Challenging Glass 3: Conference on Architectural and Structural Applications of Glass [1 ed.] 9781614990611, 9781614990604
There are two things everybody knows about glass: it is transparent, and it breaks! These are also the properties that c
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Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Challenging Glass 3
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Conference on Architectural and Structural Applications of Glass Faculty of Civil Engineering and Geosciences, Delft University of Technology June 2012 www.challengingglass.com ISBN 978-1-61499-060-4 (print) ISBN 978-1-61499-061-1 (online)
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Conference on Architectural and Structural Applications of Glass Faculty of Civil Engineering and Geosciences Delft University of Technology
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
June 2012
Bos, Louter, Nijsse, Veer (Eds.)
IOS Press
iii Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
© 2012 The authors and IOS Press. All rights reserved. ISBN 978-1-61499-060-4 (print) ISBN 978-1-61499-061-1 (online) Published by IOS Press under the imprint Delft University Press PRINTED IN THE NETHERLANDS Publisher IOS Press BV Nieuwe Hemweg 6b 1013 BG Amsterdam The Netherlands tel: +31-20-688 3355 fax: +31-20-687 0019 email: [email protected] www.iospress.nl Legal notice The publisher is not responsible for the use which might be made of the following information. Cover credits Background: Andreas Keller Photo ribbon, from back left to front right: Erick van Egeraat, Rogier van der Heide, Tim Macfarlane, Erick van Egeraat, David Sunberg (provided by JCDA), JCDA, SOM (2x), Timothy Hurstley (courtesy of Israel Museum; provided by JCDA)
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Editors Bos, Louter, Nijsse, Veer Organizing Committee Freek Bos Christian Louter
Scientific Committee Rob Nijsse, chair (NL) Fred Veer, secretary (NL) Jan Belis (B) Fabrice Bernard (FR) Freek Bos (NL) Paulo Cruz (PT) Martina Eliasova (CZ) Jean-Paul Lebet (CH) Christian Louter (CH) Jens Schneider (D) Geralt Siebert (D) Holger Techen (D) Bernhard Weller (D) Frank Wellershoff (D)
iv Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Foreword Dear reader, Once again, glass engineering, research and design specialists gather in the historical town of Delft, for the third edition of the Challenging Glass Conference (CGC3) at the TU. The proceedings of this event lie before you. Relative to the two previous occasions, the conference has made a considerable growth spurt and now features some 90 papers, distributed over seven topics, as well as five key note addresses. Fascinating contributions can be found under each topic. ‘Curved & Bended Glass’ has grown significantly, ‘Laminates & Composite Designs’ as well as ‘Projects & Case Studies’ are traditionally well represented. Under the topic ‘Joints, Fixings & Adhesives’, it is clear that structural adhesive bonds in glass construction are on the rise and here to stay.
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But a quarter of all papers is still related to the topic ‘Strength, Stability & Safety’. Clearly, there is, even now, much to learn about the basics of glass design. We urge the authors to grab every opportunity for discussion and debate: there is still a considerable way to go before we will have reached a common understanding of the nature of glass failure and how we should translate that into design guidelines. Preparing these proceedings has been a privilege, and we trust any participant in Challenging Glass 3 will move on with new ideas and inspiration to apply in his/her own work. We would like to express our gratitude to the key note speakers as well as to the other presenters and authors. Furthermore, we thank the Scientific Committee members, the supporting organizations, our main sponsor Glas Trösch, as well as our other sponsors, and, of course, all participants. Welcome to Challenging Glass!
Wishing you a stimulating and enjoyable conference,
Freek Bos, Christian Louter Joint Chairmen of the Organizing Committee Rob Nijsse, Fred Veer Chairman and Secretary of the Scientific Committee
v Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Sponsors, Support & Partners Platinum Main Sponsor Glas Trösch Gold Sponsors APG International Dow Corning Eckersley O’Callaghan Silver Sponsors DC Mat Glasimpex GlasStress Ltd. Groep Leroi / Lerobel Octatube Scheldebouw Van Noordenne Groep / Vindico
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Supporting Organizations IABSE Dutch Group Kenniscentrum Glas COST Action TU0905 Structural Glass Host & Partners TU Delft EPF Lausanne Witteveen+Bos U-Dispuut
vi Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Contents Keynote papers
1
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2
Light in the Public Realm James F. Carpenter
3
Emotion Erick van Egeraat
7
Fusing Design, Innovation and Light Rogier van der Heide
9
Engineering Invention in Glass Architecture Tim Macfarlane
11
Case Study 1 World Trade Center – Podium Wall Design Development Christoph Timm
17
Projects & Case studies
39
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40
The Glass Screens of the Japan Post Tower Lucio Blandini, Werner Sobek
41
The Glass Sphinx: A Massive Stacked Glass Sculpture Freek Bos, Tom van der Heijden, Pieter Schreurs
47
The Apple Glass Cube: Version 2.0 James O'Callaghan, Charles Bostick
57
Future Application of Structural Use of Glass Thomas Henriksen
67
A Laminated Glass Wall Will Protect Warnemünde From High Water Frank Heyder, Franziska Paulu
75
Lincoln Center Canopies – Performance in Glass Jan Knippers, Jochen Riederer, Matthias Oppe
83
Project for the Eiffel Tower: Constructive Geometry Nicolas Leduc, Jacques Raynaud, Niccolo Baldassini
93
vii Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenges in the Design, Fabrication and Installation of Glass Structures Comprising of Super Jumbo Glass Sheets Peter Lenk, Harriet Lambert Glass Walls Carrying the Roof and Withstanding the Wind Load on the Façade: Conservatory of the Museum in Dordrecht and Raaks Glass Cube in Haarlem. Rob Nijsse
111
Inclined Glass Fins for the King Abdulaziz Center for World Culture Silvia Prandelli, Damian Rogan
121
Design of Suspended Glass Ceiling Structure in High Sesimic Hazard Zones Toru Takeuchi, Kenichi Sugizaki, and Koichi Yasuda
129
Designing a Glass Pavillion to Protect an Ancient Greek Temple Fred Veer, Phaedra Oikonomopoulou, Regina Bokel
139
A True All-Glass Staircase Ernst Wälchli, Bruno Kassnel-Henneberg
151
Two Lines – Arup with David Chipperfield Architects Felix Weber
157
Torre Iberdrola, Bilbao, Spain Axel Zemborain
167
Joints, Fixings & Adhesives
175
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101
176
Experimental Investigation of Unconventional Canopy Prototypes, Suspended by Adhesive Bonds Jan Belis, Arno Van Hulle, Dieter Callewaert, Jonas Dispersyn, Bas Out
177
Connecting Through Reinforcement – Experimental Analysis of a Glass Connection Using Perforated Steel Plates Paulo Carvalho, Paulo J. S. Cruz, Frederic Veer
187
Determination of Adhesives Properties for Non-linear Numerical Simulation of Structural Steel-Glass Connections Vincent Dias, Oliver Hechler, Christoph Odenbreit
195
Shear Capacity in Adhesive Glass Joints Maria Fröling, Kent Persson, Oskar Larsson Experimental and Numerical Analysis of Edge Seal Spacers of Insulated Glass Units for Structural Sealant Glazing Applications Anneliese Hagl viii
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Contents
Tensile Loading of Silicone Point Supports – Revisited Anneliese Hagl, Oliver Dieterich, Andreas Wolf, Sigurd Sitte
235
Investigation of Stress-Whitening in Transparent Structural Silicone Adhesive Anneliese Hagl, Andreas Wolf, Sigurd Sitte
249
Designing a Glass Bearing Connection with a Probability to EN1990 CC2 Ron Kruijs
259
Influence of Various Factors on Mechanical Properties of Adhesive Joint in Glass Structures Klára Machalická, Martina Eliášova Seismic Behaviour of Point Supported Glass Panels Luís Martins, Raimundo Delgado, Rui Camposinho, Tiago Silva The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System Shelton Nhamoinesu, Mauro Overend Load Carrying Behaviour of Metal Inserts Embedded in Laminated Glass Kerstin Puller, Werner Sobek
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Direct Glass Fabrication – New Applications of Glass with Additive Processes Lisa Rammig
267
281
293
307
315
Analytical Solutions for Detail Problems in Structural Glazing Matthias Seel, Geralt Siebert
323
Glazing with Countersunk Point Fittings Geralt Siebert, Tobias Herrmann
335
Reduction of Edge Effect in Adhesive Joints of Glass Details Olena Soroka, Yurii Rodichev, Alexander Shabetia
349
Strength, Stability & Safety
359
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360 361 362
Improvement of Quality of Tempered Glass with Numerical Modeling Antti Aronen, Reijo Karvinen Analytical Approaches for Buckling Verification of In-plane Loaded Laminated Glass Columns and Panels Claudio Amadio, Chiara Bedon ix
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Contact Damage Near the Supporting Pillars in Vacuum Glazing Units Minxi Bao, Jiang Yang, Xiaogen Liu, Yiwang Bao
387
Towards a European Structural Glass Network: COST Action TU0905 Jan Belis, Jürgen Neugebauer, Jens Schneider, Mauro Overend, Danijel Mocibob
397
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How to Model Failure in Load-Bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations Fabrice Bernard, Bouazza Fahsi, Baghdad Krour
405
New Expressions for the Effective Thickness of Laminated Glass Laura Galuppi, Gianni Royer-Carfagni
419
A Study of Polishing Performance of Glass Using Fluid Jet Polishing Anders Jönsson, Pia Lindahl, Johan Fredin, Christina Stålhandske
431
Design of Arches Strengthened with Cables for Glass Roofs Wim Kamerling
441
Design of Cable Strenghtened Beams for Glass Structures Wim Kamerling
455
The Design of an All Glass Roof to EN1990 Ron Kruijs
467
Stability Analysis of Structural Glass Systems Peter Lenk, Franklin Lancaster
475
Numerical Simulation of Façade / Window Glazing Fracture Under Impact Loading Christoph Müller de Vries
489
Glazing Under Long Term Loads Induced by Water Arthur Pistora, Barbara Siebert
501
Energetic Approach of Elastic Strain Energy of Thermally Tempered Glass Stefan Reich, Bernhard Weller, Nora Dietrich, Stephan Pfefferkorn
509
Surface Cracked Layer and Damage Resistance of Glass Under Contact Loading Yurii Rodichev, Yurii Yevplov, Helen Soroka, Frederic Veer
523
Surface Defects and Statistical Characteristics of Glass Strength Yurii Rodichev, Yurii Yevplov, Helen Soroka, Frederic Veer, Nikolay Tregubov, Vladimir Polivyany
535
Load-Bearing Capacity of Thin Film Photovoltaic Modules Jens Schneider, Johannes Kuntsche, Jonas Kleuderlein
553
x Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Contents
Stress Distribution of Tension Structural Glass Plates Tomas Serafinaviius, Jörg Hildebrand, Gintas Šauiuvnas
565
Polishing Glass with Fluid Jet Technology Christina Stålhandske, Maria Lang, Marita Jansson, Kent Persson, Anders Jönsson
579
Influence of the Load History on the Edge Strength of Glass with Cut Edge Finishing Marc Vandebroek, Jan Belis, Christian Louter
587
The Relation Between Fracture Morphology and Failure Strength in Annealed Glass Frederic Veer, Yurii Rodichev
597
Strength of Flat Glass Subjected to Thermal and Mechanical Loads Vladimir Zubkov, Nadezhda Kondratieva
607
Laminates & Composite Designs
619
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620 621 622
Laminated Glass Panels in Combination with Timber Frame as a Shear Wall in Earthquake Resistant Building Design David Antolinc, Roko Žarni, Franci epon, Vlatka Raji, Mislav Stepinac
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Anchoring Triangular Glass Panels to Prevent Collapse Graham Dodd, Leroy Reed
623
633
Through-Cracked Tensile Delamination Tests with Photoelastic Measurements Daniele Ferretti, Marco Rossi, Gianni Royer-Carfagni
641
Composite Structures Made of Glass and Ultra High Performance Concrete Current Research Bernhard Freytag, Gerhard Santner, Lutz Sparowitz, Franz Götschl
653
The Influence of Parameter Setting on the Mechanical Properties of PVB in Lamination Processes Maurizio Froli, Leonardo Lani
669
Rectangular Plate Finite Element for Triplex Laminated Glass Ivelin Ivanov, Dimitar Velchev, Nikolay Georgiev, Ivo Ivanov Reinforced Glass Beams Composed of Annealed, Heat-Strengthened and Fully Tempered Glass Christian Louter, Jan Belis, Freek Bos, Fred Veer xi
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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The Applicability Evaluation of Hybrid Glass Structure Using Pre-stressing as Structural Member Naoya Miyasato, Akira Okada, Masao Sitoh, Keisuke Nomoto Structural Design of Composite Steel-Glass Elements Michal Netusil, Martina Eliasova
715
In-plane Loaded Glass-Steel Elements Geralt Siebert, Andreas Haese
725
Load-Bearing Behaviour of Non-Monolithic Glass Laminate Beams for Wide Spans Erich Trösch, Ernst Wälchli, Thomas Baumgärtner
735
Experimental Investigations on Continuous Glass-GFRP Beams; Preliminary Non-linear Numerical Modelling Luís Valarinho, João R. Correia, Fernando Branco, José Sena-Cruz
745
Design of Glass-Polycarbonate Composite Panels Thorsten Weimar
759
Further Research About the Short and Long-Term Breakage Behaviour of Hybrid Glass-Steel Elements Bernhard Weller, Philipp Krampe, Stefanie Retsch
769
Curved & Bended Glass
783
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703
784
Durability of Cold Bent Insulating-Glass Units Keith Besserud, Matt Bergers, Andrew J. Black, Lawrence Donald Carbary, Arkadiusz Mazurek, Donald Misson, Kenneth Rubis
785
Application of Thermally Curved Glass in the Building Industry Michael Elstner, Markus Kramer
819
Cold-Bent Single Curved Glass; Opportunities and Challenges in Freeform Facades Mark Feijen, Ivo Vrouwe, Peter Thun
829
Quality Control of Bent Heat-Strengthened and Fully Tempered Glass by the Application of Photoelasticity Markus Feldmann, Pietro di Biase, Ruth Kasper
837
Layout Strategies and Optimisation of Joint Patterns in Full Glass Shells Thiemo Fildhuth, Sebastian Lippert, Jan Knippers
xii Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Contents
Special Aspects in Planning of Thermally Curved Glass: Structural design, Constructional Hints Markus Kramer, Michael Elstner Curved Glass in Four-Point Bending Bernhard Weller, Michael Engelmann, Philipp Krampe, Stefan Reich
865
Architectural Design & Lighting
879
Glassolutions LED-in-Glass Outdoor at Oskomera Group HQ Rens Demarteau, Esther Hebly, Paul Roman, Rino Messere
881
Special Glazing Christian Eckhardt
885
Architectural Aspect of Structural Design of Glass Façades / Glass Skin Applications Aleksandra Krstic-Furundzic, Tatjana Kosic, Jefto Terzovic
891
Cones Made of Glass Juergen Neugebauer
901
Green Houses – Why Can´t They Be Built as Our Ancestors Did? Holger Techen, Matthias Michel
907
Glass in Façades
915
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857
916
Novel Testing Techniques for Building Glass in Service Conditions Yiwang Bao, Xiaogen Liu, Yan Qiu, D.T.Wan, Minxi Bao, JiangYang
917
Fire Resistance without Fire Resistant Glazing Csilla Csoke, Johan Koudijs
925
Building Design Might Soon Be Driven by Energy Requirements Only Christof Erban
933
Ceramic Digital Printing - Customizing Glass Façade Design Bernd Hoffmann
943
Behaviour of Electrochromic Glass in the Mediterrean Area Gianraffaele Loddo, Daniela Ludoni, Marco Pittaluga, Gian Piero Cossu
957
Building Integrated Photovoltaics Barbara Siebert
971
Design Methods and Structural Components of Blast Enhanced Facades Frank Wellershoff
981
xiii Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Indices
997
Author Index
999 1007
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xiv Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Key Notes
1
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-3
Light in the Public Realm James F. Carpenter James Carpenter Design Associates Inc, 145 Hudson Street, 4th Floor, New York, NY 10013, USA, www.jcdainc.com, [email protected]
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1. Preview The material properties of glass and its ongoing technological development offer particular opportunities for daylighting and lighting. Our own approach is to consider the possibility of approaching glass as an opportunity for the reestablishment of experiential light in public realm. Electrical lighting at night is one area where quantity is suppressing the possibilities of presenting subtle qualities of light.
Figure 1: Israel Museum, Jerusalem, Israel. Photo: Timothy Hurstley (courtesy of Israel Museum).
Today, in keeping with our prioritizing of light in the public realm, we continue to explore many materials, but glassy materials such as glass continue to be of particular interest for their specific ability to unravel and reveal the density of information 3
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
inherent in light. Though we used to focus on the structure of transparency when talking about glass a decade ago, we always placed transparency within a spectrum of characteristics. Today, the transmission, reflection, refraction and absorption of light still defines our approach to glass. Integrating structure within the glass, the use of oversize panels, coatings and other developments serve these interests for us, be it in daytime or nighttime conditions.
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There are many steps toward changing prevailing attitudes towards overabundant electric lighting in the public realm, many that due to city, state, federal and national codes seem intractable. However, is there a place for the glass industry in the discussion of public attitudes and eventual changes in practice? Can glass become a material that demonstrates the opportunities for lower, more diverse and better deployed levels of light in the public realm? We believe glass is rich with potential – just as we have always explored the depth of light information that can be revealed within glass, so we believe that glass as it is used in the public realm, be it curtain walls or future applications emerging from thin glass films and computer technology, can be designed to enhance a denser and darker environment with subtle qualities of light that can provide enough illumination, wayfinding and safety while enhancing our human experience with a powerful sense of nature, both day and night.
Figure 2: Dichroic Light Field, New York, 1994.
4 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Light in the Public Realm
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Figure 3: 7 World Trade Center Podium and Envelope, New York, 2002-2006. Photo: David Sundberg.
Figure 4: Ice Falls, Hearst Tower, New York. Photo: Andreas Keller.
5 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-7
Emotion Erick van Egeraat Designed by Erick van Egeraat, Rotterdam, NL 1. Preview Glass is one of the true marvels discovered by men. The mere heating and cooling of ever-present silica allows for a transformation and opportunity which is unparalleled. To me, glass incorporates an enduring quality I strive for in each of my projects. Not as a mere opening within a structure but an integral part of Architecture. Glass and Light are a one, without the one the other cannot shimmer, shine, reflect or capture. If architecture is gravity, then glass is the illusionist allowing light(ness) and interaction. We have been pushing the boundaries of glass throughout the centuries. And like the glass in the Gothic Cathedrals it tells a story for those who wish to listen and observe. The opportunities to tell this story as an Architect are endless: etching, coloring, sandblasting deforming of glass, to name just a few, make it one of the most versatile materials. This richness in treatment and effect make it still the favorite in the development of our contemporary world.
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To use Glass as an Architectural asset requires determination, skill and a love for detail. As our Gothic predecessors it still is much a process of ‘Learning by doing ‘. Prototypes and tests are still very much a part of making Glass work. At our offices in Rotterdam, Moscow and Budapest you can still witness these samples from which our Architecture was derived. Beside today’s incorporated technology, Glass to me remains a primarily emotional element. It invites light to structure defining our comfort zone and well-being. 2. Re-creation For our design of the new Leipzig University we use Glass to re-create an emotional reminder. In the sixties of the 20th century the East-German regime at the time destroyed one of the oldest churches in the region. This Pauline-church at the time was believed to be the center of the critics of the regime. This symbol of freedom will now be re-created as reminiscence to it. The Gothic arches and columns will be made of out of ceramics and Glass, allowing light to shimmer, shine and reflect and at night transform into lighting elements. Our world is covered with Glass which we mostly take for granted. Let’s aim for a world in which we can enjoy the richness Glass can offer.
7 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figures 1a, b: Office Tower, Amsterdam.
Figure 3: New Leipzig University.
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Figure 2: City Hall, Alphen a/d Rijn.
Figure 4: Extension of InHolland University, Rotterdam.
8 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-9
Fusing Design, Innovation, and Light Rogier van der Heide Philips Lighting, Rotterdam, NL
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1. Preview Rogier van der Heide is Vice President and Chief Design Officer of Philips Lighting. In that role it is his mission to inspire architects, interior designers, artists and lighting designers around the world with products and solutions that unleash one's creative freedom. As a thought leader and designer himself, Rogier has completed many projects on all continents. He specializes in the creation of spatial experiences that are imaginative, colorful and stimulating.
Figure 1: Buckminster Fuller’s Fly’s Eye Dome.
9 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Figure 2: Force Field, London.
Figure 3: Galleria West Façade, Seoul.
10 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-11
Engineering Invention in Glass Architecture Tim Macfarlane Glass Light and Special Structures Limited, London, UK
The introduction of new structural configurations within the field of glass engineering is the topic of this address. The generation of these design ideas and the process by which they are realized is particular to the production of architecture and although there is considerable cross fertilization with the world of product design there are some fundamental differences in the two processes that highlight in what circumstances architectural invention can best thrive. Keywords: Engineering history, invention, glass structures
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1. Architecture and the Engineering Consultant At around the end of the 19th Century structural engineers were not part of the architects design team. In the field of building construction the engineer was challenged with inventing uses for the newly emerging construction materials which at that time were reinforced concrete and steel. As a result of this effort a number of patented frame systems appeared on the market which were used in the construction of factory sheds and other simple building types. The development of these patented frames was in every way similar to the way in which products for the mass market are introduced: a large amount of design and testing followed by the production of a large number of units. The larger the number, the greater the return. The architect would have been acutely aware of these new building technologies and although the architectural critic Ruskin was in this period declaring that the introduction of ferrous metals into the fabric of architecture would be a corruption of its very soul there were a number of ‘modern’ architects who could see that reinforced concrete and steel would be the construction materials of the future. The problem was that the means of design and production was in the hands of the contractors and the engineers who worked for them. The relationship between the contractor, the architect and the client then as now meant that access to the contractors design knowledge to allow the architect to fit the structure to the architecture was limited. The contractors focus is on building safe economic structures and building the same solution more than once gives him the opportunity to reduce risk and increase profit. His natural tendency is therefore to avoid embarking on something he has not done before and which during the bidding period he has insufficient time to investigate. A further disincentive is that he is often only one of a number of contractors and there is no guarantee that any effort he might make to understand the full implications of a new design idea will be rewarded. 11 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Architects, when designing a work of ‘Architecture’ are in almost all instances proposing a bespoke solution within which their control of the construction materials of the building is critical. In order to bridge this gap between the architect’s desire for a bespoke solution and the contractor’s desire to reduce risk the engineer was invited to be a consultant to the design team. This meant that the architect could use the engineers skill to develop bespoke solutions during the design process and thereby relieve the contractor of the design responsibility for the proposed structural configuration and thereby his risk. This new partnership gave rise to the creation of Associations of Consulting Engineers in many countries in Europe between 1900 and 1910. The independence of the engineer from the commercial world meant that proprietary technical knowledge could be brought into the public domain and ultimately codes of practice and standards for designing in these materials came into existence
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2. The Emergence of Glass as a Structural Element The two structurally significant inventions in the manufacture of glass which happened in the middle of the 20th Century were the float line process for making glass in a continuous ribbon and a method for strengthening glass by tempering. In addition to these two major developments, the improvement of laminating techniques, which had first been invented in the late 19th century, allowed the production of thicker glass panels with significantly enhanced fail safe performance. These three techniques offered architects the opportunity of developing a new design vocabulary for glass which, however, required a comprehensive understanding of its structural behavior. Up until the mid 1980’s Pilkington, the company that patented the float line process, controlled the way that glass manufactured by their process was used in building structures. Glass processors and installers were bound by Pilkington’s rules as the company held patent rights on all the float line machines. This made it very difficult for an architect to investigate new uses for glass as fabricators were unable to provide glass which did not conform to Pilkington’s strict guidelines. After the patent rights ran out in the mid 1980’s there was an opportunity for architects to begin to think of new uses for this fundamentally traditional material. They found, however, that as much as they were able to imagine a floor made of glass, they were unable to persuade fabricators to design and build these structures. 3. The Era of the Structural Glass Consultant The structural design of glass was not a part of the academic training of a Structural engineer until recently and in the mid 1980’s there were very few sources for determining the physical properties of glass and no codes that a practicing engineer could consult. Information of this type was jealously guarded by the glass manufacturers who could use their technical expertise to offer proprietary systems. Architects reasonably thought that structural consultants should be able to help them develop original design ideas and engineers were encouraged by a number of ambitious architects during this period to start thinking about how to design glass structures. 12 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Engineering Invention in Glass Architecture
The following examples indicate the progress we have made since 1988 as glass engineering consultants. And although there are still no current codes for the structural design of glass, there are now a number of extremely useful handbooks to consult which means more engineers can now offer this support to the architect 4. Inventions in the use of Structural Glass Our progression in understanding the structural properties and behavior of glass started with the design of a simple staircase tread. Through subsequent projects over the following 25 years, we were able introduce radical ideas that expanded the vocabulary of glass architecture. The following projects illustrate the structural glass inventions that we introduced during that period.
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Figure 1: Glass and acrylic treads, 1988.
Figure 2: Laminated glass floor plates.
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Figure 3: Simple glass beams and columns.
Figure 4: Bolted glass beams.
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Figure 5: Friction grip laminated glass beams and columns.
Figure 6: Parallel cable supported glass walls.
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Figure 7: Two side supported glass treads using ionoplast laminates.
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-17
1 World Trade Center – Podium Wall Design Development Christoph Timm Skidmore, Owings & Merrill LLP, New York, USA, [email protected], www.som.com On the new 1 World Trade Center Tower an exterior permeable façade treatment was to be designed for the lower 20 floors cladding a concrete shear wall and mechanical louvers. Engineering and design had to be balanced with the client’s desire to streamline maintenance issues for the tallest office building in the western hemisphere. The scope of the podium façade treatment includes over 12.000 m2 in total area with more than 4.000 glass fins each free spanning 4m in height between attachments. Various glass fin-metal connection details were evaluated for aesthetic and performance criteria. Keywords: Laminated Glass, Glass Metal Connection, LED Lighting, Aero Elastic Testing, 1 World Trade Center
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1. General Upon completion 1 World Trade Center will be the tallest building in the western hemisphere with a symbolic 1776’ (541m) in height and 104 floors. Its outer skin will have a total of about 88.000 m2 (945,000 sf), comprised of 75.000 m2 (807,000 sf) of tower office curtain wall starting at the first office floor at Level 20, podium wall below 12.200 m2 (132,000 sf) and cable net wall systems at each of the 4 entrances on all sides of the 62,48m x 62,48m (205’ x 205’) square building. This paper focuses on the expedited development of the podium wall design process. Particular emphasis is given to selection of the glass fin make up and engineering of the glass/ metal attachment to the podium wall units, its components, and the choice of glass in the context of aesthetics and performance. 1.1. Project Delivery Method The podium section of World Trade Center One was previously designed with a prismatic glass enclosure that had been using the traditional Design-Bid-Build Delivery Method. When the contractor who had been awarded the scope failed to deliver his work in a timely and acceptable manner the decision was made to abandon the original scheme and develop an alternate design under an expedited schedule. Therefore the Design Assist Method was chosen for delivery and the new podium design developed to a level typical for a mid construction document phase in the US. Bid documents included engineered key details and illustrations showing the architectural intent for the entire scope of work.
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In May 2011 the construction manager Tishman Construction engaged Benson Industries Inc., the curtain wall contractor delivering the tower office curtain wall to assist the design team in developing the new scheme. By the beginning of the summer the client decided to bid the podium wall scope of work and bidding guidelines prevented Benson Industries to be further involved in the development in order to stay eligible for bidding. APG International (APG) took over Benson’s role in assisting the design team with further development, providing in depth technical assistance, cost estimation services and eventually a full size proof of concept mock-up that convinced the client and design team that the new scheme was feasible and met all aesthetic expectations. At the end of 2012 Permasteelisa North America Corp. (PNA) was awarded the contract for the podium wall through an RFQ and RFP process. They immediately went to work together with the design team, construction manager and client.
Figure 1: Rendering World Trade Center One [1]
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1 World Trade Center One – Podium Wall Design Development
1.2. Building Ventilation Requirement Air intake, Exhaust All office floors of World Trade Center One are enclosed in a glass envelope without major louver interruptions. Therefore the building “breathes” below and above the office section with extensive louver areas. Figure 2 illustrates the extent of the podium ventilation zone on World Trade Center that wraps around the entire building. It shows the unclad podium portion of the building being visually bifurcated into a lower part that consists of concrete shear walls extending up to the top of the cable net entrance portals and an upper part that is comprised of recessed mechanical louvers set back 6’ behind the façade system, structural steel lattice beams and columns. This 6’ zone between permeable podium wall façade and mechanical louvers is used as a plenum for air to mix and freely move in and out of the building. All intake louvers are located on the North and South Façade and all air exhaust louvers positioned on the East and West Façade. Baffles at the corners between the plenums prevent air from short circuiting and ensures that exhaust air is not simply being reused as fresh air. Due to tenant changes and potentially changing mechanical requirements extend of the active mechanical louvers will change over time but will not be perceptible through the decorative face.
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Figure 3 demonstrates the unifying character of the decorative podium wall as it screens the lower concrete shear walls and the mechanically active upper section of the podium. The podium wall is an aesthetic device and not a thermal envelope and not watertight.
Figure 2: Construction Photo, South East Podium Corner (June 2011)
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Figure 3: Rendering of Finished Podium Wall South East Corner, note the north pool waterfall of the World Trade Center Memorial in the foreground of the image
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2. System description 2.1. General The 4,06 m x 1,52 m (13’-4” x 5’-0”) grid of the podium wall is an extension of the unitized office tower curtain wall grid above. The podium itself is vertically divided into 14 tiers; each full tier encompassing 40 typical podium wall panels and two half corner units per façade. At the base of the wall there is a short tier that includes a wall panel with stone cladding below that meets the plaza on the east and west side of the building and the street sidewalk on the north and south. Figure 4 illustrates the repetitive nature of the design with over 90% of the panels being identical except for the angle of the glass fins as discussed later in the paper. The efficiency of this system translated directly into cost reduction.
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Figure 4: Podium Wall Panel Types
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2.2. Unitized Podium Wall Components The podium wall panels are in principal a curtain wall system without the requirements for air and water tightness. In fact, the opposite is required as the panels will have to allow for free air movement to ventilate the building. The unitized panels will arrive prefabricated at the site, ready to be hung off of previously installed anchor assemblies on the face of the building. Each panel is comprised of a series of layers that as an ensemble screens the inside of the building but allows air to travel through. The outermost layer of the design are two 3,96m x 0,60m (13’ x 2’) laminated glass fins that cantilever off each of the typical podium wall panels. The fins are dynamically oriented in varying angles across the façade with a more closed appearance at the top and bottom tiers of the podium and a more open configuration for maximized air throughput at the mid section. Structurally siliconed to a stainless steel extrusion receiver shoe at the top and bottom of the glass, each fin assembly is bolted to a stainless steel outrigger that fixes the angle. At the center of the unit between the fins is a vertical channel located that houses the LED lighting system which is serviced from the exterior of the building only. Behind the glass fins are horizontal stainless steel slats attached to the unit framing adding visual surface to the assembly and a notion of weaving. At the back of the painted aluminum panel framing an aluminum perforated sheet metal screen is mounted and serves 3 functions: It screens the plenum particularly where the glass fins are more open, acts as a projection surface when lit at night and prevents birds from entering the plenum.
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Figure 5: Explosion Axon of Typical Wall Panel
2.3. Varying fin angles The primary design intent for the glass fins is to create ever-changing reflections of the sky and context, and refract light in infinite angles - different in medium, but very similar in concept to the waterfalls at the World Trade Center Memorial site nearby. Throughout the day and season the play of light and shadow will animate the façade as well as the observer’s changing vantage points. This dynamic character of the façade is amplified by the changing of the angle that the glass fins form with the building face. While a set of fins parallel to the building face always defines the corners and volume of the podium on every one of the 14 tiers, all other fins change angles in a carefully composed way. See Figure 6, 7 and 8.
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Figure 6: Plan Detail showing Corner Panel and two typ. Panels with Varying Angles Tier 1-14
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Figure 7: Dynamic Glass Fin Angles vary with Tiers
Figure 8: Close up Perspective Diagram at Corner
2.4. Ventilation Performance of Podium Wall Units Air traveling through the podium wall panels finds its way through the various layers of the panel - glass fins, slats, perforated metal, framing, etc., with all components causing some level of resistance (pressure loss). This resistance and its impact on the mechanical system had to be evaluated. Initial desk top calculations performed by Rowan Williams Davies and Irwin Inc. (RWDI) indicated acceptable pressure loss in the plenums but further verification was required with computational fluid dynamics modeling (CFD). In an effort to develop accurate input data for the CFD model, a full scale mockup with all relevant layers of the podium wall system was constructed and pressure loss across the system measured at varying fin angles (Figure 9). Data for the various fin angles under intake and exhaust mode were then plugged into the CFD analysis (Figure 10).
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Figure 9: Wind Tunnel Testing of Podium Wall Assembly
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The objective of this task was to estimate the average static pressure differences across the plenums of each facade. Based on a review of the mechanical and architectural drawings, it was anticipated that the performance of the intakes on the south facade would reflect the worst case conditions. CFD analysis showed that the expected static pressure differences across the facades would be in a range well within the limits that would allow the mechanical system to function as engineered.
