3 + x2  dc Þ + a3  c3  B3  Kp  f 0 cc ðg3  c3 + x2  dc Þ  a0 3  c4  B4  Kp  f 0 cc   g03  c4 + x3  dc + a4  c4  B4  Kh  f 0 cc  ðg4  c4 + x3  dc Þ

(9.3.15c)

392

Hybrid composite precast systems

At the maximum load limit state Four simplified zones with the concrete stress-strain profiles at the maximum load limit state similar to those of the yield limit state are shown in Fig. 9.3.2C [10]. Equations for the maximum and the ultimate load limit states were derived to conduct an analytical investigation of the steel beams encased in the structural concrete [10]. The equilibrium equations are given in Eq. (9.3.16) at the maximum load limit state where the neutral axis is c1. Faxial ðzero when there is no axial loadsÞ + Cc + FRcompression + Fsteelcompression ¼ FRtension + Fsteeltenstion or Faxial ¼ FRtension + Fsteeltenstion  Cc  FRcompression  Fsteelcompression

(9.3.16)

Here, the internal forces in the tension zone contributed by the structural components of the section are shown as follows: FRtension ¼ Ar1  fyR  Fsteeltenstion ¼ As1 + As2 + 0:5As3  fyS

(9.3.16a) (9.3.16b)

where As1 ¼ bf  tf1, As2 ¼ (ds + h  c1  tf1)  tw, As3 ¼ (ds + h  c1  tf1)  tw. The compressive forces due to the concrete block are given by the following equations:
 Cc ¼ a1  c11  B1  f 0 c + 0:5  c12  B1  f 0 c + fecm1  a0 1  c21  B2  f 0 c
 0:5c22  B2  f 0 c + fecm2 + a2  c2  B2  f 0 cc  a0 2  c3  B3 f 0 cc + a3  c3  B3  Kp  f 0 cc  a0 3  c4  B4  Kp  f 0 cc + a4 c4  B4  Kh  f 0 cc

(9.3.16c)

The unconfined concrete is based on the Mander curve (refer to green region of Fig. 9.3.2C). The concrete components in Eq. (9.3.4) were replaced as follows: Cc11 ¼ a1  c11  B1  f 0 c
 Cc12 ¼ 0:5  c12  B1  f 0 c + fecm1 C0 c11 ¼ a0 1  c21  B2  f 0 c
 C0 c12 ¼ 0:5  c22  B2  f 0 c + fecm1

(9.3.16d1) (9.3.16d2) (9.3.16d3) (9.3.16d4)

The compressive forces due to the concrete block are given by the following equations for the confined concrete based on the Mander curves (refer to cyan region of Fig. 9.3.2C): Cc2 ¼ a2  c2  B2  f 0 cc

(9.3.16d5)

Cc2 ¼ a0 2  c3  B3  f 0 cc

(9.3.16d6)

The compressive forces due to the concrete block are given by the following equations for the partially confined concrete based on the Mander curves (refer to yellow region of Fig. 9.3.2C): Cc3 ¼ a3  c3  B3  Kp  f 0 cc

(9.3.16d7)

C0 c3 ¼ a0 3  c4  B4  Kp  f 0 cc

(9.3.16d8)

Finally, the compressive forces due to the concrete block are given by the following equations for the highly confined concrete based on the Mander approach (refer to orange region of Fig. 9.3.2C): Cc4 ¼ a4  c4  B4  Kh  f 0 cc and the mean stress factors a for the four zones are obtained by:

(9.3.16d9)

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

393

ð 0:002 a1 ¼

fc1 dec

0

(9.3.16d10)

0:002f 0 c

ð 0:002 0

a1¼ fc2 dec

0

f 0 cc ecm2

;ecm2 ¼ eyS  ð ecm3

a0 2 ¼ ð ecm3 a3 ¼

0

Kp

ð ecm3 Kp fc2 dec f0

cc ecm3

¼

0

ð ecm4

a0 3 ¼

0

c2 ds + h  c1

(9.3.16d12)

fc2 dec

0

(9.3.16d13)

f 0 cc ecm3

fc2 dec

f0

(9.3.16d11)

0:002f 0 c

ð ecm2 a2 ¼

fc1 dec

0

cc ecm3

;ecm3 ¼ eyS  ð ecm4

Kp fc2 dec

¼

0

c3 ds + h  c 1

(9.3.16d14)

fc2 dec

Kp f 0 cc ecm4 f 0 cc ecm4 ð ecm4 ð ecm4 Kh fc2 dec fc2 dec c4 ¼ 00 ;ecm4 ¼ eyS  a4 ¼ 0 0 Kh f cc ecm4 f cc ecm4 ds + h  c 1

(9.3.16d15)

(9.3.16d16)

Here, the centroid factors g are given as: ð 0:002

g1 ¼ 1 

ec fc1 dec ð 0:002 0:002 fc1 dec 0

(9.3.16d17)

0

ð 0:002

g0 1 ¼ 1 

ec fc1 dec ð 0:002 0:002 fc1 dec 0

0

ð ecm2

g2 ¼ 1 

(9.3.16d18)

ec fc2 dec ð ecm2 ecm2 fc2 dec 0

(9.3.16d19)

0

ð ecm3

ec fc2 dec ð g 2 ¼1 ecm3 ecm3 fc2 dec 0

0

(9.3.16d20)

0

ð ecm3
ð ecm3  ec Kp fc2 dec ec fc2 dec 0 ð g3 ¼ 1  0 ð ecm3
 ¼1 ecm3 ecm3 Kp fc2 dec ecm3 fc2 dec 0

0

(9.3.16d21)

394

Hybrid composite precast systems

ð ecm4
ð ecm4  ec Kp fc2 dec ec fc2 dec 0 ð g0 3 ¼ 1  0 ð ecm4
 ¼1 ecm4 ecm4 Kp fc2 dec ecm4 fc2 dec 0

ð ecm4

g4 ¼ 1 

ð ecm4

0

ec ðKh fc2 Þdec ec fc2 dec ð ecm4 ¼ 1  0 ð ecm4 ecm4 ðKh fc2 Þdec ecm4 fc2 dec 0

0

(9.3.16d22)

(9.3.16d23)

0

The internal forces in the compression zone contributed by the structural components of the section are then calculated as follows: FRcopression 5Ar2  Er  es1 

c 1  d2 ds + h  c 1

where the tensile strain of es1 at the steel flange was obtained as 0.0055.

 c 1  ds + t f 2 c1  ds + 0:5tf 2 + As5  Es  es1  Fsteelcompression ¼ 0:5  As4  Es  es1  ds + h  c 1 ds + h  c 1

(9.3.16e)

(9.3.16f)

where As4 ¼ [c1  (ds + tf2)]  tw, As5 ¼ bf  tf2. Finally, the nominal moment strength at the maximum load limit state is obtained using Eq. (9.3.17): Mnominal ¼ MR=centroid + Msteel=centroid  MConc=centroid

(9.3.17)

where the flexural moment capacities provided by the structural components with respect to the centroid (calculated by Eq. 9.3.16) are calculated as follows: c 1  d2  ð d2  dc Þ (9.3.17a) d s + h  c1
 
 
  Msteel=centroid 5 As1  fyS  ds1  dc + As2  fyS  ds2  dc + 0:5As3  fyS  ds3  dc

 c1  ds + tf 2 c1  ds + 0:5tf 2   (9.3.17b) 0:5As4  Es  es1   ds4  dc  As5  Es  es1   ds5  dc ds + h  c 1 ds + h  c 1 h
 MConc=centroid 5 a1  c11  B1  f 0 c  ðg1  c11 + c12  dc Þ + 0:5  c12  B1  f 0 c + fecm1  ð0:5c12  dc Þ
 a0 1  c21  B2  f 0 c  ðg0 1  c21 + c22 + x1  dc Þ  0:5c22  B2  f 0 c + fecm2  ð0:5c22 + x1  dc Þ MR=centroid 5Ar1  fyR  ðd1  dc Þ  Ar2  Er  es1 

+ ½a2  c2  B2  f 0 cc  ðg2  c2 + x1  dc Þ  a0 2  c3  B3  f 0 cc  ðg0 2  c3 + x2  dc Þ h i + a3  c3  B3  Kp  f 0 cc  ðg3  c3 + x2  dc Þ  a0 3  c4  B4  Kp  f 0 cc  ðg0 3  c4 + x3  dc Þ + ½a4  c4  B4  Kh  f 0 cc  ðg4  c4 + x3  dc Þ where the lever arms for the moment calculations are given as follows: ds1 ¼ ds + h  0:5tf 1

 eyS ds2 ¼ 0:5 ds + h  c1  1 +  0:5tf 1 + c1 es1 





2 eyS  ds3 ¼  d + h  c1 + c1 3 es1 s  1
ds4 ¼ c1 + 2ds + 2tf 2 3 ds5 ¼ ds + 0:5tf 2

(9.3.17c)

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

395

9.3.2.4 Verification analysis Verification model The computing algorithm developed by Nguyen and Hong [10] shown in Fig. 9.3.2F was used to estimate the neutral axis and the corresponding nominal moment capacity of the test Specimen C6, introduced in Fig. 2.5.1 of Chapter 2. The material properties of the steel section (H-250  250  9  14) with a yield strength of 350 MPa and reinforcing steels (4-HD25) with a yield strength of 550 MPa were obtained from the test samples when the axial loads were not applied. Compressive and tensile strengths of 21 and 2.1 MPa were used for the concrete encasing the steel sections and rebars. Young’s moduli of 200,000 and 21,538 MPa were implemented for the steels/rebars and concrete, respectively. In Fig. 9.3.2B, the compressive strains at the extreme fiber of the concrete and at the steel flange were found as 0.0017 and 0.00043, respectively, at the yield limit state. In Fig. 9.3.2C, the compressive strains at the extreme fiber of the concrete and at the steel flange were also calculated as 0.00384 and 0.00038 for the maximum limit state, respectively. Fig. 9.3.3 presents the influence of the confined concrete established by the confining factors including Kh and Kp, (provided by the steel section) on the nominal moment capacities at the yield, maximum load, and ultimate load limit state. Confinement factors, Kh and Kp, were used to simplify the concrete zone confined by the steel flange, which were then validated by the experimental data and the numerical results based on the nonlinear finite element analysis considering concrete plasticity. Nonlinear finite element analysis based on the concrete plasticity The concrete confined by the rebars and steel sections was modeled using 268,061 total elements with the element types as shown in Fig. 9.3.3A, in which the definition of the interactions between the reinforcing bars, steel sections, and the concrete were also developed [10]. In this model, the tie contact model allowed the concrete surface to be tied with the reinforcing bars and H-steels. Fig. 9.3.3B shows the overall FEA model, where the master surfaces (H-steels and reinforcing bars) and the slave surface (concrete surface) are defined (refer to Fig. 9.3.3C). The relative motion between the two surfaces cannot occur when the tie constraint method fuses together the master and slave surfaces; however, the rotations between the contacts were permitted with the buckling of the embedded elements. The local failure of a single node in the FEA model was prevented by applying a displacement to a rigid body object (JIG) with a dimension of 300  500 mm to distribute stress. The proposed FE models with a tie modeling technique accurately predicted the postyield behavior of the tested steel-concrete composite beam. Verification of the analytical model with the finite element analysis results The nonlinear finite element analysis and their results shown in Legends 2–4 of Fig. 9.3.3D were compared with the postyield behavior of the precast composite beams obtained based on the iterated strain compatibility approach (refer to equations in Section 9.3.2.3, and Legends 1A–D of Fig. 9.3.3D) at the yield, the maximum load, and the ultimate load limit states [10]. The moment-strain relationships for the shallow beam, represented by Legends 2, 3, and 4 in Fig. 9.3.3D, were obtained based on the varied confining factors (Kh and Kh) representing the confined concrete effects by the steel section. Differences of 6.58% (indicated by the red dots) and 7.45% (indicated by the black dots) at the yield and the maximum load limit state, respectively, were found between the analytical results with confining factors of Kh with 2.0 and Kp with 1.5 (refer to Legend 4 in Fig. 9.3.3D) of the shallow beam model and the FEA data (refer to Legend 1A in Fig. 9.3.3D). The greater load capacities of the deep beams were delivered than those of the shallow sections with a pure flexure. A compression force combining the load and the reaction was caused in deep beams creating significant shear deformations by a nonlinear strain distribution. For deep beams, the shape of the concrete compressive stress block may not be parabolic at the ultimate limit state and the stress distribution is not linear even in the elastic stage. The influence of the plasticity of the concrete on the postyield deformation of the deep beams with an L/d ratio of 3.9 at the maximum load limit state was more significant than that at the yield limit state, resulting in the greater moments strength which were observed for the maximum load limit state. Ignoring the plastic rotation caused by the inelastic energy dissipation in the analytical estimation of the curvatures in equations (refer to Section 9.3.2.3) based on the strain compatibility was partly responsible for the difference between the analytical and the numerical models at the maximum load limit state. The plastic rotations of the sections between cracks, which accompany the inelastic energy dissipation associated with diagonal concrete cracks, should be accounted for to achieve an accurate prediction of the postyield deformation of the composite beams at a maximum load limit state. The prediction should also include the stiffening effect of the concrete tension between cracks and plastic strains occurring in the steel section. The differences in the flexural capacity obtained by

396

Hybrid composite precast systems

between the numerical investigation (refer to Legend 1d of Fig. 9.3.3D with 9 m shallow beam and with a L/d ratio of 20) and the strain compatibility-based study with confining factors of Kh (2.0) and Kp (1.5) (refer to Fig. 9.3.2D and Legend 4 of Fig. 9.3.3D) reduced to 4.68% and 2.93% at the yield and the maximum load limit state, respectively. The moment-strain relationship represented by Legend 2 in Fig. 9.3.3D demonstrated a greater discrepancy when the confining effect offered by the steel sections was ignored with Kh and Kp being implemented as 1. Influence of the buckling effect of the reinforcing steels on the flexural strength The influence of the buckling effect of the reinforcing steels in compression on the flexural strength of the composite section was explored for the varied compressive concrete strains and tensile steel strains [10], respectively, as shown in Fig. 9.3.3E and F. A moment-steel strain relationship of all analyses (refer to Fig. 9.3.3D and E) is illustrated in Fig. 9.3.3F. The flexural strength of the composite section with the buckling of the reinforcing steels in the compression

(B)

FEA model for verification; overall model with load application

FIG. 9.3.3 Parameters influencing the flexural strength of the steel section encased in structural concrete; FEA compared with test data; momentcompressive concrete strain relationship based on tie models with fixed base (with base vs. without base) [10].

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

(C)

FIG. 9.3.3, cont’d

FEA model for verification; definition of interactions (H-steel, reinforcing bars, and concrete)

9

397

398

Hybrid composite precast systems

FIG. 9.3.3, cont’d

zone degraded more rapidly than one that did not consider the buckling of the reinforcing steels in compression when the confining effect offered by the steel section was considered. This can be seen with Fig. 9.3.3F, in which the flexural strength with considering the rebar buckling indicated by Legends 4, 5, and 6 of Fig. 9.3.3F degraded faster than the flexural strength without considering the rebar buckling indicated by Legends 1, 2, and 3, respectively, when considering the confining effects offered by the steel section. The highly and partially confined zones of the compressive concrete at the yield and the maximum load limit state were small, preventing the confining factors from significantly influencing the flexural load resisting capacity, when compressive buckling failure was not considered. Accurate flexural capacities of composite beams can be obtained when the rebar is modeled with the buckling in the compression zone. Table 9.3.1 summarizes the moment capacities at the maximum load and the design load limit states [10], which were identified from Fig. 9.3.3D and E. The design load limit state is defined at a concrete strain corresponding to 0.003. Verification of the algorithm Test specimens shown in Fig. 9.2.1 and the test results shown in Fig. 9.2.3 were used to verify the program algorithm based on the iterated strain compatibility. The input window shown in Fig. 9.3.4 assisted all parameters to be updated easily and fast for calculations. In Fig. 9.3.5A, the analytical results based on the iterated strain compatibility were compared with test data TABLE 9.3.1 Flexural capacities at the maximum load and the design load limit states [10].

Kp

Kh

Maximum load/ concrete strain

Maximum moment/concrete strain

Design load (concrete strain 5 0.003)

Design moment (concrete strain 5 0.003)

Elasto-plastic (steel + rebar) in both tension and compression, confined Mander curve, Fig. 9.3.3D Legend 2

1.0

1.0

380.6 kN/0.0046

647.0 kN-m/0.0046

373.0 kN

634.1 kN-m

Legend 3

1.2

1.5

382.7 kN/0.0046

650.5 kN-m/0.0046

373.5 kN

634.9 kN-m

Legend 4

1.5

2.0

384.1 kN/0.0046

652.9 kN-m/0.0046

374.3 kN

636.3 kN-m

Elasto-plastic (steel + rebar) in both tension and compression except EL-buckling for rebar in compression, confined Mander curve, Fig. 9.3.3E Legend 2

1.0

1.0

379.7 kN/0.0042

645.5 kN-m/0.0042

373.5 kN

635.0 kN-m

Legend 3

1.2

1.5

381.5 kN/0.0042

648.5 kN-m/0.0042

374.1 kN

635.9 kN-m

Legend 4

1.5

2.0

382.8 kN/0.0042

650.8 kN-m/0.0042

374.9 kN

637.3 kN-m

FIG. 9.3.4 Input window of the computing algorithm based on strain compatibility.

Strain compatibility (1.44 Million iterations)

TEST Specimen Load (kN)

Nominal moment (kN-m)

No. #1 (Push)

511

561.5

No. #1 (Pull)

790

865.7

No. #2

726

791.2

No. #3

899

984.2

No. #4

1065

1238.7

(A)

Load (kN) 505.4 (Error +1.1%) 779.1 (Error +1.4%) 712.1 (Error +1.9%) 885.8 (Error +1.5%) 1114.8 (Error –4.7%)

Nominal moment (kN-m) 581.4

Load (kN) 523.3 (Error –2.4%)

-

-

822.4 1000.2 1298.4

740.2 (Error –2.0%) 900.2 (Error –0.13%) 1168.6 (Error –9.7%)

Analytical results compared with test and plastic stress distribution method Nominal moment-Concrete strain relationship

1000

300 Neutral axis

Nominal moment

250

600

200

400

Nominal moment-Concrete strain curve

150

200 0

100 0

0.005 0.01 Concrete strain

´10–3

50

0.015

(1) Moment-compressive concrete strain 8

Neutral axis-Concrete strain curve

0

0.005 0.01 Concrete strain

0.015

(2) Neutral axis- compressive concrete strain

Top rebar strain-Concrete strain relationship 8

7

´10–3 Strain at upper flange-Concrete strain relationship

Strain at upper flange

7

6 5 4 3 Top rebar strain-Concrete strain curve

2

6 5 4 3 Strain at upper flange-Concrete strain curve

2 1

1 0

Neutral axis-Concrete strain relationship

350

800

Top rebar strain

Plastic stress distribution (PSD, ASCE)

0 0

0.005

0.01

0.015

Concrete strain

(3) Upper rebar-compressive concrete strain

(B) FIG. 9.3.5 Verification of the algorithm.

0

0.005

0.01

0.015

Concrete strain

(4) Upper steel flange-compressive concrete strain Strain analysis

400

Hybrid composite precast systems

12,500

SG1

SB1

SB1

SG1

SG2

SB1 : H-396 ´ 199 ´ 7 ´ 11 SG1 : H-496 ´ 199 ´ 9 ´ 14 SG2 : H-700 ´ 300 ´ 13 ´ 24

SG2

(A)

Conventional steel beam module 12,500 1

2

MHSG2 2

1

4

6

5

MHSG1

5

MHSB1

3

MHSB1

4

MHSG1

8700

3

6

MHSG2

4160

4180

4160

PLAN VIEW

(B) Proposed composite beam (MHS) module FIG. 9.3.6 Composite beams compared with conventional steel beams [19].

presented in Fig. 9.2.3 and the plastic stress distribution method (refer to Section 9.3.1), demonstrating a good correlation with both data. Fig. 9.3.5B exhibits selected strains relationships with the nominal flexural strength, neutral axes, rebars, and steel sections, enabling fast but accurate design of the composite beams with economy. The concrete compression zone of the beam section subjected to moment was found to be small; thus, the confinement effect provided by steel sections was insignificant, resulting in insignificant influence on the flexural load resisting capacity. Besides, the strain analysis efficiently identified the damage evolutions of the composite components predicting the failure modes of the composite beams. Fracture criteria of the concrete encased steel composite beams can be proposed when the double confinements provided by both transverse reinforcements and a wide flange steel section in the compression zone were accounted for.

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

401

FIG. 9.3.6, cont’d

Reduced beam depth using the composite beams The design of the conventional steel frames and their structural quantities of the module shown in Fig. 9.3.6A were compared with those of the composite frames shown in Fig. 9.3.6B. The composite beam sections designed based on the algorithm [10] shown in Fig. 9.3.2F are presented in Fig. 9.3.6C. The steel beam depth with 900 mm, including a slab of 150 mm and fire proofing, was reduced to a depth of 750 mm including the slab depth for the proposed composite beams (designated as for MHSG2 in Fig. 9.3.6B). The structural quantities of the steel were also significantly reduced, as shown in Fig. 9.3.6D, even if the concrete and rebars were added into the proposed composite beams. In the investigation shown in Fig. 9.3.6, the concrete strength of 28 MPa was used, whereas the yield strength of the rebars and steel sections were 500 and 315 MPa, respectively.

402

Hybrid composite precast systems

Steel Top rebar

MHSG2

Bottom rebar

H-446x199x8x12

Weight (kgf)/m 74

0.17 0.01 0.02 0.01 0.20

HD29 (end) HD13 (middle) HD13 (end) HD13 (middle)

Total rebar weight

Concrete Original steel weight

Steel Top rebar

MHSG1

Bottom rebar Total rebar weight

Concrete Original steel weight

Steel Top rebar

MHSB1

Bottom rebar

Concrete volume (m3)

Dimension (m)

Weight (ton)

3

0.60x0.40x12.5

7.5

Weight (kgf)/m 32

Weight (ton) 0.28

Original steel weight

(D)

Area (m2) Number

0.00066 0.000133 0.000133 0.000133

Length (m)

4 2 2 2

8 5 8 5

185 kgf/m

H-298x149x5.5x8 HD19 (end) HD13 (middle) HD13 (end+middle)

Concrete volume (m3) 0.9135

0.07 0.01 0.02 0.09 Dimension (m) 0.35x0.30x8.7

Weight (ton) 2.28375

Weight (kgf)/m 18

Weight (ton) 0.16

Area (m2) Number

0.000283 0.000133 0.000133

Length (m)

5 2 2

6 3 8.7

80 kgf/m

H-175x90x5x8 HD13 (end+middle) HD13 (middle) HD13 (end)

0.02 0.01 0.01 0.04

Total rebar weight

Concrete

Weight (ton) 0.93

Concrete volume (m3) 0.783

Dimension (m) 0.30x0.30x8.7

Area (m2) Number

0.000133 0.000133 0.000133

Length (m)

2 3 2

8.7 4 6

Weight (ton) 1.9575

57 kgf/m

Structural quantities of the composite beams vs. conventional steel beam size

FIG. 9.3.6, cont’d

9.4

Assembly of the steel beam-column joints with a skewed beam section

9.4.1 Conventional steel erection The conventional steel brackets with straight cuts for the assembling steel frames are shown in Fig. 9.4.1A. For heavy precast frames, the conventional steel joints with the brackets having straight cuts would require significant crane operation time to install all bolted stiffeners. The steel beams encased by the precast concrete can weigh more than 200 kN when they are designed for the floor loadings of 20 kN/m2. In the conventional steel assembly shown in Fig. 9.4.1A and B, the bolt holes are in the proper relative positions using the splicing plates of up to eight pieces (six plates for the upper and lower flanges and two plates for the web), which are temporarily installed to hold the column and beam brackets in a position before removing the cranes. This requires significant crane operation time. All the splicing plates are held together by a number of temporary bolts, with up to 20% of the total bolts at the joints, keeping the bolt holes aligned. The temporary web plates should also be replaced by the plates with the full bolt holes, requiring the extra time to connect the steel beam sections to the column brackets.

9.4.2 New erection method; splicing plates and bolting beyond critical path 9.4.2.1 Noncritical installation of the splicing plates and bolting The hybrid precast concrete encasing the steel beams can be heavy when they are designed for heavy floor loadings. These beams are difficult to erect and assemble via the conventional erection method since these precast beams usually have a deep depth with multiple bolts and heavy stiffeners. This section introduces a new erection method for the heavy precast

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

403

FIG. 9.4.1 Conventional column-beam connection with the temporary splicing plates and temporary bolting as critical path before removing cranes.

frames with heavy stiffeners and multiple bolts to replace the conventional erection method. Hong et al. [15] proposed to preinstall a pair of L-shaped channels to assemble T-shaped steel beams for the fast assembly of the beam-column joints subjected to heavy loads. This method allows a web of T-shaped steel beams without lower flanges to be inserted into the preinstalled L-shaped guide pockets (Fig. 9.4.2C). However, the mismatches will occur for the wide-flange steel beams with lower flanges. This mismatch can be resolved by introducing a novel beam-column joint consisting of a straightskewed web, shown in Fig. 9.4.2A and B [16], for easing the erection of the precast frames. This is accomplished by preparing skewed cuts for both the lower flanges of the column brackets (Fig. 9.4.2B-(1)) and the steel beam section (Fig. 9.4.2B-(2) and C).

9.4.2.2 Preinstallation of the L-shaped pocket The new connections, having the skewed cuts with the three types of web cuts, straight-skewed, skewed, and crank type, as shown in Fig. 9.4.2A, allowed the lower flange of the beam steel to be guided and placed between the two L-shaped pocket channels. As shown in Fig. 9.4.2B-(1), (2) and C, the lower flange of the column bracket and beam are partially removed to avoid bumping the bottom flange of the H-shaped steel beam into the L-shaped guide pockets (refer to Fig. 9.4.2D-(1)) preinstalled on the column bracket (refer to the upper pocket shown in Fig. 9.4.2D-(2)) when the bottom flange of the steel beam was inserted in the L-shaped pockets. The tolerances for the assembly of the column-beam frames with the wide flange steels were provided by preparing slot holes in the L-shaped pockets (refer to Fig. 9.4.2D-(1)), accounting for the misalignments of the holes during the manufacture of the L-shaped channels. The washer plates were used for the long slot holes. The guide pockets consisting of a pair of continuous L-shaped channels hold H-shaped steel sections [16] whereas the T-shaped beam [15] is to be placed in the pocket shown below Fig. 9.4.2D-(2) without cut. Fig. 9.4.3 shows the full-scale assembly and the connection details with a lifting simulation using the skewed web (refer to Fig. 9.4.3). Novel connections with the cuts along the steel web of columns and beams (the lower flange of column bracket and the beam was

(1) Web preparation of column bracket with a skewed cut

(2) Preparation of H-type beam steels with a skewed cut

(B)

Preparatin of joint steels

FIG. 9.4.2 Preinstallation of the L-shaped pocket; novel connection for assembling heavy precast frames.

H shaped and T shaped Steel beams

(C)

Preparation of H-type (a skewed cut) and T-type beam steels (a straight cut)

(1) L-type channel used for pocket with long slots

H-shaped steel (upper)

T-shaped steel (Lower)

(2) L-shaped guide pockets pre-installed at column bracket

(D) FIG. 9.4.2, cont’d

Installation of L-shaped guide pockets

406 Hybrid composite precast systems

FIG. 9.4.3 (A) Installation of steel beam sections having a skewed web in the L-shaped pockets. (B) Lifting of beam with skewed web for being guided/inserted into the preinstalled pockets.

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

407

FIG. 9.4.4 SRC (steel and concrete) precast joints.

partially removed) were developed to hold heavy frames in the preinstalled L-shaped pocket angles, helping position the steel beams in the L-shaped pockets (Fig. 9.4.3A and B-(1)). The installation of the temporary splicing plates for flange, web, and the temporary bolting being with a critical path are removed. The use of such bolts is reduced significantly, requiring only a few bolts, as demonstrated in the full-scale assembly test shown in Fig. 9.4.3B-(2) and (3), which shows one temporary erection bolt (or drift pin) used to hold the steel beams in the preinstalled L-shaped pockets on the column bracket (Fig. 9.4.2B-(3)). The proper relative positions (refer to Fig. 9.4.3B) were ensured, allowing the fast removal of the cranes, thus leading to the significantly reduced crane operation time. The proposed assembly method established

408

Hybrid composite precast systems

FIG. 9.4.5 Deformations and strains at the joints with/without bolts when cranes were removed.

noncritical works for bolting, removing the temporary bolting. This method provides an assembly time faster than that of the conventional steel assembly which requires the temporary bolts to hold the connections before removing cranes. Another test erection of the beam-to-column connection for the steel and concrete composite precast joints is demonstrated in Fig. 9.4.4, where the beam steels in each end of the precast beams were placed in the L-shaped guide channels similar to the one shown in Fig. 9.4.2D. They were then bolted with the stiffener plates. Fig. 9.4.4 shows photographs of the

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

409

test erection of the beam-to-column connection for the SRC precast joints, where the rebars were connected to the columns through couplers. The U-shaped precast beam sections were utilized to reduce the weight of the beam section.

9.4.2.3 Numerical evaluation of the proposed connections In Fig. 9.4.5, the finite element analysis was performed to explore the relative deformations of the empty bolts holes when the bolts are not used to hold the beam-column connections upon the removal of cranes. The finite element analysis predicted the dislocation of the bolt holes less than 0.1 mm at all bolt holes when no bolts are used to hold the joints, respectively, as shown in Fig. 9.4.5A. In Fig. 9.4.5B, the bolt strains are plotted against the gravity loads when one erection bolt was used. The curve indicated by Legend 9 elicits the strain of Bolt 5 as a function of the vertical uniform loads. This plot can be used to determine the strain levels of the permanent erection bolts against the given gravity loads for the design of the hybrid joints.

9.4.2.4 Conclusions A skewed web of the steel beam sections, shown in Fig. 9.4.3, was placed and bolted in the L-shaped pockets. It was held by the drift pins and the erection bolts until the permanent stiffener plates were bolted. The lower flange of the steel beam was prevented from colliding with the upper flange of the guide channels during the assembly. The easy and fast installation of the heavy precast members was demonstrated, minimizing the crane operation time by placing the steel beams in the guide pockets prior to bolting with the permanent splice plates. Efficient assembly times similar to those of the steel structures were demonstrated for the assembly of the precast frames subjected to the heavy loads. This assembly method is expected to be more efficient when multibay steel frames with vertical and horizontal modules carrying heavy loads are to be assembled. This method also can be used to erect the conventional steel frames even if it was originally proposed for the precast frame construction.

9.4.3 Precast column spliced by the rebars extended in holes In Fig. 9.4.6, the steel-concrete composite columns were spliced as shown in the drawing for the test erection. In Fig. 9.4.7, the steel sections and rebars of the composite precast columns are spliced. The holes indicated by “s” in Fig. 9.4.7A-(1) were provided to splice rebars. Rebars from the upper precast column were spliced in the holes as shown in Fig. 9.4.7A-(2), where the rebars were overlapped with the required length. The conventional sleeve couplers for rebars were used frequently when the splice length at the connection joints was not sufficient. The splicing holes were, then, grouted with high-strength mortar. Splices of the SRC precast columns are not common due to the difficulties in splicing both steel columns and rebars. In Fig. 9.4.7B, the steel section of the SRC precast columns was spliced through guide angles, which were prepared at the lower steel column.

FIG. 9.4.6 Erection test plan.

FIG. 9.4.7 Splice of precast columns.

410 Hybrid composite precast systems

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

411

9.5 Application of the hybrid composite precast frames with the beam depth reduction capability to high-rise buildings 9.5.1 Application to a 19-story building 9.5.1.1 Original design The hybrid precast frames with reduced beam depth capability were applied to high-rise buildings, adding one additional floor while the overall building height was maintained [2]. The 68-m tall, 18-story steel building was redesigned as a 19-story building using the hybrid precast beams, which combine the merits of the ductile steel and concrete components to withstand external loading while reducing floor height. The original steel beams, wherein the depths of the beam members were designed for the original 18-story building, are shown in Table 9.5.1. Table 9.5.2 summarizes the dimensions of the precast composite beams (refer to Fig. 9.1.3A) (including steel sections, reinforcing steel, and precast concrete), which replaced the steel frames. The depths of these members are also listed in this table. Table 9.5.3 shows the dead and live loads used in the design of the building. The compressive concrete strength was 24 MPa. The yield strengths of the reinforcing steel and structural steel were 400 and 330 MPa, respectively. Table 9.5.4 compares the design flexural moment strength and the factored moment demand for the new composite beams, and the same comparison for the original steel beams is shown in Table 9.5.5.

9.5.1.2 Reduction in floor height The reduction of the floor depth is obtained by employing composite beams as shown in Fig. 9.5.1, which compares the floor depth obtained using composite beams with that of the original steel beams. Floor depths greater than 220 mm were TABLE 9.5.1 Original steel beam sections by floor. Member

SB1 (2F-3F)

SB1 (4F-6F)

SB1 (PIT)

SB1 (7F-19F)

SB1(Roof)

Depth (D)

506 mm

506 mm

596 mm

596 mm

344 mm

H-Steel

506  201  11  19

506  201  11  19

596  199  10  15

596  199  10  15

344  348  10  16

TABLE 9.5.2 New composite beam sections by floor. Member

SB1 (2F-3F)

SB1 (4F-6F)

SB1 (PIT)

SB1 (7F-19F)

SB1(Roof)

Width (B)

400 mm

400 mm

400 mm

550 mm

550 mm

Depth (D)

650 mm

650 mm

650 mm

500 mm

550 mm

H-Steel

500  200  10  16

500  200  10  16

500  200  10  16

344  348  10  16

344  348  10  16

Compressive reinforcement

2-D25

2-D25

2-D25

2-D25

4-D25

Tensile reinforcement

2-D25

2-D25

2-D25

2-D25

4-D25

TABLE 9.5.3 Dead and live loadings. Public facility (2F-3F)

Floor loads 2

2

Business facility (4F-6F) 2

Residential facility (7F-19F)

PIT 2

2

Roof

Dead load (kN/m )

5.9 kN/m

5.3 kN/m

14.4 kN/m

10.9 kN/m

7.0 kN/m2

Live load (kN/m2)

4.0 kN/m2

2.5 kN/m2

3.0 kN/m2

2.2 kN/m2

2.0 kN/m2

412

Hybrid composite precast systems

TABLE 9.5.4 Comparison of the design flexural moment strength to the moment demand for the new composite beams. Member

SB1 (2F-3F)

SB1 (4F-6F)

SB1 (PIT)

SB1 (7F-19F)

SB1(Roof)

Design flexural moment strength

944.2 kN-m

944.2 kN-m

944.2 kN-m

957.6 kN-m

957.6 kN-m

Moment demand

545.9 kN-m

419.6 kN-m

894.2 kN-m

479.0 kN-m

334.7 kN-m

Accepted

O.K.

O.K.

O.K.

O.K.

O.K.

TABLE 9.5.5 Comparison of the design flexural moment strength to the moment demand for the original steel beams. Member

SB1 (2F-3F)

SB1 (4F-6F)

SB1 (PIT)

SB1 (7F-19F)

SB1(Roof)

Design flexural moment strength

676.5 kN-m

676.5 kN-m

1349.3 kN-m

677.0 kN-m

445.7 kN-m

Moment demand

545.9 kN-m

419.6 kN-m

894.2 kN-m

479.0 kN-m

334.7 kN-m

Accepted

O.K.

O.K.

O.K.

O.K.

O.K.

reduced with the composite beams relative to the depth of the conventional steel sections. This comparison was based on the same design code and specification. Composite beams consisted of steel sections and rebars encased in precast concrete, which helped reduce the floor depth.

9.5.1.3 Design of the composite frames A computer model of the building with 19 floors is shown in Fig. 9.5.2. The construction of high-rise buildings utilizing the precast steel-concrete composite beam is presented, resulting in both reduced floor height and a shortened construction schedule as compared with conventional concrete construction practices. The successful application of the composite beams introduced in this chapter transformed an 18-story building to one with 19 stories, adding one additional floor on the top of the building without increasing overall height of the building. Pour forms were prepared at both ends of the beam-to-column joint. The pour forms, however, could have been removed when mechanical joints with endplates introduced in Chapter 2 were used instead. The slabs were subsequently installed on the top edges of the U-shaped precast concrete instead of on the top of the wide steel flanges, reducing the floor depth (refer to Fig. 9.1.2). The new section of the proposed composite beams with the reduced depth is shown in Fig. 9.5.1A and B, for the second to sixth floors and the seventh to nineteenth floors, respectively. The composite beams with the reduced depth designed for the 19-story building are compared with the conventional steel depth in Fig. 9.5.1C. The top 150 mm accounts for the depth of the concrete slabs. The total depth of the original steel beam consisted of the fire spray coating, beam and slab depth of 786 mm for the residential floors (sixth floor to eighteenth floor). However, as shown in Fig. 9.5.1C, the depth of the new composite beams was only 500 mm (i.e., reduced by 286 mm from that of the original steel beams). The composite beam sections were designed based on the analytical equations shown in Section 9.3.1 of this chapter.

9.5.1.4 Design summary Table 9.5.6 describes the building with the precast composite frames as having a gross area of 24,368.53 m2. The building consists of both residential and office space. Although originally designed as an 18-story with steel frame, the design was changed to 19-stories with precast composite frames to meet the project budget. Table 9.5.7 presents the total reduction in the height of the building obtained by using the precast composite beams. The height of the building (66.40 m) re-designed with 19 stories decreased by 1.24 m from that of the 18-story building (67.64 m). It is also recognized in this table that a reduction in the floor by 3.922 m was achieved, enabling the addition of one more floor within the height that was permitted by the city regulations. The average reduction of the floor depth per floor was 220 mm. The height from the slab to the ceiling was not altered. The use of the precast concrete encasing steel beams also helped make the construction schedule similar to that of steel structures, but shorter than that of reinforced concrete structures. The quality assurance program helped improve

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

FIG. 9.5.1 Composite beam sections with shallow depths [2].

9

413

414

Hybrid composite precast systems

FIG. 9.5.2 Computer modeling of the 19-story building [2].

TABLE 9.5.6 General information related to 19-story building with precast composite frames [2]. Site

Seoul, Korea

District

Commercial district, district plan zone, central aesthetic zone

Site area

2071.10 m2

Building type

Residential housing, public facility, business facility

Stories

6 below ground, 19 superstructure

Structural system

Steel and concrete composite structure

Building area

1235.32 m2

Gross area

24,368.53 m2

Building coverage

59.65%

Bulk rate to building lot

699.91%

construction quality and save the cost involved with the corrections. Fig. 9.5.3 illustrates the composite beam in its complete manufactured form. The bottom flange was encased in the precast concrete, which provided the beam with additional flexural capacity. Fig. 9.5.4 shows the manufactured precast products being transported. Fig. 9.5.5 shows the beam-to-column connections after the pour forms were removed. Completed buildings with facade are also shown in Fig. 9.5.6.