Figure 10: CFD Analysis shows Correlations w/ Mechanical Louver [5]
2.5. Glass selection The idea for the glass fins on the podium wall is to match the visual reflectivity of the tower curtain wall above to the largest degree possible in an effort to visually unify the building. Knowing that different lighting conditions on the office floors and mechanical floors would make the glass appear differently, the design team focused on matching reflectivity of both glass assemblies as a means to visually tying them together. The Viracon VRE-54 Insulated Glass Units on the tower curtain wall with a reflectivity of 33% the target, the team selected Interpane’s Ipasol Bright White coating due to its extremely high light transmittance of 58%. Typically used in solar-control applications, its unique characteristics result in a reflective and bright light appearance. As a monolithic glass lite, Ipasol Bright White’s has a reflectivity of about 36% which 24
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1 World Trade Center One – Podium Wall Design Development
decreases by half if laminated into a safety glass assembly with a clear lite. To counter this effect and to maintain the high reflectivity, the final glass assembly will feature the Interpane coating on the #2 and #3 surface resulting in a reflectivity matching almost exactly the 33% of the office curtain wall above the podium.
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Besides the aesthetic appearance characteristics, the Bright White coating also features the technical advantage of not requiring an edge deletion due to absence of silver in the coating design that could degrade when exposed to humidity. Edge deletion would create a vertical line and visual frame destroying the homogenous and scale-less appearance of the fin’s glass surface.
Figure 11: Reflectivity of Tower Glass vs. Podium Glass
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Figure 12: Surface Characteristics of Glass Fins
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Studies with the reflective glass were undertaken and it became clear that under certain lighting conditions the glass would come close to matching the tower curtain wall appearance. With a change of lighting conditions and a different vantage point however, the fins tended to lose their presence and amplified the horizontal slats at the back of the podium wall due to their reflective nature. To counter this effect and add luminosity to the assembly, an acid etch finish was added to the back surface of the glass. This was for important aesthetic considerations as described and was not required structurally.
Figure 13: Renderings, W/O and W/ Acid Etched Back Layer
26 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 14: Surface Characteristics of Glass Fins
2.6. Structural analysis of glass make up A series of varying glass assembly make-ups were studied for their structural performance and feasibility on the system. The following base criteria were established: x x
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x x x
Structural deflection limits for glass fins < l/100 typically as the glass fins only serve as decorative components of the façade Maximum acceptable deflections within dimensional boundaries of the units illustrated in Figure 15, the fins cannot hit each other or have contact with the stainless steel slats behind Design wind load +/- 2,87 kPa (+/- 60 psf) 1.52mm Ionoplast interlayers All glass to be heat strengthened
Based upon finite element analysis (FEA) Glass make up GL-01 and GL-03 were found to meet all criteria and were specified in the bid documents (see Figure 16, 17)
Figure 15: Dimensional Boundaries for Glass Fins [2]
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Figure 16: Structural Analysis Glass Make up Option GL-01 [2]
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Figure 17: Structural Analysis Glass Make up Option GL-03A with Stainless Steel Embed [2]
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2.7. Glass Fin – Podium Wall Unit Attachment Initially two schemes were developed for the attachment of the glass fin assembly to the curtain wall unit. As the base bid scheme a traditional “U” shaped stainless steel extrusion clamps the glass at its horizontal edges from both sides with structural silicone in between.
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Figure 18: Base Scheme Attachment Glass – Podium Wall Unit – Stainless Steel U- Extrusion
Figure 19: Alternate Scheme Attachment Glass – Podium Wall Unit – Stainless Steel Embed
The alternate scheme also attaches only at the top and bottom of the glass fins, but instead of the clamping action of the shoe, a stainless steel fitting is embedded into the glass during the lamination process in the autoclave. This integrated approach may have reduced the appearance of solid metal that was deemed distracting from the glass itself. During the bidding process none of the three invited bidders wanted to entertain the alternate scheme with the embedded stainless steel fitting and therefore the more traditional shoe approach was selected with the potential to revisit the precise attachment detail during the design assist process. 30
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Figure 20: Three Variation Schemes: “J”, “L” and “U” Stainless Steel Extrusion [3]
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After award of the contract Permasteelisa North America investigated this attachment detail further together with the design team. Variations of the Shoe shaped extrusions were investigated but eventually discarded in favor of the “U” extrusion (Figure 20).
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2.8. Aeroelastic calculations and modeling During the design development phase the issue of the glass fins starting to vibrate under certain wind loading conditions related to the natural frequency of the assembly was examined. Two independent computer finite element studies for the natural frequencies of the glass fin assembly were undertaken to determine if vortex shedding, flutter and galloping concerns could be ruled out for the design. Both studies returned favorable results as the frequencies were calculated to be higher and the assembly to be stiffer than what is generally considered as critical (2HZ). However, during the shop drawing phase of the project the computer calculations will be confirmed by the contractor via two 1:10 physical aeroelastic section models that will be tested in a wind tunnel setup under expected wind loading conditions using material representing stiffness and distributed weight of the full scale assembly.
Figure 21: FEA Study Natural Frequency Mode 1-3 [4]
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1 World Trade Center One – Podium Wall Design Development
3. Lighting Developing a design scheme for the podium wall that would look engaging and dynamic throughout the diurnal cycle cannot focus on daylight hours only. The same design intents that apply to daytime, also apply to night time hours with its play of (ambient) light and shadow. Therefore an (artificial) lighting scheme was developed that would allow the base of 1 World Trade Center evolve into an ever changing light choreography as the sun sets. The final lighting program is still under development, but the system being proposed has a high degree of flexibility and programmability. Ideas similar to giving resident artists a canvas to paint on with light at the podium have been floated but no decision made on how to put to work a lighting system that can be controlled in real time to a pixel size of 0,3 m x 1,52 m (1’ x 5’) in color.
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The genesis of the overall podium wall unit design can to a degree be traced back to an initial design decision to illuminate only from the inside. In fact the physical light source itself is not visible at all in the podium wall unit and only its light effect mysteriously illuminates the base of the building like a lantern. The only place to locate the fixture symmetrically and economically was the center of each unit, dividing it vertically into two sides with two sets of stainless steel slats and two glass fins, one on each side. Evenness of the lighting was a primary goal and a max. 1:4 luminance ratio across the perforated screen as the receiving screen specified. Furthermore the light fixtures will be serviced from the front due to the lack of access from the back at the lower podium section at the shear walls. For the purpose of access, a vertical snap cap can be removed at each of the 3 stacked light fixtures per panel.
Figure 22: Plan Detail Lighting in Podium Wall Unit
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Figure 23: Full Scale Lighting Mock-up Testing and Evenness Verification
The advent of LED lighting technology has revolutionized the possibilities of illuminating buildings particularly in situations where allocated space for the fixture is limited and performance requirements for optics are challenging. Both criteria are prevalent on this podium wall, making LEDs the light source of choice in this application. The custom LED fixture specifications on the project were developed by Brandston Partnership Inc. (BPI) as Lighting Designer with Lumenpulse as a fabricator. During the bidding process Color Kinetics/ Phillips was subcontracted to develop the specifications further into a final fixture.
Figure 24: APG Mock-up At Night time
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Figure 25: At Daytime close up
Figure 26: Suspended 150’ in the Air
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4. Full Scale Proof of Concept Mock-up at APG With the design and engineering task for the bid documents finalized, a visual proof of concept mock-up was constructed by APG with the help of Lumenpulse. For glass comparison purposes, two additional tower wall units were also added above the podium wall. To evaluate the design at various heights off the ground, the mock-up was built around a (12.5’ x 7.5’ x 33’) structural steel cage that could be elevated by truck crane. Furthermore the mock-up was constructed with a glass fin attachment detail allowing for various fin angles as depicted e.g. in Figure 25/26. The mock-up was extremely helpful to the design team as it influenced further decision making in many ways. It verified the design concept and gave key decision makers a comfort level needed to proceed with this unusual design.
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5. Outlook With World Trade Center One about to top out in the summer 2012, fabrication and installation of the podium wall panels will get on the way at about the same time if performance testing goes according to plan. Installation of the panels is planned to last about a year for the over 2000 typical panels with the last leave out panels to be installed 2014/ 2015.
Figure 27: World Trade Center One, 20 April 2012
36 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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6. Acknowledgements The success of any project depends largely on the expertise and enthusiasm of those who direct it: First and foremost, I would like to thank Roger Duffy (FAIA), TJ Gottesdiener (FAIA), Ken Lewis and Nicholas Holt for their leadership and guidance heading the SOM efforts. I would like to take this opportunity to express my gratitude to team mates Frank Mahan, Christian Kotzamanis, Andrea H. Wong and Scott Matthews of BPI who have all made this design process memorable. Special thanks go to Nicole Dosso, Donald Marmen and Benjamin Reich whose contribution was instrumental for converting a design idea into a soon to be reality. Thanks also go to structural engineers Charles Besjak and Dmitri Jajich of SOM for volunteering their time at a critical junction of the design process. Architects do not build their design; this huge task is left to the construction manager and contractors who literally put it together. Everyone stepped up along the way to the final design. Thank you Tishman Construction for managing the process and APG International with Ed Zaucha, Dirk Schulte and Bob Unruh whose dedication to the project was extraordinary. Thank you Permasteelisa with Alberto De Gobbi and team for adding refinement to the overall design together with Phillips Color Kinetics and Interpane. There was never a moment where I felt this project was treated as business as usual! Finally, I would like to acknowledge the ownership on the project, The Port Authority of New York and New Jersey and the Durst organization for challenging us in a healthy and productive way and allowing us to work on this once in a lifetime project. 7. References Rendering by Dbox Schulte, Dirk, Structural Analysis Podium Wall, APG International, 08-07-2011 Drawings and renderings by Pemasteelisa North America Corp. Studies by Wacker Ingenieure Studies by RWDI Consulting Engineers
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[1] [2] [3] [4] [5]
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Projects & Case Studies
39
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-41
The Glass Screens of the Japan Post Tower Lucio Blandini, Werner Sobek Werner Sobek Stuttgart, Germany, www.wernersobek.com The Japan Post Tower is a 200 m tall building, rising on the site of the former Tokyo Central Post Office in the Marunouchi business district, Tokyo. The complex, designed by Helmut Jahn, integrates in the base area the restored historic façade of the old Post Office. On the north side, the façade of the highrise is characterized by three asymmetrical folds and by four glass screens framing the unitized glass façade. Such screens have to reach a high degree of transparency, while still being able to withstand tornados (up to 8.5 kN/m2) and high earthquake loads (up to 1.2 g).
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Keywords: Glass Screens, Highrise Buildings
Figure 1: Japan Post Tower - Architectural Rendering (© Murphy/Jahn Architects, Chicago)
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1. Introduction The redevelopment of the historic Tokyo central post office, designed by Helmut Jahn, Chicago, is a 200 m high tower rising out of the renovated historic building. The tower main façade, located on the north side, is characterized by three asymmetrical folds as well as by four almost dematerialized glass screens, which frame the unitized glass façade. The two external fold lines are inclined, and the middle fold line is vertical; thus the façade surface is defined by a vertical plane (on the outer parts on the left and right sides) as well as by two spatially inclined planes in the central part. The 31 m high top screen is the most challenging high-transparency screen due to its size, the loadings and the fold geometry. Further screens are the wings on the two sides (5.4 m wide and 129 m high) and a 6 m high screen enclosing the unitized glass façade at the bottom.
Figure 2: Japan Post Tower – North Facade (© MJS, Tokyo)
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The Glass Screens of the Japan Post Tower
2. The Top Screen The top screen (61 m wide and 31 m high) is designed to withstand tornado loadings up to 8,5 kN/m2 and earthquake accelerations up to 120% of the earth gravital acceleration. Nevertheless, it reaches a high degree of transparency, due to the fact that forces are mainly transferred to the main steel structure (see figure 3, red profiles) by means of tension and compression members, thus allowing for minimal profile sizes. The glass panels (made of 2 x 12 mm laminated fully tempered glass) are 1,80 m wide and have different heights varying between 4.55 m and 4.90 m. The glass dead load is carried by means of welded tapered T profiles, which are hung at the top. The wind loads are transferred at every level from the vertical T profiles to stainless steel tapered wind needles ending with spherical hinges. The façade steel structure is braced by a discrete number of diagonal needles and by a slender hollow steel profile running horizontally parallel to the façade surface, in order to increase the facade capacity of withstanding earthquake forces. Double hinge endings have been designed and engineered for the nodes where two needles, a straight one and a diagonal one, converge.
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All the arising vertical and horizontal forces are transferred by the needles and by the tapered T-profiles to the main steel frame, which is set on a vertical plane located behind the folded façade. The distance between the folded façade surface and the main steel frame varies between 1.1 m in the middle and 3.6 m on the sides.
Figure 3: Top Screen - Steel Structure Rendering (© Werner Sobek Stuttgart)
43 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
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Figure 4: Top Screen – View from outside (© MJS, Tokyo)
Figure 5: Top Screen – View from inside (© MJS, Tokyo)
44 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Glass Screens of the Japan Post Tower
3. The Wings The wings are placed on the outer left and right sides of the north façade between level 8 and level 36. They are 5,40 m wide and have an overall height of 129 m. They are subdivided in blocks of 5 to 6 levels; structurally speaking, these blocks are completely independent of each other. The horizontal loads are transferred from the glass panel to the T Profile in the same way as in the top screen. These forces are transferred at every level from the T Profile to the slab by means of a horizontal welded hollow steel profile, hinged at one end and supported horizontally at 2/3 of the span by means of a tapered wind needle. The vertical forces are transferred by the T profiles every 5 to 6 levels to three vertical inclined tension rods. A fourth vertical tension rod secures the system at the bottom in case of uplifting earthquake forces.
Tension rods
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Hinged support Figure 6: Wings - Steel Structure Rendering (© Werner Sobek Stuttgart)
Figure 7: Wings – View from below (© MJS, Tokyo)
45 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
4. The Bottom Screen The bottom screen is 61 m wide and 6 m high. Horizontal loads are transferred by the glass panels to the T profiles. These are hung on top and horizontally supported by a tapered wind needle at the bottom. Diagonal needles brace the system horizontally. A cable connects all the T profile, thus stabilizing the structure horizontally. The cable is anchored on the two ends of the bottom screen to a stiff system made of two diagonal and two horizontal wind needles and by a horizontal profile connecting them.
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Figure 8: Bottom Screen - Steel Structure Rendering (© Werner Sobek Stuttgart)
Figure 9: Bottom Screen - View from outside (© MJS, Tokyo)
5. Conclusions The four glass screens of the Japan Post Tower Tokyo demonstrate impressively how light and transparent glass structures can be designed for regions with very high seismic and wind loads. 46
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-47
The Glass Sphinx: A Massive Stacked Glass Sculpture Freek Bos Witteveen+Bos Consulting Engineers, the Netherlands, [email protected], www.witteveenbos.nl Tom van der Heijden, Pieter Schreurs Scheuten Absoluut Glastechniek, The Netherlands, [email protected], www.scheuten.nl The refurbishment of the Meuse river boulevard in Venlo instigated Scheuten Glass to donate a giant-sized, 6 metre high version of the stacked glass statue the Sphinx, which had originally been made as a 80 cm sculpture to commemorate the city’s 650th anniversary back in 1993. Many hurdles had to be taken to, starting with the preliminary feasibility study, on to adhesive selection, joint design, glass selection, cutting methods, glass sheet layout, and final construction procedure.
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Keywords: Stacked Glass, Adhesive Tape, Construction, Manufacturing
1. Introduction In 1993, the city of Venlo, in the South Eastern province of Limburg, the Netherlands, celebrated its 650th anniversary. For the occasion, the Venlo-based glass company Scheuten had local sculptor Fons Schobbers produce a piece solely out of glass. The result was the Sphinx, Figure 1a and b, a massive stacked glass object, in a free, asymmetrical gate-like shape, approximately 80 cm high. The large round head on one side stands on a slender leg, while the lower side across rests on a broad leg, with an sort of arch connecting both sides.
Figure 1a and b: The original Sphinx sculpture.
47 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Now, with the refurbished Meuse river boulevard completed and the decennial Floriade World Horticultural Expo putting Venlo in the spotlight, Scheuten offered the city a larger-than-life version of the statue. With a height of 6 m and a weight of well over 100,000 kg, the Glass Sphinx is a giant copy of the original. Figure 2 gives an indication of the size.
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Figure 2: Impression of the large Sphinx.
The Sphinx has been constructed on a prominent spot on a perpendicular corner of the Meuse rive dike just south of the new yacht harbour and refurbished river front. It is well visible from a major entrance road into the city, the historical city centre as well as the new city district ‘De Kazerne’ on the other side of the river. The object is placed on a pile supported concrete block foundation that cantilevers out of the dike by approximately 0.5 m. It will be constructed in the summer of 2012. Witteveen+Bos consulting engineers conducted a feasibility study to construct the sculpture completely in stacked glass. Scheuten Absoluut Glastechniek took care of detail engineering, manufacturing and construction. 2. Feasibility Study 2.1. General A review of similar objects showed the Sphinx would be the largest of its sort in weight, albeit not being the highest. Figures 3 and 4 show similar projects: the Police Memorial in London [1] and the Angel sculpture in Zwolle (the Netherlands) [2]. These sculptures show two different methods to obtain stability. The Police Memorial relies on vertical prestress induced by five prestress rods. There is no intermediary material between the glass sheets. Alternatively, the glass sheets of the Angel are connected by 3M VHB
48 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Glass Sphinx: A Massive Stacked Glass Sculpture
adhesive foil. This is more suitable for geometrically irregular shapes, but raises some questions regarding durability, contamination, and crushing of the adhesive.
Figure 3: Police Memorial, London.
Figure 4: Angel statue, Zwolle, the Netherlands
Potential problems that were to be expected included intrusion of water (freezing causes glass breakage), dimensional inaccuracies in the seams, and deviations in glass thickness of different glass sheets (EN 572-2 [3] for float glass allows ± 0.3 mm). Literature [4] also reports differences in glass thickness across the width of the ribbon of float glass (thin in the middle, thicker to the sides), measuring 0.3 to 0.5 mm.
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Settlements, thermal expansion differences, and concrete shrinkage should also be accounted for. Section 3 discusses how all of these issues have been addressed. 2.2. Preliminary FE-Analysis Additional to the general feasibility study, an explorative FE analysis was conducted. Three models of the Sphinx were analysed: a massive model (1), a layered model (2) and a massive hollow model (3), Figures 5a, b, c. The first model served to gain a quick insight in the structural behaviour and order of magnitude of stress. The effect of the soft interlayers was investigated with the second model. In this model, layers of 10 cm were applied (instead of 10 mm), to avoid long modeling and analysis times. For the interlayer thickness, a tenfold was also applied. In the third model, a hollow sphere was introduced in the Sphinx head. The aim was to reduce overall weight (material cost and foundation loading), make the weight distribution between both legs more balanced and also to create more interesting visual effects (a solid head would absorb a lot of light). Wind loading was applied to all models as well as uneven settlement underneath the legs. A temperature load analysis was made on model 1. The effect of step-by-step stacking of the glass on stress distribution was analyzed using model 3. The stresses due to wind loading remain extremely low, well beneath 1.0 MPa (Table 1). In the layered model, the stresses were significantly lower than in the other two as the soft interlayers allow for more distribution of the stresses. 49 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Figures 5a, b, c: FE models for feasibility study: massive, layered, and massive hollow. Table 1: Maximum tensile stresses in FE Models of feasibility study due to wind loading. LC
Description
Massive
Layered
Hollow
1
Self weight
[MPa]
0.11
0.16
0.11
2
Self weight + wind dir. 1
[MPa]
0.25
0.20
0.36
3
Self weight + wind dir. 2
[MPa]
0.11
0.09
0.21
4
Self weight + wind dir. 3
[MPa]
0.33
0.21
0.32
5
Self weight + wind dir. 4
[MPa]
0.08
0.07
0.13
Uneven settlements may cause much more severe stresses. Table 2 gives the maximum stress per length of uneven vertical settlement between the legs. Assuming an allowable permanent stress of 8.0 MPa, it also gives the estimated allowable uneven settlement. It ranges from 2.80 mm for model 1 to 8.79 mm for model 3. However, with a sound foundation design, such uneven settlements should be avoidable.
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Table 2: Uneven vertical settlement. LC
Description
6
Under slender leg
Massive
Layered
Hollow
Max tensile Stress/length [MPa/mm]
2.86
0.91
2.82
Estimated max allowable uneven settlement [mm]
2.80
8.79
2.84
The stacking process does increase the maximum stresses relatively significantly. However, in absolute terms, they still remain very low. For the thermal analysis a rather extreme situation was modeled as a starting point: a temperature rise in the object from -20 ºC to + 80 ºC in 8 hours. This leads to a maximum stress of 23 MPa. It is remarkable that even after 8 hours (28,800 s), only the outer approximately 20 cm of the sculpture has risen above 0 ºC. The inner 40 cm (in a 120 cm wide section) remains at -20 º C (Figures 6a, b and 7). This means that in reality the Sphinx will never come close to having that core temperature, but will rather have one close to the local annual average, of about 10 ºC. When it is furthermore considered
50 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Glass Sphinx: A Massive Stacked Glass Sculpture
that the actual Sphinx will be much more flexible (segmentation and layers) than the massive model 1, there seems to be no reason to expect thermal breakages. The results of the feasibility study were promising enough to continue work on the development of the Sphinx.
Figure 6a, b: Temperature and stress distribution in Sphinx after 8 hours. 90 80
0sec
70
5.000sec 10.000sec
Temperatuur [ 0C]
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60 50
15.000sec 20.000sec
40
25.000sec 28.800sec
30 20 10 0 2,900 -10
3,100
3,300
3,500
3,700
3,900
4,100
-20 -30 Y-Coordinaat [mm]
Figure 6a (top) and b (bottom): Temperature distribution in Sphinx after 8 hours.
3. Sphinx Design 3.1. Glass For the Sphinx a transition glass is used, which is obtained when a float line oven is switching from normal glass to extra clear low iron glass (Scheuten Super White). The transition glass is almost color neutral. A very clear glass was selected as a normal ironcontaining glass would result in an almost opaque sculpture because of its size. 51
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Furthermore, a darker glass would lead to higher thermal stresses as it would result in a higher temperature gradient in the object. 3.2. Adhesive AFTC Silver Tape 8502 was selected as adhesive for the sculpture. This is a transparent modified acrylate tape with a nominal thickness of 0.25 mm. It consists of 100 % adhesive, i.e. it has no carrier or filler. Table 3 provides some properties, taken from the product data sheet [5].
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Table 3: Some properties of selected adhesive foil, AFTC Silver Tape 8502 [4]. Property
Code
Value
Unit
Thickness
-
0.25
mm
Thickness tolerance
-
0.1
mm
Density
-
840
kg/m3
Peel adhesion
ASTM D3330
2.6
N/mm
Tensile strength
ASTM D897
0.75
MPa
Shear strength
ASTM D3654
0.72
MPa
Solvent resistance
-
Excellent
-
UV resistance
-
Excellent
-
Temperature resistance, long term
-
100
ºC
Temperature resistance, short term
-
160
ºC
Several tests have been carried out to determine suitability of the adhesive. Standard conformity testing according to ASTM D412, D897, D3654, D1002 and D3330 is performed on the adhesive. Additionally, adhesive glass-glass connections were subjected to heating at 80 ºC and visually inspected, but no defects were encountered. Also, no sideways flow of the adhesive was detected, thus relieving worries that surplus adhesive might spill out of the seams of the Sphinx. The adhesive is applied to one side of the glass sheets (the smaller one respective to the one it connects to), in the workshop using a custom made roller construction. Adhesive foil rolls of 900 and 500 mm wide were used. The protective cover is removed on site. The glass surface is covered completely by adhesive foil to avoid air inclusions, contamination, or water (vapour). During curing, the adhesive slightly expands, thus filling possible small gaps caused by deviations in glass thickness and driving bubbles out. 3.3. Foundation-to-Sphinx Joints The Sphinx will be placed on a concrete foundation block covered in unpolished black stone slabs, similar to ones that have been used in the new yacht harbor. The use of black stone makes the issue of differential thermal movements between foundation and sculpture more important. These are accommodated by designing the connection of the broader leg to the foundation as a sliding joint. Figure 8 shows the detail.
52 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Glass Sphinx: A Massive Stacked Glass Sculpture
Cover plate (stainless steel) Filler plate (stainless steel) Top plate (stainless steel) Teflon strips Base plate (stainless steel)
Grout filling M16 positioning bolts Concrete foundation Figure 8: Sliding joint between foundation and broad Sphinx leg.
The joint consists of a 20 mm thick stainless steel plate positioned on the concrete foundation block using M16 bolts. The space underneath is filled with grout poured through holes in the plate. 10 cm wide strips of Teflon are applied to the top of the plate. Another stainless steel plate is placed on the Teflon strips and connected to the lower plate by bolts in slots, so that they can slide relative to one another. A filler plate comes next and then, finally a top plate is applied, 5 cm wider than the footprint of the glass. From there on, the stacking of adhesive foil and glass sheets starts. The connection under the slim leg is similar, but without the teflon strips and slots, so that it can not slide.
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3.4. Glass Sheet Layout The size of the glass sheets that could be applied was limited for two reasons. Firstly, small pieces introduce flexibility and dilations. Secondly, the sculpture is constructed by hand, so the sheets can not be too heavy. Thus, each layer ended up consisting of 6 to 16 sheets. A major concern in determining the glass sheet layout was avoiding over- and underpressure in the seams between the sheets, as particularly underpressure attracts moisture, dust and dirt, which could make the sculpture dirty on the inside. This has been solved by interconnecting (almost) all seams through vertical channels and two small openings, one in each leg (with a filter). In each layer, the glass sheets are rotated with regard to the previous layer, to assure structural integrity. As introduced in the FE study, a 2 m diameter hollow sphere was introduced into the Sphinx head. This reduces the overall weight by some 16 %, from 111,813 kg to 93,725 kg. The seams of the Sphinx are sealed from the outside with a clear MS polymer. This sealant is more durable than clear silicone, and -more importantly- is compatible with the acrylic adhesive foil. If water nevertheless penetrates through a seal, glass breakage by stand still water freezing is avoided by designing the seams so that they grow wider towards the Sphinx interior, from 8 to 25 mm. This also allows for some liberty in dimensional accuracy of the sheets. 53 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
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Figures 9a – e show the sheet layout of subsequent layers 334 through 338.
Figure 9a - d: Glass sheet layout of layers 334 - 337.
54 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Glass Sphinx: A Massive Stacked Glass Sculpture
Figure 9e: Glass sheet layout of layer 338.
4. Manufacturing and Construction 4.1. Glass production The glass for the Sphinx was produced in a single batch (some 7-8 hours of production time) by her sister company f glass in Osterweddingen, Germany. Thus, all glass sheets have an identical thickness, which is essential to avoid problems when stacking layers that consist of multiple sheets of glass. The thickness across the ribbon was measured. However, contrary to what has been reported in literature [4], no significant differences were found. If they were even there, they were smaller than the adhesive layer thickness (i.e. < 0.25 mm).
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4.2. Cutting the glass panels For shaping the glass panels, ‘ordinary’ glass cutting was selected. The artist preferred the ragged, but clear glass edge that results over smoother translucent edge that would result from laser- or waterjet cutting. However, cutting glass in these shapes proved to be a challenge. Normally, plateaus are being carved in an optimal pattern by machine, supplied with cutting oil and also broken by machine, in a fast pace. However, the irregular curved sheets for the Sphinx had to be broken by hand after being carved by machine. Personnel had to be trained specifically to do this properly. Carefully breaking the glass costs a lot of time, otherwise a running crack will leave the applied carve line, and go straight. Breaking glass slowly, on the other hand, causes the cutting oil to dry out too soon. The cutting oil was therefore adjusted to stay fluid longer. Also, additional cutting oil was applied to the carves during the breaking process. 4.3. Construction All together, the glass sheets of the Sphinx provide an unsolvable puzzle. Therefore, all sheets are numbered by layer and position. To obtain the Sphinx shape out of these individual pieces on the building site, a number of vertical wood fiber boards are erected. Their edges have been sawed to follow the Sphinx contour, derived from a digital 3D model. The boards are positioned radially around two center points. In between the boards, working floors have been constructed. The whole building site was covered by a 20 x 15 x 7 m tent so that construction could take place free of weather influences, humidity and contamination. 55 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
The construction procedure was as follows. Adhesive foil is pre-applied to one side of each glass sheet, on the side where it will meet a larger sheet (i.e. the smaller sheet has the foil applied). At the site, all sheets of layer y are initially placed on layer x without removing the protective covering of the adhesive layer. Thus, the right position of each sheet can be determined. Subsequently, markers are used to fix the position of each sheet. Each sheet is then lifted individually, the protective adhesive covering is removed, and the sheet is replaced at the right position using the markers. This process is executed very carefully as sheet can not be removed after it is glued to the adhesive foil. The size of the seams will make it possible to accommodate dimensional deviations, which, due to the cutting process can easily vary between + and -3 mm. Finally, the sculpture is brushed with glass powder (glass grinded to dust). The reason for this is that the edges of the adhesive foil remain sticky and do not solidify. This would attract dirt. The glass powder adheres to the adhesive foil edge and protects it from moisture while simultaneously avoiding contamination. Scaling a 80 cm art piece to a 6 m sculpture introduced a host of expected and unexpected challenges. But it results, finally, in a fascinating landmark for the city of Venlo. 5. References [1] [2]
[3]
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[4] []
Smith, A., Mass Glass Structures, Challenging Glass 2, Delft, the Netherlands, May 2010. Nijsse, R., Glass walls carrying the roof and withstanding the wind load on the façade: Conservatory of the Museum in Dordrecht and Raaks Glass Cube in Haarlem, Challenging Glass 3 (this conference), Delft, the Netherlands, June 2012. NEN-EN 572-2: Glass in Building – Basic soda lime silicate glass products – Part 2: Float glass, July 2004. Wurm, J., Stacking of Glass –Structures and Sculptures, Glass Performance Days, June 2007. AFTC High Performance Tapes, Silver Tape, Industrial 85 serie, Product Information 04.2010.
56 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-57
The Apple Glass Cube: Version 2.0 James O'Callaghan Eckersley O’Callaghan, United Kingdom, [email protected], www.eckersleyocallaghan.com Charles Bostick seele sedak GmbH&Co.KG, Germany, [email protected], www.seele.com This paper describes engineering and fabrication innovation behind the rebuilding of the Apple 5th Avenue Glass Cube in New York City. The original of which was completed in 2006 and as a result of a number of years of glass fabrication and connection innovation, with which the authors have been instrumental, a proposal for a replacement structure embracing all the technology and techniques mastered was enacted. Keywords: Structural Glass, Connections, Lamination, Fabrication innovations
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1. Introduction The subject of the paper is renovation through innovation with structural glass. In 2005 the companies to which the authors are associated were intrinsically involved in the design and construction of a structural glass cube for Apple Inc at their high profile 5th Avenue store location. The design concept at the time was to find an enticing way for people to be encouraged to shop below ground, a retailing challenge. This challenge was addressed with architecture and solved by the architects Bohlin Cywinski Jackson through the proposal of an all glass entrance building so iconic that it would encourage curiosity and hence people to investigate its purpose. Ultimately over the following years the products developed and sold by Apple have been so popular that the original architectural intention has been overtaken by shear demand. However, this does not diminish the success of the structure and the interest it has captured from New Yorkers and tourists alike. 2. Why Over the last five years Apple, EOC and seele sedak have developed a number of design and fabrication technologies as a result of a drive to develop the language of glass within the Apple retail environments. These developments have been both in the fabrication techniques and the methods of connecting glass together. Significantly, the production of much larger panels of glass has led to laminated and tempered panels now being achievable up to 15m x 3.6m. The concept of metallic inserts being laminated in the glass build up has also been advanced further to the extent that more sophisticated details have been developed that facilitate entirely embedded joints. These particular techniques were pursued and partially applied on other projects but it was decided that these advancements in glass technologies would be most notably honed and illustrated should there be an opportunity to rebuild the 5th Avenue glass cube. Hence, it was with 57 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
these concepts in mind that in 2010 both Apple and the architect began to investigate what result these advancements would have on the design of the glass cube. 3. Concept The original concept of a glass cube structure 10m in dimension was unaltered for the revised version. Given the size parameters by which the glass panels are achievable it was concluded that the dimensional split of each side into six could now be done in three. In addition to this the length to which panels could now be fabricated resulted in the need for only one over the height of the cube. Therefore it was possible to reduce the number of panels per side from 18 to 3. Multiplying this theory over the entire cube resulted in reducing the façade and roof glass panels from 109 to 20 in total, less than 20% of the original number required. A significant consequence of the reduced panels is the reduced number of connections required, it being only necessary to have three per vertical joint. This represented a massive reduction in fittings, which when combined with the reduction in panels and subsequent joints resulted in a dramatically more transparent glass structure. The concept was quickly modeled and rendered for presentation and discussion with Apple.