Precast steel-concrete hybrid composite structural frames with monolithic joints Chapter

9

TABLE 9.5.7 Comparison of floor height between the two designs [2]. Steel beam (18 stories) Depth (mm)

Floor height (m)

–

5.65

696

4.25

3F

696

4.25

4F

696

4.25

Story

Floors

1F

Public facility

2F

MHS composite beam (19 stories) Depth (mm)

Floor height (m)

Floor height reduction (m)

–

5.6

0.046

650

4.2

0.046

650

4.2

0.046

650

3.4

0.046

650

3.4

0.136

650

3.4

0.136

Floors Public facility

Business facility

5F

Business facility

696

3.54

6F

Residential facility

786

3.39

PIT

PIT

786

1.49

PIT

650

1.2

0.286

7F

Residential facility

786

3.39

500

3.1

0.286

786

3.39

Residential facility

500

3.1

0.286

9F

786

3.39

500

3.1

0.286

10F

786

3.39

500

3.1

0.286

11F

786

3.39

500

3.1

0.286

12F

786

3.39

500

3.1

0.286

13F

786

3.39

500

3.1

0.286

14F

786

3.39

500

3.1

0.286

15F

786

3.39

500

3.1

0.286

16F

786

3.39

500

3.1

0.286

17F

786

3.59

500

3.3

0.286

18F

786

3.33

500

3.3

0.034

–

–

500

3.4

–

534

–

500

–

–

66.4 m

3.922 m

8F

19F Roof

–

Sum

FIG. 9.5.3 Manufacturing plant [2].

67.64 m

Sum

415

416

Hybrid composite precast systems

FIG. 9.5.4 Transport of composite precast beams.

FIG. 9.5.5 Completed beam-column joint.

FIG. 9.5.6 Completed buildings with fac¸ade.

9.5.2 Erection and assembly of the hybrid composite beams Table 9.5.8 elucidates the construction schedule for the erections of the composite beams and columns [2]. Four-story steel columns were lifted for the first 5 days of the first week, as shown in Fig. 9.5.7. The erection of the beams followed as shown in Figs. 9.5.8–9.5.9, whereas the metal deck plates were prepared for the concrete casting to form slabs for the first four floors as shown in Fig. 9.5.10. The steel columns of the next four floors continued to be erected as shown in Fig. 9.5.11. This process was repeated until the completion of the entire building frames as shown in Figs. 9.5.12 and 9.5.13, which illustrate the completion of both the columns and composite girders on the 12th–15th floors and 16th–19th floors, respectively. Fig. 9.5.13 also shows the steel

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TABLE 9.5.8 Construction schedule [2]. Field work

2nd week

1st week 1

2

3

4

5

6 7

8

9

10

11

12

3rd week 13

14

15

16

17

18

4th week

19

20

21

22

23

24

25

5th week

26

27

28

29

30

31

32

33

34

35

Steel work Erection of steel column

first unit column (1F–4F)

Installation of MHS composite beam

1F

2nd unit column (5F–8F) 2F

3rd unit column (9F–12F)

3F

4F

4th unit column (13F–16F) 5F

6F

5th unit column (17F–19F) 7F

8F

9F

10F

11F

RC work Installation of metal deck plate Installation of pour form Pouring & curing of concrete

1F

2F

1F

3F 2F

1F

4F 3F

2F

5F 4F

3F

4F

FIG. 9.5.7 Erection of the columns for the first 4 story unit.

FIG. 9.5.8 Erection of the composite beam.

columns of the 16th–19th floors being completed, whereas the installation of composite girders on the lower floors was in progress, and was completed shortly. A period of 35 days was required to finish the structural frame of the first four floors. The concrete cured for 7 days in the summer and 10 days with heating in the winter. The use of the precast concrete with the steel beams significantly reduced the use of supports and temporary pour forms, contributing to the fast construction that

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FIG. 9.5.9 Connections with high strength bolts.

FIG. 9.5.10 Installation of metal deck plates.

FIG. 9.5.11 Erection of columns for the next 4 story unit.

cannot be achieved when adopting the conventional concrete construction practices. The construction schedule would have been significantly delayed if all the concrete had been cast in the field. In addition to the shortened construction schedule, it was found that the quality assurance program for the precast concrete was executed more effectively than the practice of casting concrete in the field. Table 9.5.9 presents a list of the selected buildings, the floor heights of which were reduced with the structural tonnage by implementing the precast composite frames. The constructions of the steel-concrete composite precast beams reflected the individual project conditions, including the limitations, restrictions, and favorites addressed to the precast composite frames.

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FIG. 9.5.12 Completion of columns and composite girders (12th–15th floors).

FIG. 9.5.13 Completion of steel columns (16th–19th floors) [2].

9.5.3 Descriptions of the selected buildings As shown in Fig. 9.5.14A–L, the hybrid composite precast beams were implemented in numerous buildings including residential, office, and sports facilities. The descriptions of each building were given in each photo with the number of floors of the buildings. The reduction capability of the beam depth was demonstrated with rapid construction periods. The proposed hybrid composite precast beams also exhibited good structural capacities, offering the hybrid precast beams with a long span length, including one as long as 22 m for a bowling alley, as shown in Fig. 9.5.14L. Building costs were saved with the steel-concrete hybrid composite precast frames compared with that of steel frames without sacrificing building schedules and construction quality. Besides, additional floors can be added when the floor height for that is secured by implementing the hybrid precast beams with the floor reduction capability.

9.6 Contributions The traditional precast concrete approach has the drawback of being difficult for connections. The construction of both concrete frames and steel-concrete hybrid composite frames traditionally required the use of concrete pour forms. The steel frame construction offers the advantage of rapid construction, but suffers from high cost and lower fire resistance. The hybrid composite precast frame is an innovative structural system offering the economic benefits of the concrete and the constructability of the structural steels. The hybrid composite precast frames have been developed to overcome the shortcomings of each traditional construction materials and methods. The hybrid composite precast frame has been shown to improve productivity and quality, while reducing cost by shortening the construction period, construction

TABLE 9.5.9 List of selected buildings [2]. Perspective

Building type

Office building

Office & residential building 2

Office & residential building 2

Culture center

Welfare facilities

7 basements

Superstructure 4 stories

12 + 2 stories

572,886 ft , 7 basements

1,097,272 ft

Building type

Office & residential building

Residential building -Link beam-

Residential building

Office building

Office & residential building

Scale

263,314 ft2, 19 + 6 stories

5,337,450 ft2, 54 stories

1 basement

332,720 ft2 Superstructure 15 stories

473,752 ft2, 26 + 4 stories

Scale

Perspective

TABLE 9.5.9 List of selected buildings .—cont’d Perspective

Building type

Research institute

Office & residential building 2

Research institute

Church

Office & residential building 818,409 ft2, 38 + 4 stories

5 + 1 stories

1,138,656 ft , 7 basements

9 + 5 stories

Superstructure 4 stories

Building type

Office building

Parking tower

Train station

Residential building (parking space)

Scale

12 + 3 stories

Superstructure 4 stories

Superstructure 2 stories

1 basement

Scale

Perspective

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resources, CO2 emissions, and construction wastes. The hybrid composite precast frame is itself a hybrid composite structural system that maintains the advantages of both precast concrete structures and steel frames. It is a structural solution that combines the steel and concrete to offer advantages in structural stability, in constructability, cost-effectiveness, and environmental friendliness. The hybrid composite precast frame has demonstrated to provide a reduction in reinforcement, concrete, formwork and steel quantities, and CO2 emissions, relative to the traditional cast-in-place concrete and steel frames. The hybrid composite precast has also been shown to reduce the construction period by up to 20%–30% (enabling construction of each floor in 3–4 days) when compared with the traditional concrete construction practices. Cost savings of 2%–10% and reduced construction waste were achieved with many other benefits. The hybrid composite precast frame has been listed in the ICC (International Code Council, AC407) online site for its innovation. The ICC evaluates and certifies innovative construction technologies and materials. The engineering and construction innovation embodied in the hybrid composite precast frame was registered in patents including one in US. The hybrid composite precast frame developed to date represented a considerable progress towards a novel building structural system and construction technology. However, efforts are being made to enhance the hybrid composite precast frame further, with considerable success. The innovative hybrid composite precast frame technology is expected to make a significant contribution to the advancement of the construction industry as well as to environmental resource conservation.

(A)

Parking structures accommodating 4 cars between columns

FIG. 9.5.14 Composite precast beams implemented in buildings.

FIG. 9.5.14, cont’d

FIG. 9.5.14, cont’d

(L) FIG. 9.5.14, cont’d

Long span application for bowling alley; using U type precast composite beam

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References [1] W.K. Hong, S.-C. Park, H.-C. Lee, J.-M. Kim, S.-I. Kim, S.-G. Lee, K.-J. Yoon, Composite beam composed of steel and pre-cast concrete (Modularized Hybrid System, MHS). Part I. Experimental investigation, structural design of tall and special, Buildings 19 (3) (2009) 275–289, https://doi. org/10.1002/tal.507. [2] W.K. Hong, S.-C. Park, J.-M. Kim, S.-G. Lee, S.-I. Kim, K.-J. Yoon, H.-C. Lee, Composite beam composed of steel and pre-cast concrete. (Modularized Hybrid System, MHS). Part III. Application for a 19-storey building, Struct. Des. Tall Spec. Build. 19 (6) (2008) 679–706, https://doi.org/ 10.1002/tal.485. [3] S.-C. Park, Study of Steel-Reinforced Concrete Composite Beam Based on Strain Compatibility, Ph.D. Thesis, Kyung-Hee University, Korea, 2010. [4] Nzabonimpa, J.D., Won-Kee Hong, and Jisoon Kim. 2017. Strength and post-yield behavior of T-section steel encased by structural concrete Struct. Des. Tall Spec. Build., 27(5), https://doi.org/10.1002/tal.1447. [5] AISC/ANSI 358, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications Specification, American Institute of Steel Construction Inc, Chicago (IL), 2005. [6] J.-M. Kim, An Experimental and Analytical Investigation of Modularized Hybrid System (MHS), Master’s Thesis, Kyung-Hee University, Korea, 2008. [7] Yang, et al., Experimental Study on Flexural Performance of Partially Precast Steel Reinforced Concrete Beams, School of Civil Engineering, Xi’an University of Architecture & Technology, Xi’an, Shaanxi, China, 2017. [8] AISC, Specification for Structural Steel Buildings, ANSI/AISC 360-10, Chicago, 2010. [9] C. Chen, Accuracy of AISC methods in predicting flexural strength of concrete-encased members, J. Struct. Eng. ASCE (2013) 338–349. [10] D.H. Nguyen, W.-K. Hong, Part 1: The analytical model predicting post-yield behavior of concrete-encased steel beams considering various confinement effects by transverse reinforcements and steels (Materials), 12 (14) (2019) 2302. [11] C.C. Chen, N.J. Lin, Analytical model for predicting axial capacity and behavior of concrete encased steel composite stub columns, J. Constr. Steel Res. 62 (5) (2006) 424–433. [12] Mirza, Skrabek, Statistical analysis of slender composite beam-column strength, J. Struct. Eng. ASCE 118 (5) (1992) 1312–1332. [13] S. El-Tawil, G.G. Deierlein, Strength and ductility of concrete encased composite columns, J. Struct. Eng. 125 (9) (1999) 1009–1019. [14] O. Bayrak, S.A. Sheikh, Plastic hinge analysis, J. Struct. Eng. 127 (9) (2001) 1092–1100. [15] W.K. Hong, G. Kim, C. Lim, Development of a steel-guide connection method for composite precast concrete components, J. Civ. Eng. Manag. 23 (1) (2017) 59–66. [16] J.D. Nzabonimpa, W.-K. Hong, Use of artificial damping factors to enhance numerical stability for irregular joints, J. Constr. Steel Res. 148 (2018) 295–303. [17] W.-K. Hong, S.-Y. Jeong, S.-C. Park, J.T. Kim, Experimental investigation of an energy-efficient hybrid composite beam during the construction phase, Energy Build. (2012). [18] S.A. Sheikh, S.M. Uzumeri, Analytical model for concrete confinement in tied columns, J. Struct. Div. ASCE 108 (12) (1982) 2703–2722. [19] KH Housing Solutions, GS Construction, Keumho Construction and Hanjin Construction. Report for the Certification 860 of New Excellent Technology, Ministry of Land, Infrastructure, and Transport of Korean Government, 2019.

Chapter 10

Artificial-intelligence-based design of the ductile precast concrete beams 10.1

Concept and structure of the artificial neural networks

10.1.1 Analogy with the biological neuron model This chapter introduces artificial neural networks (ANNs) exhibiting a learning and memory capability similar to that of the human brain. Typical biological neurons (Fig. 10.1.1A) are activated by an electrical input, sending out pulses through their axons. These cells collect the electromechanical signals between their dendrites to transmit the voltage spikes biologically along their axons to a part of the body associated with the particular neuron. For ANNs, the voltage output is modeled by an activation function such as the sigmoid and rectified linear unit (ReLU) functions [1].

10.1.2 ANNs for structural engineering Similar to the biological neurons, an ANN comprising a large number of the interconnected nodes and deep layers was developed to integrate all incoming signals, in which all incoming input signals are mapped onto the output-design parameters (Fig. 10.1.1B). The nonlinear numerical computations are linked using the weighted interconnections and bias through an activation function. Inputs (x1 to xn) for the precast concrete beam design (Fig. 10.1.1) are relayed to the neurons of the successive layers fully connected using weights at each neuron and bias in each hidden layer. The layers are then summed for the output (Fig. 10.1.1B). The neural networks are formulated to have the ability to generalize trends (recognized as the machine learning) between inputs and outputs for the engineering applications rather than being based on the engineering mechanics or knowledge [3]. In this chapter, the ANNs have been implemented in the structural engineering to design ductile precast concrete beams by training large structural-design datasets. The accuracy of the trained data was compared with the design values, resulting in the close correlations between the two datasets.

10.2

Multilayer perception

10.2.1 Weights and bias The process of the artificial multilayer perception (MLP) was investigated with the connection weights between
1 and 1 (negative or positive wij) that were multiplied to the input signals to model the synaptic connections shown in Fig. 10.2.1 [5]. Fig. 10.2.1A depicts an MLP configuration with multiple hidden layers, each with multiple neurons. MLP, first inspired by the biological neural system, typically comprises input layers, multiple hidden layers, and output layers [6, 7]. The relayed value to node j (Fig. 10.2.1A and B) is computed through the following two equations (Eqs. 10.2.1, 10.2.2):  X wij xi + bk zj ¼ (10.2.1)   yj ¼ f zj (10.2.2) where xi (or ai) represents all inputs; wij is the weight of the connection between the nodes (hidden layers) i and j; b is the bias term for the regularization; zj is the temporary value; and yj ¼ the output value for node j, which is computed by passing zj through an activation function f [6]. Fig. 10.2.1B [4] shows the deep neural network in a matrix form, where each node in the hidden or the output layer is fully connected with all nodes of the previous layer, and these layers are connected by the weighted combination of the Hybrid Composite Precast Systems. https://doi.org/10.1016/B978-0-08-102721-9.00010-8 © 2020 Elsevier Ltd. All rights reserved.

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FIG. 10.1.1 Analogy between (A) a biological neuron model [1] and (B) an artificial neural network (ANN).

Dendrite

Axon terminal y1 y2

X1 Cell body

X2

ym Xn Myelin sheat Myelinated axon

Inputs (A) X1 X2 X3

Y1 Y2

X10

(B) nodes and bias of the previous layer, calculating values at the neurons of the first and second hidden layers. The weights are adjusted during the training of the neural networks through an iterative processing. The collected information of the connection weight is captured and stored when the iterative processes have converged [3]. The deep neural network to design the doubly reinforced precast concrete beams is illustrated in Fig. 10.2.1C, where the input and output dataset (9 inputs and 7 outputs with the multiple neurons) are shown as the input and output neurons. Results of the artificial intelligence (AI)based neural networks are presented in Section 10.3.

10.2.2 Backpropagation by adjusting weights The weights connecting layers can be adjusted to correlate the calculated output values with the target data through the backpropagation [8–10] until the networks are improved (Fig. 10.2.1D). Good neural networks can replace the conventional computation based on the engineering mechanics by mapping inputs to target outputs through minimizing cost functions. The output layer is calculated as the output predictions y of the previous layer at the end of a forward training and is succeeded by the computation of the derivatives of the loss L between these predictions and the training targets with respect to the predictions y. Then, the derivatives of the loss L is backward propagated to the previous layer to revise the weights and bias until the training results provide the acceptable correlations between the calculated output values and target values. Fig. 10.2.1D illustrates the flow of the data through the backpropagation of the neural-network, adjusting the weights and bias with the multiple hidden layers. The number of neurons may be reduced to improve trainings when an overfitting occurs, which is indicated by the performance of the good training compared to significantly worse test-set performance [7, 11]. However, the number of the neurons may be increased when the training performance is poor.

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FIG. 10.2.1 Artificial deep neural network: (A) fully connected networks between all layers with weighted combinations (wij) of the nodes and bias (bk), (B) Artificial Neural Network (ANN) in matrix form [4], (Continued)

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FIG. 10.2.1, Cont’d (C) multilayer perception (MLP): nine inputs and seven outputs with multiple neurons (see Table 10.3.2), and (D) backpropagation by adjusting weights without a hidden layer.

10.2.3 Activation functions related to the structural-engineering applications In the neurobiological systems, a neuron activates an outgoing signal only if the combined input stimuli to the cell build to a threshold value. In the artificial algorithm, the activation functions similar to the stimuli of the neurobiological systems are introduced to process the weighted sum of the previous input signals (Figs. 10.2.1A and 10.2.2) [5]. The engineering inputs and design outputs that have been selected for the neural networks are mapped based on the complex nonlinear functions. The relayed output signal would be obtained from a simple linear-regression model when the activation fuction is not applied. A neural network without using activation functions cannot represent complex nonlinearity between input and output trends, being unable to map the complex functional relationships from the data, whereas very complicated input-output relationships can be trained efficiently with the activation functions, helping an artificial neural network to extract the mapping trends from the big datasets, not based on the engineering knowledge [3, 12]. The outputs obtained from the activation functions are treated as an input to the next neurons in the network [5]. One of the important considerations is to select the activation functions for the hidden and output layers of an artificial neural network, which are differentiable because the activation function gradient must exist to update ANN parameters during the backpropagation to minimize the error signal (cost functions). Fig. 10.2.2 shows some activation functions that are widely used in the neural networks. The last activation function should be a sigmoid or tanh function when the outputs need to be between 0 and 1.

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(a) Tanh(x) A hyperbolic tangent (tanh) activation function (Fig. 10.2.2A) limits the output to the range
1 to 1. The tanh function reflects a nonlinearity between the engineering inputs and design outputs that have been selected for the neural networks. (b) Sigmoid A sigmoid function (Fig. 10.2.2B) is a mathematical function having a characteristic “S”-shaped or sigmoid curve, which is a special case of the logistic function. A sigmoid activation function squashes to limit the output to a range of 0 to 1 [13]. However, one of the detriments of the sigmoid activation function is the gradient-vanishing problems in the deep layers. The gradient of sigmoid values between 0 and 1 vanishes during the backpropagation because the gradients are repeatedly multiplied, finally vanishing, in the deep networks. (c) ReLU The hyperbolic tangent (Fig. 10.2.2A) and logistic sigmoid functions (Fig. 10.2.2B) [13] were the widely used activation functions prior to 2011, whereas since 2017, the rectifier has been the most popular activation function for the deep neural

FIG. 10.2.2 Activation functions: (A) tanh(x), (B) sigmoid function [8], (Continued)

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FIG. 10.2.2, Cont’d (C) ReLU, and (D) leaky ReLU.

networks [8, 14, 15]. The hyperbolic tangent neurons (tanh) work better than the logistic sigmoid neurons for training multilayer neural networks, whereas the logistic sigmoid neurons are more biologically plausible. Glorot et al. [16] presented the rectifying neurons that more closely resemble the biological neurons, yielding an equal or better performance than the hyperbolic tangent networks despite the severe nonlinearity and nondifferentiability at zero, creating sparse representations with true zeros, which seem remarkably suitable for the naturally sparse data [16]. The ReLU (Fig. 10.2.2C) is used in the deep-learning neural network. The ReLU activation function becomes 0 for any negative input whereas a simple linear function represents the ReLU activation for any positive input. It can be written as f(x) ¼ max(0,x), graphically shown by Fig. 10.2.2C. Even if the ReLU is a simple bilinear function, the deep-learning models using the ReLU with many diverse types of a nonlinearity are created by the different bias terms for each node, thereby allowing locations to shift where the slope changes. The deep neural networks using the ReLU are quickly compared with the hyperbolic activation functions such as the sigmoid functions. The vanishing problem can be overcome by the ReLU activation function by allowing a linear function that increases more than the sigmoid function. However, the drawback of the ReLU is that the nodes having negative inputs are ignored and thus are no longer trained, leading to inaccurate results for the simple networks. The ReLU may have a vanishing-gradient problem as the ReLU neurons may be

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pushed into the different states. This results in being inactive for essentially all inputs in which no gradients flow backward through the neuron, thereby becoming stuck in a perpetually inactive state and decreasing the minimizing capacity of the cost function when the learning rate is set too high. The Leaky ReLUs (Fig. 10.2.2D) mitigated the problem that typically arises with the ReLU by assigning a small positive gradient of 0.01 when the unit is not active (to the left of x ¼ 0) [15]. The Leaky ReLUs can be written as f(x) ¼ max(0.01x, x).

10.2.4 Initialization The weights are randomly initialized to elaborate networks when they are built and compiled. The weights are set with random numbers—typically one random number per weight—and normally distributed, having a mean value of 0 and a standard deviation of 1 [17]. He et al. [18] proposed the initialization of the weights based on the ReLU (including Leaky ReLU) that was able to resolve problems for the large models that take a long time to train. Their method is the same as Xavier’s initialization except for using the tanh activation function. In both methods, the vanishing- and exploding-gradient problems were mitigated, avoiding a slow convergence, and oscillating off the minima to minimize the variance of the weights. The weights are initialized as neither much larger than 1 nor much smaller than 1.

10.2.5 Data normalization The input and output of the design variables were normalized in the range of 0 to 1 with a mean of 0 and a standard deviation of 1. The outputs of the layers of each convolutional and fully connected layer were normalized using a batch-normalization layer, such that the predictions of the network were normalized at the start of training. The network training may fail to converge when the response is poorly scaled. The predictions of the trained network must be transformed to obtain the predictions of the original response in cases where the response was normalized before training. The nonlinear transformations of the dataset, such as a logarithmic, must be performed before training the network when the distribution of the input or response is very uneven or skewed. However, normalizations are not necessary when the dataset is distributed evenly.

10.2.6 Three ways to train ANNs in Matlab 10.2.6.1 Using neural-network toolbox fitting application The one of the easiest and fastest ways to run an ANN is to use the neural-network toolbox in Matlab, shown in Fig. 10.2.3 [19]. In the command window of the Matlab, type nnstart to start the toolbox and choose “Fitting app” (Fig. 10.2.3A). Then follow steps shown in Fig. 10.2.3A–E: Click “Next” to import the input and target dataset (Fig. 10.2.3B), click “Next” to select percentages for the validation and testing data (Fig. 10.2.3C), select the number of neurons (Fig. 10.2.3D), and choose a training algorithm (refer to Fig. 10.2.3E) to start training in the next window. In this toolbox, the number of the hidden layers cannot be changed, and all other network parameters shown are the defaults, including the number of the input and output neurons (Fig. 10.2.3D). Three training algorithms, including one by Levenberg-Marquardt, are available (Fig. 10.2.3E).

10.2.6.2 Using neural-network toolbox data manager In the command window of the Matlab [19], type nntool to start the toolbox and choose “Data Manager” (Fig. 10.2.4A). Then follow steps shown in Fig. 10.2.4A–D: Select the “Import” button to import the input and target dataset (Fig. 10.2.4A); select the “New” button to create the neural network ((1) of Fig. 10.2.4B); choose options including “Network type,” “Training function,” “Performance function,” “Number of hidden layers,” and “Number of neurons” (2–4 of Fig. 10.2.4B); close the windows and open the new network; select the “Train” tab; and then select “Training Parameters” (Fig. 10.2.4C) to modify parameters if necessary. The “Training Info” tab under “Training Data” (Fig. 10.2.4D) reveals the input and target dataset; names for the “Outputs” and “Errors” must also be provided in “Training Results” (Fig. 10.2.4D). After finishing all these steps, click on the “Train Network” button to start training. All network parameters are defaults that can be changed.

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FIG. 10.2.3 Running an ANN in a MATLAB Neural Network Toolbox: (A) start toolbox by choosing “Fitting app,” (B) select inputs and targets data, (C) select percentages on validation and testing data, (D) selecting number of neurons (10 is the default), and (E) choose a training algorithm and start training.

10.2.6.3 Writing Matlab code Users can write a Matlab code for a customized ANN (Table 10.2.1). Those who are not familiar with writing Matlab codes are advised to use “Data Manager” (Fig. 10.2.4), whereas those familiar with writing code can train ANNs in moreversatile ways, such as by having 20 hidden layers and 25 neurons as shown in the ANN of Section 10.3. Matlab also provides the customized code for the network details including the number of neurons, the number of layers, the maximum

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FIG. 10.2.4 Running ANN using the Neural Network/Data manager in MATLAB: (A) type “nntool” in the command window of MATLAB to show the Data Manager, (B) start the “Data Manager” in the Matlab and follow the next steps, (C) Go to the “Train” tab and select “Training Parameters” to modify parameters if necessary, (Continued)

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FIG. 10.2.4, Cont’d (D) select the “Training Info” tab to select the data for “Inputs’, “Targets”, and to put the names in the “Training Results” area (“Outputs” and “Errors”). Click on "Train Network" button to start training and the network is being trained as shown in (E).

of epochs, and the maximum of the validation. Using this code, a 13,000-observations dataset was trained, and the training results were discussed in Section 10.3.

10.3

Artificial neural network-based design of the ductile precast concrete beams

10.3.1 Generation of the big structural data; a ductile design of the doubly reinforced precast concrete beams Strain compatibility-based ductile design of the doubly reinforced precast concrete beams spanning 3–10 m (Fig. 10.3.1A) described in Section 9.3.2 of Chapter 9 was implemented to generate large structural datasets. A large dataset of the random variables for the design parameters was generated by the Autobeam (Fig. 10.3.1A) based on a strain compatibility-based algorithm to train an ANN. The design parameters shown in Fig. 10.3.1B can be placed in either input or output sides based on the design types. In Fig. 10.3.1B, the ANN input dataset includes the moment demand Mu (kNm); yield strength of rebars fy (MPa); concrete compressive strength fc (MPa); beam width b (mm), depth d (mm), and span length L (m); concrete cost per cubic volume, rebar cost per tonf, and cost of beam/meter (including costs of manufacturing, materials, and construction). The ANN target values are the tensile and compressive steel ratios, r and r0 , respectively; c/d (neutral axis/ effective beam depth); beam deflection D (mm); tensile and compressive strains of rebars, et and ec, respectively; and beammanufacturing cost per 1 kNm moment. The mean values and standard deviations of the random design parameters of the generated big structural data are presented and described in Table 10.3.1, Figs. 10.3.1B and 10.3.2. To cover a wide range of

Artificial-intelligence-based design Chapter

TABLE 10.2.1 Customized ANN using MATLAB code (25 neurons and 20 hidden layers). % Import data from text file. Input = importdata(’InputData.txt’); % InputData.txt includes 13000 dataset Target = importdata(’Target.txt’); x = Data; t = Target; % Choose a Training Function % ’trainlm’ is usually fastest. % ’trainbr’ takes longer but may be better for challenging problems. % ’trainscg’ uses less memory. Suitable in low memory situations. trainFcn

= ’trainlm’; % Levenberg-Marquardt backpropagation.

% Create a Fitting Network NumNeurons = 25; % Number of neurons in one layer NumLayers = 20; % Number of layers RangeLayer = zeros(1,NumNeurons); RangeLayer(:) = hiddenLayerSize; net = feedforwardnet(RangeLayer); % Choose Input and Output Pre/Post-Processing Functions net.input.processFcns = {’removeconstantrows’,’mapminmax’}; net.output.processFcns = {’removeconstantrows’,’mapminmax’}; % Setup Division of Data for Training, Validation, Testing net.divideFcn = ’dividerand’; % Divide data randomly net.divideMode = ’sample’; % Divide up every sample net.divideParam.trainRatio = 70/100; net.divideParam.valRatio = 15/100; net.divideParam.testRatio = 15/100; % Choose a Performance Function net.performFcn = ’mse’; % Mean Squared Error net.trainParam.epochs = 1000 ; % Maximum of epochs, default value is of 1000 net.trainParam.max_fail = 6;

% Maximum of validation (default value is of 6)

% Choose Plot Functions net.plotFcns = {’plotperform’,’plottrainstate’,’ploterrhist’, ... ’plotregression’, ’plotfit’}; % Train the Network [net,tr] = train(net,x,t); % Test the Network y = net(x); e = gsubtract(t,y); performance = perform(net,t,y) output = y; % Recalculate Training, Validation, and Test Performance trainTargets = t .* tr.trainMask{1}; valTargets = t .* tr.valMask{1}; testTargets = t .* tr.testMask{1}; trainPerformance = perform(net,trainTargets,y) valPerformance = perform(net,valTargets,y) testPerformance = perform(net,testTargets,y) % View the Network view(net)

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437

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FIG. 10.3.1 Neural network mapping the design conditions to the design of the ductile precast beam: (A) strain compatibility based structural design algorithm (Autobeam) and (B) big structural data used to train neural network.

Artificial-intelligence-based design Chapter

10

439

TABLE 10.3.1 List of the random variables and corresponding ranges. Mean (m)

Standard deviation (s)

Variance (V)

499.6

58.13

3379.1

38.8

12.4

153.8

Beam width, b (mm)

399.8

117.1

13,705.4

Beam effective depth, d (mm)

650.5

229.8

528.08.0

Beam length, L (mm)

8000.3

2894.5

8,378,130.5

Concrete unit cost (won/m )

12,658.3

2686.5

7,217,282.3

Rebar unit cost (won/m)

958.6

19.0

361

rtension rebar

0.0163

0.0093

0.0000865

rcompression rebar

0.0049

0.0044

0.0000194

Rebar strength, fy (MPa) Concrete strength, f

0

c

(MPa)

3

the designs, the random datasets for the rebar yield strength fy in the range 400–600 MPa and for concrete compressive strength fc in the range 18–60 MPa were generated. Other random datasets were also generated based on the ranges of the random variables (Table 10.3.1; Figs. 10.3.1B and 10.3.2), based on the probability-density functions that can be adjusted to accommodate designers’ needs. The design parameters can be located in either the input or the output to investigate the trends of the parameters of interest. The nine parameters are used as input neurons whereas the seven parameters are used as output neurons, as shown in Fig. 10.2.1C.

10.3.2 Supervised training 10.3.2.1 Numbers of datasets, hidden layers, neurons, and training functions The higher training accuracy was obtained based on the 13,000-observations input dataset than that with 1000 random variables when the same number of hidden layers (20) and neurons (25) were used. The training accuracy also significantly decreased when only 5 hidden layers and 5 neurons were used with the same 13,000-observations dataset. Three types of the functions are available in the Matlab neural toolbox [19]. Levenberg Magaredt’s optimization function was implemented in this section.

10.3.2.2 Factors influencing neural training The obtained big structural datasets (Fig. 10.3.1; Tables 10.3.1 and 10.3.3) were appropriately normalized, resulting in well-defined cost functions (Fig. 10.3.3A), whereas the input datasets and target values that are not appropriately normalized for the neural networks can result in distorted cost functions (Table 10.3.2), hindering the convergence of the gradient descents and failing to prevent the cost-function gradients from an overshooting or being kept at the local minima (Fig. 10.3.3B). To prevent the drawbacks caused by the nonnormalized data, the datasets are normalized, leading to welltrained datasets, which enable a close matching of the output dataset with the target values (Table 10.3.3). The meansquared errors and regression coefficients for the three types of the neural networks are influenced by the numbers of the datasets, hidden layers, and neurons (Fig. 10.3.4). The minimum tensile strain of the rebar for the ductile behavior of concrete beams (obtained by mapping the input dataset to the output dataset) was validated by the target values using a normalized dataset with 20 hidden layers and 25 neurons (Fig. 10.3.5). The input data was well-trained with the target values when a large dataset (13,000 input values, Fig. 10.3.4A) was used to efficiently minimize the cost function compared to those based on a smaller dataset (1000 input values) (Fig. 10.3.4B). The R values with a large dataset shown indicate the almost perfect correlation between the input and output-design parameters. It is also noted in Fig. 10.3.4C that the hidden layers and neurons large enough should be used to yield a good correlation of the networks even if a large dataset was used. The training, validation and testing were performed on 70%, 15%, and 15% of the large datasets, respectively, when using the Matlab deep-neural-network toolbox [19]. The rebar tensile strains less than 0.004 should be avoided for the design of the ductile precast concrete beams (Fig. 10.3.5), as recommended by the American Concrete Institute in ACI 10.3.5. The tensile rebars should be decreased to increase the rebar strains for the concrete beams with the rebars of the tensile strains less than 0.004.

440 Hybrid composite precast systems

× 10–3 6

Probability distribution

0.03

0.025

5 Histogram

0.015

3

0.01

2

0.005

1

0 350

400

450 500 550 Rebar strength, fy (MPa)

(A)

0 650

600

Probability distribution

0.06

Histogram Uniform distribution

0.05

Probability

(B)

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0 15

Density

4

Uniform distribution

20

25

30

35 40 45 50 Concrete strength, f⬘c (MPa)

55

60

Density

Probability

0.02

0 65

FIG. 10.3.2 Ranges of the random variables with probability-density functions: (A) rebar strength, (B) concrete strength, (Continued)

10.3.2.3 Training results and numbers of data values versus hidden layers The output values (tensile and compressive steel ratios, r and r0 , respectively; tensile and compressive rebar strains, et and ec, respectively (Fig. 10.3.6A–D); deformation; c/d ratio; and beam-manufacturing cost per 1 kNm design moment (Fig. 10.3.6E, F)) were derived (from a dataset comprising 13,000 data values) by training the networks with 20 hidden layers and 25 neurons against the target values (Fig. 10.3.6). The input dataset was accurately mapped to the output dataset, as validated by the target values when the sufficient hidden layers and neurons were used with the normalized data. However, the mapping was poor when the insufficient hidden layers and neurons were used even with the normalized data (Fig. 10.3.7). Thus, the use of enough hidden layers and neurons is important for the effective dataset training; the more hidden layers and neurons are required for the larger datasets. The similar results for the deformations and manufacturing beam cost per design moment (kNm) to those related with the information of the rebars (Fig. 10.3.6A–D) were found as shown in Fig. 10.3.6E and F. The neural outputs poorly correlated with the target values for all design parameters (including tensile and compressive steel ratios r and r0 , respectively; tensile and compressive rebar strains, et and ec, respectively; deformation; c/d ratio; and

Artificial-intelligence-based design Chapter

0.035

× 10–3 4

Probability distribution Histogram Uniform distribution

3.5 3

Probability

0.03

2.5

0.025

2

0.02

1.5

0.015

1

0.01

0.5

0.005 0

150

441

Density

0.04

10

200

250

300

350

400

450

500

550

600

0

650

Beam width, b (mm)

(C) 0.035

× 10–3

Probability distribution Histogram Uniform distribution

1.6

0.03 1.4 1.2

0.02

1 0.8

0.015

Density

Probability

0.025

0.6 0.01 0.4 0.005 0 200

0.2

300

400

500

600

700

800

900

1000

0 1100

(D) Beam effective depth, d (mm) FIG. 10.3.2, Cont’d (C) beam width, (D) effective depth of the beam, (Continued)

beam-manufacturing cost per 1 kNm design moment) when they are not nonnormalized even with sufficient hidden layers (Fig. 10.3.7). Thus, the data normalization is important to yield a good correlation between the target and the output data. The AI network will not improve the training results with the nonnormalized data, even when enough hidden layers are used. However, the Matlab algorithm trains data well when the nonnormalized data are neither much larger nor much smaller than one. In Table 10.3.2b, the nonnormalized deformation data are closer to one compared with those of the tensile rebar ratios, resulting in the better-trained data for the deformation data (Fig. 10.3.7E) than those of the tensile rebar ratios (Fig. 10.3.7A). The training results similar to those of the deformation data were found with the tensile rebar strains (Fig. 10.3.7B), the nonnormalized data of which were neither too big nor too small than one (Table 10.3.2b).

10.3.3 Test networks and the design results The accuracy of the tested design parameters was verified by the design programs based on structural mechanics. The tested design values included tensile and compressive steel ratios (r and r0 ), tensile and compressive rebar strains (et and ec), deformation, and beam-manufacturing cost per 1kNm design moment (Table 10.3.4). The input dataset of the neural network includes beam sizes (defined by the depth d, width b, and length L, as required in the architectural specifications),

442 Hybrid composite precast systems

0.03

× 10–4 1.2

Probability distribution Histogram Uniform distribution

1

0.02

0.8

0.015

0.6

0.01

0.4

0.005

0.2

0

3000

4000

5000

6000

7000

8000

Density

Probability

0.025

0

9000 10,000 11,000 12,000 13,000 14,000

Beam length, L (mm)

(E)

Probability distribution

0.05

Histogram Uniform distribution

0.045

0.02

0.04 0.035

0.025 0.01

0.02

Density

Probability

0.015 0.03

0.015 0.005

0.01 0.005 0 80

(F)

90

100

110 120 130 140 150 Concrete unit price (¥1000 won/m)

160

170

0 180

FIG. 10.3.2, Cont’d (E) beam length, (F) concrete unit cost, (Continued)

moment demand Mu (kNm), rebar yield strength fy (MPa), compressive concrete strength f’c (MPa), concrete cost per cubic volume, rebar cost per tonf, and beam-manufacturing cost/m (including materials and construction). The test (design) results obtained from a trained neural network based on 13,000 datasets with 20 hidden layers, 25 neurons were better compared than those obtained from 1000 datasets with 20 hidden layers, 25 neurons when the target values were not used during the neural networking (Fig. 10.3.8). The accuracy of the neural networks based on 13,000 datasets with 20 hidden layers, 25 neurons was also better compared than those based on 13,000 datasets with 5 hidden layers and 5 neurons. The 1000 test (design) data were validated, whereas the 100 test (design) data were graphically compared with the results based on the mechanics (Fig. 10.3.8). An accuracy was significantly lower for the networks using insufficient data and fewer hidden layers, neurons, indicating that the neural networks with big-data and sufficient hidden layers, neurons yield better results. Substantially enhanced accuracies of all test (design) outputs were achieved when the large target datasets were used during the training process, thereby effectively minimizing the cost function. The test (design) results obtained from training based on the 13,000 data values and using 20 the hidden layers and 25 neurons (Table 10.3.4) are found to correlate well with the results based on the engineering mechanics by referring the errors in Table 10.3.4.