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4. The Decision The compelling model and renderings clearly illustrated that the advancements in glass design and fabrication that Apple have supported over the last 5 years. The crystal clear structure bereft of joints and fittings was a clear demonstration of the original goal of an all glass cube. Ideally if it had been possible when the first cube was conceived it would have been made from only 5 pieces of glass and hence this latest incarnation was drawing closer that that ideal. Apple and the design team deliberated as to whether the original cube should be replaced and this debate called in to question the appropriateness of replacing an already iconic glass structure with one that was to the untrained eye, much the same. There were those who preferred the original because the increased amount of detail defined it more clearly and related it better to the building it sits in front of. Ultimately it came down to the CEO, Steve Jobs, to make the call and his thought process was typically crystal clear. He made the point that if we had shown him the version we could now create when we first designed it in 2005, he would have chosen it back then, so why would he not endorse it now. 5. Existing Conditions The existing conditions were familiar to us having created them in 2005. This was a major advantage when reanalyzing the support structure for the new cube. At the time of the original build we had not anticipated this latest move and as such the structure supporting the cube had been carefully design to accommodate the point loads from 5 fins. The total structural weight of the new cube is actually marginally heavier because the envelope glass is thicker given its larger span between fins. Therefore this combined with the concentration of load from 3 rather than 5 fins caused a slight over stress in the existing steel and a deflection greater than desired for the unbalanced loading conditions. 58 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Apple Glass Cube: Version 2.0
A result of this being that the existing structure had to be reinforced for its new conditions and a more complex approach to supporting the fins and glass panels needed to be devised so as to even out these deflections over the width of the cube glass. 6. Detailed Design and Modeling The structure of the cube is similar in nature to its original relative in that the overall stability of the structure is maintained by the stiffness of the sidewalls. The main difference other than the fewer elements is the fact that the roof now is only two single spanning glass beams rather than a structural grillages as originally devised. The glass fins support the glass roof beams at the front and rear of the cube, with secondary roof beams spanning from the sides and between the primary roof beams (see Figure 1). The roof plate consists of three cold bent laminated panels which achieve the minimum run off for water and maintenance. The roof panels are bent to a subtle but complex two dimensional curve embracing a technique that seele sedak has developed and mastered.
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As with all glass structures beyond the concept design we pay particular attention to the modeling of the connections in order to be confident of their behavior under different loading conditions (see Figure 2). This is typically done by extracting the local conditions from the global modeling in to detailed solid models. These give a more accurate reflection of how the glass, interlayers and fittings interact.
Figure 1: Global Model
Figure 2: Local Connection Model
7. Connection Advancements The reduction of the number of glass units in the cube’s facades meant fewer glass fins – two per side instead of five – which led to fewer façade to fin units connections, which begged the question how could they “disappear” altogether. One of the key reasons why the rebuilding of the cube was considered was the opportunity to demonstrate the connection advancements that we had developed in concept and worked with seele sedak to realize. We were very keen to take the idea of embedded fittings to the next stage whereby they were used structurally and in an façade/building. seele sedak had, by this time, already carried out a lot of testing on laminated inserts and felt confident that the concept of using them to connect planes of glass together would be successful. The challenge was to ensure that they connection of the planes of glass with their respective laminated inserts could be achieved without seeing bolts of screws 59
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
from any visual aspect. We developed a detail that hollowed out the insert allowing a metal tab to rotate info the insert from having been aligned with the vertical joint. The rotation could be done through the joint itself and then once secured could be siliconed over to cover the mechanics of the connection. This detail has worked perfectly and has resulted in there being no fittings on any side of the cube protruding from the face of the glass itself. This adds real magic to the structure and results in perfectly reflective and flat surfaces on each face of the structure (see Figure 3).
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Figure 3: Insert Fitting
Figure 4: Roof Structure
8. Comparison In 2005-2006, Eckersley O’Callaghan structural design and seele sedak designed and built the first glass cube (see Figure 5) – a 10x10x10 meter self supporting all glass structure with laminated glass columns that doubled as vertical beams to take wind load upon which a glass beam roof grid sat, braced by the façade and roof panes against racking and twisting. Fabrication of the laminated columns, beams and façade panes in 2005 stretched the capabilities of glass processing technology in size and quality.
Figure 5: Original Cube Structural Density
Figure 6: New Cube Structural Density
In 2010-2011, Eckersley O’Callaghan structural design and seele sedak were asked to rebuild the glass cube with larger units, fewer columns and beams, per the latest glazing technology (see Figure 6). Between the two cubes, lay 5 years of development during 60
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Apple Glass Cube: Version 2.0
which more than forty all glass structures of all sorts were executed, each project pushing the limits of glass construction a bit farther. The advance in technology can be seen in part in the following comparison of the two glass cubes (see Table 1): Table 1 Building Part
Cube 1
Cube 2
columns
5 per elevation x 4 = 20
2 per elevation x 4 = 8
façade panels (incl. doors)
72
12 + 2 doors + 2 side lights = 16
roof beams
25 @ 3.3m + 10@ 1.6m = 35
2 @ 10m + 7 @ 3.3m = 9
roof panels
36
3
entrance canopy
1
1
Subtotals
Total
109 panels
20 panels
20 fin columns
8 fin columns
35 beams
7 beams
164 glass units
35 glass units
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Less than 22% of the number of glass units were used in the new Cube. This list however does not explain why less units were necessary. Nor does it explain how it was possible to use a lesser number of glass units. Following are the various building parts and their technological advances. 8.1. Larger Façade Panels The original cube had 10m x 10m façades using glass units 6 across and 3 high of 3x SGP laminated glass in approximately 1.66m wide x 3.33m high unit size. When the original cube was fabricated there was no autoclave for laminating glass in lengths of more than around 8.4meters. In addition, the use of smaller panes allowed more movement and less stringent deflection requirements for the overall structure. For the 10m high glass fin columns, the use of an autoclave from an experimental aircraft company where carbon fiber wings were laminated had to be arranged, a not so perfect cobbled manufacturing solution. The reason for the formation of seele sedak in the year 2005 was to fill this manufacturing void. An autoclave specifically made for laminating glass in maximum 12 meter lengths and soon after another autoclave for 15 meters lengths have been the heart of seele sedak from the beginning. Five years of experience laminating all sorts of glass, different interlayers, extra jumbo sizes and extra thick laminations provided the basis for the engineering and fabrication of the Cube 2 oversize façade panels in 3.280m width x 10.30m height. This was a long process of testing, experience in doing oversize laminations, adjusting processes and slowly improving quality, the results of which were a defined process for maximum high quality, almost bubble free, large size laminated glass that eventually was given the brand name, “glascobond”®.
61 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 7: Jumbo glass
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Figure 8: “Woven” glass beam grid
Figure 9: Simple glass beam structure
8.2. Longer, fewer roof beams The structural concept of the first roof was of a “woven” glass beam grid or “grillage” that sat upon the glass fin columns with pin connections leaving the bracing of the cube against parallel racking and twisting to the façades (see Figure 8). The “grillage” was achieved with shorter 3.30m long beams connected to the middle of a traverse beam of similar length with moment stiff connections achieved thru specially milled stainless steel “saddle” connectors. This lent an economy as well as a bit of redundancy providing safety thru many small glass members, no great single spans and little roof load per member - still a monumental achievement at the time to do a 10m span. The new cube actually achieves the span with a simple 10m spanning beam braced laterally at the third points with shorter glass members (see Figure 9). The advance here is the experience in fabricating and having tested a glass beam of this length with the proper end connections that can carry more than 30 square meters of roof area safely.
62 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Apple Glass Cube: Version 2.0
8.3. Larger roof panels On top of the “grillage” glass beam roof structure sat, in six by six rows, 36 laminated glass units, each 1.66m x 1.66m, with corner patch fittings (see Figure 8). What few people realize is that the roof was actually a pyramid with minimal slope in order drain rainwater. A pyramid normally has visible, diagonally running, corners but in the original cube these were made ‘invisible’ by heat bending the units at the diagonals with a fold to create the pyramid. In the new cube the new structural concept and large unit manufacturing capability demanded that there be only three roof units, each approximately 3.3 meters wide and 10.0 meters long (see Figure 9). A heat bent pyramid shape was out of the question due to the units’ size so, cold bent lamination was used to give the roof a domed shape – this means that the panels have a double curved form – a first in that size of unit.
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9. Fabrication The glass units in the New Cube are all larger which means that structurally they have to span more. However the existing steel did not allow much more glass weight, ergo not a lot more glass thickness. So the new glass build up selected was 3x 12mm fully tempered glass as opposed to the original 3x10mm heat-strengthened units. A new tempering oven installed in the early part of 2011 allowed seele sedak for the first time to temper the glass in house allowing better control over the end result. The façade panes at 3.28 meters (!) wide were a bit of a challenge but the real hurdle was the tempering of the outside roof panels that hang over the façade units, just ever so slightly, meaning that they needed to be more than 3.28 meters in width. After trials, the fabricating machines decided the final width would be 3.295 meters. In addition, the lamination of the fittings into the units, as well as keeping the laminated units bubble free and flat, posed problems that eventually thru trial and test were solved. 10. Installation With the development of large glass unit fabrication came the need for large glass installation technology. The first large glass units requiring new expertise in installation were fabricated for the Apple Store in Sydney, Australia. Large size vacuum packs that can handle the dimensions but, also the several tonnes weight of such units were specially designed and made. The installation crews practiced on one of the first 13.5m x 3.05m three times laminated units – picking it up in its horizontal position from an imaginary flat bed truck, raising it and tilting it upright (see Figure 10). Since then, large glass units for facades and fins have been installed in the retail store on Broadway in Manhattan as well as in two stores in Shanghai, one in Hong Kong and a few others. The new Cube presented a challenge in that installation was only allowed at night. Cranes could not be left standing during the day limiting their size – the set up and take down times of a large crane would not allow time for installing glass. In addition the store was not to be closed so that two construction enclosures had to be built – one to the inside and one to the outside, the outside one being operable, opening up its top at night to allow material access by crane only from above (see Figure 11). As usual a “template” scaffold was installed. This has pre-surveyed and positioned guides for all large glass members so each unit, weighing from one to two tonnes, can be simply dropped in place – a necessity when the construction tolerances have to be plus/minus 1 millimeter! During construction, it appeared that we may have been taunting the gods. Right before the first fins were to be installed, there was an earthquake on the East 63 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Coast causing a hasty survey check of the template scaffold to make sure it was still aligned. After a good portion of glass was installed there came tail winds from a hurricane that closed the construction site for a few days and finally, just days before opening, a snow storm dropped the outside temperatures, slowing down silicon jointing work. In the end it all was done, on time, beautifully.
Figure 11: Placement of the large roof units
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Figure 10: Practicing lifting + turning
64 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Apple Glass Cube: Version 2.0
11. Cube Version 2.0 The new Apple store on 5th Avenue was unveiled on November 4th, 2011, after the store that never closes, closed for a day, to a welcome reception (see Figure 12).
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Figure 12: Completed
12. Acknowledgements We would like to thank the people on the project teams at the architects, Cywinski Bowlin Jackson, the seele Group partner in Manhattan, seele Inc., as well as our colleagues at Eckersley O’Callaghan and seele sedak without whom both of the cube structures would not have been possible. It almost goes without saying that Apple Corporation, through their vision, backed with their commitment to excellence, and contributions in time and money as the instigator of both cubes earns our deepest gratitude. The cube has become a symbol of Apple to the point that it is Apple – a well earned badge.
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-67
Future Application of Structural Use of Glass Thomas Henriksen Waagner Biro, [email protected] The structural use of glass has been explored extensively over the last decade, especially with Apple stores where the boundaries for their application have been advanced significantly. This paper reviews the history and also the state of the art in the structural use of glass. The aim of this paper is to discuss a way forward in relation to glass as a structural material, so that future innovations are not driven solely by the ability to produce and laminate large pieces of glass. Future challenges lie in having a unified understanding of glass as a structural material, high-lighting current limitations when designing with structural glass in relation to current codes in different parts of the world. A continued dialogue on the wider applications of structural glass will advance the state-of the art beyond its current range of use.
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Keywords: Glass, code of practice, Residual Stress
1. Introduction Contemporary structural use of glass dates back to the Victorian greenhouses [1], in particular the Bicton greenhouse for it’s minimalistic and transparent structure. The greenhouse was erected in approximately 1830 and is the one of the few preserved structures, where the glass is part of the structural system. The glass is located in between thin steel elements. The interaction between the glass and the steel ensures structural stability. The green house is shaped as a half dome and is then supported to the north by a brick wall. In Figure 1 the Bicton greenhouse viewed from outside and from inside.
Figure 1a, Figure 1b. Bicton green house.
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The many small glass rectangles allow sufficient redundancy in the half dome if some pieces should break. This is one of the reasons why it still remains intact today. The question which arises is; why do similar contemporary glass structures not exist today? One answer could be that these structures were developed based on trial and error, using a very labour intensive construction method. With increased requirements from safety regulations and the necessary detailed documentation of the structural system it has not been possible so far to build similar structures today. For more simple structural systems it has been possible to advance the structural use of glass. This has enabled an increase in the structural use of glass over the last two decades. Early pioneering work in the structural use of glass has been done by Rob Nijsse [2] and Duwhurst MacFarlane [3]. The most significant development is evident in the many Apple flagship stores around the world engineered by Eckersley O’callaghan [4]. Figures 2a and 2b show the Apple glass staircases in Amsterdam and in Hamburg, respectively.
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Figure 2a. Apple store in Hamburg
Figure 2b Apple store in Amsterdam. Photo EOC
One of the greatest challenges which the designer face when realising such glass structures is local building control, and acquiring the required building permits, since the local building control often has limited experience in dealing with structural use of glass. At the same time the lack of a unified code of practice for structural use of glass is also globally recognised. The building controls are therefore often reluctant to give the approval without asking for excessive 1:1 glass tests to be performed. The Apple stores have to some degree helped with this situation since all the stores are situated in a public domain; the performance requirements for the glass structures were more onerous. It is therefore to some extent now easier to convince the building control of a new glass project by referring to existing Apple stores. The presence of other Apple stores, worldwide have ensured meaningful discussion with local building control in that city and that experience forms the main topic of this paper. Is it possible to find a way forward towards a unified global design method for the structural use of glass? This paper will discuss the outstanding issues in terms of stress in the material, safety factors and combinations of loads over different time durations.
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Future Application of Structural Use of Glass
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2. Design methodology for structural use of glass The current design methodology for the structural use of glass is mostly represented by 3 different approaches; American, European and Australian. The American code [5] and the Australian code [6] mainly refer to glass as an infill panel in a primary structural system and currently not intended for the structural use of glass, but in Europe there is no consensus for a Eurocode for glass, as is the case for steel and concrete. A future code of practice for structural use of glass is planned. There exists a draft version for an EN Standard [7] that addresses glass as primary structure; however this standard has not been released in its current version. Widely recognised are the German TRLV [8] and the TRAV [9] for determining the allowable stresses in glass, but again these do not address glass as a primary structural element and refer to infill panels. On this basis it is understandable that building controls have difficulties in accessing structural calculations for structural use of glass, and demand 1:1 testing. It is important to state that it is outside the scope of this paper to critically appraise the approaches in the above mentioned design recommendations, but as stated in section 1, to highlight the remaining issues that need to be addressed to archive a coherent design methodology for the structural use of glass. 2.1. Stresses in heat treated glass Stresses in heat treated glass, toughened (fully tempered) or heat strengthened have in the past been one of the main points for discussion, since the residual compression surface stress (RCSS) in heat treated glass could vary depending on the thickness of the glass, the tempering line, operation of the tempering line and the ambient temperature of the air used in the quench. In the past the recognised quality assessment of the residual stress in a thermally toughened glass was the destructive testing of a 360mm x 1100mm glass sample [10]. Current research by Tallin University of Technology [11], shows that RCSS in a thermally toughened glass may be measured without having to perform a destructive test. This makes it possible to determine the actual RCSS of a heat treated glass pane, and it is then possible to lower the safety factor, which is added to the assumed characteristic RCSS. The safety factor is added to compensate for the uncertainty of the actual RCSS in the heat treated glass today, without measuring the RCSS. It is suggested by the Author to make it mandatory to perform stress check of all glass panels used as primary structural elements, and that the glass panels have the measured residual stress printed on the glass. 2.2. Safety factors for glass Safety factors exist to reduce any risk of material failure and such factors are usually added to the material by reducing the characteristic stress to an allowable design stress. It is common to link the glass codes to the same country’s code of practice, e.g. the prEN 13474 [7] is linked to the Eurocode – Basics of structural design [12]. Designing with glass according to the Eurocode means that a safety factor is added both to the glass, a material safety factor and a similar safety factor is added to the load. The safety factor on the material is necessary because of the determination of the strength of the annealed glass. If the strength of a heat treated glass pane was determined separately from the residual strength then it would probably be possible to reduce the safety factor which is added to the material side of glass. The strength of annealed glass is currently 69 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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the cause of much debate in advancing towards a European structural glass code. The topic has been discussed by Fred Veer [13]. To progress from the issue of the assessment of the strength of annealed glass is the Author of this article suggestion to ignore the annealed strength and allow the glass to work within the RCSS alone. This would, in theory, mean that the surface cracks in the glass would never open, except from accidental loads, which are not accounted for in the assessment of the RCSS, but by laminating several glass plys together. This could be a short term solution to the assessment of the strength for annealed glass in relation to structural design with heat treated glass. With the possibility to measure the exact residual strength of a heat treated glass as mentioned in section 2.1, it would be possible to lower the safety factor currently added to heat treated glass. 2.3. Time dependent strength of the glass The strength of annealed glass is dependent on the time duration of the load. In the most simple cases this is because the surface cracks in the glass open slowly over time and thereby reduce the strength for long term loads [14][15][16]. The time dependent reduction factor for glass can be described by [17]:
kmod
0,663t
1 16
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Where t is the load duration in hours. In the prEN13474 [7] the factor kmod has a maximum value of kmod = 1 and a minimum value of kmod = 0.25. Interestingly enough, the kmod factor does not comply for short term loads, wind gusts under 1.2 sec, blast loads, or impact loads. The corresponding strength of annealed glass for time durations of less than 3 seconds is not determined. Jens Schneider have investigated the strength of glass for impact loads [18], but besides his research work very limited information exists for short term loading with a duration of less than 3 seconds. The time dependent strength of the glass is valid area for debate. If the glass is heat treated the issue of static crack propagation over time can be neglected, since the RCSS prevents the surface cracks from propagating. However, in the case of impact loads the residual strength from the tempering process might not be sufficient to withstand the magnitude of the load and it is necessary to take the additional annealed strength into account. 2.4. Combined loads with different load duration Load combinations of different load duration (wind load, snow load etc.) are normally governed by the code of practice from the different code systems. Usually different safety factors are added to the loads, dependent of which load is the governing load case. For most engineering materials this is not problematic since the strength of the materials are not dependent on the load durations unless it is a dynamic load. For glass; the load durations as mention above have a significant impact on the strength. Therefore it is important to understand how to combine loads of different duration, and at the same time determine the correct corresponding allowable stress in the glass. This topic has been discussed frequently over the last decades and is evident in the different revisions 70 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Future Application of Structural Use of Glass
to prEn 13474 [7]. Mauro Overend [19] suggested in 2010 the use of a stress-history interaction equation. The equation takes into account short term loads, (wind loads), medium term loads, (snow loads), and long term loads, (dead load). This argument is based on the long and medium term loads causing static crack growth in the surface cracks, thereby weakening the glass. In the Cost C13 JM Andersen [20] presented results showed that, loads with different load durations acting together, cannot directly be linked, and that especially glass under wind loads did not have a time dependent reduction in the strength. However it also stipulated that the number of tests were limited, and that further enquires was necessary. It is the author’s opinion that these considerations only apply to annealed glass where no RCSS are in place to force the surface cracks to remain closed. If heat treated glass is used, it can be assumed, for the purposes of design, that the strength is not dependent on the load duration, if the heat treated glass is designed in a way that the residual stress is not overcome in bending. This would ensure that the surface cracks always remain closed. This would be valid for most design cases. But there still exist situations where this design assumption cannot be fulfilled and the additional annealed strength has to be considered. This was the case for the design of the work of art by Olafur Eliasson ‘Your Rainbow Panorama’ in Aarhus, Denmark [21], shown in Figure 3a & 3b.
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Figure 3a and 3b. “Your Rainbow Panorama” Work of Art by Olafur Oliasson, Aarhus, Denmark. Photo SOE.
In this work the glass walls are the primary structural elements. In this instance the issue of combining loads with different load duration became relevant. The local municipality requested that the load bearing glass walls be dimensioned for; self-weight, wind load, snow loads and an impact load according to En12600 [22] acting at the same time. All the loads have different time durations. The sizing of the glass would be possible according to the TRAV [9] if the impact load was not considered. But the coincident impact load adds an additional tensile stress in the glass pane so the allowable stress in the glass is exceeded. Normally in this situation it is necessary to perform a 1:1 test to prove that the glass has sufficient capacity to accommodate the loads with different time durations but it should be possible to design with glass without having to do such tests each time.
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3. Designing with structural use of glass Designing the structural use of glass is challenging given the lack of guidelines or codes of practice. Local building control often follows guidelines that are not up to date compared to the current research for contemporary built glass structures. Besides the necessary structural requirements, the safety aspects of glass structures also need to be considered. This aspect is rarely covered in the guidelines. This is mostly because safety is linked to local governmental building regulations. The topic has been discussed by Stephan Niderehe [23] and Freek Bos [24]. The safety aspect often leads to additional glass layers being added to ensure redundancy in the structure if one layer should fail. Today most glass fins and beams are designed with a minimum of 3 layers of glass where 1 of the 3 layers ensures redundancy in the structure, which means that only 2 layers is necessary structurally. When designing with glass most of the design possibilities are governed by the limitations to the manufacture of glass. Post fracture integrity of glass structures is also important to minimise the risk of failure. Post fracture integrity can be ensured by laminating heat strengthened glass with toughened glass. The difference in breakpatterns will ensure that the panel will be self-supported until temporary measures are in place.
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The size of glazing has long been governed by the maximum dimensions of “Jumbo” sized glass, 6m x 3.21m. This is still the most economical size of glass and any building grid conforming to this size has less waste glass from the cutting process. Additionally most Post-processing plants are only equipped to handle these sizes or smaller. If the sizes are above the standard size of 6m x 3.3m, which is the case in most Apple stores, then far fewer suppliers is available. The overall size of individual glass sheets becomes an issue when considering the control of the continuity of the residual stress in the heattreated glass.
Figure 4a. Police Memorial, Fosters & Partners. London.
Figure 4b. Glass Bench intended for Plantation place.
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If glass with holes and notches are used in structural design it is important to follow the guidelines in terms of edge distance to ensure that that the parts get cooled correctly in the quench. Laminated glass is always used when designing with glass for structural use. But the understanding of the interlayers’ ability to transfer shear loads under different temperatures is not fully covered by any guidelines. Much research has been undertaken in Germany on this topic; the works of Wellershof [25] can be used as a reference for design purposes. The research only covers pvb as an interlayer limited but additional research has been undertaken for Sentry glass interlayer. There are many more aspect which are important to understand when designing for structural use of glass dependent on the application. With lack of extensive experience in the topic it is recommended to undertake a 1:1 test of the glass structure to ensure capacity and the post breakage behaviour.
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4. Conclusion In this paper the current development regarding the structural use of glass has been discussed. A design methodology for the structural use of glass which alone utilizes the residual strength in heat treated glass, has been suggested. This would minimise some of the issues in understanding the brittle behaviour of glass. This, together with a clear redundancy scheme, would enable a code of practice for structural use of glass to be drafted. It is clear that workmanship is still an important issue in maintaining the robustness of glass structures. Also understanding the stress distribution in glass structures, especially when glass elements are mechanically connected via bolted connections, is necessary. The emphasis needs focus on the quality checks of the residual stress in the glass, but as already mentioned will depend on existing equipment capable of reliably measuring this residual stress. It is necessary to conduct further research into understanding the issues mentioned in section 2, to be able to advance towards a comprehensive code of practice. 5. Acknowledgements The Author would like to thank Dr. Stephen Lo and Dr Stephen Morse for reviewing this paper.
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6. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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[25]
Koppelkamm, Stefan, Glasshouses and Wintergardens of the Nineteenth Century, Rizzoli International Publications, INC, NY, USA, 1981. Nijsse, Rob, Glass in Structures. Elements, Concepts, Designs, Birkhäuser, Basel, Switzerland, 2003. Structural use of Glass in Buildings, p 75. , IstructE, Dec 1999 O’Callaghan James. Thinking big with Structural Glass, GPD proceedings 2009, Finland ASTM 1300-9a, Standard practice for determining load resistance for glass in buildings, June 2009. AS 1288-2006, Glass in Buildings-Selection and Installation. Jan 2006 prEN14373-3, June 2008, Glass in building - Determination of the strength of glass panes- Part 3: General method of calculation and determination of strength of glass by testing. TRLV, Techniches Regeln für die Vervendung von linienförmig gelagerten Verglasungen. Techniche Report, Mitteilungen des Deutschen Instituts für Bautechnick, Berlin, 2006 TRAV, Technische Regeln für die Verwendung von absturzsichernden Verglasungen, Fassung Januar 2003. EN12150-1:2000, Glass in buildings - Thermally toughened Soda lime Silicate Safety glass. Anton, J, et al. On the inhomogeneity of Resiudal Stress in Tempered Glass Panels, GPD, Finland, 2011 EN 1991-2005, Action on Structure. Veer, Fred, et Al. The strength of architectural glass, Challenging Glass 1, 2008 Griffith, A.A, The Phenomena of Rapture and flow in Solids, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of Mathematical or Physical Character, Vol. 221 (1921) pp. 163-198. Charles, R.J. Static fatigue of glass. I, J. Appl Phys., 1958, 29, 1549 Charles, R.J. Static fatigue of glass. II, J. Appl Phys., 1958, 29, 1554 Brown, W.G., A practicable formulation for the strength of glass and its application to large plates, Publication No. NRC 14372, National Research Council of Ottawa, 1971. Schneider, J. ‘Festikeit und Bemessung punktgelagerter Gläser und stossbeanspruchter Gläser“PhD. Thesis, TUDarmstadt, Institut für statik, 2001. Overend, Mauro, Recent development in design methods for glass structures, The Structural Engineer, IStructE-Journal-issue-88, London, UK, 2010. Andresen J.M. et A, Proposal for a Code Calibration Procedure, EU COST C13, Glass and Interactive Building Envelops IOS Press, 2007 Henriksen T: ARoS, Your Rainbow Panorama, .GPD proceedings, Finland, 2009. EN12600:2002, Glass in buildings – Pendulum test – Impact test method and classification for flat glass. S. Niderehe, Glass structures and their structural reliability – a discussion, Challenging Glass 1, 2008 Bos, F, Safety Concepts in Structural Glass Engineering, Towards an Integrated Approach, PhD TUDelft, Dec 2009. Wellershoff, F. Bemessungsschubmodulwerte für Verbundglasscheiben, Stahlbau 76, 2007, Heft 3.
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-75
A Laminated Glass Wall Will Protect Warnemünde From High Water Frank Heyder, Franziska Paulu hpl-Ingenieure, Germany, [email protected] Warnemünde is a former fishing village on the Baltic coast, now part of the city of Rostock. A new flood protection wall is due to be built along a river in an architecturally sensitive inner-city area. Transparent or movable solutions are necessary, while the barrier must withstand water, flotsam, ice and the impact of boats of up to two tons weight. Here the optimum solution is a 4-layer laminated glass wall. The article describes the research required to establish realistic impact loads (via transient-dynamic finite element analysis), the safety concept and the applied design criteria for glass sections.
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Keywords: flood prevention walls, laminated glass, flotsam and boat impact, transient-dynamic finite element analysis
1. Planning objectives Flood protection structures at the Baltic Sea are required to protect against windinduced seasonal flooding rather than tidal floods. The typical flood season is winter. An existing concrete flood protection wall is no longer considered stable or sufficiently high, due to an increase of predicted peak water level. The client brief for the new wall was challenging: The flood barrier must not hinder the current usage of the quay for boat moorings, and must not disturb the view from adjacent houses to the river and vice versa. After a flood warning there is very little time and only a limited workforce available to close temporary openings or to erect mobile walls, and therefore mobile elements must be reduced to a minimum or made fully automatic. All solutions must also function in winter under freezing conditions or after heavy snowfall. There is only a narrow strip of land available for any flood prevention construction between quay and street. The waterfront architecture is of historic interest and must not be spoiled by technical constructions. 2. Feasibility studies, alternatives, comparison The following solutions have been considered: moving walls (flaps, miter gates, elevating walls) as a permanent mechanical solution; removable walls, which are erected only when a storm flood has been forecast, but with a permanent sub construction and coupling points in the pavement; and, finally, rigid walls. All three solutions have drawbacks: moving walls may fail to work in severe winter conditions, and need plenty of maintenance. The removable walls require more time and many workers for erection. Rigid walls are less complex and require comparatively little maintenance, but can greatly disturb the surrounding architecture and block riverside views if not transparent. Thus, the optimum solution is a combination of all these 75
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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alternatives: Rigid concrete for the base, rigid-transparent (glass) in the upper part of the wall where transparency matters most, and mobile walls for openings, giving access to moorings and the quay.
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Figure 1: Proposed solution with a glass-topped wall, left [2]
3. Optimum solution The optimum solution for the flood protection wall is an integrated approach which solves both the technical issues and the objectives for maintaining Warnemünde’s architectural unity. The technical and optical functions go hand in hand: The glass balustrade protects the historic city against high water, while ensuring an unobstructed view in both directions from the small fishing houses to the water. The wide quay is not only designed for mooring, but also creates a new space for tourists and inhabitants – a pedestrian zone at the water’s edge which serves as a small harbour for recreational and fishing boats. The formerly dreary embankment becomes an attractive part of the town. The concrete lower section at the water’s edge is constructed as a sheet pile wall. The upper section is a glass-steel-construction, which not only protects against flooding, but also serves as a transparent balustrade for pedestrians. Gates at various stations offer barrier-free access via stairs or ramps to the lower section.
Figure 2: Future view from the river Alter Strom to the storm flood protection wall [2]
76 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
A Laminated Glass Wall Will Protect Warnemünde From High Water
The laminated glass wall consists of 4 layers: 2 inner layers of heat-strengthened glass (TVG) and 2 outer layer of fully tempered glass (ESG), with 3 layers of foils inbetween. Additional exterior foils create a no-scratch coating. The glass construction is shown in Figure 5. The posts (Figure 3) and the handrail bar (Figure 4) are made of stainless steel, elastically embedded in the concrete construction.
Figure 3: Cross section of lower beam
Figure 4: Handrail design
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Figure 5: Cross section of laminated glass
Figure 6: Cross section of flood protection wall as optimum solution, compared with current situation
77 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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4. Structural design 4.1. Safety Concept The proposed wall is one element of a wider storm flood safety scheme for the entire coastline of Mecklenburg-Vorpommern, and for Rostock-Warnemünde in particular [1,2]. A special safety concept was required for the laminated glass wall due to the special fracture behaviour and stability of glass structures. The concept assumes that when any glass section shows signs of distress, such as cracking, the distressed section will remain watertight for sufficient time to allow a temporary stoplog to be installed. A first step was to determine the behaviour of the laminated glass for typical loads (wind, hydrostatic, flotsam as static force) according to codes of practice to ensure the usual level of building safety. In a second step, a probabilistic risk assessment investigated the probability of glass failure under the impact of larger flotsam and abandoned boats, for which no codes of practice exist. This allowed an estimation of the annual costs for glass replacement and the number of stoplogs and workers required to cope with heavy flooding. The proof of water tightness of broken laminated glass is part of the experiment described in Section 5. 4.2. Loads To calculate the impact loads which the laminated glass walls will have to bear, the effect of insufficiently moored boats striking glass sections was investigated. First, the 100 boats currently moored at the quay were listed and classified. Eight typical categories of boats where modelled in Strand7 FEA-Software to calculate the typical stiffness of the boat hull. The mass was taken from known examples. The average impact velocity and wind loads were calculated using design parameters typical to boat construction. Table 1: Loads of various boat categories Boat category
Stiffness [N/m]
Velocity [m/s]
Mass [kg]
1.8 x 106
2,50
2000
(wood)
2,00
2000
3.5 x 10
2,50
2000
(steel)
2,00
2000
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Heavy boats 1
with build-up without build-up
2
with build-up without build-up
3
with build-up without build-up
7
6
1.0 x 10
2,50
2000
(composite)
2,00
2000
1.8 x 106
2,20
1000
(wood)
1,70
1000
Lighter boats 4
with build-up without build-up
78 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
A Laminated Glass Wall Will Protect Warnemünde From High Water
4.3. Calculation method The numeric simulation of impact was calculated using an FE-model in Strand7. All elements (glass wall, steel posts and bars) are plate elements. The posts are elastically embedded in the wall’s foundation.
Figure 7: Model laminated glass wall with elastic posts in the ground and handrail as crossbar with Impact 1 situation
The calculations were carried out as a nonlinear transient-dynamic FE analysis for a hard impact. The model has three different impact situations:
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x x x
Impact 1: Impact in the centre of the glass section (area 50 cm x 50 cm) Impact 2: Impact at the top of the post Impact 3: Impact in the middle of handrail (crossbar)
Each impact is analysed under the load of all boot categories 1-4 with and without build-up. The analysis of Impact 1 shows the maximal glass stresses, the Impact 2 and 3 the maximal internal forces in the steel sections. The following stress limits for impact loads according to TRAV[4], based on [3] and [6], were used to assess the breaking probability of the glass: RD = 170 N/mm² (ESG) RD = 120 N/mm² (TVG) The 4-layer VSG-glass sections are modelled as isotropic plate elements with full composite effect, acting like a full cross section. This is justified by the extremely short loading time during impact and by the typically low temperatures during winter storm flooding. Wellershoff describes the dependence of G (shear modulus) of the composite interlayer (PVB, SGP) vs. load duration and temperature in [5].