Artificial-intelligence-based design Chapter

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443

Probability distribution 0.04

Histogram Kernal distribution

0.025

0.035 0.02

0.025 0.015 0.02

Density

Probability

0.03

0.01

0.015 0.01

0.005 0.005 0 910

920

930

(G)

940 950 960 970 Rebar unit price (won/kg)

980

990

0 1000

Probability distribution 0.06 Histogram Kernal distribution

40 35

0.05

30 25 0.03

20

Density

Probability

0.04

15

0.02

10 0.01 5 0

(H)

0

0.005

0.01

0.015

0.02

0.025

0.03 rtension rebar

0.035

0.04

0.045

0.05

0

FIG. 10.3.2, Cont’d (G) rebar unit cost, (H) tensile rebar ratio, and (Continued)

444 Hybrid composite precast systems

Probability distribution 0.12

Histogram Kernel distribution

80 70

0.1

60 50 0.06

40 30

0.04

20 0.02

0 –0.005

10

0

(I) FIG. 10.3.2, Cont’d (I) compressive rebar ratio.

0.005

0.01 rcompression rebar

0.015

0.02

0 0.025

Density

Probability

0.08

Artificial-intelligence-based design Chapter

10

445

FIG. 10.3.3 Well-defined cost function vs cost function due to nonnormalized data: (A) well-defined cost function based on an appropriate normalization and (B) distorted cost function due to an inappropriate normalization.

446 Hybrid composite precast systems

TABLE 10.3.2 Sample of the inputs and target dataset that is not normalized, causing distorted cost functions for the neural networks (20 hidden layers, 25 neurons; 9 inputs, 7 outputs) (see Fig. 10.3.3B). (a) Nonnormalized input data (original dataset) Input Mu (kNm)

fy (MPa)

fc (MPa)

b (mm)

d (mm)

Length (mm)

Concrete unit price (per 1 m3)

Rebar unit price (per 1 kg)

Manufacturing cost (won/m)

235.49

439

23

290

370

10,250

94,073.8

938.21

32,103.1

645.79

445

29

235

535

7200

102,476.5

940.55

54,094.0

2901.22

439

44

375

805

4250

137,142.1

938.21

163,823.9

173.2

433

22

475

460

3350

92,605.7

935.87

34,548.8

507.62

454

45

325

465

8600

139,403.0

944.06

54,325.0

1948.83

415

48

600

510

5300

146,365.1

928.85

182,211.2

312.16

582

29

425

375

9450

102,476.5

983.32

37,660.8

1721.67

479

56

210

805

5400

165,008.9

953.81

94,894.7

1121.59

416

47

580

545

9950

144,044.4

929.24

111,374.5

1003.93

490

58

315

740

7000

169,622.7

958.1

77,336.9

1209.54

452

18

335

980

4250

87,365.5

943.28

68,494.9

460.84

452

45

495

280

9050

139,403.0

943.28

76,852.7

2449.38

532

37

495

975

3950

120,936.3

970.32

126,367.6

2789.35

475

34

590

760

7200

113,769.5

952.25

162,006.3

2739.67

407

20

445

1005

11,000

89,880.2

925.73

136,921.0

4263.36

470

29

430

965

9750

102,476.5

950.3

185,314.9

3338.62

577

39

540

970

10,900

125,711.1

982.02

159,163.5

435.1

489

57

275

375

10,450

167,315.8

957.71

52,143.6

2127.29

584

20

490

1010

12,650

89,880.2

983.84

96,490.0

1143.55

414

24

360

835

5500

95,542.0

928.46

72,996.3

88.18

493

41

295

260

3200

130,359.4

959.27

22,208.9

305.78

594

57

240

555

7750

167,315.8

986.44

37,043.3

195.57

532

51

260

305

6100

153,345.6

970.32

30,004.8

7587.28

564

56

595

925

9600

165,008.9

978.64

316,306.4

1090.9

526

45

320

505

5650

139,403.0

968.76

88,593.1

1381.81

590

52

415

785

9150

155,684.7

985.4

93,968.0

1041.25

598

41

375

560

3750

130,359.4

987.48

75,051.3

320.34

548

28

240

420

5050

100,751.5

974.48

32,095.6

130.09

506

22

290

345

7050

92,605.7

963.56

20,363.4

2021.88

461

53

275

845

3750

158,023.8

946.79

108,597.7

151.11

442

20

590

460

6650

89,880.2

939.38

35,808.7

1588.63

493

54

490

775

6400

160,362.9

959.27

116,629.2

2835.34

499

22

320

975

4850

92,605.7

961.61

120,130.7

Artificial-intelligence-based design Chapter

10

447

TABLE 10.3.2 Sample of the inputs and target dataset that is not normalized, causing distorted cost functions for the neural networks (20 hidden layers, 25 neurons; 9 inputs, 7 outputs)—cont’d (a) Nonnormalized input data (original dataset) Input Mu (kNm)

fy (MPa)

fc (MPa)

b (mm)

d (mm)

Length (mm)

Concrete unit price (per 1 m3)

Rebar unit price (per 1 kg)

Manufacturing cost (won/m)

972.63

474

27

375

740

8400

99,026.5

951.86

65,817.7

1849.89

587

31

540

760

6350

106,593.5

984.62

107,715.7

(b) Target data not normalized Target «tension of rebars in term of «y

«compression of rebars in term of «y

Manufacturing cost per kNm

rtension

rcompression

c/d

Deformation (mm)

0.016998

0.004887

0.3076

31.58

3.0758

1.0065

1397.34

0.027042

0.010141

0.3520

11.74

2.4817

1.1336

603.10

0.032435

0.015569

0.2385

2.58

4.3630

1.1532

239.99

0.004636

0.001982

0.0974

1.21

12.8455

0.4575

668.24

0.019670

0.001721

0.2576

17.98

3.8085

0.9906

920.37

0.036481

0.015961

0.2542

6.14

4.2414

1.1112

495.54

0.011448

0.000172

0.3083

31.60

2.3128

0.7634

1140.10

0.031332

0.014256

0.2138

4.42

4.6072

1.0342

297.64

0.019031

0.001618

0.2202

18.46

5.1065

1.0818

988.04

0.014031

0.001684

0.1554

7.13

6.6528

0.9051

539.24

0.009898

0.003712

0.2029

1.90

5.2133

1.1272

240.67

0.033336

0.011834

0.3255

36.11

2.7512

0.8905

1509.24

0.011580

0.003155

0.1730

1.88

5.3923

0.9272

203.79

0.021841

0.004041

0.3427

8.46

2.4225

1.1177

418.18

0.018572

0.006268

0.3297

12.81

2.9978

1.3407

549.75

0.027900

0.011927

0.3514

12.57

2.3563

1.1637

423.80

0.013347

0.006540

0.1622

15.78

5.3705

0.8416

519.64

0.029006

0.004423

0.3142

37.82

2.6776

0.9146

1252.37

0.009538

0.000238

0.3580

20.77

1.8422

0.9422

573.78

0.013871

0.001075

0.2948

3.68

3.4670

1.2726

351.08

0.010727

0.005122

0.1546

3.70

6.6544

0.3088

805.95

0.008094

0.002206

0.1069

11.28

8.4357

0.4996

938.87

0.018982

0.000949

0.2756

15.83

2.9643

0.7253

935.88

0.031794

0.014228

0.2721

14.59

2.8454

0.9370

400.21

0.031041

0.015443

0.2842

8.71

2.8727

0.9023

458.84

0.010801

0.001998

0.1524

13.22

5.6539

0.7620

622.23

0.018530

0.004262

0.3076

3.69

2.2590

0.8286

270.29

0.017737

0.004523

0.3643

8.32

1.9105

0.8802

505.97

0.009379

0.000352

0.2774

16.08

3.0894

0.8140

1103.56

0.027665

0.004634

0.2909

2.03

3.1730

1.1427

201.42 Continued

448 Hybrid composite precast systems

TABLE 10.3.2 Sample of the inputs and target dataset that is not normalized, causing distorted cost functions for the neural networks (20 hidden layers, 25 neurons; 9 inputs, 7 outputs)—cont’d (b) Target data not normalized Target «tension of rebars in term of «y

«compression of rebars in term of «y

Manufacturing cost per kNm

rtension

rcompression

c/d

Deformation (mm)

0.003167

0.000158

0.0905

2.61

13.6494

0.3788

1575.86

0.012981

0.000909

0.1614

5.70

6.3244

0.9251

469.86

0.022863

0.011146

0.3525

3.20

2.2089

1.0974

205.49

0.012363

0.001391

0.2598

10.65

3.6060

1.0683

568.43

0.012146

0.004403

0.2187

7.11

3.6508

0.8377

369.75

TABLE 10.3.3 Sample of the normalized inputs and target values establishing well-defined cost functions for the neural networks (20 hidden layers, 25 neurons; 9 inputs, 7 outputs) (see Fig. 10.3.3A). (a) Normalized input data Normalized input Mu (kNm)/ 20,000

fy (MPa)/ 1000

fc (MPa)/ 100

b (mm)/ 1000

d (mm)/ 1200

Length (mm)/ 20,000

Concrete unit price (per 1 m3)/ 200,000

Rebar unit price (per 1 kg)/1000

Manufacturing beam cost (won/m)/ 500,000

0.01177

0.439

0.230

0.290

0.3083

0.5125

0.4704

0.9382

0.0642

0.03229

0.445

0.290

0.235

0.4458

0.3600

0.5124

0.9406

0.1082

0.14506

0.439

0.440

0.375

0.6708

0.2125

0.6857

0.9382

0.3276

0.00866

0.433

0.220

0.475

0.3833

0.1675

0.4630

0.9359

0.0691

0.02538

0.454

0.450

0.325

0.3875

0.4300

0.6970

0.9441

0.1086

0.09744

0.415

0.480

0.600

0.4250

0.2650

0.7318

0.9289

0.3644

0.01561

0.582

0.290

0.425

0.3125

0.4725

0.5124

0.9833

0.0753

0.08608

0.479

0.560

0.210

0.6708

0.2700

0.8250

0.9538

0.1898

0.05608

0.416

0.470

0.580

0.4542

0.4975

0.7202

0.9292

0.2227

0.05020

0.490

0.580

0.315

0.6167

0.3500

0.8481

0.9581

0.1547

0.06048

0.452

0.180

0.335

0.8167

0.2125

0.4368

0.9433

0.1370

0.02304

0.452

0.450

0.495

0.2333

0.4525

0.6970

0.9433

0.1537

0.12247

0.532

0.370

0.495

0.8125

0.1975

0.6047

0.9703

0.2527

0.13947

0.475

0.340

0.590

0.6333

0.3600

0.5688

0.9523

0.3240

0.13698

0.407

0.200

0.445

0.8375

0.5500

0.4494

0.9257

0.2738

0.21317

0.470

0.290

0.430

0.8042

0.4875

0.5124

0.9503

0.3706

0.16693

0.577

0.390

0.540

0.8083

0.5450

0.6286

0.9820

0.3183

Artificial-intelligence-based design Chapter

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449

TABLE 10.3.3 Sample of the normalized inputs and target values establishing well-defined cost functions for the neural networks (20 hidden layers, 25 neurons; 9 inputs, 7 outputs)—cont’d (a) Normalized input data Normalized input Mu (kNm)/ 20,000

fy (MPa)/ 1000

fc (MPa)/ 100

b (mm)/ 1000

d (mm)/ 1200

Length (mm)/ 20,000

Concrete unit price (per 1 m3)/ 200,000

Rebar unit price (per 1 kg)/1000

Manufacturing beam cost (won/m)/ 500,000

0.02176

0.489

0.570

0.275

0.3125

0.5225

0.8366

0.9577

0.1043

0.10636

0.584

0.200

0.490

0.8417

0.6325

0.4494

0.9838

0.1930

0.05718

0.414

0.240

0.360

0.6958

0.2750

0.4777

0.9285

0.1460

0.00441

0.493

0.410

0.295

0.2167

0.1600

0.6518

0.9593

0.0444

0.01529

0.594

0.570

0.240

0.4625

0.3875

0.8366

0.9864

0.0741

0.00978

0.532

0.510

0.260

0.2542

0.3050

0.7667

0.9703

0.0600

0.37936

0.564

0.560

0.595

0.7708

0.4800

0.8250

0.9786

0.6326

0.05455

0.526

0.450

0.320

0.4208

0.2825

0.6970

0.9688

0.1772

0.06909

0.590

0.520

0.415

0.6542

0.4575

0.7784

0.9854

0.1879

0.05206

0.598

0.410

0.375

0.4667

0.1875

0.6518

0.9875

0.1501

0.01602

0.548

0.280

0.240

0.3500

0.2525

0.5038

0.9745

0.0642

0.00650

0.506

0.220

0.290

0.2875

0.3525

0.4630

0.9636

0.0407

0.10109

0.461

0.530

0.275

0.7042

0.1875

0.7901

0.9468

0.2172

0.00756

0.442

0.200

0.590

0.3833

0.3325

0.4494

0.9394

0.0716

0.07943

0.493

0.540

0.490

0.6458

0.3200

0.8018

0.9593

0.2333

0.14177

0.499

0.220

0.320

0.8125

0.2425

0.4630

0.9616

0.2403

0.04863

0.474

0.270

0.375

0.6167

0.4200

0.4951

0.9519

0.1316

0.09249

0.587

0.310

0.540

0.6333

0.3175

0.5330

0.9846

0.2154

(b) Normalized target data Normalized target rtension × 15

rcompression × 30

c/ d × 1.5

Deformation (mm)/100

«tension of rebars in term of «y/40

«compression of rebars in term of «y/2

Beam unit price per kNm/8000

0.254974

0.146610

0.4614

0.3158

0.07690

0.503275

0.17467

0.405624

0.304218

0.5280

0.1174

0.06204

0.566776

0.07539

0.486532

0.467070

0.3578

0.0258

0.10908

0.576605

0.03000

0.069544

0.59460

0.1461

0.0121

0.32114

0.228733

0.08353

0.295043

0.051633

0.3864

0.1798

0.09521

0.495304

0.11505

0.547218

0.478816

0.3813

0.0614

0.10604

0.555621

0.06194

0.171727

0.005152

0.4625

0.3160

0.05782

0.381713

0.14251

0.469977

0.427679

0.3207

0.0442

0.11518

0.517115

0.03720

0.285465

0.048529

0.3303

0.1846

0.12766

0.540915

0.12351

0.210462

0.050511

0.2331

0.0713

0.16632

0.452570

0.06741 Continued

450 Hybrid composite precast systems

TABLE 10.3.3 Sample of the normalized inputs and target values establishing well-defined cost functions for the neural networks (20 hidden layers, 25 neurons; 9 inputs, 7 outputs)—cont’d (b) Normalized target data Normalized target rtension × 15

rcompression × 30

c/ d × 1.5

Deformation (mm)/100

«tension of rebars in term of «y/40

«compression of rebars in term of «y/2

Beam unit price per kNm/8000

0.148473

0.111355

0.3044

0.0190

0.13033

0.563604

0.03008

0.500036

0.355025

0.4883

0.3611

0.06878

0.445231

0.18865

0.173694

0.094663

0.2595

0.0188

0.13481

0.463599

0.02547

0.327620

0.121220

0.5141

0.0846

0.06056

0.558837

0.05227

0.278578

0.188040

0.4946

0.1281

0.07494

0.670355

0.06872

0.418500

0.357818

0.5271

0.1257

0.05891

0.581828

0.05298

0.200205

0.196201

0.2433

0.1578

0.13426

0.420799

0.06496

0.435093

0.132703

0.4713

0.3782

0.06694

0.457305

0.15655

0.143065

0.007153

0.5370

0.2077

0.04605

0.471081

0.07172

0.208062

0.032250

0.4422

0.0368

0.08668

0.636320

0.04389

0.160912

0.153671

0.2319

0.0370

0.16636

0.154379

0.10074

0.121408

0.066168

0.1604

0.1128

0.21089

0.249781

0.11736

0.284725

0.028473

0.4134

0.1583

0.07411

0.362667

0.11698

0.476905

0.426830

0.4082

0.1459

0.07114

0.468522

0.05003

0.465619

0.463291

0.4263

0.0871

0.07182

0.451135

0.05736

0.162021

0.059948

0.2286

0.1322

0.14135

0.381010

0.07778

0.277952

0.127858

0.4614

0.0369

0.05647

0.414289

0.03379

0.266058

0.135690

0.5465

0.0832

0.04776

0.440110

0.06325

0.140692

0.010552

0.4161

0.1608

0.07723

0.407013

0.13794

0.414972

0.139016

0.4364

0.0203

0.07932

0.571331

0.02518

0.047511

0.004751

0.1358

0.0261

0.34123

0.189416

0.19698

0.194717

0.027260

0.2421

0.0570

0.15811

0.462552

0.05873

0.342948

0.334375

0.5288

0.0320

0.05522

0.548720

0.02569

0.185443

0.041725

0.3897

0.1065

0.09015

0.534158

0.07105

0.182191

0.132089

0.3281

0.0711

0.09127

0.418843

0.04622

Best validation performance is 9.6007e–05 at epoch 115 100 Train Validation Test Best

Mean squared error (mse)

10–1

10–2

10–3

10–4

10–5 0

50

100

200

150

250

300

350

350 Epochs

(1) Mean squared error

0.8

Validation: R=0.9982

Output ~= 1*Target + 0.00057

Output ~= 1*Target + 0.00067

Training: R=0.99842 Data Fit Y=T

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.2

0.4 Target

0.6

0.8

Data Fit Y=T

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0.8

0

Output ~= 1*Target + 0.00071

Output ~= 1*Target + 0.001

Data Fit Y=T

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

(A)

0.2

0.4 Target

0.6

0.4 Target

0.6

0.8

AII: R=0.99818

Test: R=0.99709 0.8

0.2

0.8

0.8

Data Fit Y=T

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.2

0.4 Target

0.6

0.8

(2) Minimization of the cost function with 13,000 input dataset

FIG. 10.3.4 Minimization of the cost function: (A) regression results with 13,000 input dataset; 20 hidden layers, 25 neurons, (Continued)

Best validation performance is 0.0020389 at epoch 14 100 Train Validation Test Best

Mean squared error (mse)

10–2

10–4

10–6

50

0

150

100

200

250

264 Epochs (1) Mean squared error

Output~= 0.94*Target + 0.015

Data

0.7

Fit Y=T

0.6 0.5 0.4 0.3 0.2 0.1 0

0.8

0.2

0.4

0.6

Fit Y=T

0.6 0.5 0.4 0.3 0.2 0.1 0

0.2

0.4

0.6

Target

Target

Test: R=0.96336

AII: R=0.97662

Fit Y=T

0.6

Data

0.7

0.8

Data

0.7

0.5 0.4 0.3 0.2 0.1

0.8

0.8

Data

0.7

Fit Y=T

0.6 0.5 0.4 0.3 0.2 0.1 0

0 0

0.2

0.4

Target

(B)

0.8

0 0

Output~= 0.95*Target + 0.014

Validation: R=0.95989

Output~= 0.96*Target + 0.012

Output~= 0.96*Target + 0.011

Training: R=0.98253 0.8

0.6

0.8

0

0.2

0.4

0.6

0.8

Target

(2) Minimization of the cost function with 1000 input dataset

FIG. 10.3.4, Cont’d (B) regression results with 1000 input dataset; 20 hidden layers, 25 neurons, and (Continued)

Best validation performance is 0.0013669 at epoch 965 100

Train Validation Test Best

Mean squared error (mse)

10–1

10–2

10–3 0

200

100

400

300

500

600

800

700

900

1000

1000 Epochs

(1) Mean squared error

Output ~= 0.95*Target + 0.011

Data Fit

0.6

Y=T

0.4 0.2 0

0

Output ~= 0.95*Target + 0.011

Validation: R=0.97375

0.8

0.2

0.4

0.6

Fit Y=T

0.4 0.2 0

0

0.2

0.6

Test: R=0.97493

AII: R=0.97411

Y=T

0.4 0.2 0

0.2

0.4

0.6

0.8

0.8

Data Fit Y=T

0.6 0.4 0.2 0

0.8

0

0.2

Target

(C)

0.4

Target

Fit

0

Data

0.6

0.8

Data

0.6

0.8

Target

Output ~= 0.95*Target + 0.011

Output ~= 0.95*Target + 0.011

Training: R=0.97401 0.8

0.4

Target (2) 13,000 input dataset

FIG. 10.3.4, Cont’d (C) regression results with 13,000 input dataset; 5 hidden layers, 5 neurons.

0.6

0.8

454 Hybrid composite precast systems

FIG. 10.3.5 Minimum tensile strain of rebars validated for the ductile behavior of concrete beam obtained based on the normalized data using, 13,000 dataset with 20 hidden layers and 25 neurons (9 Inputs, 7 outputs).

Artificial-intelligence-based design Chapter

10

455

(1) Neural outputs vs target values: 13,000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(2) Neural outputs vs target values: poorly trained by 1000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(A)

(3) Neural outputs vs target values: poorly trained by 13,000 dataset with 5 hidden layers and 5 neurons (obtained based on normalized data)

FIG. 10.3.6 Trained data, comparing 20 hidden layers and 25 neurons versus 5 hidden layers and 5 neurons (9 inputs, 7 outputs): (A) tensile rebar ratios, (Continued)

456 Hybrid composite precast systems

(1) Neural outputs vs target values: 13,000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(2) Neural outputs vs target values: poorly trained by 1000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(B)

(3) Neural outputs vs target values:poorly trained by 13,000 dataset with 5 hidden layers and 5 neurons (obtained based on normalized data)

FIG. 10.3.6, Cont’d (B) tensile rebar strains, (Continued)

Artificial-intelligence-based design Chapter

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457

(1) Neural outputs vs target values: 13,000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(2) Neural outputs vs target values: poorly trained by 1000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(C)

(3) Neural outputs vs target values: poorly trained by 13,000 dataset with 5 hidden layers and 5 neurons (obtained based on normalized data)

FIG. 10.3.6, Cont’d (C) compressive rebar ratios, (Continued)

458 Hybrid composite precast systems

(1) Neural outputs vs target values: 13,000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(2) Neural outputs vs target values: poorly trained by 1000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(D)

(3) Neural outputs vs target values: poorly trained by 13,000 dataset with 5 hidden layers and 5 neurons (obtained based on normalized data)

FIG. 10.3.6, Cont’d (D) compressive rebar strains, (Continued)

Artificial-intelligence-based design Chapter

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459

(1) Neural outputs vs target values: 13,000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(2) Neural outputs vs target values: poorly trained by 1000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(E)

(3) Neural outputs vs target values: poorly trained by 13,000 dataset with 5 hidden layers and 5 neurons (obtained based on normalized data)

FIG. 10.3.6, Cont’d (E) deformation, and (Continued)

460 Hybrid composite precast systems

(1) Neural outputs vs target values: 13,000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(2) Neural outputs vs target values: poorly trained by 1000 dataset with 20 hidden layers and 25 neurons (obtained based on normalized data)

(F)

(3) Neural outputs vs target values: poorly trained by 13,000 dataset with 5 hidden layers and 5 neurons (obtained based on normalized data)

FIG. 10.3.6, Cont’d (F) manufacturing beam cost per design moment (kNm).

Artificial-intelligence-based design Chapter

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461

FIG. 10.3.7 Poorly trained data due to nonnormalized data with sufficient hidden layers: 13,000 data with 20 hidden layers and 25 neurons (9 inputs, 7 outputs): (A) tensile rebar ratios, (Continued)

462 Hybrid composite precast systems

FIG. 10.3.7, Cont’d (B) tensile rebar strains, (Continued)

Artificial-intelligence-based design Chapter

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463

FIG. 10.3.7, Cont’d (C) compressive rebar ratios, (Continued)

464 Hybrid composite precast systems

FIG. 10.3.7, Cont’d (D) compressive rebar strain, and (Continued)

Artificial-intelligence-based design Chapter

FIG. 10.3.7, Cont’d (E) Deformation.

10

465

466 Hybrid composite precast systems

TABLE 10.3.4 Comparison of the test (design) results based on neural networks (13,000 dataset with 20 hidden layers (a) Normalized data Normalized f 0c

Normalized fy

Input in mechanic and neural network

Normalized rtension Results based on engineering mechanics

Neural network results

Normalized rcompression

Errors

Results based on engineering mechanics

Normalized ration c/d

Neural network results

Errors

Results based on engineering mechanics

Neural network results

Errors

0.56

0.590

0.181026

0.18133

0.17%

0.06698

0.06660


0.57%

0.2372

0.24153

1.83%

0.59

0.506

0.715346

0.71087


0.63%

0.65097

0.65890

1.22%

0.4932

0.48761


1.13%

0.34

0.589

0.069203

0.07311

5.65%

0.03460

0.03769

8.93%

0.1404

0.14053

0.10%

0.58

0.531

0.245243

0.24450


0.30%

0.02207

0.02432

10.17%

0.3186

0.32091

0.73%

0.25

0.445

0.152612

0.15458

1.29%

0.14956

0.14789


1.12%

0.2226

0.22023


1.06%

0.58

0.445

0.293928

0.30158

2.60%

0.27482

0.27416


0.24%

0.2423

0.24623

1.62%

0.57

0.488

0.483586

0.47798


1.16%

0.39896

0.39950

0.14%

0.3869

0.37735


2.47%

0.57

0.458

0.127194

0.12916

1.55%

0.11193

0.10993


1.79%

0.1206

0.12271

1.75%

0.44

0.486

0.313239

0.31096


0.73%

0.25999

0.25813


0.71%

0.2991

0.30004

0.32%

0.49

0.594

0.192412

0.19164


0.40%

0.07697

0.07910

2.77%

0.2825

0.28152


0.35%

0.31

0.535

0.323551

0.32925

1.76%

0.29120

0.29164

0.15%

0.4194

0.42921

2.34%

0.38

0.588

0.216985

0.21514


0.85%

0.14321

0.14862

3.78%

0.3747

0.37794

0.87%

0.37

0.459

0.228273

0.23074

1.08%

0.21344

0.21784


2.06%

0.2772

0.27762

0.15%

0.51

0.415

0.472385

0.46094


2.42%

0.02362

0.03086

30.67%

0.5414

0.53132


1.86%

0.22

0.495

0.205167

0.20737

1.08%

0.12105

0.11076


8.50%

0.4316

0.45813

6.15%

0.19

0.542

0.05653

0.05459


3.43%

0.01244

0.00943


24.18%

0.1932

0.19516

1.01%

0.35

0.585

0.19814

0.19655


0.80%

0.14563

0.14481


0.57%

0.3236

0.32003


1.10%

0.56

0.440

0.06721

0.06792

1.06%

0.03764

0.03111


17.35%

0.0747

0.07392


1.04%

0.2

0.477

0.26288

0.26123


0.63%

0.22476

0.21860


2.74%

0.4727

0.49560

4.84%

0.26

0.476

0.17118

0.17089


0.17%

0.02482

0.02510

1.11%

0.3908

0.39357

0.71%

0.48

0.567

0.14441

0.14364


0.53%

0.06498

0.06554

0.86%

0.1991

0.20077

0.84%

0.25

0.439

0.09699

0.09420


2.88%

0.00485

0.00242


50.04%

0.2252

0.22001


2.30%

0.28

0.552

0.15196

0.15401

1.35%

0.04711

0.04596


2.44%

0.3627

0.36118


0.42%

0.44

0.578

0.18443

0.18382


0.33%

0.12633

0.12477


1.23%

0.2529

0.25146


0.57%

0.4

0.510

0.17313

0.17156


0.91%

0.06925

0.06718


2.99%

0.2814

0.28112


0.10%

0.43

0.464

0.20285

0.19995


1.43%

0.12678

0.12313


2.88%

0.2529

0.25134


0.62%

0.54

0.452

0.30557

0.30140


1.36%

0.23224

0.23282

0.25%

0.2309

0.22836


1.10%

0.25

0.547

0.12378

0.12441

0.50%

0.07365

0.07412

0.63%

0.2678

0.26520


0.97%

0.24

0.505

0.11951

0.11935


0.14%

0.07350

0.07150


2.72%

0.2586

0.25878

0.07%

0.6

0.422

0.52522

0.50579


3.70%

0.04727

0.05118

8.28%

0.5219

0.51788


0.77%

0.5

0.496

0.27635

0.27489


0.53%

0.11607

0.11506


0.87%

0.339

0.33641


0.76%

0.52

0.475

0.55941

0.55651


0.52%

0.38040

0.38481

1.16%

0.4884

0.47881


1.96%

0.31

0.594

0.15327

0.15365

0.25%

0.10193

0.10154


0.38%

0.2946

0.29483

0.08%

0.29

0.589

0.12495

0.12663

1.35%

0.04248

0.04207


0.98%

0.2993

0.29879


0.17%

0.19

0.533

0.13178

0.13457

2.12%

0.12387

0.12979

4.78%

0.2799

0.27511


1.71%

0.52

0.553

0.14355

0.14428

0.51%

0.00861

0.01225

42.26%

0.2157

0.21675

0.48%

0.44

0.571

0.20604

0.20517


0.42%

0.01648

0.01622


1.60%

0.3665

0.37019

1.01%

Artificial-intelligence-based design Chapter

10

467

and 25 neurons) with results based on the engineering mechanics.

Normalized deformation Results based on engineering mechanics

Neural network results

0.1213 0.1047

Normalized «tension in term of «y

Errors

Results based on engineering mechanics

Neural network results

0.12065


0.53%

0.13538

0.10355


1.10%

0.06051

0.1252

0.12212


2.46%

0.4196

0.42707

0.0179 0.1552

Normalized «compression in term of «y

Errors

Results based on engineering mechanics

Neural network results

0.13293


1.81%

0.406376

0.06456

6.69%

0.523979

0.24667

0.24371


1.20%

1.78%

0.10476

0.10539

0.60%

0.01521


15.05%

0.19336

0.19869

2.76%

0.15356


1.06%

0.17504

0.17353


0.86%

0.0546

0.05189


4.96%

0.08845

0.09058

2.41%

0.1762

0.17763

0.81%

0.37465

0.37429

0.0639

0.06420

0.47%

0.12389

0.1355

0.13943

2.90%

0.10889

0.1829

0.17689


3.29%

0.6593

0.65898

0.1602 0.0483

Normalized manufacturing cost per kNm

Errors

Results based on engineering mechanics

Neural network results

Errors

0.40986

0.86%

0.06476

0.06383


1.44%

0.52649

0.48%

0.04747

0.03858


18.72%

0.301328

0.30429

0.98%

0.13097

0.13177

0.61%

0.395177

0.40189

1.70%

0.16886

0.17174

1.71%

0.396122

0.38952


1.67%

0.04722

0.05166

9.41%

0.288761

0.29027

0.52%

0.16305

0.16325

0.12%

0.440331

0.43848


0.42%

0.05773

0.06067

5.09%


0.10%

0.222378

0.22331

0.42%

0.22279

0.22517

1.07%

0.12374


0.12%

0.469901

0.47264

0.58%

0.05482

0.05508

0.47%

0.11039

1.38%

0.393266

0.39321


0.01%

0.07169

0.07249

1.12%

0.07222

0.07098


1.72%

0.502905

0.49669


1.24%

0.05651

0.05587


1.13%


0.05%

0.07663

0.07453


2.74%

0.302464

0.30098


0.49%

0.23628

0.23002


2.65%

0.15696


2.02%

0.1442

0.14448

0.20%

0.316668

0.31718

0.16%

0.1574

0.15716


0.15%

0.05279

9.30%

0.06402

0.06710

4.81%

0.635798

0.63469


0.17%

0.04595

0.04949

7.70%

0.0226

0.02027


10.33%

0.07501

0.06798


9.38%

0.509591

0.51169

0.41%

0.03151

0.02996


4.91%

0.1371

0.13636


0.54%

0.18717

0.18913

1.05%

0.392371

0.40001

1.95%

0.14443

0.14435


0.05%

0.2163

0.21757

0.59%

0.09322

0.09507

1.99%

0.398718

0.39934

0.15%

0.09008

0.08922


0.96%

0.0176

0.01980

12.49%

0.65084

0.64285


1.23%

0.059179

0.06647

12.32%

0.19018

0.19064

0.24%

0.1926

0.19098


0.84%

0.06836

0.06480


5.21%

0.504166

0.50934

1.03%

0.10512

0.10330


1.73%

0.155

0.15679

1.15%

0.08945

0.08978

0.37%

0.533484

0.53242


0.20%

0.08733

0.08744

0.12%

0.0411

0.04595

11.80%

0.17295

0.17018


1.60%

0.412943

0.41136


0.38%

0.04153

0.03939


5.16%

0.1556

0.15068


3.16%

0.19344

0.19864

2.69%

0.263212

0.24543


6.76%

0.24011

0.24313

1.26%

0.0791

0.07492


5.29%

0.0852

0.08636

1.36%

0.339171

0.33631


0.84%

0.08895

0.09043

1.67%

0.0505

0.05192

2.82%

0.12802

0.12933

1.02%

0.385144

0.38645

0.34%

0.04695

0.04559


2.89%

0.128

0.12988

1.47%

0.12735

0.12439


2.33%

0.226501

0.22915

1.17%

0.1559

0.15747

1.01%

0.3891

0.39251

0.88%

0.15947

0.16133

1.16%

0.292491

0.28681


1.94%

0.25784

0.25824

0.15%

0.1379

0.13800

0.08%

0.18244

0.17975


1.47%

0.523089

0.52259


0.10%

0.07752

0.07624


1.65%

0.1501

0.15057

0.31%

0.12619

0.12407


1.68%

0.440645

0.43789


0.63%

0.08074

0.08390

3.91%

0.2823

0.28044


0.66%

0.14261

0.14109


1.06%

0.374084

0.37851

1.18%

0.17867

0.17784


0.47%

0.0448

0.05332

19.03%

0.06664

0.06866

3.03%

0.641229

0.64192

0.11%

0.03806

0.04145

8.92%

0.1554

0.15939

2.57%

0.10359

0.10448

0.86%

0.337186

0.33426


0.87%

0.13455

0.13653

1.47%

0.2503

0.24996


0.14%

0.06541

0.06608

1.02%

0.554505

0.55664

0.39%

0.0836

0.08620

3.11%

0.0512

0.05184

1.24%

0.10332

0.10416

0.81%

0.399377

0.40245

0.77%

0.04294

0.04300

0.14%

0.0321

0.03130


2.49%

0.10216

0.10391

1.71%

0.385828

0.38595

0.03%

0.04063

0.04247

4.52%

0.0602

0.06244

3.71%

0.1227

0.12585

2.56%

0.449727

0.44076


1.99%

0.05187

0.04951


4.56%

0.0264

0.02617


0.87%

0.16147

0.16514

2.27%

0.401048

0.40071


0.09%

0.04023

0.04068

1.12%

0.1176

0.12067

2.61%

0.08127

0.08189

0.77%

0.41603

0.41583


0.05%

0.07097

0.06724


5.25%

Continued Continued

468 Hybrid composite precast systems

TABLE 10.3.4 Comparison of the test (design) results based on neural networks (13,000 dataset with 20 hidden layers (a) Normalized data Normalized f 0c