79 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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4.4. Conclusion Glass failure is only associated with impact by a category “boat 2 with build-up”, for which stress limits are exceeded. However, as the number of boats in category “boat 2 with build-up” is limited to 8 % of all boats, there is only a low probability that a wall section will in fact be breached. For all other categories, the loads and corresponding stresses are below critical level and do not result in glass failure. The steel-frame construction resists all kinds of boat impact.
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Figure 8: Glass stress from boat impact (category “boat 2 with build-up”)
Figure 9: Stress on steel elements from boat impact (category “boat 2 with build-up”)
5. Experimental verification In an experiment undertaken at Dresden’s Technical University, Prof. Weller’s team investigated the load bearing capacity and the deformation of broken laminated glass sections under hydrostatic water pressure (1.10 m water column to ground-level glass section) resulting from storm flooding. In the experiment, two different composite constructions were investigated, one with PVB foil and the other with SGP interlayers. During the whole experiment duration of 9 hours, no relevant deformation could be detected, and the two composite constructions did not display any differences in terms of deformation [7]. However, in an additional test with a free falling compact mass, the 80
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
A Laminated Glass Wall Will Protect Warnemünde From High Water
SGP glass turned out to have a significant better resistance against local penetration than the PVB glass.
Figure 10: Water filling of the specimen [7]
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6. Outlook The project is now fully designed and in its authority approval phase. Detailed design and the tender is planned for 2013. The construction phase is scheduled to run from 2014 to 2016. As the pictures show, the Warnemünde flood protection wall is a highly versatile solution, suitable for many locations worldwide with similar design requirements. Hopefully, the Warnemünde project will become a model for the successful application of laminated glass in flood protection walls in visually sensitive inner-city areas.
Figure 11: Future riverside view [2]
81 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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7. Abbreviations Table 2: Abbreviations Abbr.
in UK
in USA
in Germany
Float
Float glass
Annealed glass (AN)
Floatglas Spiegelglas
TVG
Heat-strengthened glass
Heat-strengthened glass (HS)
teilvorgespanntes Glas (TVG)
ESG
Toughened glass
Fully tempered glass(FT)
Einscheiben-Sicherheitsglas (ESG)
ESG-H
toughened glass with heat-soak test
fully tempered glass with heat soak test
Einscheiben-Sicherheitsglas mit Heißlagerungstest
PVB
Polyvinyl butyral
Polyvinyl butyral
Polyvinylbutyral
SGP
Sentry glas (plus)
Sentry glas ( plus)
Sentry glas (plus)
TRAV Strand7
see reference [4] Finite Element Software package
8. Acknowledgements The project’s client, the Staatliche Amt für Landwirtschaft und Umwelt Mittleres Mecklenburg, Dezernatsgruppe Küste, was fully confident that the glass wall would prove to be the right solution for the project, long before the laboratory tests had been carried out by TU Dresden, Institut für Baukonstruktionen. The authors are grateful to both these institutes for their confidence and professional advice. 9. References [1]
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[2]
[3] [4] [5] [6] [7]
Regelwerk Küstenschutz Mecklenburg-Vorpommern, Übersichtsheft, published by Ministerium für Landwirtschaft, Umwelt und Verbraucherschutz, Schwerin, Germany, 2009. Sturmflutschutz Warnemünde, Alter Strom, Süd, folder, published by Staatliches Amt für Landwirtschaft und Umwelt Mittleres Mecklenburg, www.sturmflutschutz-warnemuende.de, Rostock, Germany, 2010. Rück, R, Voelker, G.E.: Untersuchung von 4-seitig linienförmig gelagerten Scheiben bei Stoßbelastung, Stuttgart, Germany, 1999. Technische Regeln für die Verwendung von linienförmig gelagerten Verglasungen (TRLV), German code of practice, 2006 Wellershoff, Frank: Bemessungsschubmodulwerte für Verbundglasscheiben, in: Stahlbau 76 (3/2007), p. 177ff, Berlin, Germany, 2007. Wörner, J.-D, Schneider, Jens: Abschlußbericht zur experimentellen und rechnerischen Bestimmung der dynamischen Belastung von Verglasungen durch weichen Stoß, Darmstadt, Germany, 2000. TU Dresden, Fakultät Bauingenieurwesen, Institut für Bauingenieurwesen, Prof. Dr.-Ing. Bernhard Weller: Prüfbericht Nr. 2010/246 Bauvorhaben: Sturmflutschutz Rostock-Warnemünde, Bauteil: Sturmflutschutzwand aus Glas; Prüfung: Experimenteller Nachweis unter statischem Wasserdruck, (10.12.2010).
82 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-83
Lincoln Center Canopies - Performance in Glass Jan Knippers, Jochen Riederer, Matthias Oppe Knippers Helbig Advanced Engineering, Germany, [email protected]
This paper concerns two cantilevering steel-glass structures recently built in New York, USA. Each structure consists of two outward tilting primary steel beams with a length of 27m, a central column, and a glass surface providing lateral stability and weather protection. Twelve panels of four-layer laminated safety glass with dimensions of 2,3×4,4m are connected to the underside of the beams. The glass panels act as the only bracing system of the structure; no additional bracing is required. The connection between glass and steel is made by custom-built point fittings with four fittings per glass panel connected by a two-part injection mortar. At the column kink a ‘glass knee’ of two frameless four-layer laminated safety glass panels is used for even load distribution. Keywords: glass structure, structural glazing, SGP-interlayer, canopy, roof, cantilever, steel-glass-structure, New York
David H. Koch Theater
Josie Robertson Plaza
Canopy I
Avery Fisher Hall
Canopy II
W63rd St
Columbus Ave
W65th Street
Vivian Beaumont Theater
W62nd Street
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1. General Introduction The Lincoln Center for the Performing Arts was built in the 1950s and is the most important cultural venue in New York. As part of a renewal of the whole complex, the architects Diller Scofidio + Renfro of New York designed the new Josie Robertson Plaza and the entrance from Columbus Avenue / Broadway (Fig. 1).
ay adw Bro
Dante Park
Figure 1: Plan View ´Lincoln Center´
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The architects developed two large cantilevering glass canopies to provide weather protection for the visitors arriving from Broadway streetside. The two structures each consist of two 27m long hollow section steel beams that cantilever 12m towards the street and rest on two steel columns. The glass panels are connected to the underside of the beams to provide lateral stability to the system. This made it possible to construct the canopies without any additional bracing elements. The steel columns are also linked together by two glass panes, the ‘glass knees’ at the column kink. Due to this sculptural geometry a distinctive and at the same time light and transparent structure has been developed (Fig. 2).
Figure 2: Canopies and Lincoln Center, New York (Photo: Keller Fotografie)
2. Construction The two canopies comprise of two slightly tilting 27m long welded steel hollow sections. They are fixed to the existing buildings by a circular hollow cross beam at one end. Together with two supporting column legs the structure rests on these four points. The beams cantilever out with a length of 11,6m (Fig. 3) towards the adjacent street. Twelve glass panels with dimensions of 2,3×4,4m are connected to the underside of the beams. The point fittings connecting the panels to the steel beams were developed using high strength steel. In order to enable correct load transfer between the glass panels and the steel structure a two-part injection mortar was used to rigidly connect the glass to the steel point fitting. During the development of the structure it was therefore possible to eliminate any additional horizontal bracing system apart from the glass panels. Each panel has a slight incline for drainage of the roof surface without requiring an additional gutter. Due to the fact that each steel beam is slightly tilted and also not parallel to each other, each single point fitting had to be custom built. A central steel column built of two welded hollow steel sections supports the roof of the canopy. The steel column has 84
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Lincoln Center Canopies – Performance in Glass
a kink that creates a Y-shape in elevation. The column is founded on the basement level, supports a pedestrian ramp, the roof, and has a total height of 8m.
Figure 3: Canopy Avery Fisher Hall (Photo: Keller Fotografie)
The two column legs are connected at approximately mid-height to allow for an even horizontal load distribution. This connection is situated at the kink and uses two structural laminated glass panels.
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3. Glass Supporting Steel 3.1. Structural system and Development of details The structure was developed in close cooperation between the structural engineer, the construction company, and the architects and client. The overall concept was progressed in several stages, beginning with the development of the structural glazing and proceeding to the detailed design of the point fittings and the connection detail between the beams and columns. By including local key decision maker a very commanding time schedule could successfully be achieved. 3.2. Design Criteria The canopies were designed using regular load cases such as snow and wind loading. Wind tunnel tests with two different models had to be performed due to the extensive cantilever and the unusual design. For the determination of the local characteristic wind speeds a surrounding area model was used, with adjacent buildings modelled in 1:350 scale (Fig. 4a). A second model built at a larger scale (Fig. 4b) helped determine the pressure distribution on the roof surface and the steel structure.
85 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 4a and b: Wind tunnel test - 1:350 Context Model- and 1:60 Detail model (Photos: Wacker Ingenieure)
With this analysis the static and dynamic effects of the wind loads could be correctly determined. The canopies are also designed for maintenance loading. Additionally, a temperature load case was applied in the structural calculations to account for variable heating of the dark steel beams and the transparent roof surface, as well as the varying coefficients of thermal expansion of the different materials. 3.3. Steel Structure The two main criteria for the geometry and detailing of the steel structure (Fig. 5 and 6) were to create a sculptural but simple structure where the beams rest on the columns without any visible connection details, and to connect the various steel members using bolted connections to prevent any site welding due to cost reasons. These goals were achieved using countersunk screws or providing steel pockets at the connection details. After construction the details were covered, sealed and painted. The beams and columns are welded hollow box sections prefabricated as variable depth custom members.
27,24 m 11,63 m
15,61 m
3
2
6
3,54 m
5
1 existing concrete structure 2 steel girder 3 suspended glass 4 pedestrian ramp 5 steel column 6 glass knee
Figure 5: Structure - Elevations
86 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
7,95 m
4
4,41 m
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1
Lincoln Center Canopies – Performance in Glass 27,24 m 11,63 m
15,61 m
4,42 m
1,41 m
2,33 m
Figure 6: Structure – Plan View
The slightly tilted primary beams are rectangular hollow sections that vary in depth from 300×55mm to 700×180mm. The sections have flange thicknesses of 50mm and web thicknesses of 10-25mm. The two column legs are also variable depth custom profiles using steel plates of 460×185mm at the column foot and 800×185mm at the column head. The heavy plate thicknesses of 40mm for the columns were determined using dynamic analysis of the overall structure. The structure is designed to American steel codes. 3.4. Suspended Roof Diaphragm The roof surface consists of twelve planar glass panels with dimensions of 2324×4420mm. The laminated safety glass consists of three 15mm thick upper and one 8mm thick lower fully tempered glass panes. The panes are laminated together using a 1,52mm thick Sentry Glass Plus (SGP) laminating foil.
1
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4420mm
2
2324 mm 1 point fitting 2 glass cutout at column
Figure 7: Top view glass panel with four point fittings / Detail – Analysis model – stress distribution (Figure: LFK Ingenieure)
The lowest panel has a silkscreen dot pattern for sun protection. The two glass panels next to the columns are cut-out to allow the columns to run through the roof surface. Each glass panel is connected by four point fittings. Four holes are drilled through the glass at each fitting with a diameter of 46mm (Fig. 7 left). Each glass panel weighs roughly 1,5 tonnes. After the structure is carefully erected to avoid any lock-in forces in the elements, the gap between the glass panel and the connecting bolt is grouted using injection mortar Hilti Hit HY 70. The grout allows the transfer of horizontal forces 87
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between the steel beam and the glass panels. The analysis of the glass panels used linear-elastic finite element methods. For this a volumetric model with three 15mm layers and a 1,52mm SGP- interlayer was constructed. (Fig 7 right) The lower 8mm glass pane is applied as self-weight only because it is not directly connected to the point fitting and therefore does not provide any load bearing function. For the SGP- interlayer the applied shear modulus depends on the loading duration (see Table 1). Table 1: Consideration of material properties SGP-interlayer Loading Duration, Load Case
Shear modulus SGP interlayer [MPa]
G, long, self-weight
2
G, long, snow
15
G, short, wind
80
The load combinations were derived from common loadings such as self-weight, snow, wind, temperature and live load, and also from earthquake loading. Additionally the restraint forces due to lateral stability are applied as point forces within the glass hole. Finally, additional accidental load cases assuming a broken upper or lower glass pane were investigated. The analysis was undertaken in accordance to American Standard ASTM E 1300-04 [1]. For the accidental load combinations the permissible stress of the glass panes was increased by 50%. 3.5. Glass Knee The so-called “glass knee” connects the two steel column legs to create one composite steel-glass column (Fig. 8).
2
314 mm
2
3
800 mm
1
314 mm
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4
185mm
236 mm
185mm
1 glass knee LG - 4x12mm FT 2 pin 3 steel column 4 continuous support - injection mortar
1 3
394 mm
Figure 8: Detail - Glass Knee (Figure: seele GmbH)
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Lincoln Center Canopies – Performance in Glass
It consists of two coupling glass panels with dimensions of 311×800mm. The build-up of the glass is derived from the maximum moment induced by the column legs. Each glass panel comprises of laminated safety glass with four 12mm fully tempered glass panes, each connected by an intermediate 1,52mm SGP-interlayer. The composite action between the column legs and the glass panes is provided by connecting the glass to the legs using four corner bolts as point fixings. Additionally a partial line support in the glass corners is provided through injecting mortar in these locations. 3.6. Point Fittings The point fitting was developed in close cooperation with Seele Sedak GmbH with the goal to achieve an even and smooth underside of the roof without any protruding point fitting or bolts (Fig. 9). Therefore, each point fitting is embedded within the lower glass pane of 8mm and covered by a cover plate. The adjacent bore holes are always linked by one point fitting. The detail is very important for the overall structural behavior it has to accommodate loads due to the bracing system as well as lock-in loads due to the varying thermal expansion of the materials glass and steel. Each point fitting was custom-built due to the variable geometry. To allow for a slim and elegant detail high strength stainless steel type 1.4462 was used. 1
2 7
5
4
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3
1 steel girder 2 point fitting 3 pin Ø 40mm 4 silicone sleeve 5 laminated glass 3x15mm FT + 8mm FT 6 cover plate 7 injection mortar Hilti HIT HY 70
6
Figure 9: Point Fitting – Vertical Section (Figure: seele GmbH)
The canopies are laterally restrained by the active connection between glass pane and steel structure. However, all loads could not be transferred if the connection would have been completely rigid. Therefore the detail was developed in an iterative process. First the glass panes were mounted without introducing any constraint forces and grouting took place only after all glass panes were in place. By doing so, the constraint forces due to self-weight were eliminated. In a second step a system was developed that provided enough stability for the structure while keeping the restraint forces in an acceptable limit. Silicone bushings of 2mm thickness where placed around each fixing 89
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steel bolt in the glass hole. These act as springs in the structural system. Additionally various bolt diameters and the effects on the structure were investigated. By selecting the correct bolt diameter and silicon bushing material with the proper hardness the forces from all load combinations that have to be transferred by the glass could be determined. Finally a dynamic analysis on the overall structural system was performed to determine the effect of the eigenvalues on the applied wind loading. The steel-glasssystem was optimised in various iterative steps and the assumptions verified by material tests for the silicone bushing (Tab. 2). Table 2: Lateral Stability System System
Spring stiffness Silicone bushing [kN/mm]
Diameter Bolt d [mm]
Eigenvalues System f [Hz]
Max. Force FK [kN]
Model 1
10
20
1,2
0,3
Model 2
10
40
1,3
1,5
Model 3
100
20
1,6
14
Model 4
100
40
1,9
19
Sleeve 2mm, 80 Shore
44 / 941
40
1,7
17
1
upper and lower bound of the measured silicone bush stiffness
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After the final system with a 2mm thick silicone bushing of shore hardness 80 was chosen, the structural system was checked again with an upper and lower bound for the spring stiffness. This took into account the varying bush hardness due to temperature difference and the slip between the bush and the steel bolt. 3.7. Performance Criteria The beams were pre-cambered to minimise the deflection of serviceability loading. The self-weight deflections at the cantilever are approximately 60mm vertical and 95mm horizontal. Thus, the beams were fabricated using stencil plates. The camber in longitudinal beam direction was constructed by partial heating. Due to the tilted shape of the beams this had to be performed in three-dimensions for the vertical and horizontal direction. 4. Fabrication and Erection 4.1. Fabrication Tolerances The general construction tolerances of +/- 3 to 5 mm for steel structures had to be exceeded significantly due to architectural demands for the appearance of the cantilever structure. A tolerance limit of +/- 1,5mm was established for the steel structure. For the glass panes, the steel bolts of the point fittings had to be placed exactly so that the silicone bush could be fitted and the injection mortar could achieve a minimum thickness of 3mm.
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4.2. Shipping and Erection Shipping and construction of the structure was been a logistical challenge (Fig. 10). The whole structure with an overall weight of 40 tonnes for each canopy had to be prefabricated in Europe, transported to North America by ship, and driven to Manhattan in the heart of New York by heavy goods transport. For this the steel structure was prefabricated in two pieces. One piece consisted of the columns including the premounted glass knee. The second piece consisted of the complete steel roof structure. On site the two pieces were connected at the column head. Because of the large prefabricated elements the construction time could be considerably shortened to keep interruption of the traffic to a minimum.
Figure 10: Shipping of steel structure (Photo: seele GmbH)
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5. Credits x x x x x x x x
Client: Lincoln Center for the Performing Arts, Inc., New York, USA Architect: Diller Scofidio + Renfro, New York, USA Conceptual Design: Dewhurst Macfarlane, New York, USA Design Development- and Construction Documents: Knippers Helbig GmbH, Stuttgart, Germany Glass Design: Knippers Helbig GmbH, Stuttgart with LFK Ingenieure GmbH, Lauffen, Germany Windtunnel Tests: Wacker Ingenieure, Birkenfeld Fabrication and Erection: Seele Sedak GmbH & Co. KG, Gersthofen, Germany Completion: 12.2009
6. References [1]
ASTM International: ASTM E 1300-04: Standard Practice for Determining Load Resistance of Glass in Buildings, 2004
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-93
Project for the Eiffel Tower: Constructive Geometry Nicolas Leduc, Jacques Raynaud, Niccolo Baldassini RFR, France, www.rfr-group.com, [email protected], [email protected], [email protected] The three pavilion facades for the renovation of the Eiffel Tower’s first floor constitute a new challenge in the field of transparent skins with free forms: this smooth double curved surface adapts to the high-performance thermal constraints of a of a unique public interior space. In avoiding the standard facetted solution, the developed project retains the full integrity of the initial Architectural proposal while guaranteeing economic feasibility. Thanks to the optimization of a parametric model, the variable double-curved surface of the transparent skin can be approximated from a quadrangular cylindrical panel surface. This process implies zero torsion at structural nodes and permits the fabrication of structural elements from developable curved sheets by welding thus enabling a standard compact detail. Keywords: Eiffel Tower, Cylindrization, Discretization, Freeform geometry, Geometrical optimization
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1. Project introduction For the third time since its construction, the first floor of the Eiffel Tower will undergo renovation. The competition organized by the SETE (Eiffel Tower Operating Company) was won by a partnership led by the architecture agency Moatti & Rivière and the general contractor BATEG by providing an appropriate response to current uses, while offering a new way of experiencing the tower’s particular space and emptiness.
Figure 1: Renovation project of the Eiffel Tower’s first floor
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The project is the planned replacement of the Gustave Eiffel and Ferrié pavilions with two new pavilions housing an auditorium, a shop and exhibition spaces along with the façade renovation of ‘restaurant 58’ to render this harmonious with the new pavilions. The three lifts which give access to the first floor will be equipped with new shelters. Visitors will be able to experience the 57 meters of void under their feet with a 1.5metre wide glazed floor which is to run around the perimeter of the centre of the tower. This experience will be reinforced by a fully glazed 2.5-metre-high balustrade inclined towards the void. All of the new structures echo the Eiffel Tower geometry in that the façades of the pavilions and shelters as well as the balustrades follow the inclined direction of the columns. This distorsion is particularly tangible for the façades of the pavilions which are oriented towards the central floor opening and have a double-curved surface.
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RFR are collaborating with Moatti & Rivière Architects for the technical design of the project’s glass works: glass floors, balustrades, pavilions and shelter façades. In this article we will focus on the design of the main feature of the project: the inclined double curved façades of the two pavilions. Moreover, from the technical point of view, the free geometry of these façades faces a dual challenge from the perspectives of a glazed skin complying with thermal constraints and those of the support structure.
Figure 2: Curved façades of pavilions
2. Morphogenesis The façade design is the result of a process where geometrical optimization is developed according to the architectural intent thus guaranteeing the aesthetic goals aimed for by the architect. In a façade with relatively modest spans, the constructive question of the skin is in the core of the challenge. 2.1. Skin Several constructive strategies of freeform glazed skins have been ruled out. While the fabrication of double-curved panels was rendered impossible due to economic feasibility reasons, the use of flat panels, whether triangular or quadrangular, was deemed inappropriate. This was especially true for a curved surface where the reading of the double curvature was a priority. 94
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Figure 3: Double-curved quadrangular panel
Figure 4: Flat triangular panels
Figure 5: Flat quadrangular panels
Figure 6: Cylindrical quadrangular panels
The adopted solution preserves the curved aspect of the façade while guaranteeing economic feasibility thanks to the use of industrially produced cylindrical panels. Today’s bending machines enable the fabrication of cylindrical panels with variable radii (See §4.1.). This solution implies two types of discontinuity between two consecutive panels: a discontinuity in position and in tangency which can be minimized with geometrical optimization. 2.2. Jointing setting-out The minimization of divergences is a major challenge from an architectural point of view as well as from a technical one (fixation of panel, watertightness, etc.). The orientation of the jointing setting-out along the lines of curvature is minimizing the divergences. Indeed, since generatrixes of cylinders are aligned with the direction of maximum curvature, it is preferable that the jointing layout adopts the same direction in order to reduce the discretization length which can be described as the maximal length of the panel in the generatrixes’ direction.
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If the principal maximum curvature is small, the cylinder orientation and therefore the jointing layout orientation are less constrained, therefore a greater freedom in the jointing layout can be implemented in the most planar zones.
d1
d
a
d2> d1
Figure 7: Divergences implied by cylindrical panels
Figure 8: Influence of the jointing layout orientation in relation with curvature lines
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2.3. Structure The principal curvature directions are also well-adapted to the geometry of curved sheet mullions: the geodesic torsion being null along those curves, the envelope of the tangential planes and the normal surfaces are developable and always perpendicular between them, which permits a much higher level of constructability (See §4.2).
Figure 9: Developable normal surfaces
Figure 10 : Developable tangential surfaces
Figure 11 : Normal & tangential surfaces
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3. Project process Placing a parametric model of the surface which integrates the architectural intention at the heart of the design process creates a synergy between architectural constraints and geometric and technical aspects. The variations of the surface parameters, such as the central rise or the tangency of the upper edge, allow rapid surface modification and the generation of families of solutions.
Figure 12: Central rise parameter
Figure 13 : Tangency parameter
For each set of parameters, the principal curvature lines as well as the corresponding jointing layout are generated. In order to regulate the panels’ dimension, the jointing layout is modified and does not follow exactly the principal curvature lines. This has a very minimal impact on divergences between panels because this decorrelation is operated in the most planar zones.
Figure 14: Example of jointing layouts for three parameter sets
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The choice within this solution matrix is made according to architectural criteria and technical performances (evaluation of divergences, panels’ size, etc.). Thanks to algorithms of global optimization, the radii and positions of cylindrical panels are finally optimized in order to minimize the divergences in position and tangency in adjacent panels (Eigensatz & Schiftner [1]). This optimization process has been carried out with Evolute and is one of the key issues of the European research project which is currently being conjointly pursued by RFR, the University of Vienna and Evolute (IAPP). The research aims at finding solutions of how to build “Architectural Freeform Structures from Single-Curved Panels” [2]. The quality of the output from the first optimization phase is very satisfactory and results in divergences in position of lower than 2mm. This led to a second optimization phase with new architectural constraints: cylinders are re-oriented to concentrate tangency discontinuities according to vertical lines to underline the ascensional character, particular to the Eiffel Tower.
Figure 15: First optimization phase
Figure 16: Smoothing of cylinders according to the vertical direction
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4. Materialisation 4.1. Glass panels The panels are insulated glazed units which are composed of an external toughened laminated sheet for public protection as the glass overhangs the public space and an internal a single sheet of tempered glass. The traditional method for fabricating curved glass is to heat flat float glass in an oven over a heat resistant mould, very often made of steel, and let it bend under gravity loading. This was not appropriate to the project for two reasons: firstly because the geometry of each individual panel requires a specific mould, which is very expensive when there is no repetitivity, and secondly because it is very difficult to create reliable heat treatments of the glass with this bending technique. Glass bending machine techniques are becoming standard practice and are able to bend the glass and provide heat treatments of good quality at the same time. These machines are derived from industrial tempering machines which have been altered in order to 97 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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bend while tempering. Instead of being bent by moulding, the glass is bent via computer controlled mechanisms which include air blowers and rollers. These systems provide good quality tempered bent glass but have two important limitations which are the consequence of their complexity: firstly the bending shape is limited to circular cylinders and secondly the bending direction is fixed. The first limitation has to be controlled by the cylinders’ optimization and the second limitation imposes a panel size constraint which is dependent on the angle between the ruling of the surface and the edges of the panel.
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Figure 17: Traditional bending on a steel mold
Figure 18: Modern bending and tempering machine without mold
4.2. Structure The 8-meter-high façade of the Eiffel pavilion is supported against its perimeter to transfer all loads to the rest of the pavilion or to the existing structure of the Eiffel Tower. Permanent dead loads are mainly transferred by vertically orientated mullions in the central part of the facade and then by cross beams. Mullions are subjected to bending in order to take wind loads. In order to reduce deflections generated by the wind, the base of mullions are rigidly connected to the lower edge beam.
Figure 19: Moment diagram
To maximize the slenderness of the mullions, we chose a rectangular section whose strong inertia is normal to the reference surface and geometric axis follows the curved glass jointing layout. We have previously observed that the normal and the tangential surfaces leaning against a principal curvature line are developable. The orthogonal offset of developable surfaces keeping its developability (Pottmann et al. [3]), the four 98
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sheets of built-up girders are therefore developable: webs are obtained by orthogonal offset of median normal surfaces and flanges by orthogonal offset of median tangential surfaces. The mullion is therefore obtained by the forming of four faces by simple bending without torsion from sheets cut in plan and then assembling by welding. Figure 20 shows the process for a built-up girder whose curvature has deliberately been accentuated.
Figure 20: Tri-dimensional modelization
Figure 21: Unfolding of sheets
Figure 22: Physical model
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4.3. Tightness Main curvature lines have one more interesting feature: normal surfaces leaning against principal curvature lines are not only developable, but also bisectors to two adjacent cylindrical panels. Thanks to this feature, the discretization angle is better distributed on both sides of the mullion. Furthermore, because divergences in position and angle are limited, it is possible to adapt a standard detail despite the geometric complexity of the façade.
Figure 23: Tightness detail on mullion
The pressure plate is fabricated on a principle similar to the one of mullions’ flanges: this is a developable surface formed by bending cut-in-plan sheet without torsion.
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5. Conclusion The refurbishment project for the first floor of the Eiffel Tower which will be inaugurated in 2013 is a successful application of cylindrical discretization principles of double-curved complex forms using double glazing. A construction feasibility approach to the glazing and structural elements helped finalize the jointing setting out thus controlling building costs. Mullions, which are free forms in space, are realized thanks to the assembly of developable surfaces. Panels are portions of cylinders shaped by industrial forming methods. The minimization of the divergences allows the use of ‘off-the-shelf’ glazing fixation products possible.
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This design process, resulting from a technical and productive reflection, intended for a unique public interior space with high-performance thermal constraints, allowed the architectural intentions to become a reality in such a prestigious historical site.
Figure 24: Execution geometry
6. Acknowledgements We would like to thank the teams we worked with for this project, particularly Alain Moatti and Marie-Pierre Guerin at Moatti & Rivière, Alexander Schiftner and Michael Eigensatz at Evolute and Alex Beeputh at RFR. References [1] [2]
[3]
Michael Eigensatz and Alexander Schiftner, Case Studies in Optimization of Glass-panelized Architectural Freeform Designs, Proceedings Glass Performance Days Conference, Finland, 2011. Research on the panelisation of free-form structures by single-curved panels is being carried out by a consortium consisting of Vienna University of Technology, RFR and Evolute, and is funded by the EU through project ARC (IAPP Project 230520). Helmut Pottmann, Andreas Asperl, Michael Hofer, Axel Kilian, Architectural Geometry, Bentley Institute Press, 2007.
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-101
Challenges in the Design, Fabrication and Installation of Glass Structures Comprising of Super Jumbo Glass Sheets Peter Lenk, Harriet Lambert Eckersley O’Callaghan, UK, [email protected] The recent works at Apple Stores in Hamburg, Germany and SoHo, New York, USA have incorporated the installation of new internal glass structures: 12m straight stairs; 10m balustrades forming the atrium perimeter of the upper storey; and 5m bridges. The design of each project elegantly balances structural glass elements with connecting metal fittings through the choice of super jumbo glass panels and inserted laminated connections. An overview of these projects is presented focusing on challenges which have arisen during design, fabrication and installation. These include the global stability and dynamic behavior of the stair and bridge; matching the limited tolerances of large glass panels with movements of existing structure; and dealing with restraints imposed by building authorities. Keywords: Structural Glass, Dynamic Analysis, Super Jumbo Glass Panels, Laminated Fittings
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1. Introduction The new glass structures installed in Hamburg and in SoHo, New York have a similar format. This is apparent in the images of Figures 1a and b. Each flat glass structural element is a single glass panel. The only exception to this is the floor edge guardrail (balustrade) at SoHo, which is divided into two panels between the stairs and bridge.
Figures 1a and b: The new internal glass structures for the Apple Stores in Hamburg and SoHo, New York.
1.1. Stair The glass stringers are the primary structural elements of the stair. They span as beams between the lower and upper floor levels. The glass stringers comprise of five sheets of 12mm thick, flat, fully tempered glass, laminated with DuPont™ SentryGlas® interlayers. They measure approximately 12m in length and 1.6m in height. The stringer 101
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supports at lower floor level are hidden within the floor build-up. They are vertically supported on bearing blocks and laterally supported between mild steel plates. The stringer supports at upper floor level are partially visible and partially hidden. They are visibly supported on two full-penetration bolts. These connect to hidden rocking brackets which provide vertical support and out-of-plane rotational stiffness. Glass treads span 2.3m between stringers as simply supported beams. The treads and landings comprise of five sheets of flat glass, laminated with DuPont™ SentryGlas® interlayers. The treads are 8mm / 8mm / 19mm / 8mm / 8mm all annealed to allow postlamination polishing for a crisp edge. Each handrail connects to each stringer at eight or nine locations and continues beyond the stringer to connect to the main structure on the lower floor and to balustrade elements on the upper floor. Connections in glass elements use metal alloy components and resin.
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Figure 2a, b and c: The bridge, staircase and balustrade of Apple Store Hamburg.
1.2. Bridge The glass guardrails are the primary structural elements of the bridges. They span as simply supported beams, connecting to the main floor edge beams. The guardrail panel supports are similar to the stringer supports at upper floor level. Glass beams span between the guardrails. Three beams are used at Hamburg; whilst only two beams are used at SoHo. The beams connect to the guardrails at four points: two points vertically and all four points laterally. The bridge walkway is supported on the main structural floor and the glass beams through direct bearing. Each handrail connects to the bridge guardrail at locations aligned with the beams and continues, connecting to the floor edge guardrail (balustrade) on each side of the bridge. 1.3. Balustrade The balustrade comprises of glass panels point-fixed to the face of the 2nd floor slab. The pairs of point fittings supporting the balustrade panels are located at approximately 1.5m centers and align with the handrail fittings above. All point fittings provide lateral restraint. Two fittings per panel provide vertical restraint.
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2. Glass Design Challenges 2.1. Global structural behavior The first step in the design of the glass elements is to study the global behavior of each glass structure. Global finite element models of each of the glass structures were created. In these models, glass panels are modeled using plate elements with calculated effective thicknesses and connections are modeled using beam elements with rigid links allowing load share between nodes in the region of each fitting. These models are used to gather results related to global behavior, such as structural deflections and reaction forces at connections.