Normalized fy

Normalized rtension

Input in mechanic and neural network

Results based on engineering mechanics

Neural network results

0.59

0.485

0.36326

0.35961

0.31

0.405

0.41838

0.45

0.408

0.18

0.572

0.44

Normalized rcompression

Errors

Results based on engineering mechanics

Neural network results


1.01%

0.03633

0.03584

0.42749

2.18%

0.30333

0.28537

0.28737

0.70%

0.07594

0.07790

2.58%

0.461

0.31149

0.31134

0.47

0.457

0.40660

0.18

0.458

0.18

0.549

0.29

Normalized ration c/d

Errors

Results based on engineering mechanics

Neural network results

Errors


1.34%

0.4202

0.41800


0.52%

0.28790


5.09%

0.4779

0.50058

4.75%

0.07990

0.08140

1.87%

0.3162

0.31511


0.34%

0.05696

0.06456

13.34%

0.2526

0.24861


1.58%


0.05%

0.21337

0.20637


3.28%

0.3042

0.30536

0.38%

0.40612


0.12%

0.04066

0.04793

17.88%

0.5367

0.52740


1.73%

0.26766

0.26552


0.80%

0.21413

0.22206

3.71%

0.5339

0.51433


3.67%

0.19484

0.19269


1.10%

0.16366

0.15816


3.36%

0.4695

0.47030

0.17%

0.421

0.50846

0.49460


2.73%

0.43982

0.46382

5.46%

0.5687

0.52181


8.24%

0.33

0.534

0.15744

0.15802

0.37%

0.11808

0.11465


2.90%

0.2393

0.23536


1.65%

0.18

0.452

0.13792

0.13593


1.44%

0.02138

0.03269

52.93%

0.4175

0.40712


2.49%

0.43

0.536

0.29936

0.30039

0.34%

0.05688

0.04879


14.22%

0.4815

0.48440

0.60%

0.24

0.530

0.18880

0.18963

0.44%

0.11517

0.10984


4.62%

0.3897

0.40458

3.82%

(b) Original data f0 c

fy

rtension

rcompression

Input in mechanic and neural network

Results based on engineering mechanics

Neural network results

56

590

0.01207

0.01209

0.17%

59

506

0.04769

0.04739


0.63%

34

589

0.00461

0.00487

5.65%

58

531

0.01635

0.01630

25

445

0.01017

58

445

0.01960

57

488

57 44

Results based on engineering mechanics

c/d

Neural network results

Errors

Results based on engineering mechanics

0.002233

0.00222


0.57%

0.1581333

0.16102

1.83%

0.021699

0.02196

1.22%

0.3288

0.32507


1.13%

0.001153

0.00126

8.93%

0.0936

0.09369

0.10%


0.30%

0.000736

0.00081

10.17%

0.2124

0.21394

0.73%

0.01031

1.29%

0.004985

0.00493


1.12%

0.1484

0.14682


1.06%

0.02011

2.60%

0.009161

0.00914


0.24%

0.1615333

0.16415

1.62%

0.03224

0.03187


1.16%

0.013299

0.01332

0.14%

0.2579333

0.25157


2.47%

458

0.00848

0.00861

1.55%

0.003731

0.00366


1.79%

0.0804

0.08180

1.75%

486

0.02088

0.02073


0.73%

0.008666

0.00860


0.71%

0.1994

0.20003

0.32%

49

594

0.01283

0.01278


0.40%

0.002566

0.00264

2.77%

0.1883333

0.18768


0.35%

31

535

0.02157

0.02195

1.76%

0.009707

0.00972

0.15%

0.2796

0.28614

2.34%

38

588

0.01447

0.01434


0.85%

0.004774

0.00495

3.78%

0.2498

0.25196

0.87%

37

459

0.01522

0.01538

1.08%

0.007115

0.00726

2.06%

0.1848

0.18508

0.15%

51

415

0.03149

0.03073


2.42%

0.000787

0.00103

30.67%

0.3609333

0.35422


1.86%

22

495

0.01368

0.01382

1.08%

0.004035

0.00369


8.50%

0.2877333

0.30542

6.15%

19

542

0.00377

0.00364


3.43%

0.000415

0.00031


24.18%

0.1288

0.13011

1.01%

35

585

0.01321

0.01310


0.80%

0.004854

0.00483


0.57%

0.2157333

0.21335


1.10%

56

440

0.00448

0.00453

1.06%

0.001255

0.00104


17.35%

0.0498

0.04928


1.04%

20

477

0.01753

0.01742


0.63%

0.007492

0.00729


2.74%

0.3151333

0.33040

4.84%

Errors

Neural network results

Errors

Artificial-intelligence-based design Chapter

10

469

and 25 neurons) with results based on the engineering mechanics—cont’d

Normalized deformation Results based on engineering mechanics

Neural network results

0.1619

0.16491

0.2061

Normalized «tension in term of «y

Errors

Results based on engineering mechanics

Neural network results

1.86%

0.07947

0.08336

0.20269


1.66%

0.07923

0.1153

0.11183


3.01%

0.1526

0.15121


0.91%

0.118

0.11645

0.0788

Normalized «compression in term of «y

Errors

Results based on engineering mechanics

Neural network results

4.89%

0.460836

0.46733

0.07501


5.32%

0.495971

0.13761

0.13990

1.66%

0.12948

0.13328

2.93%


1.32%

0.12793

0.12724

0.08324

5.64%

0.05891

0.0896

0.08577


4.28%

0.228

0.22567


1.02%

0.0191

0.00853

0.2001

0.20532

Normalized manufacturing cost per kNm

Errors

Results based on engineering mechanics

Neural network results

Errors

1.41%

0.10377

0.10329


0.47%

0.50514

1.85%

0.16034

0.16574

3.37%

0.629613

0.62603


0.57%

0.07252

0.07222


0.41%

0.264957

0.25901


2.24%

0.17456

0.17241


1.23%


0.54%

0.540093

0.54458

0.83%

0.06612

0.06560


0.79%

0.06031

2.38%

0.585892

0.58771

0.31%

0.0508

0.05096

0.32%

0.05927

0.06323

6.68%

0.589292

0.59050

0.21%

0.05506

0.05178


5.96%

0.05997

0.06086

1.49%

0.470544

0.46983


0.15%

0.08669

0.08960

3.36%


55.36%

0.05836

0.06610

13.26%

0.642536

0.63835


0.65%

0.02519

0.02547

1.10%

2.61%

0.148

0.14942

0.96%

0.421863

0.42441

0.60%

0.09824

0.10307

4.92%

0.1663

0.16718

0.53%

0.08607

0.09145

6.25%

0.591805

0.58813


0.62%

0.08966

0.09515

6.13%

0.331

0.33265

0.50%

0.0592

0.05816


1.75%

0.459106

0.46548

1.39%

0.11689

0.11932

2.08%

0.0547

0.05808

6.18%

0.08065

0.07647


5.18%

0.492171

0.49837

1.26%

0.03985

0.03990

0.13%

Neural network results

Neural network results

«compression

«tension

Deformation (mm) Results based on engineering mechanics

Errors

Results based on engineering mechanics

Neural network results

Errors

Results based on engineering mechanics

Manufacturing cost (won per kNm)

Neural network results

Errors

Results based on engineering mechanics

Errors

12.13

12.07


0.53%

0.0160

0.0157


1.81%

0.00240

0.00242

0.86%

518.08

510.63


1.44%

10.47

10.35


1.10%

0.0061

0.0065

6.69%

0.00265

0.00266

0.48%

379.76

308.68


18.72%

12.52

12.21


2.46%

0.0291

0.0287


1.20%

0.00177

0.00179

0.98%

1047.76

1054.16

0.61%

41.96

42.71

1.78%

0.0111

0.0112

0.60%

0.00210

0.00213

1.70%

1350.88

1373.94

1.71%

1.79

1.52


15.05%

0.0172

0.0177

2.76%

0.00176

0.00173


1.67%

377.76

413.31

9.41%

15.52

15.36


1.06%

0.0156

0.0154


0.86%

0.00128

0.00129

0.52%

1304.4

1306.01

0.12%

5.46

5.19


4.96%

0.0086

0.0088

2.41%

0.00215

0.00214


0.42%

461.84

485.33

5.09%

17.62

17.76

0.81%

0.0343

0.0343


0.10%

0.00102

0.00102

0.42%

1782.32

1801.33

1.07%

6.39

6.42

0.47%

0.0120

0.0120


0.12%

0.00228

0.00230

0.58%

438.56

440.61

0.47%

13.55

13.94

2.90%

0.0129

0.0131

1.38%

0.00234

0.00234


0.01%

573.52

579.91

1.12%

18.29

17.69


3.29%

0.0077

0.0076


1.72%

0.00269

0.00266


1.24%

452.08

446.98


1.13%

65.93

65.90


0.05%

0.0090

0.0088


2.74%

0.00178

0.00177


0.49%

1890.24

1840.20


2.65%

16.02

15.70


2.02%

0.0132

0.0133

0.20%

0.00145

0.00146

0.16%

1259.2

1257.31


0.15%

4.83

5.28

9.30%

0.0053

0.0056

4.81%

0.00264

0.00263


0.17%

367.6

395.90

7.70%

2.26

2.03


10.33%

0.0074

0.0067


9.38%

0.00252

0.00253

0.41%

252.08

239.70


4.91%

13.71

13.64


0.54%

0.0203

0.0205

1.05%

0.00213

0.00217

1.95%

1155.44

1154.81


0.05%

21.63

21.76

0.59%

0.0109

0.0111

1.99%

0.00233

0.00234

0.15%

720.64

713.73


0.96%

1.76

1.98

12.49%

0.0573

0.0566


1.23%

0.00026

0.00029

12.32%

1521.44

1525.11

0.24%

19.26

19.10


0.84%

0.0065

0.0062


5.21%

0.00240

0.00243

1.03%

840.96

826.37


1.73%

Continued

470 Hybrid composite precast systems

TABLE 10.3.4 Comparison of the test (design) results based on neural networks (13,000 dataset with 20 hidden layers (b) Original data f0 c

fy

rtension

Input in mechanic and neural network

Results based on engineering mechanics

Neural network results

26

476

0.01141

0.01139

48

567

0.00963

rcompression

Errors

Results based on engineering mechanics

Neural network results


0.17%

0.000827

0.00084

0.00958


0.53%

0.002166

0.00218

c/d

Errors

Results based on engineering mechanics

Neural network results

Errors

1.11%

0.2605333

0.26238

0.71%

0.86%

0.1327333

0.13385

0.84%

25

439

0.00647

0.00628


2.88%

0.000162

0.00008


50.04%

0.1501333

0.14667


2.30%

28

552

0.01013

0.01027

1.35%

0.001570

0.00153


2.44%

0.2418

0.24078


0.42%

44

578

0.01230

0.01225


0.33%

0.004211

0.00416


1.23%

0.1686

0.16764


0.57%

40

510

0.01154

0.01144


0.91%

0.002308

0.00224


2.99%

0.1876

0.18741


0.10%

43

464

0.01352

0.01333


1.43%

0.004226

0.00410


2.88%

0.1686

0.16756


0.62%

54

452

0.02037

0.02009


1.36%

0.007741

0.00776

0.25%

0.1539333

0.15224


1.10%

25

547

0.00825

0.00829

0.50%

0.002455

0.00247

0.63%

0.1785333

0.17680


0.97%

24

505

0.00797

0.00796


0.14%

0.002450

0.00238


2.72%

0.1724

0.17252

0.07%

60

422

0.03501

0.03372


3.70%

0.001576

0.00171

8.28%

0.3479333

0.34525


0.77%

50

496

0.01842

0.01833


0.53%

0.003869

0.00384


0.87%

0.226

0.22427


0.76%

52

475

0.03729

0.03710


0.52%

0.012680

0.01283

1.16%

0.3256

0.31921


1.96%

31

594

0.01022

0.01024

0.25%

0.003398

0.00338


0.38%

0.1964

0.19655

0.08%

29

589

0.00833

0.00844

1.35%

0.001416

0.00140


0.98%

0.1995333

0.19920


0.17%

19

533

0.00879

0.00897

2.12%

0.004129

0.00433

4.78%

0.1866

0.18341


1.71%

52

553

0.00957

0.00962

0.51%

0.000287

0.00041

42.26%

0.1438

0.14450

0.48%

44

571

0.01374

0.01368


0.42%

0.000549

0.00054


1.60%

0.2443333

0.24680

1.01%

59

485

0.02422

0.02397


1.01%

0.001211

0.00119


1.34%

0.2801333

0.27866


0.52%

31

405

0.02789

0.02850

2.18%

0.010111

0.00960


5.09%

0.3186

0.33372

4.75%

45

408

0.01902

0.01916

0.70%

0.002663

0.00271

1.87%

0.2108

0.21008


0.34%

18

572

0.00506

0.00519

2.58%

0.001899

0.00215

13.34%

0.1684

0.16574


1.58%

44

461

0.02077

0.02076


0.05%

0.007112

0.00688


3.28%

0.2028

0.20357

0.38%

47

457

0.02711

0.02707


0.12%

0.001355

0.00160

17.88%

0.3578

0.35160


1.73%

18

458

0.01784

0.01770


0.80%

0.007138

0.00740

3.71%

0.3559333

0.34289


3.67%

18

549

0.01299

0.01285


1.10%

0.005455

0.00527


3.36%

0.313

0.31353

0.17%

29

421

0.03390

0.03297


2.73%

0.014661

0.01546

5.46%

0.3791333

0.34788


8.24%

33

534

0.01050

0.01053

0.37%

0.003936

0.00382


2.90%

0.1595333

0.15691


1.65%

18

452

0.00919

0.00906


1.44%

0.000713

0.00109

52.93%

0.2783333

0.27141


2.49%

43

536

0.01996

0.02003

0.34%

0.001896

0.00163


14.22%

0.321

0.32294

0.60%

24

530

0.01259

0.01264

0.44%

0.003839

0.00366


4.62%

0.2598

0.26972

3.82%

Artificial-intelligence-based design Chapter

10

471

and 25 neurons) with results based on the engineering mechanics—cont’d «tension

Deformation (mm) Results based on engineering mechanics

Neural network results

15.5

15.68

4.11

Errors

Results based on engineering mechanics

Neural network results

1.15%

0.0085

0.0085

4.59

11.80%

0.0196

15.56

15.07


3.16%

7.91

7.49


5.29%

5.05

5.19

12.8

«compression

Manufacturing cost (won per kNm)

Errors

Results based on engineering mechanics

Neural network results

0.37%

0.00254

0.00253

0.0193


1.60%

0.00234

0.0170

0.0174

2.69%

0.0094

0.0095

1.36%

2.82%

0.0148

0.0150

12.99

1.47%

0.0130

0.0127

38.91

39.25

0.88%

0.0148

0.0150

1.16%

13.79

13.80

0.08%

0.0165

0.0162


1.47%

15.01

15.06

0.31%

0.0138

0.0136


1.68%

28.23

28.04


0.66%

0.0144

0.0143

4.48

5.33

19.03%

0.0056

15.54

15.94

2.57%

0.0103

25.03

25.00


0.14%

0.0062

5.12

5.18

1.24%

0.0123

0.0124

0.81%

0.00237

0.00239

0.77%

343.52

344.01

0.14%

3.21

3.13


2.49%

0.0120

0.0122

1.71%

0.00227

0.00227

0.03%

325.04

339.73

4.52%

6.02

6.24

3.71%

0.0131

0.0134

2.56%

0.00240

0.00235


1.99%

414.96

396.05


4.56%

2.64

2.62


0.87%

0.0179

0.0183

2.27%

0.00222

0.00222


0.09%

321.84

325.45

1.12%

11.76

12.07

2.61%

0.0093

0.0094

0.77%

0.00238

0.00237


0.05%

567.76

537.93


5.25%

16.19

16.49

1.86%

0.0077

0.0081

4.89%

0.00224

0.00227

1.41%

830.16

826.30


0.47%

20.61

20.27


1.66%

0.0064

0.0061


5.32%

0.00201

0.00205

1.85%

1282.72

1325.95

3.37%

11.53

11.18


3.01%

0.0112

0.0114

1.66%

0.00257

0.00255


0.57%

580.16

577.78


0.41%

15.26

15.12


0.91%

0.0148

0.0152

2.93%

0.00152

0.00148


2.24%

1396.48

1379.27


1.23%

11.8

11.64


1.32%

0.0118

0.0117


0.54%

0.00249

0.00251

0.83%

528.96

524.79


0.79%

7.88

8.32

5.64%

0.0054

0.0055

2.38%

0.00268

0.00269

0.31%

406.4

407.68

0.32%

8.96

8.58


4.28%

0.0054

0.0058

6.68%

0.00270

0.00270

0.21%

440.48

414.24


5.96%

22.8

22.57


1.02%

0.0066

0.0067

1.49%

0.00258

0.00258


0.15%

693.52

716.84

3.36%

1.91

0.85


55.36%

0.0049

0.0056

13.26%

0.00271

0.00269


0.65%

201.52

203.74

1.10%

20.01

20.53

2.61%

0.0158

0.0160

0.96%

0.00225

0.00227

0.60%

785.92

824.58

4.92%

16.63

16.72

0.53%

0.0078

0.0083

6.25%

0.00267

0.00266


0.62%

717.28

761.24

6.13%

33.1

33.26

0.50%

0.0063

0.0062


1.75%

0.00246

0.00249

1.39%

935.12

954.53

2.08%

5.47

5.81

6.18%

0.0085

0.0081


5.18%

0.00261

0.00264

1.26%

318.8

319.22

0.13%

Errors

Results based on engineering mechanics

Neural network results

Errors


0.20%

698.64

699.49

0.12%

0.00233


0.38%

332.24

315.11


5.16%

0.00116

0.00108


6.76%

1920.88

1945.03

1.26%

0.00187

0.00186


0.84%

711.6

723.46

1.67%

1.02%

0.00223

0.00223

0.34%

375.6

364.76


2.89%


2.33%

0.00116

0.00117

1.17%

1247.2

1259.75

1.01%

0.00136

0.00133


1.94%

2062.72

2065.91

0.15%

0.00236

0.00236


0.10%

620.16

609.95


1.65%

0.00241

0.00240


0.63%

645.92

671.17

3.91%


1.06%

0.00189

0.00191

1.18%

1429.36

1422.71


0.47%

0.0058

3.03%

0.00271

0.00271

0.11%

304.48

331.64

8.92%

0.0104

0.86%

0.00167

0.00166


0.87%

1076.4

1092.27

1.47%

0.0063

1.02%

0.00263

0.00264

0.39%

668.8

689.61

3.11%

472 Hybrid composite precast systems

FIG. 10.3.8 Accuracy of the test (design) results of the neural networks: 20 hidden layers, 25 neurons, 9 inputs, 7 outputs (neural test results vs results based on the engineering mechanics): (A) tensile rebar ratio, (Continued)

Artificial-intelligence-based design Chapter

10

473

FIG. 10.3.8, Cont’d (B) tensile rebar strain, (Continued)

474 Hybrid composite precast systems

FIG. 10.3.8, Cont’d (C) compressive rebar ratio, (Continued)

Artificial-intelligence-based design Chapter

10

475

FIG. 10.3.8, Cont’d (D) compressive rebar strain, (Continued)

476 Hybrid composite precast systems

FIG. 10.3.8, Cont’d (E) deformation, and (Continued)

Artificial-intelligence-based design Chapter

FIG. 10.3.8, Cont’d (F) manufacturing beam cost per design moment kNm.

10

477

478 Hybrid composite precast systems

10.3.4 Conclusions The artificial neural networks (ANNs) exhibited a learning and memory capability similar to that of the human brain, which is activated by an electrical input, sending out pulses through their axons. For ANNs, the voltage output is modeled by an activation function whereas the human cells collect the electromechanical signals between their dendrites. The entangled input and output relationships for the design of the doubly reinforced concrete beams were established by an ANN, not based on the engineering mechanics, which memorized how the input dataset was mapped onto the output-design parameters. The design results obtained using an ANN were verified by the test datasets. Readers are encouraged to extend the artificial neural networks to solve the diverse engineering problems of their interests, and to verify the designs. A methodology similar to the one used in the design of the doubly reinforced concrete beams can be implemented for the designs of the structural components, including columns, slabs, walls, and foundations with appropriate input and output parameters. The application of the deep learning models based on the convolution neural network architectures containing layers including convolution layers, activation layers, and pooling layers was not described in this chapter, but are reserved for the next discussion.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

https://en.wikipedia.org/wiki/Artificial_neural_network. R.D. Vanluchene, S. Roufei, Neural networks in structural engineering, Microcomput. Civ. Eng. 5 (1990) 207–215. B. Abbes, Artificial neural networks in structural engineering: concept and applications, Eng. Sci. 12 (1) (1999) 53–67. 3Blue1Brown, https://www.youtube.com/watch?v¼IHZwWFHWa-w. P. Hajela, L. Berke, Neural networks in structural analysis and design: an overview, Comput. Syst. Eng. 3 (1–4) (1992) 525–538. I.A. Basheer, M. Hajmeer, Artificial neural networks: fundamentals, computing, design, and application, J. Microbiol. Methods 43 (1) (2000) 3–31, https://doi.org/10.1016/S0167-7012(00)00201-3. R.-T. Wu, M.R. Jahanshahi, Deep convolutional neural network for structural dynamic response estimation and system identification, J. Eng. Mech. 145 (1) (2019) 04018125. Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature 521 (7553) (2015) 436–444. Bibcode:521..436L, https://doi.org/10.1038/nature14539. PMID 26017442. A.E. Bryson, A gradient method for optimizing multi-stage allocation processes, in: Proceedings of the Harvard Univ., April, 1961. https://en.wikipedia.org/wiki/Backpropagation. Matlab (Getting Started Manual). https://towardsdatascience.com/activation-functions-and-its-types-which-is-better-a9a5310cc8f. https://towardsdatascience.com/derivative-of-the-sigmoid-function-536880cf918e. P. Ramachandran, Z. Barret, V. Le Quoc, Searching for activation functions, 2017. arXiv:1710.05941[cs.NE]. Rectifier (Neural Networks), https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#cite_note-glorot2011-3. X. Glorot, A. Bordes, Y. Bengio, Deep sparse rectier neural networks, in: Proceedings of the 14th International Conference on Arti_cial Intelligence and Statistics (AISTATS), volume 15 of JMLR:W&CP 15, 2011. Weight Initialization explained j A way to reduce the vanishing gradient problem, https://www.youtube.com/watch?v¼8krd5qKVw-Q. Kaiming He, Xiangyu Zhang, Shaoqing Ren, Jian Sun, 2015, “ Delving deep into rectifiers: surpassing human-level performance on image net classification”, IEEE International Conference on Computer Vision (ICCV), pp. 1026–1034. Matlab User Guide.

Index Note: Page numbers followed by f indicate figures and t indicate tables.

A Abaqus model, 108, 152–153f Artificial neural networks (ANNs) biological neuron model, analogy with, 427 ductile precast concrete beam design big structural data, 436–439, 438f multilayer perception (MLP) (see Multilayer perception (MLP)) random variables, ranges of, 436–439, 439t, 440–444f strain compatibility based structural design algorithm, 436–439, 438f structural engineering, 427 supervised training, 439–441 test networks and design results, 441–477

B Backpropagation, 428–429, 429–430f Base template, offsite modular construction, 328, 329f Beam-column frames concrete strain, nominal strength, 220 high-rise buildings, multibay L-type hybrid composite precast frames, 219 nonlinear numerical model column-girder joints, 218 contact element, 218 FEA elements, 214–218, 225t first-order three-dimensional beam element, 214–218 R3D4 elements, 214–218 reduced integration element, 214–218 strain evolutions mechanical joints, 220–223 plates, structural components attached to, 223–225 Beam endplates, 275–277, 276–277f Beam-to-column connections beams installed on corbels/steel inserts, 8–9, 9–11f cast-in-place construction methods, 8 via hardware, 10–12 mechanical joints design of stiffness of column plates and bolts, 28 for moment connections, 19–20, 21–25f moment-resisting connection, 8 pinned connections, 8–9 pour forms, 8, 8f steel-concrete hybrid composite beams, 64–76

failure modes of mechanical joint, 68–76, 70–73f, 75–76f instrumentation of test specimens, 67, 67–68f tested specimen and test set-up, 64–67, 65t, 65–66f test results and design recommendations, 67–76, 69f, 69t structural performance, 77

C Cast concrete, 348 Cast-in-place methods, 345 Cast-in-place monolithic concrete, 275–277, 289–291, 297–300 Column-to-column connections activation of rebars, steel sections, and metal plates, 64, 64f cast-in-place concrete with pour forms, 1–2, 2–6f column-to-foundation, 7, 8f concrete columns without steel sections, 54 design of test specimens, 40t, 56 derived equation on strain compatibility, 54–56 fabrication of test specimens, 56–58, 57–58f test results, 59–64, 59–63f mechanical joints (see Mechanical joints) one-touch interlocking couplers, spliced precast columns, 249–250, 250–252f replacing couplers, 255–256 stacked connections, 6 steel-concrete hybrid composite columns concrete filler plate, 29–32, 33–34t, 35f instrumentation of test specimens, 32–36, 36–38f metal filler plate, 28–29, 29–32f, 33–34t strains evolution, 41–53, 54–55f test results and design recommendations, 36–41, 39t, 41–51f test erection, 251–255, 253–254f using bolted plate, 7, 7f using grouted splice sleeve connectors, 2–6 using plastic shim, dowel pin and welding, 6 Concrete-based frames beam-to-column connections (see Beam-tocolumn connections) beam-to-column joints, 336–338 column-to-column connections (see Columnto-column connections)

concrete cores and hybrid composite precast frames, 344t estimated construction period, 344t high-rise building application, 334–336, 335–337f lateral stability of structural systems, 341–344, 342–343f L-shaped hybrid composite precast frames, 335–336 mechanical joints (see mechanical joints) pipe-rack frames and parking structures, 336–338, 338–340f test assembly with column-to-column connections, 77–78, 79–81f full-scale erection model properties, 79–81, 84t full-scale precast columns, 77, 78f significance of mechanical connection, 77 using laminated metal plates, 79–81, 82–87f three-dimensional frame analysis, 340–341, 341f Concrete-steel hybrid composite frames, 331 Concrete strain, 220 Constraints, 198

D Deep neural network, 427–428, 429–430f, 432–433 Design verification concrete strain, beam-column frames, 220 high-rise buildings, multibay L-type hybrid composite precast frames, 219 interlocking mechanical couplers, precast frames, 264–268 low-rise buildings, precast frame construction period reduction, mechanical connection, 297–298 construction quantities, 297 energy consumption reduction and CO2 emissions, 298–299, 300t rates of strain, 292–297, 296–297f strain activation, structural components at connection, 292–297, 295–296f nonlinear numerical model, beam-column frames column-girder joints, 218 contact element, 218 FEA elements, 214–218, 225t

479

480

Index

Design verification (Continued) first-order three-dimensional beam element, 214–218 R3D4 elements, 214–218 reduced integration element, 214–218 strain evolutions, beam-column frames mechanical joints, 220–223 plates, structural components attached to, 223–225 Drucker-Prager hyperbolic plastic potential function, 264–266 Ductile precast concrete beam design, ANN big structural data, 436–439, 438f multilayer perception (MLP) (see Multilayer perception (MLP)) random variables, ranges of, 436–439, 439t, 440–444f strain compatibility based structural design algorithm, 436–439, 438f structural engineering, 427 supervised training, 439–441 test networks and design results, 441–477

E Embedded elements, 198, 280, 283t Endplate connection extended plates, 19–20, 64–67, 65f for steel frames, 15 mechanical moment connections, 15f steel moment joint, 15f Extended endplates, low-rise buildings column-to-girder connection, 291 girder-to-beam connection, 286–291 headed studs, design of, 289–291 mechanical connections, 286–289

F Finite element analysis (FEA), 278–280 Finite element (FE) models with foundation, 198–203 without foundation shear center, load applied at, 206 test center, load applied at, 206 Flexural capacity of connection, 271–273 Floor framing, 256–260 Full-scale precast frame column-to-column connections one-touch interlocking couplers, spliced precast columns, 249–250, 250–252f test erection, 251–255, 253–254f girder-to-column connections and test erection, 256–264

G Girder-to-column connection mechanism, 256–264, 256–259f

H High-rise building construction erections of hybrid composite beams and columns, 416–418, 417–419f, 420–421t multibay L-type hybrid composite precast frames, 219

19-story building completed beam-column joint, 412–414, 416f floor height between two designs (18th and 19th), 412, 415t floor height reduction capability, 411–412, 413f hybrid composite precast beams transportation, 412–414, 416f manufacturing plant, 412–414, 415f selected buildings with hybrid frames, 419 Host elements, embedded element, 198 Hybrid composite pipe rack frames with monolithic joints, 304, 305–307f Hybrid composite precast frames with mechanical joints, nonlinear finite element analysis. See Nonlinear finite element analysis, hybrid composite precast columns

I Incremental dynamic analysis (IDA), 338–339 Interlocking mechanical couplers, precast frames full-scale precast frame column-to-column connections, 249–256 girder-to-column connections and test erection, 256–264, 256–259f numerical investigation design verification, mechanical connections for, 264–268 finite element model, proposed joint, 268 flexural capacity of connection, 271–273 verification of, 268–271 significance of, 249 Intermediate moment frame, 300

L Laminated metal plates hybrid mechanical joint, L-type precast concrete frames flexural capacity, interior bolts on, 179 grouted sleeve connections, 179 specimen details, 179, 183t structural capacity, 179 test preparation, 179–183, 183t nonlinear finite element analyses, L-type columns, 203–206 Linear variable differential transformers (LVDTs), 32–36 Load-displacement relationship, 198–200 Low-rise buildings, precast frame advantages and challenges, 275 beam endplates, nuts anchoring rebars, 275–277, 276–277f bolted beam-to-column connection, 275–277, 276–277f column-to-column connections, 275–277, 276–277f column-to-girder connections, 275–277, 276–277f design verification

construction period reduction, mechanical connection, 297–298 construction quantities, 297 energy consumption reduction and CO2 emissions, 298–299, 300t rates of strain, 292–297, 296–297f strain activation, structural components at connection, 292–297, 295–296f erection test, steel-reinforced concrete precast frames, 275–277, 276–277f extended endplates column-to-girder connection, 291 in girder-to-beam, 286–291 girder-to-beam connections, 275–277, 276–277f laminated mechanical plates, 275 mechanical assembly method, 275 mechanical joints, building design load combination and conventional design, 277–278 mechanically layered plates, nonlinear finite element analysis, 278–280 numerical model and nonlinear finite element analysis parameters connection plates, 280–285 contact properties, 280 discretization, 280 embedded elements (re-bars and H-steels), 280 pour forms, 275, 298–300 precast frames test, mechanical connections, 275–277, 276–278f L-type precast concrete frames, 180–182f beam-column frames (see Beam-to-column frames, design verification of) columns, nonlinear finite element analyses (see Nonlinear finite element analyses, L-type columns) hybrid mechanical joint, laminated metal plates flexural capacity, interior bolts on, 179 grouted sleeve connections, 179 specimen details, 179, 183t structural capacity, 179 test preparation, 179–183, 183t irregular L-shaped frames, test erection of (see Test erection, irregular L-shaped frames)

M Machine learning, 427 Matlab, ANN in data manager, 433 fitting application, 433 writing Matlab code, 434–436 Mechanical joints beam-to-column connections design of stiffness of column plates and bolts, 28 for moment connections, 19–20, 21–25f building design load combination and conventional design, 277–278

Index

mechanically layered plates, nonlinear finite element analysis, 278–280 column-to-column connections bolts design, 22–24 column plates design, 20 connection plates design, 27t for moment connections, 16–19, 18–20f nominal bearing strength of plates at bolt holes, 20–22, 26f pretension in bolts, 25–27, 27f tension in bolts, 24 constructability, 345 detachable, 301 economics, 345 erection verification, 16, 16–17f flexural capacity, interior bolts on, 179, 195 full-scale precast frame, interlocking couplers column-to-column connections, 249–256 girder-to-column connections and test erection, 256–264, 256–259f grouted sleeve connections, 179 hysteretic energy dissipation capacities, 193–195 numerical investigation, interlocking couplers design verification, mechanical connections for, 264–268 finite element model, proposed joint, 268 flexural capacity of connection, 271–273 verification of, 268–271 precast column-to-column joint, structural elements contribution, 189–193 precast concrete-based frames (see Concretebased frames) significance, interlocking couplers, 249 specimen details, 179, 183t specimen LC1, L-type precast concrete frames vs. LC2 and LC3, 189 structural behavior and associated failure modes, 184–186 specimen LC2, L-type precast concrete frames vs. LC1 and LC3, 189 structural behavior and associated failure modes, 187–189 specimen LC3 (monolithic specimen), L-type precast concrete frames vs. LC1 and LC2, 189 structural behavior and associated failure modes, 183 structural capacity, 179 structural performance via numerical investigation, 28 structural response, 345 test specimens preparation, L-type precast concrete frames, 179 cyclic loads, application of, 180–183, 192f fabrication, 182, 190f linear variable differential transformers (LVDTs), 182–183 material properties, structural elements, 182, 191t quasi static testing, 182–183 sample test, 182 strain gauges, 180–181, 187–188f, 189t Modular construction

advantage of, 331 cellular-type modules and intra-module connection, 331, 332f for high-rise buildings, 332–334, 333–334f inter-module connection, 331–332, 332f lifting of modular structure, 331 low-rising buildings, 331, 332f with mechanical joints constructability, 345 precast concrete-based frames (see Concrete-based frames) structural response, 345 modular steel building with braced frames, 340, 341f seismic responses for braced modular structures, 338–339 structural and connection systems light steel material, 331 module classification, 331, 332t time saving process, 331 Multilayer perception (MLP) activation functions, structural-engineering applications, 430–433 backpropagation, 428–429 data normalization, 433 initialization, 433 Matlab, ANN in data manager, 433 fitting application, 433 writing Matlab code, 434–436 weights and bias, 427–428

N Nonlinear finite element analyses, L-type columns constraints, definition of, 198 elements and discretization, selection of, 195–196 embedded elements, definition of, 198 FE models with foundation, 198–203 without foundation, 206 host elements, definition of, 198 interactions, definition of, 196–198 laminated metal plates, structural behavior of, 203–206 load application, test center, 198–203 strain evolution, monolithic and mechanical joints with no axial force, 206–209 surface-to-surface contact, definition of, 196–198 Nonlinear finite element analysis, hybrid composite precast columns with concrete filler plates design recommendations, 137 FE models, 131–132 influence of metal and concrete plates, 136–137 load-deflection relationships estimation, 131, 132f plate deformations, 131–132, 133–134f structural performance, 132–135, 134–135f with metal filler plates, 113–131 bond-slip method, 116

481

calibration of numerical data, 116–125, 121–127f contact elements modeling, 113–114, 115–116f embedded region technique, 114–115 geometric configurations of specimens, 113, 114f load-displacement relationship for specimens, 114–115, 120f nonlinear FEA model, 128–130 plate deformation and strains, 125–127, 127–130f, 127t reinforcing bars and steels in steel-concrete hybrid composite members modeling, 114–115, 117f seismic performance, 130–131 tested specimens, 113 numerical investigation of metal plates influence of headed studs, 149 influence of high-yield metal plates, 144–149, 144–145f, 146t, 147–149f parameters, 138–144, 139f, 139–140t specimen with mechanical joints, 141–144 specimen with monolithic joint, 138–141, 140–143f strains activation, 149–150, 150f Nonlinear finite element analysis, of beam-tocolumn connections, 165 with concrete filler plates, 165–176 numerical modeling, 165–167, 168–169f stiffness of metal and concrete plates, 168–174, 169–174f strain evolution, 94f, 95–98, 175f with metal filler plates, 151–165 concrete damaged plasticity model, 154, 156f contact elements modeling, 154–157, 157f contribution of metal plates, 162–164, 164–167f, 164t finite element (FE) models, 152 geometric configuration for specimen, 152, 152–153f mechanical joints with laminated plates, 151, 151f mesh density, 157, 157f mesh discretization, 157 monolithic model, calibration of, 158, 159–160f partially restrain moment connection, 159–162, 161–163f stress vs. strain relationships, 152–153 Nonlinear finite element models, 300 Nonlinear-inelastic finite element analysis damaged concrete plasticity model, 89–90, 90f stress-strain relationship, 91 uniaxial tension and compression stress behavior, 90–91, 92f dilation angle definition, 95 Drucker-Prager hyperbolic plastic potential function, 95–98 eccentricity, 96–97 identification of, 97–98

482

Index

Nonlinear-inelastic finite element analysis (Continued) and interlocking concept, 95–96 viscosity parameter, 98 volumetric dilations and, 94–95, 94f FEA parameters, 91 for calibrations, 91, 93t yield surface of concrete, 91–93, 127t plastic potential surface and yield surface, 89 Nonlinear numerical model, 283f Nonlinear structural behavior, steel-concrete hybrid composite structures conventional strain compatibility approach, 382–383, 382–388f verification analysis, 395–401, 396–402f, 398t without axial loads, 383–401

O Offsite modular construction, using base template, 328, 329f One-touch interlocking couplers, 249–250, 250–252f

P Pipe rack frames advantages and challenges, 301–302 bolted connections, 301–302 case study, 314–328 conventional and hybrid composite steel pipe rack with concrete cover, 303f conventional steel frames with braces seismic deflections, 317–321, 326f determining ductility and plastic strain concentration, 301 dynamic characteristics, 321, 327t fast track construction based on hybrid frames, 321, 328f with fire-proofing, 328t guidelines, 301–302 historical development, 301–302 innovated types, 301–304 offsite modular construction with base template, 328, 329f pinned steel-concrete composite precast frames material data, 314–317, 317t moment demands, 314–317, 318f with nonstructural concrete cover, 314–317, 316f seismic deflections, 324–325f, 327t sizes without braces, 317, 319–323f with prestressed frames, 314, 315f reduction of material quantity, 321–327, 328t with rigid joints precast concrete-based pipe rack frames (see Precast concrete-based pipe rack frames) prestressed precast frames, 314, 315f rigid steel frames, 314, 315f significance of, 302–304 Plates, structural components attached to, 223–225

Precast concrete-based pipe rack frames with mechanical joints, 304–314 for assembly of frame module, 308 assembly sequence, 308–309, 308–314f numerical investigation, 309–314 with rigid monolithic beam-to-column connections, 304, 305–307f Precast concrete beam design, ANN. See Artificial neural networks (ANNs) Precast concrete structure advantages, 1 beam-to-column connections beams installed on corbels/steel inserts, 8–9, 9–11f cast-in-place construction methods, 8 moment-resisting connection, 8 pinned connections, 8–9 pour forms, 8, 8f via hardware, 10–12 column-to-column connection cast-in-place concrete with pour forms, 1–2, 2–6f column-to-foundation, 7, 8f stacked connections, 6 using bolted plate, 7, 7f using grouted splice sleeve connectors, 2–6 using plastic shim, dowel pin and welding, 6 definition, 1 disadvantages, 12 collapse of concrete frames, 12 construction waste and concrete pour forms at joints, 12 structural failure, 12, 13f vs. precast steel-concrete hybrid composite frames, 12–14, 13f prefabricated beams and columns, 1 quality control and facile installation, 1

R Rectified linear unit (ReLU), 427, 431–432f, 432–433 Reinforced concrete (RC), 280–284 Replacing couplers, 255–256

S Steel-concrete hybrid composite frames with monolithic joints advantages, 348, 419–422 beam-to-column connection with skewed beam section erection test, 408–409, 409f noncritical installation of temporary splicing plates and bolting, 402–403 preinstallation of L-shaped pocket, 403–409, 404–405f splice of precast columns, 409–410, 410f steel erection, 402, 403f benefits of, 348–352 cost reduction, 348–349 floor depth reduction, 349–350, 349f high-rise building with reduced beam depth (see High-rise building construction)

hybrid precast beams, seismic capacity of, 373–376, 374t, 374–377f modular constructions of, 349–350, 350–353f nonlinear structural behavior conventional strain compatibility approach, 382–383, 382–388f verification analysis, 395–401, 396–402f, 398t without axial loads, 383–401 pour forms, 348, 348f prestressed precast beam monolithically integrated with columns, 376–377, 378–381f specimen, 351–352, 354f structural behavior, 352–381 T-shaped steel section, 377–381 experimental investigation, 355–356, 360–361f, 361t finite element analysis, 3D mesh for, 361–362, 362f instrumentation and test set-up, 357–360, 362f load-strain relationship based on strain compatibility, 367, 368f parameters for nonlinear numerical model, 363, 363t rebars and damage assessment, 370–371, 370–372f sensitivity of dilation angles and damage variables, 368–369 tensile cracks evaluation, 371–372, 372–373f test results and numerical data, 363–364, 363–365f, 365t unsymmetrical precast composite beams, 365–366, 366–367f viscosity, 369, 369f, 369t wide steel flanges encased in, 352–355 experimental investigation, 352 flexural strength, 352 full scale hybrid composite beam with slab, 352, 354f load bearing strength, 354–355, 358–359f load displacement relationships of test specimens, 352, 355–357f moment capacity at deflection corresponding to L/360, 353–354, 358t Steel-concrete hybrid composite precast frames, 334–335 beam-to-column connections (see Beam-tocolumn connections) column-to-column connections (see Columnto-column connections) mechanical joints (see Mechanical joints) with moment connections, 314–321, 316f, 317t, 318–326f, 327t vs. precast concrete structure, 12–14, 13f test assembly with column-to-column connections, 77–78, 79–81f full-scale erection mock-up model properties, 79–81, 84t full-scale precast columns, 77, 78f significance of connection, 77

Index

using laminated metal plates, 79–81, 82–87f Steel moment resisting frame (SMRF) modules, 340 Steel-reinforced concrete (SRC), 280–284

T Test erection, irregular L-shaped frames column-to-column connection column-to-column assembly, 230–232 connection mechanism, 229 girder-to-column connections column-to-beam assembly, 235–237

connection mechanism, 233–235 verification, 238–239 significance of, 228 Torque gage, 256–260 T-shaped steel section, 377–381 experimental investigation, 355–356, 360–361f, 361t finite element analysis, 3D mesh for, 361–362, 362f instrumentation and test set-up, 357–360, 362f load-strain relationship based on strain compatibility, 367, 368f parameters for nonlinear numerical model, 363, 363t

483

rebars and damage assessment, 370–371, 370–372f sensitivity of dilation angles and damage variables, 368–369 tensile cracks evaluation, 371–372, 372–373f test results and numerical data, 363–364, 363–365f, 365t unsymmetrical precast composite beams, 365–366, 366–367f viscosity, 369, 369f, 369t

V Von Mises equivalent effective stress, 96

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