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A significant design challenge was the lateral flexibility of the staircase stringers which arises due to the extensive free-spanning length of these elements. The upper and lower floor level stringer supports are designed with some lateral rigidity to increase the stiffness of the system. Despite this, the lateral stiffness of the system remains inadequate if all glass-glass connections are designed with full rotational releases. Several structural systems were investigated to address this. The addition of diagonal bracing rods below tread level and the addition of vertical risers between treads were both considered. Both of these approaches are effective in increasing the lateral stiffness. However, both were rejected by the client on aesthetic grounds. Designing the treads as fixed struts between stringer panels (forming a Vierendeel truss) is very effective in increasing the lateral stiffness. However, stress concentrations develop in the glass elements at the rigid connections which are too high for a glass element, of reasonable thickness, to resist. The approach which offered the best solution was to design the tread connections as semi-rigid and to increase the thickness of the stringer panels. The design of connections is controlled to achieve an optimum balance between the lateral stiffness of the system and the magnitude of stress in the glass. The design of the connections also accounts for manufacturing accuracies and installation tolerances. In the bridge, a lateral stability structural system is used which is similar to the staircase, as described above. The shorter span and horizontal form of the bridge (with a single continuous walkway panel) means that it is inherently stiffer laterally than the staircase. The bridge guardrails are thinner in build-up than the staircase stringers. 2.2. Connection design The next step in the design of the glass elements is to study the local behavior of the glass and fittings in the region of glass-glass and glass-structure connections. Having discussed some aspects of the connection design in the above section, it is apparent that the global design and local design stages are not entirely independent. The two processes interact and iterations in the design are required. Detailed local finite element analysis models are used. These use three-dimensional brick elements and cover a region of approximately 300mm in all directions from the center of the connection being investigated. All of the fittings in these projects are innovative designs; having evolved from the fitting designs used in previous Apple Stores; they are used for the first time in these projects. The majority of the fittings used are laminated insert fittings: such as at the connection between the bridge beams and bridge guardrails. Some fittings use throughbolts and rocking bracket bearings; such as at upper floor level staircase stringer 103 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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connections. Several design challenges were faced at this stage. Two are presented below which relate to the magnitude of forces transferred: firstly, at the bridge beam to bridge guardrail fittings; and secondly, at the upper floor staircase stringer connections.
Figures 3a and b: The bridge beam to guardrail laminated insert fitting: vertical and horizontal sections
Figure 4: Local FEA stringer connection model - bolt hole stress contour plot.
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The bridge beams connect to the guardrails via two laminated insert fittings at each end. These fittings penetrate two plies of the three-ply laminated glass guardrails, and continue into the central ply of the five-ply laminated glass beams. See figures 3a and b. One fitting per pair transfers vertical and horizontal loads, whilst the other fitting only transfers horizontal loads. At SoHo, the bridge has two beams. The loads transferred in each fitting for the SoHo bridge are easily accommodated by the glass. However, the stress developed in some fitting components is close to design capacity. To carry out an accurate analysis of these components it is necessary to account for non-linear material behavior, allowing for plastic deformation of some metal parts. It was decided that physical testing of the fitting is the most appropriate design assessment method for these components. Two fitting specimens, manufactured by TriPyramid Structures, Inc. were tested. They were fixed to mild steel plates in a testing rig. A shear force across the fitting was increased in steps until breakage. The minimum breakage load was found to be 54.5kN. This is 3.7 times greater than the applied load. The connection at the top of the staircase transfers high reaction loads. Unfortunately, the capacity of the minimalistic and neat laminated insert fitting is insufficient at this location. The use of through-bolts allows for more uniform distribution of load through the element thickness, reducing peak stresses. By connecting to a hidden rocking bracket, load-share between two through-bolts is achieved. Analyses accounted for the possibility of the breakage of both outer glass plies and for the possibility that forces may not distribute evenly between the two bolts – allowing for an extreme case of a 70:30 load share. See figure 4. 2.3. Failsafe Design The failsafe condition is achieved through redundancy within the laminated glass sheets. Failure of an outer ply of any single glass panel will not result in successive failure of the remaining plies. Any glass panel with a broken ply will continue to function under full loading for a short period of time, and will remain in position without causing successive failure under self-weight for a minimum of one day. 104 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 5: Residual capacity test of stair tread
Figure 6: Impact test of balustrade
A series of impact and residual capacity tests were carried out by Labor fur Stahl- und Leichtmetallbau GmbH which confirmed the analytical results. See figures 5 and 6. In the impact tests, the glass is allowed to break but the connections must not fail, the glass element must not be penetrated by the impactor and there is to be no dangerous debris falling from the test specimen. All components passed this series of tests. 2.4. Dynamic Analysis The staircase structure has a relatively low stiffness to mass ratio which means it is likely to have a relatively low natural frequency. There is a significant potential that such a structure will be dynamically excited by human-induced loading. An assessment of the dynamic behavior of the staircase is conducted to ensure that the structure does not trigger human discomfort in normal use. As the stair is more flexible in the lateral direction, this study focuses on the lateral dynamic behavior.
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A significant amount of research into human-induced vibration of structures has been carried out in recent years. Valuable information can be found in [2], [3], [4] and [8]. From these resources, the following can be stated: x x x x
Human induced loading varies in magnitude and in range of frequencies. According to [1], ‘about 10% of the vertical loading, which is about 4% of pedestrian’s weight, works laterally when people walk’. People ascend and descend staircases at a mean frequency of 2Hz. Major lateral load components are associated with frequencies of 1Hz and 3Hz.
Figure 7: Harmonic load components (Fourier amplitudes) [1]
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In Figure 7, the harmonic load components induced by a 60kg person are presented. This highlights the significance of the two major lateral load components associated with frequencies of 1Hz and 3Hz. A modal analysis was carried out to calculate the natural frequencies of the structure using Strand7 FEA software. A 10% live load mass was applied in addition to the selfweight mass. There is little guidance available on the damping properties of glass structures. This topic is discussed further in [7]. Analyses were carried out with 1% and 5% critical damping to cover a range of values for this fundamental dynamic property. A parametric study was carried out to investigate the sensitivity of the dynamic behavior to variations in connection stiffness. The study concluded that within the limited range of stiffness for the semi-rigid connection design, the variation in dynamic behavior was minor.
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A harmonic analysis was carried out with a lateral 70N force oscillating sinusoidally at mid-span of the stair. This force was identified as appropriate for two 90kg people walking simultaneously on the stair. The results are presented in Figures 8a and b. Distinct peaks in acceleration are apparent at particular frequencies which correspond with the natural frequencies identified during the modal analysis. The maximum acceleration is located at 4m which corresponds with the 1st mode shape.
Figures 8a and b: Results of harmonic analysis. Lateral acceleration of the stringer panel at 1m spaced positions over a frequency range 0Hz to 20Hz for models with (a) 1% damping and (b) 5% damping. Note the difference in magnitude of node accelerations along the vertical axis for the two graphs.
Figures 9a and b: Results of time history analysis. Lateral acceleration of the stringer at 2m-spaced positions (a) at tread level, and (b) at handrail level.
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A time history analysis was carried out for two 90kg people walking simultaneously up and down the stair. Results are presented in figures 9a and b. It is apparent that lateral accelerations at tread level are greater than at handrail level. The maximum peak lateral acceleration experienced by the stair, with 1% critical damping, is 1.7m/s2 at tread level and 0.5 m/s2 at handrail level. This result corresponds well with the harmonic analysis presented in figure 8a. Finite element software incorporates fast Fourier transformation signal post-processing methods providing further information on the dynamic behavior and distribution of energy across the frequency range of the analyzed structure. In figures 10a and b, power spectral density plots are presented which have been post-processed from the results of the time-history analyses presented in figures 9a and b.
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Figures 10a and b: Power spectral density plots processed from figures 8a and b respectively.
A set of reference curves describing the human perception of continuous vibration is presented in [5] see figure 11. Human perception of a vibration depends on its frequency, its acceleration and its direction relative to the human body. In these curves, vibration is rated relative to the vibration at the threshold of human perception. A recommended performance target for indoor bridges is R100% when measured in tension on a tensile-adhesion joint with dimensions as defined in ISO 8339 [8]. The resulting joint design with a bond thickness of minimum 6 mm allows compensation of thermally induced movements and dimensional tolerances between the substrates, which is a necessity for linear structural bonded bearings. However, for adhesively bonded point-fixed bearings, a higher Young’s modulus is desirable to achieve higher stiffness with a smaller bonding area that still allows carrying significant out-of-plane loads [4]. This paper presents experimental data obtained on a Transparent Structural Silicone Adhesive (TSSA), a one-component, heat-curing silicone film adhesive showing high transparency, superior mechanical performance, thermal stability and excellent weatherability. TSSA is provided as pre-manufactured sheets with thicknesses of typically 1 mm. Due to its appealing mechanical properties, point supports for glass 249
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facades are identified as primary target application for the market introduction of this next generation silicone adhesive material. The novel material has been described in more detail in previous papers [9, 10]. The test campaign presented in this paper covers tensile and shear tests for point supports of diameters 20 mm, 50 mm and 80 mm. In total, more than 100 test runs were performed using representative circular point support specimens. Special attention was given to the identification of the load level which leads to a significant transparency change (stress whitening) of the adhesive material. 2. Experimental Procedure 2.1. Test Equipment The tensile and shear tests of the point support specimens up to 10 kN maximum load were performed on an INSTRON series 5566A dual column load frame. The load frame was equipped with a 10 kN load cell and an advanced video extensometer (AVE) using a lens of 55 mm for a field of view of 200 mm. Tests involving loads above 10 kN were performed at the Institute for Lightweight Structures of the University of Munich. 2.2. Test Specimens Test specimens, i.e., circular point support assemblies of diameters 20 mm, 50 mm and 80 mm were prepared by bonding stainless steel buttons with the TSSA (1 mm film thickness prior to compression) to standard (uncoated) float glass coupons in a typical autoclave process used for the production of laminated glass. The following procedure was used for the manufacture of the point-fixing specimens: 1.
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2. 3. 4. 5. 6. 7.
8.
Cleaning of glass and steel surface using Dow Corning® R40 Universal Cleaner; Application of Dow Corning® 92-023 Primer on both glass and steel surfaces; Removal of polyester film cover on one side of the structural silicone film adhesive and placing of the steel button on the film adhesive; Removal of excess film adhesive around the button by cutting; Removal of second polyester cover from the adhesive and placement of steel button with the film adhesive face on the glass substrate; Use of manual load equipment, placing pressure of approximately 0.7 MPa on the button for a short period of time (10 s); Placement of glass vertically with attached buttons in standard autoclave process for laminated glass with the lamination process run at 13 bars and 140 °C for 4 hours; Cutting of glass by water jet to generate individual test specimens.
The above process conditions were chosen primarily based on their suitability to fit into a standard glass lamination process. The point supports made of stainless steel were bonded to glass pieces typically based on a nominal adhesive thickness of 1 mm. In addition, some specimens showed an adhesive thickness of 3 mm allowing the evaluation of film thickness effects (in this case, three layers of TSSA film were laminated together).
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Investigation of Stress-Whitening in Transparent Structural Silicone Adhesive
2.3. Test Procedures A key objective of this test campaign was the identification of the load levels at which a change in the transparency of the adhesive material occurs (stress whitening). Due to the peculiarities of the silicone film adhesive, test set-up and test procedures sometimes differed significantly from conventional tests used for gun-grade RTV silicone sealants. Thus, special fittings and attachments had to be developed and applied in order to allow recording of the behavior of the silicone film adhesive through the glass of the specimen with the help of a web cam. After fixing the specimen in the testing machine and launching the test sequence the web cam was activated. Synchronization between the test result stream and the web cam recording was done later via the identification of the failure event recorded in both media. Figure 1 presents a sketch of the tensile test set-up including a bracket which was designed to be applicable for all point support diameters and the associated load levels and ensuring optical access to the glass side of the test specimen from above.
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Figure 1: Tensile test set-up for monitoring optical characteristics of silicone adhesive (schematic).
Figure 2 presents the bracket tailored to fit the tensile test specimens of various diameters. Due to the expected high loads for the 80 mm point supports, the design was substantiated with respect to strength issues in order to ensure the required load bearing capabilities. The web cam (not shown here) was fixed to the bracket from its top side in order to ensure a constant perspective during the test run. Figure 3 displays a sketch of the shear test set-up. The glass was put in place vertically by an L-shaped support structure allowing optical access.
Figure 2: Tensile test set-up for monitoring optical characteristics of silicone adhesive (photo).
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Figure 3: Shear test set-up for monitoring optical characteristics of silicone adhesive (schematic).
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A photograph of the shear test set-up is shown in Figure 4. The shear load was applied by a fork-like device moved downwards during the test run. The curvature of this forklike pushing device was selected in order to be applicable to all investigated diameters of point supports. In order to minimize the (unwanted) moment due to the out-of-plane offset of the load introduction area, the test set-up is adjusted in such a way as to minimize the distance between fork and glass.
Figure 4: Shear test set-up for monitoring optical characteristics of silicone adhesive (photo).
Tests were performed at room temperatures (approx. 20°C - 25°C) and under typical indoor humidity conditions (approx. 40% r.h.). Use of the video extensometer required the provision of two markers on the specimen. One marker was applied on the point support itself, the other marker was applied on a screw attached to the glass pane as for geometric reasons it was not possible to directly provide markers at the adhesive boundaries.
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Investigation of Stress-Whitening in Transparent Structural Silicone Adhesive
2.4. Determination of Onset of Stress Whitening The onset of the stress whitening was determined in the post-processing of the video streams recorded by the web cam. Figure 5 shows typical whitening patterns that occurred for the TSSA material and Figure 6 shows the earliest signs (onset) of the whitening. This onset of whitening was used to determine the associated load levels.
Figure 5: Typical whitening patterns (shown here for point supports of 80 mm diameter, adhesive thickness of 1 mm (left) and 3 mm (right).
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Figure 6: Local onset of stress whitening.
Figure 7: Determination of whitening point WP and associated load level.
253 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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The procedure used to determine the load at the whitening point is shown in Figure 7. Synchronization between video stream and load data stream was performed with the help of the failure event. The recording speed for the web cam is usually set at 60 frames per second; only for cyclic load schemes this rate was significantly reduced due to the long duration of the test run. 3. Test Results 3.1. Tensile Tests The test series can be partitioned into baseline tests, i.e., tests with monotonous loading and without water immersion; tests with specimens exposed to water immersion (monotonous loading); and tests with specimens exposed to cyclic loading (without water immersion). The load levels and nominal stresses (referring to the nominal diameter of the point support specimens) at which stress whitening was observed are listed below for the various tensile test series. Table 1 presents the results of the tensile tests of point supports of 20 mm diameter and 1 mm adhesive thickness under baseline conditions, i.e., room temperature, monotonous loading and no water immersion. The test series covers ten specimens labeled 20-Z-01 to 20-Z-10.
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Table 1: Whitening point for baseline tensile tests with 20 mm diameter and adhesive thickness of 1 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
1
20-Z-01
657.6
2.09
1
20-Z-02
698.2
2.22
1
20-Z-03
618.0
1.97
1
20-Z-04
606.3
1.93
1
20-Z-05
644.3
2.05
1
20-Z-06
701.1
2.23
1
20-Z-07
489.7
1.56
1
20-Z-08
719.0
2.29
1
20-Z-09
717.9
2.29
1
20-Z-10
669.6
2.13
Max
WP
719.0
2.29
Min
WP
489.7
1.56
Mean Value
WP
652.2
2.08
254 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Investigation of Stress-Whitening in Transparent Structural Silicone Adhesive
Table 2 displays the results of the tensile tests of point supports of 20 mm diameter subjected to room temperature, monotonous loading, and water immersion. After water immersion the specimens were conditioned at room temperature and humidity for 24 hours. The test series covers five specimens labeled 20-Z-W-01 to 20-Z-W-05. Table 3 shows the results of the tensile tests of point supports of 50 mm diameter and 1 mm adhesive thickness under baseline conditions, i.e., room temperature, monotonous loading and no water immersion. The test series covers eight specimens labeled 50-Z-01 to 50-Z-05 and 50-Z-10 to 50-Z-12. In addition, Table 4 presents the results of a test series that was performed under baseline conditions for four specimens of 3 mm adhesive thickness (labeled 50-Z-06 to 50-Z-09). Table 2: Whitening point (in tensile) for 20 mm diameter after water immersion, adhesive thickness of 1 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
1
20-Z-W-01
756,2
2,41
1
20-Z-W-02
770,2
2,45
1
20-Z-W-03
796,2
2,54
1
20-Z-W-04
459,8
1,46
1
20-Z-W-05
622,5
1,98
Max
WP
796,2
2,54
Min
WP
459,8
1,46
Mean Value
WP
681,0
2,17
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Table 3: Whitening point (in tensile) for baseline tests of 50 mm diameter, adhesive thickness 1 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
1
50-Z-01
4,174.50
2.13
50-Z-02
3,089.97
1.57
1
50-Z-03
4,549.42
2.32
1
50-Z-04
4,422.90
2.25
1
50-Z-05
4,049.45
2.06
1
50-Z-10
3,934.89
2.01
1
50-Z-11
3,555.89
1.81
1
50-Z-12
3,837.50
1.96
Max
WP
4,549.42
2.32
Min
WP
3,089.97
1.57
Mean Value
WP
3,951.82
2.07
255 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 4: Whitening point in (tensile) for baseline tests of 50 mm diameter, adhesive thickness of 3 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
3
50-Z-06
3,387.35
1.73
3
50-Z-07
4,037.28
2.06
3
50-Z-08
4,158.00
2.12
3
50-Z-09
3,868.45
1.97
Max
WP
4,158.00
2.12
Min
WP
3,387.35
1.73
Mean Value
WP
3,862.77
1.97
Table 5 presents the results of the tensile tests of point supports of 50 mm diameter under room temperature, monotonous loading and with water immersion. After water immersion the specimens were conditioned in a room climate for 24 hours. The test series covers five specimens labeled 50-Z-W-01 to 50-Z-W-05.
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Table 5: Whitening point (in tensile) for 50 mm diameter after water immersion, adhesive thickness of 1 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
1
50-Z-W-01
3165,7
1,61
1
50-Z-W-02
4740,7
2,42
1
50-Z-W-03
3800,1
1,94
1
50-Z-W-04
4852,8
2,47
1
50-Z-W-05
5011,5
2,55
Max
WP
5.011,46
2,55
Min
WP
3.165,74
1,61
Mean Value
WP
4.314,15
2,20
Table 6 displays the results of the cyclic loading scheme defined by 200 N and 2000 N as lower and upper boundary, respectively, based on three specimens. Table 6: Whitening point (in tensile) for 50 mm diameter after cyclic loading, adhesive thickness of 1 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
1
20-Z-C2-01
4011,48
2,04
1
20-Z-C2-02
4525,42
2,31
1
20-Z-C2-03
4632,00
2,36
Max
WP
4.632,00
2,36
Min
WP
4.011,48
2,04
Mean Value
WP
4.389,63
2,24
256 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Investigation of Stress-Whitening in Transparent Structural Silicone Adhesive
Table 7 shows the results of the tensile tests of point supports of 80 mm diameter and 1 mm adhesive thickness under baseline conditions, i.e., room temperature, monotonous loading and no water immersion. The test series covers four specimens. Table 7: Whitening point (in tensile) for baseline tests of 80 mm diameter, adhesive thickness of 1 mm. TSSA Thickness [mm]
Test No.
Load [N]
Stress [MPa]
1
80-Z-01
6.452,93
1,28
1
80-Z-02
5.773,08
1,15
1
80-Z-03
5.181,47
1,03
1
80-Z-04
3.507,44
0,70
Max
WP
6.452,93
1,28
Min
WP
3.507,44
0,70
Mean Value
WP
5.228,73
1,04
3.2. Shear Tests Table 8 shows the results of the shear tests of point supports of 20 mm diameter point supports subjected to room temperature, monotonous loading and water immersion. After water immersion the specimens were conditioned at room climate for 24 hours. The test series covers five specimens labeled 20-S-W-01 to 20-S-W-05. Table 8: Whitening point (in shear) for 20 mm diameter and adhesive thickness of 1 mm (after water immersion). TSSA Thickness
Test No.
Load [N]
Shear Stress [MPa]
1
20-S-W-01
541,3
1,72
1
20-S-W-02
507,0
1,62
1
20-S-W-03
252,6
0,81
1
20-S-W-04
407,6
1,30
1
20-S-W-05
651,2
2,07
Max
WP
651,2
2,07
Min
WP
252,6
0,81
Mean Value
WP
471,9
1,50
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
[mm]
In contrast to 20 mm point supports, no whitening point could be detected for point supports of 50 mm and 80 mm diameters in shear. Nevertheless the ultimate shear stresses observed for 50 mm and 80 mm point supports were of the same magnitude.
257 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
4. Conclusions The onset of stress whitening in the transparent structural silicone adhesive (TSSA) occurs relatively consistently at around 2 MPa when subjected to tensile loading. Under shear loading, stress whitening was only observed for point supports with 20 mm diameter. For bonded point supports with larger diameter no stress whitening was observed in shear prior to failure. This raises the question whether this behavior depends on the ratio of the diameter of the point support to the thickness of the TSSA layer. Further tests in shear loading with increased adhesive thickness are planned for point supports of 50 mm diameter and larger. Water immersion has a negligible on stress whitening. 5. References Tasche, S., Strahlungshärtende Acrylate im Konstruktiven Glasbau, Ph.D. Thesis, Technische Universität, Dresden, Germany, 2007. [2] Weller, B. and Tasche, S., “Experimental Evaluation of Ultraviolet and Visible Light Curing Acrylates for Use in Glass Structures”, Durability of Building and Construction Sealants and Adhesives, 3rd Volume, A.T. Wolf, Ed., ASTM International , West Conshohocken, PA, USA, 2010, pp. 135-156. [3] Hagl, A., “Bonded Point-Supports: Understanding Today – Optimizing for the Future”, Challenging Glass 2, Conference on Architectural and Structural Applications of Glass, F. Bos and C. Louter, Eds., University of Technology, Faculty of Architecture, Delft, The Netherlands, 2010.. [4] Hagl, A., “Silicone Bonded Point Supports – Behaviour under Cyclic Loading”, Engineered Transparency – International Conference at Glasstec, Düsseldorf, Germany, J. Schneider and B. Weller, Eds., Technical University of Dresden, Dresden, Germany, 2010, pp. 139-148. [5] Parise, C.J., Science and Technology of Glazing Systems, STP1054, ASTM International , West Conshohocken, PA, USA, 1989. [6] ASTM Standard C1401-09a, 2009, “Standard Guide for Structural Sealant Glazing”, Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA, USA. [7] EOTA Recommendation, ETAG 002 Structural sealant glazing systems, Part 1: Supported and unsupported systems, 1999; Part 2: Coated aluminum systems, 2002; Part 3: Thermal breaks, 2003, European Organization for Technical Approvals (EOTA), Brussels, Belgium. [8] ISO Standard 8339, 2005, Building construction - Sealants - Determination of tensile properties (Extension to break), International Standardization Organization (ISO), Geneva. [9] Sitte, S., Brasseur, M.J., Carbary, L.D., and Wolf, A.T., “Preliminary Evaluation of the Mechanical Properties and Durability of Transparent Structural Silicone Adhesive (TSSA) for Point Fixing in Glazing”, Journal of ASTM International, Vol. 8, No. 10, Paper ID JAI104084. [10] Hagl, A., Dieterich, O., Wolf, A.T., and Sitte, S., “Tensile Loading of Silicone Point Supports – Revisited”, Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass, Bos, Louter, Nijsse, Veer (Eds.), TU Delft, June 2012.
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[1]
258 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-259
Designing a Glass Bearing Connection with a Probability to EN1990 CC2 Ron Kruijs Glasimpex Schiedam, Holland, [email protected] Member of TC129WG8, TC250WG3 and the Dutch construction glass workgroup Deutscher Ausschuss für Stahlbau (DAst) [1] published a report about steel-glass connections, Mascha Batinger [2] did her thesis about this subject. In both publications an analytic model for bearing hole connection is presented. To verify this analytic models experiments have been performed. The ultimate tensile strength at the holes in those experiments are usually (almost)lower than the residual stress from the tempering process. Analysing the design of the bearing hole connection of both publications several problems were highlighted. In contrast to the publication the load bearing capacity in this paper is designed from a stress point of view. The acceptable level of stress is related to probability of EN1990.
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Keywords: Glass, bearing hole, EN1990
1. General There are no standards are available for the design of a glass connection. The design has to be based on scientific publications and experiments. The subject of bearing hole connection has been investigated by several authors. This connection has a number of different parameters which have a function in the load capacity. The geometric parameters as well as glass strength (residual part and annealed part) and condition of the hole are important. In the design of the bearing hole connection in this paper the geometric parameters and condition of the hole are as perfect as possible. The residual stress part of the test samples are known. So when the experimental bearing strength is known we can derive the tensile stress. And make a connection to CC probability. 2. Test results of DASt and Thesis Table 1 and 2 present the results of the test from DASt and thesis. The failure load of the test samples in table 1 and 2 can’t be compared. The failure load has a function in sample size and hole position. In this paper the topic is the failure tensile stress. 2.1. Deutscher Ausschüss für stahlbau (DASt) DASt 2/2007 table 4.17.1.4 shows results of the performed tests. The geometric parameters of the hole where diameter 44mm, Hy50/70 ring 5mm and a metal insert size unknown. The results of the test on axial loading are summarise at table 1. Only the results with now residual stress from the tempering process are of interest.
259 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 1: Results test DASt 2/2007 Toughened glass
Failure Load
Residual stress hole
Failure stress
Annealed part
10 mm
40,43 kN
96,00 N/mm2
90,48 N/mm2
5,52 N/mm2
10 mm
49,38 kN
96,00N /mm2
110,51 N/mm2
14,51 N/mm2
10 mm
42,73 kN
85,60 N/mm2
113,25 N/mm2
27,65 N/mm2
50,13 kN
2
2
46.88 N/mm2
10 mm
85,60 N/mm
132,84 N/mm
2.2. Zur bemessung van SL-belasteten anschüssen im konstruktiven glasbau Thesis von Mascha Baitinger [2] Table 8.7 shows results of performed tests. The geometric parameters of the hole were diameter 44mm, Hy70 ring 5mm, 2mm aluminium ring and a bolt M30. The average results of the test on axial loading are summarise at table 2.
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Table 2: Mean results test thesis Mascha Baitinger. Toughened glass
Failure Load
Residual stress hole
Failure stress
Annealed part
10 mm
44,34 kN
96,00 N/mm2
116,36 N/mm2
20,36 N/mm2
10 mm
50,86 kN
96,00 N/mm2
112,98 N/mm2
16,98 N/mm2
10 mm
41,43 kN
85,36 N/mm2
104,39 N/mm2
19,02 N/mm2
2x10 mm
88,59 kN
83,25 N/mm2
99,04 N/mm2
15,76 N/mm2
3x10 mm
141,54 kN
99,84 N/mm2
107,69 N/mm2
7,85 N/mm2
2x15 mm
115,77 kN
87,12 N/mm2
88,02 N/mm2
0,10 N/mm2
2x8 mm
86,02 kN
97,52 N/mm2
120,20 N/mm2
25,88 N/mm2
10 mm
49,03 kN
83,87 N/mm2
109,63 N/mm2
25,86 N/mm2
12 mm
52,81 kN
91,36 N/mm2
118,09 N/mm2
26,73 N/mm2
10 mm
57,33 kN
78,24 N/mm2
73,73 N/mm2
4,51 N/mm2
2.3. Remark The tests are performed with new glass samples. The annealed part of the strength should have an average about 60N/mm2. The average value here is much lower. So a other parameter should be responsible for this phenomenon. 3. Design of the holes It is known that the strength of annealed glass is covered by the condition of the cracks at the high stress region. The maximum stress at a bearing hole connection is positioned on the facet of the hole. For the test performed in this paper we used polish hole . On the facet of the polish holes no cracks are visible (there are cracks only small ones), in contrary to the holes used in [2] and assumable in [1].
260 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Designing a Glass Bearing Connection with a Probability to EN1990 CC2
Figure 1 Polished hole
Figure 2: Normal hole
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4. Design of the insert. Design figure 3 is used in [1] and [2]. The materials used from glass hole to middle are mortal 5mm, aluminum 2mm and bolt. Design figure 4 is used in this paper. The materials used are mortal 10mm, and stainless steel insert. Stainless steel insert size diameter 70mm with tread M16. In this way there is no space left in the bearing connection between bolt and hole in the pane.
Figure 3
Figure 4
5. Load introduction The deformation of the mortal insert during load condition is about 0,5mm. So relative small space between components lead tot asymmetric introduction of load and stress concentration.
261 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
5.1. DASt and Thesis The load introduction by figure 5 is combined with hole design Figure 3. This load introduction will be asymmetric for the following reasons: x x x x
Space between the aluminum insert and the bolt. Displacement in hole positions in steel plates. Small different in hole size. Possibility of stress concentration in mortal because of deformation of aluminum insert.
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Figure 5
5.2. This paper The load introduction figure 6 is combined with figure 4 and 7. This load introduction will be symmetric for the following reasons: x x x
The stainless steel disc has a threat M16. No space between bolt and disc. The stainless steel disc will not deform, no stress concentration will be introduced in the mortal. Injection bolts are used, so displacements in hole positions or differences in hole size will be avoided .
262 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Designing a Glass Bearing Connection with a Probability to EN1990 CC2
Figure 6
Figure 7
6. Experiments produced for this paper Two sets of five samples are produced with a different hole design. The aim is to test two bolts ad a row. The connection between glass and steel plates is made of four bolts M16 10.9 and the connection between steel/steel is made of two bolds M16 10.9.
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6.1. Bearing hole figure 1 All three plates of the laminated are produced with a hole of 90mm. The connection is only bearing. 6.2. Combination of bearing and pretension bolt, hole figure 8. The outer two ply of the laminated plate have a hole of 90mm and the inner plate has an hole of 25mm. The advantage of this system is that an eccentric in the load introduction at the hole is almost impossible. There is a low level of eccentricity because it is not possible to use the injection bold on both site of the connection plates. The bearing connection and the pretension bold load capacity can’t be activated together. The pretension part needs too much displacement.
263 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Figure 8
6.3. First tests The test result of both types were limited by bolt capacity. Both connections failed about 180KN. 6.4. Second test For the second test two bolts M16 were added ad the steel/steel connection. The test result of both types were again limited to bolt capacity. Both connections failed at about 312KN. Meaning that 2 holes at a row using 12mm toughened glass had a bearing capacity of more than 156KN.
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6.5. Third test only figure 8 hole type The aim was to test 2 bold at a row with a symmetric load introduction. We did the following chances. We dismantled one bold and lost the pretension. In this way we had the bearing connection at one hole and introducing an eccentricity. The level of eccentricity is not known. The results are summarized in table 3. Table 3: Results of test for this paper hole type par.6.2 Toughened glass
Failure Load
Residual stress at hole
Failure stress
Annealed part
2x12 mm
268 kN
136,80 N/mm2
184,48 N/mm2
47,68 N/mm2
2x12 mm
267 kN
136,80 N/mm2
183,79 N/mm2
46,99 N/mm2
2x12 mm
221 kN
136,80 N/mm2
153,13 N/mm2
16,33 N/mm2
2x12 mm
233 kN
2
136,80 N/mm
2
160,39 N/mm
23,59 N/mm2
2x12 mm
312 kN
136,80 N/mm2
214,76 N/mm2
77,97 N/mm2
264 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Designing a Glass Bearing Connection with a Probability to EN1990 CC2
The calculated failure stress did not take into account the eccentricity of load introduction. The first two results had a low eccentricity. The next two had a very high eccentricity. The last one had no eccentricity, but did not break. 6.6. Conclusion Compare table 3 with 1 and 2, and you can see that in table 3 the annealed part of the glass strength is more like it would aspect to be. We know that the results are in no way exact but it shows that when using a perfect hole and a symmetric load introduction, the strength of this bearing hole connection is governed by glass strength. When testing bearing hole connections it is important to know the failure stress and the residual stress from the tempering process. The problem of using bearing test results for calculation of bearing capacity is that there is now correction for the parameters that together form glass strength. These parameters are: a) b) c) d) e)
Time-depending of the annealed part Aging of the annealed part The influence of environment on the annealed part The high variation of strength from new annealed glass. The high difference in residual stress from the tempering process between different manufactures.
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So when only bearing results are used in statistics, this can lead to unsafe design.
7. Design to the probability of the EN1990 CC2 Using ultimate stress as a design aid we use the Dutch standard NEN2608 to derive the permitted ultimate stress. The level of ultimate stress in this standard is related to CC2. fmt;u;d
k e u k a u k mod u k sp u fg;k
J m;A
k e u k z u fb;k k sp u fg;k
J m;V
fmt;u;d ultimate stress; factor for edge quality ke = 1; ke factor for size effect ka = 1; ka kmod factor for load duration kmod =0,29 ; ksp factor for the glass surface profile ksp =1; fg;k is the characteristic value of the bending strength fg;k = 45 N/mm2; Jm;A; is the material partial factor Jm;A = 2,0; is the correction factor for hole residual stress kz =0,65 ; kz fb;k is the characteristic value of the residual stress of the tempering proces fg;k = 120 N/mm2 (EN12150); Jm;V is the material partial factor Jm;A =1,2; 265
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 4: Ultimate strength hole. Standard/ product
Residual stress
Kz
Ym;v
Residual stress + annealed part ad hole
Ultimate stress
EN12150/NEN2608
75 N/mm2
0,65
1,2
40,62 + 6,66 N/mm2
47,28 N/mm2
Securipoint minimum
125 N/mm2
0,8
1,0
100 + 6,66 N/mm2
106,66 N/mm2
PaperCC2 testsamples
152,25 N/mm2
0,8
1,0
121,80 + 6,66 N/mm2
128,86 N/mm2
Table 4 shows the different hole strength in relation with the level of residual stress. When using only CE (EN12150) toughened glass the ultimate stress is 47,28N/mm2. Only when higher demands are set for residual stress, in combination with a procedure to control this minimum level of residual stress , higher levels of stress can be accepted. Kz = 0,8 for other that NEN2608 ultimate stress design because of hole position. [3] 8. Conclusion When table 4 is compared to table 3 to 1 you can see the enormous difference between CE ultimate stress and the derivate experimental ultimate stress. Especially the level of residual stress from the tempering process has a significant influence on bearing strength. So when tests are done to derive a bearing strength of a connection. The level of residual stress must be known. The level of residual stress of the toughened glass used on site must, at least, be the same as the level of residual stress measured at the test samples. 9. References Bailinger, Mascha, Zur bemessung von SL-belasteten Anschlüssen in konstructiven DASt,2/2007,Untersuchung von Stah-Glas-Verbindungen im Hinblick auf die Nielsen, Jens Henrik, Tempered Glass bolted connections and related problems.
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[1] [2] [3]
266 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-267
Influence of Various Factors on Mechanical Properties of Adhesive Joint in Glass Structures Klára Machalická, Martina Eliášová CTU in Prague, Faculty of Civil Engineering, Department of Steel and Timber Structures, Czech Republic, [email protected], [email protected] Ability of adhesive connection to distribute stress in uniform manner due to relative large bonding area is a significant advantage in brittle and stress concentration sensitive glass. For the glued joint design there are many aspects which have an essential influence on shear load carrying capacity and behaviour of joint under increasing load. The shear strength of adhesive connection is affected by correct choice of glue for specific joint in the first place, but there are many other important factors which have to be taken into the consideration during adhesive joint design. Research is focused on effect of thickness of adhesive layer, different joining materials including their surface preparation and surface roughness and exposure to environment conditions for several chosen adhesives with different mechanical properties.
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Keywords: Adhesion, Artificial ageing, Glass structures, glued joint, Environmental factors, Shear bonded connection, Thickness of adhesive layer
1. General The contemporary architecture uses widely glass as a structural element due to great advantage of transparency and glass structures are often combined with other materials, too. Adhesive joint is more appropriate way how to make connection in glass structures because of glued joint ability to distribute the loads arising from connection in more uniform manner in comparison to bolted connection. There are other benefits like possibility of joining different and also thinner materials, reduction in weight, easier reaching of composite action of built – up sections, transparency and aesthetical quality. Adhesive connections can be produced chemical resistant, depending on choice of the adhesive. Adhesive layer can act, if it is necessary, also as a sealing. These above mentioned advantages have a practical meaning for designing structures with a glass as a load bearing elements. Thanks to intensive research and development in improving material properties of polymer adhesives in recent years there are many types of glue with different properties. But missing standards or guidelines and lack of data about behaviour of adhesive in particular joint are some of the difficulties, which have to be solved before correct and safe design of adhesive connection.
267 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
1.1. Research experimental program The research is focused on various types of adhesives and different joining materials to examine influence on joint behaviour under increasing shear load and also specific part of research is aimed at environmental and ageing effects. Investigation of adhesive connections deals with elastic adhesives (one-component and two-component polyurethanes), semi-rigid adhesives (two-component acrylic adhesive) and transparent adhesives (UV-curing systems), which can be suitable in case of glass-to-glass bonding. The research covers glass to glass and glass to metal (steel, stainless steel and aluminium) joints with smooth or coarsened glass surface because of adhesion improvement possibility. Adhesives have been applied in two different thicknesses to determine influence on behaviour of the joint. Particular part of the research has been performed for glued connection exposed to environmental conditions - changing temperature (from -20 °C to 80°C), UV-radiation and increased relative humidity at the same cycle of artificial ageing.
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2. Choice of adhesives Adhesives are polymer materials that are consisted of monomer units chained into macromolecules. Chemical composition, molecular structure and cross-linking rate of polymer determine the polymer properties. Adhesives used in glass structures can be divided according to their modules of elasticity and shear modulus into flexible-elastic or rigid systems. 2.1. Flexible adhesives Flexible connection is created by using adhesive with low modulus of elasticity applied in several millimetres thickness. Flexible adhesives (typically silicones or polyurethanes) can be classified according to thermo-mechanical properties like elastomers. Elastomers have low cross-linking rate and thus they can be stretched easily several times their unstretched length and they rapidly return to their original dimensions when the applied stress is removed. Elastomers have low tensile strength (about 1 to 10 MPa) and high elongation at break even more than 350%. Due to low modulus of elasticity they can easy distribute stress in uniform manner. The flexible adhesives are very suitable for linear connections, accepting dynamic loads, damping sound transmission between the components and functioning as a seal. Two flexible adhesives have been selected to the research program – one-component and twocomponent polyurethane. They have higher strength values then silicone and elongation more than 200%, so they are suitable for flexible load-bearing connection of glass and other material. 2.2. Rigid adhesives Adhesives which can be classified according to their thermo-mechanical properties like plastomers (thermosets or thermoplastics) can create rigid connection. Thermosets have, due to their high cross-linked polymer chains, very high strength and low elongation at break. Rigid adhesives (typically epoxy resins or acrylic adhesives) can be differentiated to contact adhesives that require small adhesive thickness (often under 1 mm) and gap-filling adhesives, that are able to perform at thicknesses in excess several millimetres [1], which can be useful for a hybrid structures due to imperfections in flatness of joining materials. Some acrylics adhesives are transparent and cured by UVradiation. After curing they are UV-resistant, which can be benefit for glass structures. 268 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Influence of Various Factors on Mechanical Properties of Adhesive Joint in Glass Structures
Three types of rigid adhesives were chosen to the research - gap filling semi-rigid two – component acrylic adhesive and two types of transparent UV-curing adhesives, which can be suitable in case glass to glass bonding. 3. Adhesion and cohesion The strength of adhesive joint depends on two main factors – adhesion and cohesion. Adhesion is a tendency of certain dissimilar molecules of adhesive and substrate to cling together due to attractive forces. In contrast, cohesion takes place between similar molecules of one material. Strong intermolecular bonds with high degree of crosslinking cause high cohesion strength of adhesive. Strong atomic bridges between glue and substrate make strong adhesive joint. Generally, failure of glued joint can happen by loss of adhesion or by cohesive strength exceeding.
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3.1. Types of adhesive joint failure Shear adhesive connection in glass structure can fail by some of the three main modes or their combination. Firstly, failure can occur as adhesive slip. This is the failure at the adhesive – glass boundary; it is caused by poor adhesion of glue to glass surface, see Fig. 1. Secondly, failure can develop within the adhesive layer by excess shear cohesive strength of glue. This mode of failure can be caused by insufficient cohesion of adhesive, see Fig. 2. Thirdly, some adhesives are stronger than the glass to which they are attached and failure can occur within the glass by exceeding tensile strength of glass. The behaviour and failure mode of the glued joint is dependent on the surface preparation (cleaning, degreasing, primer coating). Adhesion is influenced by materials, which are bonded together, as well as every surface treatment. Etching or sandblasting of glass surface can improve the adhesion but it will reduce the strength of glass. Furthermore, roughened surface can improve adhesion only with sufficiently liquid adhesive. Glue with high viscosity can wet only surface protrusions and this can lead to reduce of bonded area and subsequently to reduce of bond strength, see Fig. 3 [2].
Figure 1: Adhesive failure.
Figure 2: Cohesive failure.
Figure 3: Surface wetting by a) adhesive with high viscosity, b) adhesive with low viscosity
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4. Environmental condition effect to adhesive joint Adhesive bond has to resist the service environmental conditions, which influence strength and durability of joint. Chemical composition and cross-linking rate of polymer affects the environmental resistance of adhesive and joint service time. Mechanical properties of adhesive connection, which depends on adhesive layer itself as well as interface between adhesive and substrate, may deteriorate upon exposure to moisture, UV radiation or temperature range that the connection has to withstand during its service life. 4.1. Glass transition temperature and thermal resistance Thermal resistance of polymer adhesive depends on glass transition temperature Tg. Temperature Tg is way to understanding molecular motion that occurs in polymeric material. The degree of molecular motion affects adhesive and cohesive forces, polymer chain and its structure, cross-linking, molecular weight, brittleness and other polymer properties. At low temperatures, less than Tg, polymer behaves like a solids in which the molecular segments has a moderate and independent motions. If the temperature of polymer is increased, molecules become more flexible and mobile. Transition of polymer from glassy to rubbery state signifies that temperature is close to Tg. If the temperature is raised above Tg, distance between molecular segments is increased and it is accompanied by increasing the specific volume of the polymeric material, [3].
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Glass transition temperature should be above the upper service temperature for high bond strength values. Elastomers have usually low Tg (below freezing) to have low modulus of elasticity, low tensile and shear strength and high elongation at break. Rigid adhesive have usually high Tg to ensure high strength values during common temperatures, but they loss their stiffness and strength if temperature increases. Furthermore, adhesive forces between substrate and glue become weaker during high temperatures, which can cause peeling off adhesive layer from one of the bonded surfaces (adhesive failure). On the contrary, with decreasing temperature contracted bonded materials will cause increasing stiffness of the bonded connection but also adhesive become brittle and the joint is prone to cohesive failure [4]. During repeated temperature changes adhesive layer has to be flexible enough to equalize different elongations of different joining materials. This can be achieved by using flexible and durable adhesive with optimal thickness of layer. 4.2. UV-radiation UV-radiation is a main cause of organic materials damage and in glass structures connection is important choose UV-resistant adhesives, because UV-radiation goes through the glass and can break external layers of adhesive. It can lead to damage of adhesive forces between glass and glue. In case of bonding glass to metal (or nontransparent) structure, there is suitable to protect adhesive layer by glass coatings (primer coating) if adhesive has not sufficient UV-resistance. 4.3. Moisture and water effect Environmental moisture or water can be absorbed into polymer material and cause swelling up of glue. But with decreasing relative humidity moisture can migrate out from polymer material and cause other volume changing. Repeating of this process can 270 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Influence of Various Factors on Mechanical Properties of Adhesive Joint in Glass Structures
lead to worsening adhesive forces. Besides, absorbed moisture in polymer material can migrate to interface between adhesive and substrate and can accumulate at microcavities. This effect can lead to deterioration of adhesive forces and subsequently to adhesive failure. In case of glass-metal bond, environmental humidity can also degrade metal substrate by corrosive attack and consecutively adhesion of whole bonded connection. Furthermore, water often in combination with heat can lead to hydrolysis and cause changes in macromolecular structure of polymer which leads to changes in material properties of polymer. 5. Performed experiments –joint thickness, material and surface treatment effects The first part of experimental analysis for chosen adhesives is focused on aspects influencing adhesion and effect of adhesive layer thickness on behaviour of joint.
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5.1. Experimental setup The small-scale tests, specialized in behaviour of adhesive joint under increasing shear load, were performed according to the scheme in Fig. 4. Different types of adhesives with different mechanical properties were chosen after consulting with SIKA CZ and ProVetro Group affiliated cooperation's partner for Czech Republic. The sphere of interest covers connecting glass with different materials (steel, aluminium, stainless steel, glass) to examine adhesion to these materials. Required adhesion was reached by using certified technologies of surface treatment and by primer coating for some of the adhesives. Glass for specimens was utilized both with smooth glass surface (only cleaned and degreased) and with roughened surface by sandblasting to obtain better adhesion of glue to the glass surface. Elastic and semi-rigid adhesives (one-component, two-component polyurethanes and two-component acrylic adhesive) were applied in 3 and 4 mm thick layer to join glass with metals. For transparent connection glass to glass two types of rigid UV – curing adhesives were chosen, which were applied in 1mm thick adhesive layer. exchangeable middle part from different materials with glued glass specimens adhesive layer float glass
adhesive layer float glass
polyamide setting blocks
Figure 4: Setup of the small-scale shear connection tests: on the left and middle – setup for metal to glass connection, on the right – setup for glass to glass or timber to glass connection
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5.2. Results For every tested adhesive, summarized diagrams were prepared for comparisons of joint types with various materials and glue thickness in one picture, see Fig. 5, 6 and 7. The summarized shear stress-strain relationships show representative curves, which were chosen according to their approaching to average values of results. One-component polyurethane adhesive at all types of specimens reached strength value approximately 4 MPa with elongation at break more then 350%. Two-component polyurethane adhesive achieved strength values approximately 4.5 MPa with elongation at break about 250%. The most of specimens made from both types of polyurethane were broken in cohesive mode of failure. Sandblasting of glass surface has no substantial effect on strength of glued joint by polyurethane adhesives because the cohesive strength of adhesive was achieved also at specimens with smooth glass surface.
3 5
1
1 3
4
2
4 5
2
1...steel + glass (3mm) 2...steel + glass (4mm) Copyright © 2012. IOS Press, Incorporated. All rights reserved.
3...steel + sandblasted glass (3mm) 4...stainless steel + glass (3mm) 5...aluminium + glass (3mm) Figure 5: Shear stress-strain relationship – PU adhesives.
Two-component acrylic adhesive got to the strength value more than approximately 6 MPa with elongation at break 100 – 150%. Failure started predominantly in adhesion manner but part of adhesive layer still behaved cohesively, so the joint was broken by combined adhesive-cohesive failure. From this reason, specimens with sandblasted glass reached up to 20% higher shear strengths than specimens with smooth glass surface and specimens with sandblasted glass was broken only by cohesive failure. Transparent glass to glass specimens achieved strength values approximately 10 – 15 MPa with elongation at break about 50 – 100 %. Difference between specimens without surface roughening (surface was only cleaned and degreased before gluing) and with surface sandblasting is showed at Fig. 6 right. Sandblasting has no essential effect on 272
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Influence of Various Factors on Mechanical Properties of Adhesive Joint in Glass Structures
strength of the glued joint, because the failure of specimens with smooth glass surface was probably broken by glue cohesive failure together with glass rupture.
3
4 5 1...steel + glass (3mm) 1
2...steel + glass (4mm)
6
3...steel + sand-blasted glass (3mm)
2
4...stainless steel + glass (3mm) 5... stainless steel + glass (4mm) 6... aluminium + glass (3mm)
Figure 6: Shear stress-strain relationship – acrylate adhesive.
b
c a a...UV-adhesive 1 (1mm); smooth glass b...UV-adhesive 1 (1mm); sand-blasted glass
d Copyright © 2012. IOS Press, Incorporated. All rights reserved.
c...UV-adhesive 2 (1mm); smooth glass d...UV-adhesive 2 (1mm); sand-blasted glass
Figure 7: Shear stress-strain relationship – UV-curing adhesives.
6. Performed experiments –environmental condition effect The second part of experimental analysis deals with the environmental effects to bonded joint. Moisture, UV-radiation, high and low (frost) temperature effect is in one typical cycle of accelerated ageing. The second series of specimens were prepared for the same adhesives and same bonding materials (substrates) like at the first part of research. Specimens were subjected to laboratory ageing conditions and subsequent there were performed shear tests according the scheme on Fig. 4. Artificial ageing effect was 273
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assessed by naked eye to find out some modifications. Shear tests results (shear strength values and failure mode) were compared for both parts of research. 6.1. Laboratory ageing Typical cycle of artificial ageing, see Fig. 7, comprises eight-hour exposure to UVradiation alternating with demineralised water showers at 20 °C (i.e. weterometer conditions). Afterwards, specimens were subjected to sixteen-hour exposure to high temperature (+80 °C) or low temperature (-20 °C). This part is repeated four times and than cycle is finished by conditioning at (20±2) °C and relative humidity (60±5) %. Whole cycle is repeated nine-times. This whole procedure replaces 5 years in exterior conditions in Czech Republic climate according to Research and Development Timber Institute´s internal regulation for polymer coatings at metal materials. temperature [°C ]
every 20 minutes UV-radiation or water shower (weterometer) increased / decreased temperature without UV-radiation and showers
Conditioning for 64 hours (20°C, 60% rel. humidity)
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time [hour ]
Figure 7: Typical cycle of laboratory ageing.
6.2. Observable modifications caused by ageing There were no significant changes at PU-adhesives observable with the naked eye. Both of PU-adhesives have low UV-resistance, but this problem was solved by primer coating to glass surface. Specimens glued by 2-component acrylate adhesive showed adhesive faults at glass surface and also there were small bubbles and small surface cracks at adhesive layer edge, see Fig. 8. These faults were probably created due to temperature changes which adhesive had to withstand. The adhesive should be thermally stable from -40°C to +80°C according to technical data sheet. But glass transition temperature Tg is around +50°C and it is within the temperature range of laboratory ageing cycle. There is assumption that changes of specific volume when temperature went repeated over the Tg, caused the small bubbles, cracks and adhesion faults in glue. 274
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Influence of Various Factors on Mechanical Properties of Adhesive Joint in Glass Structures
Figure 8: Faults caused by artificial ageing at 2C-acrylate adhesive.
Figure 9: Unsealed specimen from UV-curing adhesive 1.
One type of the UV-curing adhesives was found out like the least ageing resistant adhesive from the selection of glues. All specimens glued by this UV-curing adhesive with smooth glass surface were unsealed spontaneously during artificial ageing. Specimens with this adhesive and roughened surface by sand-blasting had no observable modifications. Because of UV-curing adhesives are UV-resistant after hardening and they are thermal stable to 100 °C with glass transition temperature Tg higher then temperature range of laboratory ageing, there is assumption that adhesion weakening and subsequent pealing off was caused by high relative humidity at weterometer.
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The second type of UV-curing adhesive had also no noticeable changes, which can affect the mechanical properties. But adhesive layer became light yellow, which can be caused by raised relative humidity during accelerated ageing. 6.3. Results of artificial aged specimens Shear test results in stress-strain relationship graphs including comparisons both research parts are showed in Fig. 10, 13 and 14. Continuous line in the graphs marks results of laboratory aged specimens and dashed line provides comparison with results of specimens which were not exposed to ageing. Specimens bonded by 1-component PU adhesive had similar shear strength and strain values like same specimens without ageing effect. 2-component PU adhesive specimens had shear strength values higher than same specimens without ageing. There is assumption that this glue needs longer time for curing than is stated in technical data sheet. Thermal and moisture resistance of these adhesives have been proved. UVresistance was sufficiently solved by black primer coating on glass surface. Cohesive failure mode was observed at majority of specimens. Specimens bonded by two-component acrylic adhesive showed similar shear strength values like specimens without artificial ageing, no negative effect of small bubbles or adhesive faults was observed. Average shear strain values were measured by 15% higher and deformation had more plastic character than deformation at specimens without ageing effect, see picture of broken specimens, Fig 11. Failure predominantly started at adhesive manner like at specimens without ageing but cohesive failure was decisive. 275 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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1 3
3 2
1*
2
3*
3*
2*
1...steel + glass, lab. aged 2... stainless steel + glass, lab. aged 3... aluminium + glass, lab. aged 1*...steel + glass 2*...stainless steel + glass 3*...aluminium + glass Figure 10: Shear stress-strain relationship – laboratory aged PU adhesives.
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2*
Figure 11: Specimen bonded by 2C-acrylate adhesive after shear test.
Figure 12: Specimen bonded by UV-curing adhesive after shear test.
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2* 1...steel + glass, lab. aged
1 1*
2... stainless steel + glass, lab. aged 3... aluminium + glass, lab. aged
3 2 3
1*...steel + glass
*
2*...stainless steel + glass 3*...aluminium + glass
Figure 13: Shear stress-strain relationship – laboratory aged 2C -acrylate adhesive.
Test specimens glued by the first type of UV-curing adhesive with sandblasted glass surface had strength reduced to only about 40% of original value and shear strain was measured by 50% higher. The glue was evaluated like unsuitable for structural bonding, because of unsealing specimens with smooth glass surface and also for unsatisfactory mechanical properties after ageing for roughened surface specimens.
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Specimens bonded by the second type of UV-curing adhesive reached about 40% lower strength values with approximately same deformation like specimens without laboratory aging. The test specimens were broken by combination of cohesive failure in glue and creating cracks in glass.
b...UV-adhesive 1; sand-blasted glass; lab. aged
b*
a*
c...UV-adhesive 2; smooth glass; lab. aged
c*
d...UV-adhesive 2; sand-blasted glass; lab. aged
d* c
a*...UV-adhesive 1; smooth glass
d
b*...UV-adhesive1; sand-blasted glass c*...UV-adhesive 2; smooth glass b
d*...UV-adhesive 2; sand-blasted glass
Figure 14: Shear stress-strain relationship – laboratory aged acrylate adhesives.
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7. Summary There were performed numerous experiments focused on different joining material (steel, stainless steel, aluminium + glass, glass + glass) including their surface treatment (sandblasted glass) for 5 various types of glue applied at different thicknesses. Sphere of interest covered also environmental influences. Influence of different materials in bonded connection was assessed in the first part of this research. There were proved that sandblasted glass surface can improve shear strength values, if pure cohesive mode of failure is not reached at joint with smooth glass surface. No decreasing strength values of sandblasted glass were observed because of the cohesive strength of adhesive was crucial in the glued joints. Influence of different metal materials in glued connection was not decisive, but it is remarkable that specimens composed of glass with stainless steel glued by 2-component PU or acrylic adhesive proved higher shear strength values then samples with common steel. Effect of thickness was noticeable at semi-rigid 2-component acrylate adhesive strength of glued connection was decreased with increasing thickness of adhesive layer, especially at glass – steel type of connection. At flexible PU-adhesives the influence of thickness was not noticeable.
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The second part of research was focused on environmental effects. Every adhesive from selection showed different behaviour after laboratory ageing, which can simulated five years at exterior conditions in middle Europe climate. PU-adhesives and 2-component acrylate adhesive had no significant deterioration of mechanical properties, but some changes, especially at acrylate adhesive specimens, were observed. One type of UVcuring adhesive was showed as unsuitable for structural use because of weakened adhesive forces after artificial ageing. The second type of UV-curing adhesive had appropriate behaviour, but strength values were reduced by 40% from original (without ageing) values. But there is important to keep in mind that dependence between ageing affect and time is not linear, so there is bad opportunity to predict behavior of joint at different time. Mechanical properties can worsen less or more based on chemical composition and macromolecular structure of particular adhesive. Except above mentioned, it is important to say that long-term load effect during exposure to environmental conditions can be significant, but one of the main goal of this investigation was evaluated environmental resistance of selected adhesives. 8. Acknowledgements This paper is carried out with a support of the project SGS10/237/OHK1/3T/11.
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9. References [1] [2] [3] [4] [5]
[8]
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[9]
Haldimann, M., Luible, A., Overend, M., Structural Use of Glass, International Association for Bridge and Structural Engineering – ETH Zürich, Zürich, 2008 Weller, B., Tasche, S., Vogt, I., Bonded Joints of Adhesives with Higher Strength, Proceedings of the International Conference on Building Envelope Systems & Technology, pp 185-195, Bath, UK, 2007 Petrie, E.M., Handbook of Adhesives and Sealants, McGraw-Hill, USA, 2007 Huveners, EMP., van Herwijnen, F., Mechanical shear properties of adhesives, Proceedings of Glass performance days, pp 367 – 370, Tampere, Finland, 2007 technical data sheets [online], Sika CZ [vid. 13.4.2012], available on: http://cz01.webdms.sika.com/fileshow.do?documentID=1790, http://cz01.webdms.sika.com/fileshow.do?documentID=1143, http://cz01.webdms.sika.com/fileshow.do?documentID=1111 product data sheet [online], univarsc [vid. 13.4.2012], available on: http://www.univarsc.com/DynamicContent/Documents/RITE-LOK%20Datasheets/RITELOK%20UV50.pdf technical data sheets [online], MEVHA [vid. 13.4.2012], available on: http://www.mevha.cz/editor/image/download1_soubory/conloc685.pdf
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-281
Seismic Behaviour of Point Supported Glass Panels Luís Martins, Raimundo Delgado Faculty of Engineering of the University of Porto, Portugal, www.fe.up.pt Rui Camposinhos Scholl of Engineering of Polytechnic of Porto, Portugal, www.isep.ipp.pt Tiago Silva FACAL - Façade Engineering, Portugal, www.facal.pt Due to its transparency today’s architectures often rely on glazed façade solutions to execute the building envelope. During a seismic event, glass breakage and fall out can occur and threaten occupants and passers. So in earthquake prone regions this must be accounted in the design project; however, there is little research on the behaviour of glazed façades under seismic loads. This papers focus on the results of a project under development to ascertain right well dimensioned and adequate solutions to glass facades using point fixing systems under seismic or wind actions. Numerical analyses were performed, using finite element commercial software, the results are compared with simplified methods and conclusion are drawn.
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Keywords: spider glass, glass façade seismic behaviour, curtain wall glass façade
1. Introduction Recent developments in science and technology allowed glass to be used in several structural demanding applications such as façades, roofs, girders and columns, etc. Due to glass’ brittle behaviour this calls for more refined analysis methods and greater design detailing to ensure structural stability and safety. Currently modern facade buildings rely on glazed curtain wall systems. These systems include either singular aluminium alloy frame glass curtain walls or frameless glass curtain walls. This is the case of the so called spider fixing systems, which are pointed supported. Although there are some research on the behaviour of glass panels under out-of-plane loads, e.g., wind loads, the combine effect of both in-plane and out-of plane loads that are applied to the panels during an earthquake is a field of research still on its early stages. In fact, seismic action brings out specific problems to designers, due to the lack of, at least well-known, international rules or regulations about this problem. The scope of this paper is to present the relevant aspects of the seismic loading in point fixed glass panels. Firstly a simplified method based upon the elastic response spectrum is introduced, then the results of a time history dynamic analyses are presented. 281
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2. Seismic design of glass façades Earthquakes cause damage to the building main structure as well as to the non-structural components. Falling façade fragments during an earthquake poses a serious hazard to pedestrians and occupants as well, so in earthquake prone regions its must be accounted in the design. Sucuo lu and Vallabhan refer broken window glass as the second most serious nonstructural damage, for example in the 1985 Mexico City earthquake over 50% of the 263 office observed buildings had experienced some sort of glass breakage [1]. During an earthquake two types of lateral loads are considered acting in the façade panels: the “in plane” loads and the “out of plane” loads. Both inertial loads are caused by the horizontal displacements of the building’s floors, yet the in-plane actions causes, mainly shear stresses, and the others give rise to extra inertial forces due to the panel’s bending. The frequency content of the dynamic loads transmitted to the panels is modulated by the building natural frequency, so if it happens that it has a value very close to the panel’s natural frequency, resonant effects occur with an agonisingly increase of the dynamic response, a well-known phenomena that must be avoided, otherwise structural safety may be compromised. As there are no design regulations for determine seismic loads in glass façades, a laboratory test procedure according the American Architectural Manufacturers Association recommendations [2, 3] is followed in order to evaluate the maximum seismic drift which may cause glass breakage and fall out of framed glass panels.
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The dynamic test procedure considers a sinusoidal drift history for the procedure testing with growing amplitudes to a maximum of 150 millimetres (Figure 1). This test method has been applied in previous studies, like (Memari et al) [4], and is going to be used to assess the seismic behaviour of point fixed glass panels in the Seismic Laboratory of the University of Porto Engineering faculty.
Figure 1: Schematic of displacement time history for dynamic crescendo test [2].
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3. Simplified method to assess the seismic forces The simplified method to assess the seismic forces transmitted to the façade panels, was adapted by Camposinhos [5] from the work of Singh [6, 7], and is based on the response spectra of Eurocode 8 (EC8) [8]. Figure 2 presents the elastic response spectrum adopted in this work.
Sa (m/s2)
Response spectrum (Seismic action type II; soil type D; seismic region 2.1; =1.0) 10 8 6 4 2 0 0
1
2
3
4
T (s) Sa Figure 2: Response spectrum [8].
Thus the dynamic load transmitted to the façade panels (equation 1) depends on the building’s natural vibration period and on the panel’s mass and natural vibration period.
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FEk
0.40 u C fZ u S DS u J E u M E RE
(1)
Where, characteristic seismic force; FEk seismic coefficient of the panel (depends on the building dynamic CfZ characteristics and the position on the panel in the building); ground acceleration value; SDS importance coefficients of the panel (ranging between 1.0 and 1.5); E panel’s mass; ME coefficient of performance of the panel (ranging between 1.5 and 3.5). RE Prior to the application of the simplified method a parametric analysis was made to evaluate the variation of seismic coefficient CfZ with the dynamic properties of the panel and its position or height in the building. Two different cases were studied: in the first case the panel is assumed to be in the last floor (m=N), and in the second, the panel was assumed to be in placed at the penultimate floor (m=N-1). Figure 3 and Figure 4 presents the variation of Cfz with the natural period of vibration of the building for different values of the natural period of vibration for the glass panel.
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CfZ
Variation of CfZ (m=N; =5%) 100 80 60 40 20 0
Tpanel=0.05s Tpanel=0.2s Tpanel=0.4s Tpanel=0.6s 0
1
2
3
4
T(s)
Tpanel=0.8s Tpanel=1s
Figure 3: Variation of Cfz (m=N).
CfZ
Variation of CfZ (m=N-1; =5%) 100 80 60 40 20 0
Tpanel=0.05s Tpanel=0.2s Tpanel=0.4s Tpanel=0.6s 0
1
2
3
T (s)
4
Tpanel=0.8s Tpanel=1s
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Figure 4: Variation of Cfz (m=N-1).
The results (Figure 3 and Figure 4) shows a very significant resonant effect for low periods and a comparison between them allow to conclude that a panel in the last floor corresponds to the most severe situation in what seismic excitation concern, with values about 40% higher, once the coefficient, CfZ is directly correlated with the maximum seismic force acting in the panel. 4. Case study 4.1. Field application In order to analyze the behaviour of different solutions of point supported glass panels systems under seismic loads a partnership study involving the Faculty of Engineering of the University of Porto and FACAL – Façade Engineering, a Portuguese company known for its work in the field of glazed façades, has been promoted. FACAL has a great experience in technical innovative solutions, namely looking for the development and easy installing thinner and lighter glazing, and is well known by the execution of famous facade glazings such as the glass system in Casa da Música in Oporto, the double skin façade Torre H in Lisbon, the glazing of the Spanish Pavilion in the International Fair in Zaragoza or the glass roof of the Metro Station at Sá Carneiro Airport in Porto. On the basis of this work is the newly-built office building of Bouygues Imobiliária in Lisbon. A particular attention was given to the safety requirements of a 20 meters high 284
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Seismic Behaviour of Point Supported Glass Panels
point-supported glass façade over the main entrance of the building. The post-breakage behaviour of the laminated safety glass panels is the primary concern. This is often a neglected problem in glass façades yet of greater importance since Lisbon as many other metropolis is prone to seismic activity. A crucial concern on this matter is essential: The integrity of the glass façade must be preserved and assured that there’s no risk of glass fragments fallings. Among the various enhancement solutions the use of laminated safety glass with the DuPont interlayer SentryGlas® provides an optimal behaviour due to its excellent postbreakage performance with the glass fragments remaining adhered to the interlayer, without falling down.
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Figure 5: Point-supported glass façade - office building of Bouygues Imobiliária in Lisbon.
4.2. Geometrical and mechanical properties This paper focus on a set of five point supported laminated glass panels. All the specimens have a surface of 2350x2300 mm2 differing on the glass thicknesses, the interlayer and distance from edges to holes (Figure 6).
Figure 6: Geometrical configuration of the glass panels: left) V1 and V2; right) V3, V4 and V5 (Drawings by: FACAL).
285 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
The panels identified as V1, V2, V3 and V4 are obtained from 10 mm strengthened glass and a 1.52mm thick interlayer together with a 8mm also tempered glass.Panel V5 is made from two 12mm tempered glass sheets. Panels V1 and V3 have a SentryGlass® film while the remaining panels have PVB interlayer. Furthermore a panel with the same geometrical configuration of that of V5 but with SentryGlass® interlayer film was additional considered in the analyses. The properties of the PVB’s Young modulus ranges from 3.2 MPa to 18 MPa [9, 10], so in the panels with this type of interlayer three different values for this parameter were considered: (i) 3.2MPa, (ii) 9.0 MPa and (iii) 18.0 MPa. In the case of SentryGlas® a the value of 300 MPa was adopted for its Young modulus, as suggested by Delincé [10]. Table 1summarises the relevant data for the studied glass panels.
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Table 1: Test specimen’s description. Glass panel
Dimensions [mm]
Total thickness [mm]
Interlayer film
Interlayer’s Young modulus [MPa]
Glass’ Young modulus [GPa]
Glass’ Poisson coefficient
V1
2350x2300
10+1.52+8
SentryGlas®
300
70
0.20
V2(i)
2350x2300
10+1.52+8
PVB
3.2
70
0.20
V2(ii)
2350x2300
10+1.52+8
PVB
9.0
70
0.20
V2(iii)
2350x2300
10+1.52+8
PVB
18.0
70
0.20
V3
2350x2300
10+1.52+8
SentryGlas®
300
70
0.20
V4(i)
2350x2300
10+1.52+8
PVB
3.2
70
0.20
V4(ii)
2350x2300
10+1.52+8
PVB
9.0
70
0.20
V4(iii)
2350x2300
10+1.52+8
PVB
18.0
70
0.20
V5(i)
2350x2300
12+1.52+12
PVB
3.2
70
0.20
V5(ii)
2350x2300
12+1.52+12
PVB
9.0
70
0.20
V5(iii)
2350x2300
12+1.52+12
PVB
18.0
70
0.20
V5(iv)
2350x2300
12+1.52+12
SentryGlas®
300
70
0.20
4.3. FE model To evaluate the structural response of the glass panels a set of numerical models were made using commercial finite element (FE) software. The glass panels and interlayer film were modelled with 8-node 3D finite elements. In the interior of the panel the maximum size of the finite elements was limited to 2 centimetres, while near the supports the maximum size was reduced to half to attend the stress concentrations near the holes to take in account the expected stress concentrations in this regions.
286 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Seismic Behaviour of Point Supported Glass Panels
Figure 7: FE mesh details - a) lateral view; b) interior of the panel; c) support region.
The degrees of Freedom (DOF) restrictions which enabled this stress concentration near the support region and the brittle nature glass leads to a several numerical model simulations stages until a solution that that correctly represent the real support condition was achieved. To assess the behaviour of the model two premises were advanced: (i) the allowance for rotations of the panel according the real behaviour; (ii) Stress distribution around the hole should be compatible with reality.
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The best solution lead to the implementation of an external node where the support constraints are included. The connection to the panel was provided throughout rigid pseudo beam elements (Figure 8).
Figure 8: Lateral view of the support solution.
287 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
5. Results 5.1. Simplified method The natural frequencies of the glass panels were determined using the FE model and are depicted in Table 2. The already mentioned simplified method was applied to assess the maximum seismic effect on the façade panel and the results are presented in Figure 9. As it can be observed, the peak values presented in the figure, nearly 10 times the panel’s self weight, confirm the expected resonant effects in the panels.
Glass panel
Natural frequency (Hz)
V1
13.4
V2(i)
10.3
V2(ii)
11.5
V2(iii)
12.2
V3
8.1
V4(i)
6.4
V4(ii)
7.1
V4(iii)
7.5
V5(i)
8.0
V5(ii)
9.0
V5(iii)
9.5
V5(iv)
10.5
Seismic forces transmited to the façade panels 30 20 FEk (kN)
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Table 2: Glass panels natural frequency.
10 0 0
1
2
(s) V1
V2(i)
V2(ii)
V2(iii)
V3
V4(i)
V4(ii)
V4(iii)
V5(i)
V5(ii)
V5(iii)
V5(iv)
Figure 9: Maximum seismic force transmitted to the glass panels.
288 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Seismic Behaviour of Point Supported Glass Panels
5.2. Time history dynamic analyses In order to qualitatively assess the results obtained by the simplified method a set of time history dynamic analyses has been performed, using the El Centro ground motion record (Figure 10) appropriately scaled so that the maximum spectral acceleration was equal to the one calculated by EC8. El Centro earthquake, May 18th 1940 (N-S)
üg (m/s2)
4 2 0 -2 -4 0
5
10
15
20
25
30
35
Time (s) Ground acceleration Figure 10: El Centro ground motion record [11].
To verify the existence of resonant effects in the panel a structure with a natural period of 0.12 s (very close to the natural period of that of panel V5(i)) was analysed with the selected ground motion record. The floor accelerations obtained, Figure 12, were then applied to the façade panel and the corresponding response was gathered, Figure 13.
Acceleration (m/s2)
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Floor accelerations 10 5 0 -5 -10 0
5
10
15
20
25
30
Time(s) Floor accelerations Figure 11: Floor accelerations.
289 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
35
Challenging Glass 3
Acceleration (m/s2)
Response of the panel V5(i) 100 50 0 -50 -100 0
5
10
15
20
25
30
35
Time (s) Panel acceleration Figure 12: Response of the panel V5(i).
The maximum response acceleration of the panel, about 81 m/s2, 10 times the peak floor acceleration, confirms the existence of resonance in the façade panel. As the simplified method does not consider any damping effects, new dynamic analyses were made considering the panel’s damping ratio ( ) ranging from 0% to 5%.
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Table 3: Differences in the panel V5(i) response for different damping ratio. Damping ratio [%]
Maximum deflection on the panel [mm]
0
16.7
2
11.8
5
8.58
Table 3 shows that there is a decay of almost 30% in the maximum deflection when a 2% damping ratio was considered. Thus in buildings with natural vibration frequencies that might induce resonance in the façade panels an energy dissipation device should be applied to reduce the dynamic response of the panel. 5.3. Numerical simulation of the test procedure according to AAMA recommendations Section 2 briefly described a test procedure to assess the maximum seismic drift causing glass breakage and fallout in framed glass panels. This test procedure was numerically simulated using the same FE models previously developed to determine the panel’s dynamic properties. Due to stress concentrations in the support region, material rupture was reached for a drift less then10 mm (Figure 13).
290 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Seismic Behaviour of Point Supported Glass Panels
(MPa)
Results for the AAMA dynamic test (Panel V1) 900 800 700 600 500 400 300 200 100 0 0
5
10
15
20
25
drift (mm) Maximum Tension in the support
Tension at 5mm from support
Tension at 10 mm from support
f annealed glass
f heatstrenghtned glass
f tempered glass
Figure 13: Example of results for the AAMA dynamic test.
The low drift level that causes material failure determined by the numerical test lead to the formulation of the hypothesis that AAMA 501.6 dynamic test aims to determine the maximum drift that causes panel’s detachment from the support rather than the material rupture.
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6. General conclusions In a FEM analysis the importance of an adequate modelling of the support conditions in the point supported glass panels is mandatory in order to control the stress concentration phenomenon. The simplified method to determine the seismic forces transmitted to façade panels seems to be able to capture the relevant aspects of the whole issue regarding resonance effects as well. The numerical simulations using time history analysis confirmed the hypothesis of resonance effects induced by the building’s natural frequency and are in agreement with the peak values determined by the simplified method. Tests showed up that the problem’s sensibility to damping is relevant. In fact a 2% damping ratio for the panels lead to a 30% decrease in its maximum deflection. It must be emphasized that in earthquake prone regions façade panels without energy dissipation devices could be seriously and dangerously excited into non acceptable limits.
291 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
7. References Sucuo lu, H. and C.V.G. Vallabhan, Behaviour of window glass panels during earthquakes. Engineering Structures, 1997. 19(8): p. 685-694. [2] AAMA, AAMA 501.6-09: Recommended dynamic test method for determining the seismic drift causing glass fallout from a wall system. 2009, AAMA. [3] AAMA, AAMA 501.4-09: Recommended static testing method for evaluating curtain wall and storefront systems subjected to seismic and wind induced interstory drift. 2009, AAMA. [4] Memari, A.M., R.A. Behr, and P.A. Kremer, Seismic behavior of curtain walls containing insulating glass units. Journal of Architectural Engineering, 2003. 9(2): p. 70-85. [5] Camposinhos, R.d.S., Revestimentos em pedra natural com fixação mecânica dimensionamento e projecto. 2009, Lisboa: Edições Sílabo. 199 ISBN 978-972-618-561-1. [6] Singh, M.P., et al., Seismic design forces. I: Rigid nonstructural components. Journal of Structural Engineering, 2006. 132(10): p. 1524-1532. [7] Singh, M.P., et al., Seismic design forces. II: Flexible nonstructural components. Journal of Structural Engineering, 2006. 132(10): p. 1533-1542. [8] CEN, Eurocode 8 - Design of structures for earthquake resistance Part1: General rules, seismic actions and rules for buildings. 2010, IPQ: Caparica. p. 230. [9] Chen, J., Q. Zhang, and B. Xie, Nonlinear finite element analysis on laminated glass panel based on APDL. Computer Aided Engineering, 2010. 19(Copyright 2011, The Institution of Engineering and Technology): p. 22-6. [10] Delincé, D., et al. Post-breakage behaviour of laminated glass in structural applications. in Challenging Glass. 2008. [11] http://www.vibrationdata.com/elcentro.htm. Access Date: 18/05/2011
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[1]
292 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-293
The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System Shelton Nhamoinesu, Mauro Overend University of Cambridge, UK, [email protected] , [email protected] High strength adhesives provide potentially efficient load-bearing steel-glass linear connections by enabling composite action. However, there is a lack of reliable models that can accurately predict their mechanical behavior. This paper describes experimental investigations undertaken to select suitable adhesives from shortlisted epoxies and acrylates. The selection was based on mechanical performance of adhesive single-lap shear joints subjected to short-duration loads. The paper also assesses the validity of an analytical and a viscoelastic-plastic numerical model used for predicting the stress-state in adhesive joints. The investigation shows that three of the tested adhesives may be suitable for use in a steel-glass composite façade system. The analytical model provides good predictions at low strains but the accuracy decreases with increasing adhesive strains. The non-linear numerical model provides reasonable predictions but is sensitive to adhesive shear modulus history.
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Keywords: Structural Adhesives, Steel-Glass Composite Façade System, SingleLap Shear (SLS) Test
1. Introduction Despite the ubiquity of bolted connections in structural glazing systems, adhesive connections are gaining popularity. Unlike bolted connections that weaken the glass in the vicinity of bolt holes, adhesive bonding ensures a more uniform load transfer between glass and the supporting elements. As a result, efficient composite behaviour between glass and the supporting elements can be achieved. Studies aimed at understanding the mechanical behaviour of adhesive joints date back to the mid-1940s when Goland and Reissner ‘[1]’ proposed an empirical moment distribution approach for determining the stress-state in a lap joint. They derived expressions for the distribution of shear stress across an adhesive in a lap-shear joint with similar adherends. More recently, Bigwood and Crocombe ‘[2]’ proposed a general elastic analysis where adherends act as cylindrically bent plates connected along adjacent interfaces by an adhesive layer capable of transmitting both shear and tensile loads. Their approach is an extension of Goland and Reissner’s empirical moment distribution but has been extended to analyse dissimilar adherends. There are many adhesives produced by different manufacturers which can be potentially used for steel to glass connections. Perhaps the best known are the structural silicone sealants which are increasingly being used to achieve flexible structural connections between glass and aluminium or steel or between glass and glass. Compared to other types of adhesives, silicones are better understood in terms of their mechanical 293
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Challenging Glass 3
performance and durability. These are well documented in several standards and codes such as BS 6262-6: 2005 ‘[3]’, EOTA 1988 ‘[4]’, AAMA CW-13-85 ‘[5]’ and ASTM C 1401-02 ‘[6]’. Structural silicone joints are relatively thick and flexible, thereby allowing them to accommodate differential thermal strains between glass and metallic sub-frames. However with tensile strengths of only 0.8 to 1.8MPa ‘[7]’ for dynamic loading, structural silicones are unsuitable for transferring the higher longitudinal shear required for composite action in a typical steel-glass composite façade system. Several studies on high strength thermosetting adhesives ‘[8], [9], [10], [11], [12], [13], [14]’ have shown that there is a possibility of using stiffer adhesives such as epoxies and acrylates for bonding metal to glass. There is however a lack of confidence in the use of such adhesives for structural applications partly because of a lack of reliable models that can accurately predict their transient and long-term mechanical behaviour. Significant research has been done to select the most suitable adhesives for metal to glass connections ‘[13]’ and ‘[14]’; this paper caries forward the selection process by adapting a selection criterion that is specific for a typical steel-glass composite façade system. Six candidate adhesives were investigated: x x x
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x
Two of the adhesives, the 3M two-part epoxy DP490 and the Huntsman twopart acrylate Araldite 2047 were chosen on the basis of previous research by ‘[13]’. The other two adhesives, 3M two-part epoxy 2216B/A and the Holdtite twopart acrylate 3295 were chosen on the basis of research done by ‘[14]’. The fifth adhesive, 3M two-part epoxy/acrylate hybrid 7271 B/A is a new product on the market that was recommended by the manufacturer as a potential metal to glass adhesive. The sixth adhesive, Dow Corning two-part silicone DC993 was chosen as a control adhesive since its material properties are well documented in the Dow Corning product data sheet ‘[15]’ and its mechanical behaviour has been extensively investigated ‘[13], [14], [16]’.
x This paper firstly outlines the determination of bulk material properties of the six candidate adhesives by uniaxial tensile tests on dumbbell specimens. The material properties were implemented into an analytical model ‘[2]’ as well as into a commercially available finite element analysis (FEA) software, LUSAS v14.3 ‘[17]’. The FEA analyses utilized a viscoelastic-plastic constitutive model as well as a simple linear elastic perfectly plastic constitutive model. The models were used to predict the mechanical performance of specially adapted steel-glass single-lap shear (SLS) joints. Validation of the models was done experimentally by steel-glass SLS tests based on ASTM D1002-99 ‘[18]’. Whilst different adhesives perform optimally at different bond thicknesses, all the specimens in this investigation were prepared with a bond thickness of 3mm which is the minimum gap-fill governed by the fitness tolerances in the endapplication. In addition to performing the tests at ambient temperature, specimens previously exposed to 800C for 48hrs were also tested to investigate the effect of extreme temperature on joint performance.
294 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System
Finally, the results of the SLS tests and the validity of the analytical and numerical models were discussed. The selection criterion for the adhesives most suitable for the steel-glass composite façade system was as follows: x x x x
cohesive or adherend failure preceded by substantial plastic strain in the adhesive relatively high joint flexibility adhesive shear strength of at least 7.5MPa minimum loss of strength after exposure to temperatures of up to 800C
2. Analytical and Numerical Predictions
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2.1. Experimental Determination of Material Properties 4mm thick dumbbells of the six candidate adhesives, sized to comply with ‘[19], [20]’ (Fig.1a) were prepared by casting the adhesives into an aluminium cut-out mould lined by a PTFE release film (Fig.1b). Air bubbles caused by the chemical reaction of the adhesive components were minimized by placing the cast mould into a vacuum chamber; the aluminium mould also acted as a heat sink that reduced bubble formation. Two different uniaxial tensile tests were performed on each of the adhesives in order to determine the following bulk material properties: (i) visco-elastic shear modulus Gv, (ii) visco-elastic decay constant Ⱦ, (iii) elasto-plastic stress-strain relationship and (iv) poisson’s ratio .
Figure 1: (a) Dumbbell geometry ‘[18],[19]’ and (b) PTFE lined aluminium mould
The first test was performed to determine the visco-elastic properties Gv and . An instantaneous tensile load was applied to the dumbbells at a high extension rate of 100mm/min up to an extension of 1mm followed by strain holding for approximately 500s while recording the decaying stress. The stress-time curve was converted into a shear modulus-time curve (Fig.2a); was determined by curve fitting of Eq.1. Gv was obtained by subtracting the residual shear modulus G from the initial shear modulus G0.
G (t )
Gv e E t
G0 Gf e Et
(1)
295 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 3 G0
200
2.5 True Stress (MPa)
Shear Modulus Gv(MPa)
250
150 Gv 100 50
2 1.5 1 0.5
G 0
0 0
100
200
300
400
500
0
0.02
0.04
0.06
True Strain
Time (s)
Figure 2: (a) Shear modulus vs. time and (b) True stress/relaxation vs. true strain curves for 3M 2216 B/A epoxy dumbbell. The dotted curve is the time-independent true stress vs. true strain
The second test was performed to determine the elasto-plastic properties of the adhesives by adopting a discrete load-step strategy on the dumbbell specimens ‘[14]’. The total loading period was divided into approximately ten intervals and at each interval; the strain was increased by 0.005 followed by strain holding for a period equal to the decay time td from Figure 2a above. A time-independent elasto-plastic relationship was obtained by curve fitting of the discrete points on the true stress vs. true strain graph (Fig.2b). The experimentally obtained material properties of the candidate adhesives are summarised in Table 1 below. Table 1: Material properties of the six candidate adhesives Poisson’s Ratio Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Shear
Elastic
Modulus
Modulus
Gv (MPa)
E0 (MPa)
Decay Constant
Time independent elasto-plastic stress-strain polynomial ߪ ൌ െʹͷͺߝ ଶ ͳ͵ͲͷǤͳߝ ͲǤͲͲͳ͵ߝ ͲǤͲͳͶ
3M DP490 Epoxy
0.38
239.0
659.6
0.001
Araldite 2047 Acrylice
0.43
211.0
603.5
0.002
3M 7271 Epxy/Acylic
0.29
559.0
1142.2
0.003
3M 2216 B/A Epoxy
0.47
192.4
565.6
0.007
Holdtite 3295 Acrylate
0.41
219.5
619.0
0.002
DC 993 Silicone
0.48
3.9
11.5
0.004
ߪ ൌ െͷͷʹǤߝ ଶ ͺͶǤͲ͵ߝ ͶǤͶͻͳͺߝ ͲǤͲͳͶ ߪ ൌ െͳͺͺͳߝ ଶ ǤͶ͵ߝ ͲǤͳͷͶͻߝ ͲǤͲʹͷ ߪ ൌ െͳ͵ͲͲǤͷߝ ଶ ͳͶͳǤ͵Ͷߝ Ǥ͵͵ͳߝ ͲǤͲʹͷ ߪ ൌ െ͵ͷ͵ͳߝ ଶ ͳʹͺ͵Ǥͷߝߝ ͲǤͲͳ ߪ ൌ െͳͺͶͷߝ ଶ ͻͶͷǤͻߝ ͳǤͶ͵ߝ ͲǤͲͳ ߪ ൌ െͳͲͷͷߝ ଶ ͳͻͻǤͳͶߝߝ ͲǤͲͳ ߪ ൌ െͳ͵͵Ǥ͵ߝ ଶ ͵͵ǤͶͻͷߝ ͲǤͳʹߝ ͲǤͲͳ ߪ ൌ െͳʹͶ͵Ͳߝ ଶ ͷʹͷǤʹͷߝ െ ͲǤͲͲͳߝ ͲǤͲͳͷ ߪ ൌ െͺͺǤͻߝ ଶ ͳͶǤߝ ͵ǤͲͲͻߝ ͲǤͲͳͷ ߪ ൌ െͳǤͳʹߝ ସ ʹʹǤͲͲʹߝ ଷ െ ͳͲǤͲͻߝ ଶ
ʹǤ͵ͷͳߝ ͲǤͲͲͲ͵
296 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System
2.2. Analytical Model Using material data from Table 1 above, stresses across the adhesive layer in a lap-shear joint (Fig.3) can be predicted by the Crocombe and Bigwood linear elastic analytical model‘[2]’. The model is based on a seventh order differential equation (Eq.2) and a sixth order differential equation (Eq.3) that describes the shear stress xy and the transverse stress ɐy distributed across the adhesive layer of a lap shear joint.
d 7W xy
dx 7 d 6V y dx 6
K1 K1
d 5W xy
dx 5 d 4V y dx 4
K3 K3
d 3W xy
dx 3 d 2V y dx 2
K5
dW xy
0
dx
K 5V y
0
(2)
(3)
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where K1 to K5 are constants dependent on the shear modulus of the adhesive and the elastic moduli of the adherends. Crocombe and Bigwood created a spreadsheet that solves equations 2 and 3 if the applied loads (P1, P2, V1, V2, M1 and M2) shown in Figure 3 above are known. The determination of the bending moments M1 and M2 is relatively complex, in this paper, values of M1 and M2 were obtained using an analytical derivation presented in ‘[21]’. The graphical presentation of the Crocombe and Bigwood elastic stress distribution across the 30mm length of the SLS joint of each candidate adhesive is shown in Figure 4 below. The stress distributions in Figure 4 correspond to the six mean failure loads P obtained from SLS experimental tests of each candidate adhesive.
Figure 3: Free-body diagram of element dx along single-lap adhesive joint ‘[2]’
297 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Adhesive Shear Stress (MPa)
25
DP490 Epoxy P=28.2kN H3295 Acrylate P=20kN A2047 Acrylic P=15.3kN 3M7271 Hybrid P=7.8kN 3M2216 Epoxy P=7.3kN DC993 Silicone P=1.6kN
20
15
10
5
0 0
5
10 15 20 Adhesive Overlap Length (mm)
25
30
Figure 4: Bigwood and Crocombe shear stress distribution plots across SLS adhesive joints
2.3. Numerical Model The steel-glass SLS test was constructed as a 2-dimensional FEA model using LUSAS v14.3 ‘[17]’. An eight node quadrilateral quadratic plane strain element type was implemented throughout the model. Since the SLS joint is symmetrical about the midpoint of the glass (line y-y in Fig.5), only half of the connection is modeled.
y
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y
y
½ glass plate
steel plate
x A
B
C
D
ݔሶ
Adhesive with dense mesh of 12 elements in thickness Figure 5: Two dimensional FEA model of the steel-glass adhesive SLS connection.
For the boundary conditions, the model was restrained in x and Mz along the symmetry line y-y and also restrained in y and Mz along the lines AB and CD which represent the contact of the steel plate to the testing machine. The glass and steel were modeled as perfectly linear elastic materials with Eglass=70GPa, glass=0.23, Esteel=209GPa and steel=0.3. The six candidate adhesives were modeled with visco-elastic and elastoplastic properties obtained from Table 1. A velocity ݔሶ was applied at the end of the steel plate, line BD and it corresponds to the experimental displacement rate of 0.2mm/min. The analysis was run as a dynamic geometric and material non-linear analysis using the implicit method and an updated langrangian approach. The results of the numerical analysis were compared to the analytical and experimental test results in Section 4.
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In addition to the non-linear analysis described above, a simple linear elastic analysis was performed. The adhesives were modeled with linear elastic-perfectly plastic material properties obtained from the time-independent elasto-plastic stress-strain plots (Fig.2b). 3. Steel-Glass Single-Lap Shear Joint Tests
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3.1. Specimen Preparation Specially adapted SLS adhesive joints (Fig.6a,b) of the six candidate adhesives were prepared based on ASTM D1002-99 ‘[18]’ guidelines. Each specimen was assembled using two 120mm by 49mm by 6mm thick black mild steel plates and one 200mm by 200mm by 10mm thick fully toughened glass plate manufactured to BS EN12150-2 ‘[22]’ standards. The bonding surface of the steel was sanded using a 220 grit sandpaper to give a consistent finish for all specimens. All steel and glass surfaces were thoroughly cleaned with acetone before adhesive application and in the case of the silicone joints; a siloxane based primer was applied to the steel surface before bonding the adherends. A specially machined aluminium jig lined with a PTFE release film was used for assembling all specimens; the jig ensured alignment of the two steel plates as well as maintaining a bond thickness of 3mm for all specimens. All joints had a bond width of 49mm and a bond length of 30mm. All the six candidate adhesives were twopart pot adhesives and mixing conformed to each of the manufacturer’s guidelines. The prepared specimens were stored at ambient temperature and approximately 40% relative humidity. 3.2. Test Procedure The SLS tests were performed on an Instron 5500R testing machine with a 150kN load cell. Specimens were attached to the testing machine by slotting steel pins into 12mm holes which are 20mm from the end of each steel plate. A displacement gauge was attached to each steel plate with the gauge probe resting on an aluminium plate glued to the centre of the glass plate (Fig.6b). The displacement gauges separately measured the vertical displacement in each adhesive joint. All tests were displacement controlled and a displacement rate of 0.2mm/min was applied for all specimens except for the very flexible silicone DC993 specimens which were tested at 1.0mm/min. Photographs were taken before, during and after each test. The tests were divided into two phases. Phase 1: Three specimens of each of the six candidate adhesives were tested at 210C. Phase 2: Three specimens of the best-performing adhesives from Phase 1 were heatsoaked in an oven at 800C for 48hrs and then tested at 210C.
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End of steel plate attached to Instron 49mm wide steel 49mm wide adhesive Displacement gauge attachment Aluminium T-plate for resting displacement gauge 200mm wide glass Displacement gauge
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Figure 6: (a) Schematic drawing and (b) photograph of the SLS test set up
3.3. Test Results Phase 1: All DC993 silicone specimens failed cohesively with very low failure loads but large extensions. Although the failure mode is desirable and the adhesive showed remarkable flexibility, the calculated mean shear strength of only 1.1MPa makes the silicone unsuitable for the steel-glass composite system being developed. All 3M DP490 epoxy joints experienced glass failure preceded by brittle partial failure in the adhesive. There was no plastic deformation observed (Fig.7) and the DP490 joints experienced the highest failure loads of up to 28kN. The lack of flexibility and lack of plastic deformation before failure makes DP490 unsuitable. The 3M 7271 epoxy/acrylate hybrid joints experienced very small strains before failure. Glass failure at relatively low loads and very low extensions was observed in all specimens. Holdtite 3295 acrylate specimens carried significantly high loads and were relatively flexible. The adhesive exhibited considerable plastic deformation (Fig.7) before local glass failure on the glued glass edges. The 3M 2216 epoxy specimens showed good flexibility but the load carrying capacity was relatively low with maximum loads of only 7.3kN. Adhesion failure at the steel-adhesive interface was observed in all 3M 2216 specimens, this seemed to suggest premature joint failure. This observation could be attributed to potential inadequate surface preparation or to large bond thickness since previous studies ‘[14]’ have shown that this epoxy predominantly fails cohesively. The Araldite A2047 acrylate showed the best results. All specimens failed cohesively after substantial plastic deformation. The joints were relatively more flexible yet they carried significantly high loads of up to 15.3kN. Phase 2: The 3M 2216 epoxy, the Araldite A2047 acrylate and the Holdtite 3295 acrylate adhesives were selected for SLS tests after heat soaking at 800C for 48hrs. At the time of writing this report, test results for the Holdtite 3295 acrylate were not yet available. Results for the 3M 2216 epoxy and Araldite A2047 showed that both adhesives became less stiff (Fig.7). The 3M 2216 joints performed poorly; failing to carry loads above 1kN. The Araldite A2047 joints still performed exceptionally well. The mean load bearing capacity of the joints reduced by only 18% after exposure to 800C (Fig.7). Failure was still cohesive with substantial plastic deformation in the adhesive occurring prior to failure. Table 2 below summarises the test results. 300
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The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System
30 Araldite A2047 Acrylate
25
DP490 Epoxy
Load (kN)
20
Holdtite H3295 acrylate 3M7271 Epoxy/Acrylate
15
3M2216 Epoxy
10 A2047 Acrylate after heat soaking
5
3M2216 Epoxy after heat soaking
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Displacement (mm) Figure 7: Typical SLS test load vs. extension curves for five candidate adhesives
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(DC993 Silicone is excluded for clarity)
301 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 2: Summary of experimental results Mean Failure Load (kN)
Extension at
Mean Shear
failure
Strength a
(mm)
(MPa)
3M DP490 Epoxy
28.2
0.56
19.2 b
Araldite 2047 Acrylic
15.3 (12.5*)
1.04 (1.28*)
10.4 (8.5*)
3M 7271 Epxy/Acylic
7.8
0.20
5.3 b
3M 2216 B/A Epoxy
7.3 (0.7*)
0.85 (1.71*)
5.0 (0.5*)
Holdtite 3295 Acrylic
20.0
1.25
13.6 b
DC 993 Silicone
1.6
5.61
1.1
Mode of failure
Glass failure, no plastic strain in the adhesive prior to failure Cohesive failure preceded by substantial adhesive plastic strain Glass failure, no plastic strain in the adhesive prior to failure Adhesion failure at the steeladhesive interface Glass failure preceded by significant adhesive plastic strain Cohesive failure preceded by high adhesive plastic strain
*
specimens subjected to 800C for 48hrs before testing based on equivalent constant shear stress along the lap joint and loading is short term b adhesive shear strength governed by glass failure
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a
4. Discussion Comparison of the linear elastic analytical Bigwood and Crocombe model to both linear elastic and non-linear viscoelastic-plastic FEA models (Fig.8) generally reveal that there is good agreement particularly for small loads. This is not surprising since the linearelastic analytical model by definition should predict the elastic deformation which is predominant at small strains. As the failure load is approached and strains become larger, the analytical model tends to underestimate the adhesive shear stress (Fig.8) by magnitudes of up to 16.7%. This is uncharacteristic since elastic stresses are expected to be larger than elasto-plastic stresses. Unlike the linear elastic FEA model, the nonlinear FEA model does not show prominent stress peaks near the joint edges at high loads, this is due to prediction of plasticity in the non-linear model.
302 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System 14 Linear FEA P=15.3kN 12
Nonlinear FEA P=15.3 Crocombe P=15.3kN
Shear Stress (MPa)
10
Nonlinear FEA P=10.2
8
Linear FEA P=10.2kN 6
Crocombe P=10.2kN
4
Nonlinear FEA P=5.1kN
2
Linear FEA P=5.1kN Crocombe P=5.2kN
0 0
5
10
15
20
25
30
Adhesive overlap length (mm) Figure 8: Analytical and numerical shear stress distribution across the Araldite A2047 acrylate SLS adhesive joint
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Despite the limitations of the analytical model, experimental mean shear strengths of the adhesives (Table.2) show very good agreement with the Bigwood and Crocombe’s predictions of adhesive shear stress at failure load (Fig.4). For most of the candidate adhesives, numerical results for load vs. extension generally showed good agreement at low strains (Fig.9). As strains in the SLS joint increased, numerical models showed varying degrees of accuracy for different adhesives. The accuracy of the non-linear model seemed to heavily depend on the value of the decay constant . Mathematical analysis of experimentally obtained shear modulus vs. time plots suggested that the shear modulus history of the tested adhesives G(t) is best described by a logarithmic function (Eq.4) below.
G (t )
D ln t J
(4)
where and are constants. However the FEA constitutive model used in this study describes G(t) by an exponential function (Eq.1). As a result, an estimation of was required to allow Eq.1 to approximate Eq.4 and this invariably limited the accuracy of the constitutive model. The predictive capability of the models is also dependent on the adhesive failure mode; lap shear joints that experience adhesion or glass failure tend to be predicted poorly compared to those that fail cohesively. In the case of the 3M 2216 Epoxy adhesive 303
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Challenging Glass 3
joints, for example, where failure was by adhesion at the steel-adhesive interface, the numerical predictions were unsatisfactory. 16 14 12
Load (kN)
10 FEA: Linear elastic and perfectly plastic constitutive model
8 6
FEA: Non-linear viscoelastic and elasto-plastic constitutive model
4 Experimental 2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Extension (mm) Figure 9: Experimental and numerical load vs. extension plots for Araldite A2047 acrylate SLS adhesive joint
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5. Conclusion The main objective of this paper was to identify suitable structural adhesives for a steelglass linearly bonded system. SLS tests on the six candidate adhesives provided significant information which indicated that at least three of the six adhesives may be suitable for the proposed system. Out of all the tested adhesives, it was concluded that the Araldite A2047 acrylate SLS joints exhibit the most desirable mechanical characteristics under short-duration testing conditions. The Araldite A2047 acrylate SLS joint: x x x x x
failed cohesively both in specimens tested before and after heat soaking at 800C for 48hrs showed good strength with mean shear strength of 10.4MPa exhibited relatively good flexibility with substantial plastic deformation preceding failure was not significantly affected by exposure to extreme temperature, with a maximum percentage drop in load bearing capacity of only 18% was relatively easy to prepare and handle.
Holdtite 3295 acrylate also performed well, the mean shear strength of 13.6MPa was based on glass failure therefore it is likely that the adhesive is even stronger than this. The Holdtite adhesive was relatively flexible and it experienced considerable plastic strain before local glass failure. Although the 3M 2216 Epoxy showed poor adhesion to 304
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The Mechanical Performance of Adhesives for a Steel-Glass Composite Façade System
the metal surface; its relatively good flexibility, significantly good strength, low cost and relatively long handling time warrants its consideration for further investigation. The other three adhesives were found to be unsuitable for different reasons ranging from significantly low strength in the case of DC993 silicone to significant lack of flexibility in the case of DP490 epoxy and 3M 7271 epoxy/acrylate hybrid. It must be noted however that the elimination of some of these adhesives did not necessarily mean they are not suitable for steel to glass connection; this study presented a specific bond line thickness of 3mm, a constraint which limits the performance of some adhesives which are otherwise suitable for bonding steel to glass. The other objective of this paper was to validate the predictive capability of an analytical model and a viscoelastic-plastic numerical model. It was shown that the linear-elastic analytical model is useful in predicting adhesive joint behaviour at low strains but the accuracy decreases as the adhesives start to experience plastic deformation at large strains. It was also shown that the non-linear numerical model provides reasonable predictions of stress distribution across adhesive joints but requires good approximation of the adhesive shear modulus history function G(t). Research aimed at improving the adhesive constitutive model by accounting for effects of hysteresis and repeated cyclic loading is underway and results are due to be published in the near future. It is hoped that these improved models can be used to predict the global adhesive joint performance in full-scale steel-glass composite façade modules. 6. Acknowledgements The study presented in this paper, which forms part of a broader ongoing research aimed at developing a steel-glass composite façade system is funded by an Industrial CASE studentship provided by the Engineering and Physical Sciences Research Council (EPSRC) and a contribution from TATA Steel, the Industrial partner. 7. References Copyright © 2012. IOS Press, Incorporated. All rights reserved.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Goland, M; Reissner, E, The stresses in cemented joints, J Appl Mech Trans ASME 66 (1944), Vol.11, ppA17-A27. Bigwood, D.A; Crocombe, A.D, Elastic analysis and engineering design formulae for bonded joints, Int J Adhes Adhes (1989), Vol.9, No.4, pp229-242. BS 6262-6: 2005, Code of practice for glazing for buildings – Part 6: Code of practice for special applications, British Standards Institution BSI (October 2005). ATAG Nr 002, European Organisation for technical Approvals EOTA, Brussels (1998). AAMA CW-13-85, Structural sealant glazing systems, American Architectural Manufacturers Association (AAMA), Schaumburg, USA (1985). ASTM C 1401-02, Standard guide for structural sealant glazing, ASTM Standards (2002). Haldimann, M; Luible, A; Overend, M, Structural use of glass, Structural Engineering Documents SED10, International Association for Bridge and Structural Engineering IABSE, Zurich, May 2008. Moibob, D; Crisinel, M, Linear connection system for structural application of glass panels in fullytransparent pavilions, Proceedings of Challenging Glass 1, Delft, Netherlands, 2008. Pye, A; Ledbetter, A, The selection of an adhesive for a glass-adhesive T-beam, Int J Adhes Adhes (1998), Vol 18, pp159-165. Wellershoff, F; Sedlacek, G, Glued connections for new steel glass structures, Proceedings of Glass Performance Days, Tampere, Finland, 2005. Louter, C; Veer, F; Hobbelman, G, reinforcing glass, effects of reinforcement geometry and bonding technology, Proceedings of Glass Performance Days, Tampere, Finland, 2007. Weller, B; Schadow, T, Design of bonded joints in glass strucutres, Proceedings of Glass Performance Days, Tampere, Finland, 2007. Belis, J; Van Hulle, A; Out, B; Bos, F; Callewaert, D; Poulis, H, Broad screening of adhesives for glassmetal bonds, Proceedings of Glass Performance Days, Tampere, Finland, 2011.
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Copyright © 2012. IOS Press, Incorporated. All rights reserved.
[14] Overend, M; Jin, Q; Watson, J, The Selection and Performance of Adhesives for a Steel-Glass Connection, Int J Adhes Adhes (2011), doi:10.1016/j.ijadhadh.2011.06.001. [15] DC993 Product Data Sheet, http://www.geocel.co.uk/dynpdfs/416.pdf, http://www.dowcorning.com/, Ref No. 62-0918H-01, Dow Corning Corporation, July 2001. [16] Moibob, D, Glass panel under shear loading – use of glass envelopes for building stabilisation, PhD Thesis, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, 2008. [17] LUSAS Finite Element System, Lusas theory manual, FEA Ltd, UK, (2012). [18] ASTM D 1002-99, Standard test method for apparent shear strength of single-lap-joint adhesively bonded metal specimens by tension loading (Metal-to-metal), ASTM Standards (1999). [19] BS EN ISO 527-1: 1996, Plastics – Determination of tensile properties – Part 1: General principles, pp. 1-16, British Standards Institution BSI (1996). [20] BS EN ISO 527-2: 1996, Plastics – Determination of tensile properties – Part 2: Test conditions for moulding and extrusion plastics, pp. 1-14, British Standards Institution BSI (1996). [21] Cheng, S; Chen, D; Shi, Y, Analysis of adhesive-bonded joints with non-identical adherends, J Engineering Mechanics (1991), Vol.117, No.3. [22] BS EN ISO 12150-2: 2004, Glass in buildings: Thermally toughened soda-lime silicate safety glass, evaluation of conformity/product standard, pp. 1-42, British Standards Institution BSI (2004).
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-307
Load-Carrying Behaviour of Metal Inserts Embedded in Laminated Glass Kerstin Puller Werner Sobek Stuttgart, Germany, [email protected] IIT (Illinois Institute of Technology), Chicago, Illinois, USA Werner Sobek Werner Sobek Stuttgart, Germany, [email protected] IIT (Illinois Institute of Technology), Chicago, Illinois, USA ILEK (Institute of Lightweight Structures and Conceptual Design), University of Stuttgart, Germany The introduction of a new interlayer material for laminated glass – SentryGlas (SG) – has enabled the development of an innovative glass connection technique in which a metal element is embedded in the interlayer of the laminate and acts as a load-carrying device. At the ILEK tensile tests on the interlayer material were performed to determine the material properties of SG and to develop a numerical material model. Pull-out tests of the proposed metal insert system were carried out to study its load-bearing behaviour under tensile loading. A numerical simulation was performed to model the pull-out tests and to verify the material models developed. This paper focuses on the evaluation of the load transfer behaviour of this connection under short-term tensile loading at various temperatures and the simulated stress distribution within this multi-material system.
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Keywords: Insert, SentryGlas, Connection technique, Laminated glass
1. Introduction With the introduction of SentryGlas (SG), the company DuPont made available an interlayer material with superior stiffness properties at room temperature compared to previous interlayer products (PVB). This allowed the glass and also the laminate thickness to be reduced. The main purpose of the interlayer material is to bond different glass panes of the laminate in a planar manner, and, due to the ductility of the polymer increase the residual load-bearing capacity of the composite compared to the individual glass panes. But the increased stiffness and the ability of SG to adhere well to metal has also presented the opportunity for a new and innovative glass connection technique. This new connection technique uses a metal insert, which is partially embedded in the interlayer material of the laminate, as load transferring element and as a connector to the surrounding structure. First architectural applications of this connection technique are the stair details of the Apple stores [1], the connection of the “Seele-staircase” presented at the Glasstec 2006 [2] and the folding roof detail of the intermediate ceiling at the Zürich swimming hall [3]. Research conducted at the ILEK (Institute of Lightweight Structures and Conceptual Design, University of Stuttgart) studied the load transfer of inserts embedded in glass 307
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Challenging Glass 3
laminates through experiments and numerical simulations, and analyzed the stress distribution within the laminate in dependence of the insert geometry [4, 5]. Different loading durations and various temperatures were considered. The present paper focuses on the evaluation of the load transfer behaviour of this connection under short-term tensile loading and the simulated stress distribution within the multi-material system. 2. Load-carrying behaviour of metal inserts embedded in laminated glass In order to be able to describe the load carrying behaviour of metal inserts embedded in laminated glass, the behaviour of the interlayer material itself (SG) was studied in tensile tests using dumbbell-shaped specimens according to DIN ISO 527 [6]. Since the mechanical behaviour of SG greatly varies with the surrounding temperature, the tests were carried out at three temperatures (23 °C, 40 °C, 75 °C) which were found to occur in glass laminates in central Europe [7]. Based on the experimental data, material models for different temperatures and deformation rates were developed and used to perform a numerical simulation with the finite element software Ansys 12.1. A detailed description of the tensile tests performed, the material models and the numerical simulation can be found in [4, 5, 8]. While the stress state in the dumbbell-shaped specimens during the tensile tests was mainly uniaxial, a three-dimensional stress state occurs in the laminate material of the proposed connection system (metal insert embedded in the laminate). Thus, it was very important to verify that the material models developed could also be used to simulate the load-carrying behaviour of the proposed system. To do so, an experimental and numerical study was carried out.
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2.1. Experimental investigations A series of pull-out tests were performed on inserts embedded in glass laminates to study the load-carrying behaviour of the connection system and to record the forcedisplacement relationship. Figure1 and 2 show the test specimens.
Figure 1: Test specimen of pull-out test – front view. Metal insert (thickness = 1 mm) embedded in glass laminate.
Figure 2: Test specimen detail of pull-out test – perspective view. Metal insert (thickness = 1 mm) embedded in glass laminate.
In order to minimize the influence of measurement errors the specimens were designed so that the majority of the deformation occurred in the SG. Due to the fact that the stiffness of SG varies significantly over the temperature range investigated, the test specimens were dimensioned differently for the lower temperatures (23 °C, 40 °C) than 308
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Load-Carrying Behaviour of Metal Inserts Embedded in Laminated Glass
for the higher temperature (75 °C). To avoid yielding of the insert under small deformations, a high-strength steel (Domex 700 MC D) with a thickness of 4,56 mm was used for the insert of the low temperature tests. The chosen thickness corresponds to two times the largest foil thickness of SG. To prevent large eigenstresses in the laminate, the large thickness SG-foils were cut out in the areas where the insert was embedded. However, this procedure was not necessary for the high temperature test specimens for which a stainless steel insert (product number according to [9]: 1.4301) with a thickness of 1 mm could be used. The dimensions of the test specimens are listed in Table 1 and a schematic drawing shows the test setup in Figure 3. Table 1: Specimen dimensions in dependence of the test temperature.
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Test temperature [°C] 23/40
75
Glass pane thickness
[mm]
10
10
Glass pane width
[mm]
400
400
Glass pane height
[mm]
300
300
SG-thickness
[mm]
6 x 2,28
2 x 1,52
Insert-thickness
[mm]
4,56
1
Embedded length of the insert
[mm]
50
50
Embedded width of the insert
[mm]
25
25
Figure 3: Test setup for metal insert pull-out tests.
309 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
To avoid failure of the glass, supports were located close to the insert (support width each: 70 mm, spacing between supports: 100 mm). The insert was directly clamped by the lower jacks of the testing machine and a crosshead displacement rate of 1 mm/min was applied for all tests. Two potentiometers on each side of the glass pane measured the differential displacement between the insert and the glass pane. By averaging the differential displacements of potentiometers on opposing glass pane sides rotational displacements could be compensated. The recorded force-displacement relationships are shown in Figure 4. Due to the fact that the stiffness of SG varies significantly over the temperature range investigated, the data curves for the different temperatures can be clearly distinguished: the stiffness of the system is reduced with a rise in temperature.
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During the 23 °C pull-out tests, glass breakage occurred for two specimens around 26 kN. For another specimen, the insert started to slip out of the clamps due to an insufficient clamping force. This reduced the applied load (at around 30 kN). Subsequently the clamping force was increased and the test specimen was further loaded.
Figure 4: Force-displacement relationship of metal inserts embedded in a SG-glass laminate, pull-out test, specimen geometry according to Table 1, crosshead displacement rate: 1 mm/min, test temperatures: 23 °C, 40 °C and 75 °C.
During the pull-out tests at 23 °C and 40 °C debonding of the metal insert and SG could be observed at the insert end (Figure 5). The debonding typically started from the insert face which was perpendicular to the loading direction. At 75 °C bubbles formed at the insert end. The size of the bubbles increased with further applied deformation. After the debonding/bubble formation occurred, the slope of the force-displacement relationship 310
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Load-Carrying Behaviour of Metal Inserts Embedded in Laminated Glass
starts to decrease. This effect is most evident for the 40 °C and 75 °C forcedisplacement-curves and corresponds to a decrease of stiffness of the connection system (consisting of the metal insert embedded in the glass laminate).
Figure 5: Photographs of the insert end with visible debonding or bubble formation, left: 23 °C (potentiometer displacement: 0,7 mm, force: 40 kN); middle: 40 °C (potentiometer displacement: 1,2 mm, force: 20 kN); right: 75 °C (potentiometer displacement: 0,8 mm, force: 2 kN).
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2.2. Numerical simulation To verify that the material models developed [4, 5, 8] can be used to simulate the loadcarrying behaviour of the proposed system (metal insert embedded in the laminate), a numerical simulation of the pull-out tests was performed using the finite element software Ansys 12.1. One main aspect of the numerical simulation was to incorporate an iterative scheme adjusting the strain-rate distinct SG material model to the strain rate which occurred during the experiments. The iterative scheme is explained in detail in [4, 5]. Figure 6 shows the simulated force-displacement curves together with the experimental results.
Figure 6: Force-displacement relationship of metal inserts embedded in a SG-glass laminate: experimental and numerical results, pull-out test, specimen geometry according to Table 1, crosshead displacement rate: 1 mm/min, test temperatures: 23 °C, 40 °C and 75 °C; Multi-linear SG-material model with von-Mises-yield condition, enhanced-strain element formulation
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In general, the results of the numerical simulation fit the experimental results quite well. The largest discrepancy between the curves occurs for 40 °C. One reason for this discrepancy may be the proximity to SG’s glass transition temperature at which its stiffness significantly drops. However, due to the good agreement of the experimental and numerical results the applied numerical procedure and the material models developed can be used to simulate the load-carrying behaviour of metal inserts embedded in glass-laminates. Since no failure models were integrated in the analysis, the numerical model cannot estimate failure loads but can instead be used to evaluate the stress-strain distribution within the multi-material system.
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3. Stress distribution within an insert connection After the numerical results showed a good coincidence with the experimental data, the numerical model could be used to evaluate the stress-strain distribution within the multi-material system. With a view to suspended glass panes in architecture, the boundary conditions of the numerical model were adjusted: instead of modelling the experimental setup with supports close to the insert, the insert itself was supported and a line load applied to the lower glass pane edge (total line load: 1 kN; Figure 7). The insert and the laminate dimensions were identical with the dimensions of the 75 °C-pullout test specimens (Table 1).
Figure 7: Support and loading conditions of the numerical model evaluating the stress distribution within an insert connection (insert embedded in laminate); schematic drawing.
Figure 8 shows the stress distribution on the exterior and the interior glass pane face, in the SG and within the stainless steel insert. Since tensile stresses lead to glass failure and debonding of the SG, the first principle stresses are evaluated for glass and SG. With metal yielding being dependent on the equivalent von-Mises-stress, this stress distribution is shown for the stainless steel insert. All numerical investigations were based on SG-material models for 23 °C and 75 °C with a strain rate of 0,0059 s-1 (This strain rate is equivalent to the observed strain rate during the pull-out tests with the identical specimen dimensions (75 °C test series)). The numerical analysis shows that the load-bearing mechanism of the proposed connection comprises two components: load is transferred over the embedded surface area of the metal insert, and at the insert end. The force transferred by each component depends on the relative stiffnesses of the different elements in the multi-material system. Around 23 °C SG is relatively stiff, and most of the force at this temperature is 312
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Load-Carrying Behaviour of Metal Inserts Embedded in Laminated Glass
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transferred over the embedded surface area. This results in high tensile stresses at the upper glass pane edge. At 75 °C, the decreased stiffness of SG results in a relatively high tensile force at the insert end which generates high local tensile stresses.
Figure 8: Stress distribution within an insert connection at 23 °C and 75 °C: first principle stresses at the exterior and interior glass pane face, and within the SG, von-Mises equivalent stress in the stainless steel insert (product number according to [9]: 1.4301), rectangular insert geometry (embedded length: 50 mm, embedded width: 25 mm), total applied line load on the lower glass pane edge: 1 kN, multi-linear SG-material model with von-Mises-yield condition, strain rate: 0,0059 s-1, enhanced-strain element formulation.
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4. Conclusion and Outlook The experimental tests with the proposed system show that a significant load can be transferred through this type of connection. But the magnitude of load and the stiffness of the system strongly depend on the polymer temperature and the loading rate. Nevertheless, the results of the experiments are very promising. The force-displacement relationships of the performed numerical simulations agree well with the experimental data. Thus, the applied numerical procedure and the material models are suitable to simulate the stress-strain distribution within an insert connection. Subsequently, the stress distribution of a suspended glass pane with an insert connection was evaluated. The evaluation showed that the load transfer of the insert consists of two components: load is transferred over the embedded surface area of the metal insert, and at the insert end. The amount of force transferred by each component depends on the relative stiffnesses of the different elements in the multi-material system. Around 23 °C SG is rather stiff, and most of the force at this temperature is transferred over the embedded surface area. At 75 °C, the decreased stiffness of SG results in a relatively high tensile force at the insert end. This load transfer generates for 23 °C high tensile stresses at the upper glass pane edge, while for 75 °C high tensile stresses occur at the insert end. An approach followed in [4, 5] uses the insight of the stiffness dependent load transfer to optimize the load-carrying behaviour of the insert-laminate-system. In that approach the insert material is systematically relocated to reduce stress concentrations in the glass and to homogenize the stress distribution within the multi-material system. With an adjusted insert geometry, the stress concentrations can be significantly reduced under the same applied load and maintained embedded metal area.
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5. Acknowledgements The research was funded by the Federal Office for Building and Regional Planning, Germany (Reference number: Z6-10.08.18.7-08.24/II2-F20-08-21). The authors would also like to thank the members of the ILEK and the sponsoring companies (seele sedak, DuPontTM, Hottinger Baldwin Messtechnik) for their support. 6. References [1] [2] [3] [4] [5]
[6] [7]
[8] [9]
O´Callaghan, James, A case study of the Apple computer stores - glass structures 2001 - 2005, Proceedings of the Glass Processing Days, Tampere, Finland, 2005. Peters, Stefan; Fuchs, Andreas; Knippers, Jan; Behling, Stefan, Ganzglastreppe mit transparenten SGPKlebeverbindungen - Konstruktion und statische Berechnung, Stahlbau, 3/2007, pp. 151–156. Willareth, Philippe; Meyer, Daniel, A new folding glass roof for the historic city swimming hall Zürich, Proceedings of the Glass Performance Days, Tampere, Finland, 2011. Puller, Kerstin, Untersuchung des Tragverhaltens von in die Zwischenschicht von Verbundglas integrierten Lasteinleitungselementen, Phd-Thesis, ILEK, University of Stuttgart, expected: 2012. Puller, Kerstin; Denonville, Jürgen; Sobek, Werner, Hochleistungsfähige, materialminimale und werkstoffgerechte Verbindungstechnik im Glasbau, Research Report, Forschungsinitiative: ZukunftBau, Research project number: Z6- 10.08.18.7-08.24, ILEK, University of Stuttgart, expected: 2012. DIN EN ISO 527-2 – Kunststoffe: Bestimmung der Zugeigenschaften, Teil 2: Prüfbedingungen für Form- und Extrusionsmassen, 1996:07, Beuth, Berlin, Germany, 1996. Sobek, Werner; Haase, Walter, Temperaturversuche an Verbundsicherheitsglasscheiben unter Sonneneinstrahlung, Research Report, Zentrallabor des Konstruktiven Ingenieurbaus (now part of the ILEK), Universität Stuttgart, 2001. Puller, Kerstin; Denonville, Jürgen; Sobek, Werner, An Innovative Glass Connection Technique Using an Ionomer Interlayer, Proceedings of the Glass Performance Days, Tampere, Finland, 2011. DIN EN 10088-1 – Nichtrostende Stähle, Teil 1: Verzeichnis der nichtrostenden Stähle, 2005:09, Beuth, Berlin, 2005.
314 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-315
Direct Glass Fabrication – New Applications of Glass with Additive Processes Lisa Rammig HS-OWL, Detmold School of Architecture, Germany Inhabit Europe Ltd., London, UK, [email protected], www.inhabitgroup.com Direct fabrication technologies for different materials have been developed to great detail, yet for glass, one of the most aesthetically pleasing materials known, developments are still in the early stages. By examining material properties, common technologies and analysing the parameters governing the direct fabrication of glass the following conclusions can be made; Fabrication technologies are available but must be adapted for the properties of glass. This case study which was elaborated as part of a master thesis, tries to show these fabrication abilities by moving away from computer-controlled additive processes to a manual process, derived from conventional welding techniques used in the chemical industry.
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Keywords: Glass-Glass connections, Case study, Welding
1. Vision Digital technologies largely determine contemporary lives. In different sectors their importance´s grow further and further. Starting in the 1970’s with the first personal computers these technologies significantly influenced the functions of economy and society. Computer technologies give the possibility of mass production processes, where manual labour is not required and accuracy and therefore optimisation can be guaranteed. The development of digital fabrication moves from mass production to a more customized and individualized fabrication. It is possible to create the perfect product without reverting to single piece - handcraft - manufacturing. The customer becomes a part of the production again; the product grows to their taste. Whilst the direct fabrication of materials such as plastics or metals are now a sophisticated technology, the fabrication of glass, perhaps one of the most fascinating building materials, is almost unexplored. Glass is strong but brittle, heavy yet looks lightweight, and it is transparent. These properties have made glass an important component of our built environment today. Several types of glass such as laminated and insulated glazing, coated, curved, and free-formed glass panes have been developed rapidly after the float glass process was developed. Besides this progress in glass production, constructions have been further developed to increase a transparent architectural appearance. Current architecture is heavily influenced by digital media and modelling software, giving us the possibility to create almost anything. In turn, this has developed the need for glass of an overall higher performance. Free formed glass panes, 315
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each one different to the other, might fit perfectly together, but are singularly produced. At this point the question arises; why not use additive fabrication methods for glass production? It would give us the possibility to produce free-formed transparent building parts, without the complexity of the classical steps of production.
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In this case study, the opportunities and limitations of such a technology have been made with respect to material properties, current technologies, design parameters, recent developments, practical testing and possible areas of further research.
Figure 1: Glass processing: Scheme with integration of glass-glass connections and possible applications
2. Method 2.1. Glass the material Glass can be described physically as a rigid inorganic silicate product of amorphous nature. In contrast to crystalline materials it is characterised by its isotropy, which means that all properties, or measured values, are the same in each direction of the structure. Conventional glass such as Lime-soda glass consists of silica sand, lime and soda, all of which are natural raw materials. By the addition of other materials, properties such as stiffness and colour can be changed. Compared to other substances like metal or plastics, which can be defined by their chemical affinity, glass is described by its structural composition, which must be seen 316
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irrespectively of the chemical composition. The advantageous properties of glass such as light transmittance, thermal behaviour and solidness result from its structure. The composition of glass is described by its molecular structure, in which a freezing process is required to change glass from a liquid to a hardened state. Silica glass has the simplest structure; consisting of only silicon dioxide. Whilst the structure of a silica crystal is sorted [Fig 1], the atomic composition in its glass state are unsorted, therefore it is not a crystalline structure. The material seems to be ‘liquid’, but does not tend to creep or flow. The high proportion of silica sand [around 75 %] expresses the hardness, strength, and brittleness of the material. A brittle material fails or breaks after minimal deformation. The composition of the glass is a fundamental factor of the viscosity of the melt and the properties of rigid glass. As described, pure Silica glass tends to crystallize but has a very low coefficient of linear thermal expansion, which makes it resistant to temperature differences and thermal shocks. To lower the melting point of 1700°C for silica glass during the production process, Alkali is added to the melt. This enhances the coefficient of linear thermal expansion of the rigid material such that it can be melted at a lower temperature. Table 1: Glass compositions SiO2
Na2O
CaO
MgO
Al2O3
4
2
Silica Glass
100
Soda lime Glass
72
14
8
Borosilicate Glass
80
4
1
B2O3
3
12
Table 2: Comparison of main properties of lime-soda and borosilicate glass Soda lime Glass
Borosilicate Glass
2490
2230
6-7
4.5
8.4
3.3
Thermal conductivity [W/m K]
450 x 30
4500
Softening point [°C]
710-735
825
1015-1045
1260
70000
63000
0.2
0.2
30
30
700-900
700-900
30-80
70
7
7
68.02
192.4
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3
Density [kg/m ] Scratch hardness on the Mohs hardness scale -6
-
Coefficient of mean linear expansion 10 [K ] (20-300 °C) 2
Processing temperature [°C] 2
Modulus of elasticity E [N/mm ] Poisson Ratio 2
Bending Strength [N/mm ] 2
Compressive Strength [N/mm ] 2
Tensile strength [N/mm ] (at constant load) Maximal thermal shock resistance Tmax [K]
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2.2. Technical Parameters This section gives a brief overview of the technical parameters governing the development of Direct Glass Fabrication (DGF): x x x
The coefficient of linear thermal expansion is an important value for the applications of glass; especially for the analysis of the material with respect to rapid manufacturing processes. The theoretical strength of the glass expresses the stiffness as a result of the bond strength of individual components and assumes a crack-free glass. This is an unrealistic assumption as small cracks occur during the production. The practical strength takes into account such cracks and is therefore significantly lower. This strength value is crucial for the dimensioning of components.
Borosilicate glass is primarily used in chemical and pharmaceutical industries because it offers better chemical resistance, and a lower coefficient of linear thermal expansion. This significantly enhances its resistance to large temperature differences induced by the additive fabrication process. As such, Borosilicate glass can be used as display materials for windows, fireplaces, and fire protection glass due to its good thermal properties.
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Another important factor is the viscous performance of the material. When a crystalline substance gets heated, it will melt at a certain temperature. Above this temperature, the substance will be liquid. In contrast to that, glass does not have a melting point; it softens continuously under the influence of temperature. The organized atomic structure of a crystal leads to a hard solid material, whilst glass on the other hand, has an irregular structure and therefore behaves like a cooled liquid. For a DGF addition on a usually fabricated glass sheet, the whole pane of glass must be heated to a uniform temperature, which is limited by the thermal shock resistance of the glass (Tmax =192.4 K) this is typically 370°C for borosilicate glass.
Figure 1: Ratio of Volume and Temperature showing the viscous performance
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3. Practical Application Different types of connections were manufactured to compare and evaluate atomic bonding. Firstly, the behaviour of glass-glass connections was tested and the degree of precision as to which they could be made. The applications of layer-by-layer fabricating were then completed to simulate a ‘real’ additive process. The testing of the welded connections showed that the failure of the material in most cases occurs within the region of the original material, confirming that the connections are stiffer than the raw material. This verifies that it is possible to manufacture glass with the additive processes to generate strong connections.
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Figure 2a and b: First experiments of layer by layer application
This first step demonstrated that glass-glass connections can be produced manually but furthermore it had to be proved that a layer-by-layer production is possible. This was done by heating a thin glass rod, elongating it to a thin wire, and then welding it on to a pane of glass. To verify that the connected layers have a constant high temperature, such that bonding with the next layer is possible. The question arises, how could such a production method be used in architecture or the façade industry and what products could it possibly develop? To develop applications from basic production principles, a glass point fixing was designed (Fig.3+4) which can be attached to the glass pane by an additive process. This was then fabricated and tested for numerous connections. The point fixings would be mounted to the sub construction with a clamp, which gathers the loads via friction.
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Figure 3: fracture mechanical testing of connections
Figure 4: conchoidal fracture
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When compared to conventional point fixations, one of the main advantages is that the quantity and size of fixings can be determined individually for each pane. Attachments are optimized based on the dead load, wind load, and other influences. The most important advantage of the point fixing however, is the removal of the need to drill the glass panes. Resulting in less stresses being induced and thermal losses are reduced, as there is no thermal bridging. The penetration of the outer pane is avoided, which means that the thermal separation of the facade is uninterrupted. This is of significant importance for the northern European climate, especially with current energy savings regulations and sustainability considerations when regarding energy resources.
Figure 5: Glass point fixing fabricated in a manual additive process
Figure 6: Scheme of point fixation via friction
320 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Direct Glass Fabrication – New Applications of Glass with Additive Processes
4. Innovation Direct fabrication technologies for different materials have been developed to great detail, yet for glass, one of the most aesthetically pleasing materials known, developments are still in the early stages. By examining material properties, common technologies, and analysing the parameters governing the direct fabrication of glass, the following conclusions can be made: x
x x x
Fabrication technologies are available but must be adapted for the properties of glass. This case study research tries to show these fabrication abilities by moving away from computer-controlled additive processes to a manual process, derived from conventional welding techniques used in the chemical industry. The major problem when dealing with larger panes of glass is that they have to be heated carefully to avoid breakage of the material. Properties in which the behaviour of the glass can be modified are its viscosity, the thermal linear expansion coefficient, and its resulting maximal thermal shock resistance (Tmax) A proper annealing process has to be guaranteed, to avoid thermal stresses in the connections.
For the fabrication of large products, which could not be built in the construction space of rapid prototyping machines, special heating and cooling components are required to provide the object with uniform heat. Partial heating of the glass would result in material breakages caused by thermal stresses.
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The developed point fixing technique highlights DGF´s applicability to facade design. By producing a fixing which connects the glass panes to the primary facade without penetration of the outer pane can lead to new opportunities in facade construction. It would be possible to construct facades without thermal breaks and without the visual
disturbance of conventional point fixings. It has been shown that the additive process of producing glass is successful, the results also encourage further research to be undertaken within the field such that products can be developed which are truly representative of such technological advances.
5. References [1] [2] [3] [4] [5] [6] [7]
Hopkinson, N; Hague, R.J.M.; Dickens, P.M; Rapid Manufacturing, John Wiley & Sons Ltd, Chichester, 2006 Neef, A.; Burmeister, K.; Krempl, S. Vom Personal Computer zum Personal Fabricator, Murmann, Hamburg, 2005 Lohmeyer, S. et al. Werkstoff Glas, Expert Verlag, Grafenau, 1979 Wörner, J.D. ; Schneider, J.; Fink, A Glasbau, Springer, Berlin, 2001 Petzold, A. ; Marusch, H. ; Schramm, B. Der Baustoff Glas, Verlag für Bauwesen Berlin, 1990 Rammig,L. Direct Glass Fabrication-New applications of glass with additive Processes, HS-OWL, 2010 Wiggington, M. Glas in der Architektur, Deutsche Verlags-Anstalt GmbH, München 2003
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-323
Analytical Solutions for Detail Problems in Structural Glazing Matthias Seel, Geralt Siebert Universität der Bundeswehr München, Germany, [email protected], [email protected], www.unibw.de/glasbau
Detail points play a crucial role in the calculation of stress in structural glazing. Drill holes, point fixing by clamps or plane discs with drill holes and glued connection are such detail points. The calculation of these details is usually done by using the finite element analysis (FEA). But the scatter of the FEA results is very big – which means that the quality can be evaluated as low. The FEA results depend on the applied FEM software and the modeling by the user. Therefore, it is always necessary to compare FEA-results with solutions of comparable problems for excluding inadequate FEA models. In this paper, several analytical solutions for detail problems in structural glazing are derived and presented. These analytical solutions can be used for validation of point fixing systems (mechanical and glued). Keywords: Detail points, Point fixing, Stress concentration, FEA validation, Plates
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1. Introduction The desire for more transparency in the architecture can be achieved by point fixings. Due to this fact, punctual supports are popular among architects and builders. The profit of transparency precludes the complex design. The calculation of stress values (e.g by finite element analysis (FEA)) in the area of a point fixing is sophisticated, if the results should be close to reality. Research activities (e.g. ‘Beyer’ [1], ‘Siebert’ [2], ‘Seel’ [3]) on the mesh quality of different FEA-models for point fixings show that stress and deformation values can be calculated more or less accurately in such cases. It is possible, that the deviation from realistic values can be more than 30 % without being identified as poor values. The FEA software offers the engineer a good possibility to calculate complex mechanical structures-like punctual supported structures-in a realistic way. Using elaborate FEA software gives the user the feeling of having covered everything. The FEA results depend on the applied FEA software and the modeling by the user. Therefore, it is always necessary to exclude inadequate FEA models by validation with solutions of comparable problems. A validation process can be done by testing or by comparison with existing analytical or numerical solutions. In the field of structural glazing, tests are used for validation of FEA results (e.g. with strain gauges and displacement sensors). These tests are necessary to validate the results, but are at the same time very time-consuming and require a lot of experience. Analytical solutions for the validation of FEA results can be more suitable than complex tests. 323 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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The aim of this paper is to present analytic solutions for detail points in structural glazing. These solutions can be used for a validation process in the field of FEA. 2. Analytic solutions for circular plates with and without a center hole 2.1. Theory The bending surface of a thin, isotropic and elastic circular plate can be described by the linear, partial inhomogeneous differential equation (ODE) of the fourth order:
§ w 2 w 1 ww 1 w 2 w · § w 2 w 1 ww 1 w 2 w · ¸¨ ¸ 2 ''w ¨ 2 2 2 ¸¨ 2 2¸ ¨ wr w G r r r r w w w M M r r r © ¹© ¹
p(r , M ) K
(1)
with w
displacement in z-direction
r
Radius
Angle
p(r, )
load function
K=Eh³/12/(1- ²)
plate stiffness.
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The detailed derivation of the Eq.(1) can be found in the relevant literature e.g. ‘Girkmann [4]’, ‘Timoshenko & Woinowsky-Krieger [5]’ and ‘Márkus [6], [7], [8]’. Eq. (1) can be solved by using numerical or analytical approaches. In few cases it is possible to get an exact solution. An exact solution must satisfy all boundary conditions and Eq. (1). A circular plate with center hole and rotationally symmetric load p(r,) is illustrated in figure 1. For such plates the equation can be solved. The presented solutions here are based on analytic approaches and the classic plate theory of Kirchhoff. In general, the solution for the unknown bending surface w consists of a homogeneous wh and a particular function wp:
w (r , M )
wh (r ,M ) wp (r ,M ).
(2)
If the displacement function w(r, ) of the plate is known, the internal forces (e.g. moments) are determined by the following equations:
mr
§ w2w § 1 ww 1 w 2 w · · ¸¸ K ¨ 2 P ¨ ¨ r wr r 2 wM 2 ¸ ¸ ¨ wr © ¹¹ , ©
(3)
mM
§ 1 ww 1 w 2 w w 2 w ·¸ 2 K ¨ P ¨ r wr r wM 2 wr 2 ¸¹ , ©
(4)
324 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Solutions for Detail Problems in Structural Glazing
mr ,M
mM , r
§ 1 w 2 w 1 ww · ¸ (P 1) K ¨ ¨ r wrwM r 2 wM ¸ © ¹.
(5)
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Figure 1: Circular plate with center hole and rotationally symmetric load p(r,) (‘Seel [3]’)
The equations for the shear forces qr and q are not shown for clarity and limits of this paper. The principal stresses H can be calculated by:
V H1/ H 2
§ § mr mM 12 ¨ mr mM z r ¨¨ 3 ¨ 2 2 h ¨ © ©
2 · · ¸ ¸¸ mr2,M ¸ ¸. ¹ ¹
(6)
The maximum/minimum stress in the cross-section is obtained by substituting z=h/2 in Eq. (6) and the location of the maximum/minimum in the whole area is given by:
wV H 1 / H 2 wr
0,
(7)
wV H 1 / H 2 wM
0.
325 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
(8)
Challenging Glass 3
Results of Eq. (2) can be determined by using adequate analytical approaches and by consideration of boundary conditions (BC) as well as transition conditions (TC). In the following sections analytical solutions (‘Seel’ [3]) are presented for some load cases. 2.2. Circular plates with center hole and rotationally symmetric load For simple cases of circular plate there are some analytical solutions available in literature e.g. ‘Márkus [6], [7], [8]’. ‘Beyer [1]’ presented a solution for partially constant loaded circular plate with a center hole. In this section, an analytical solution for partially loaded circular plate is presented ‘Seel [3]’. The plate with center hole and linearly varying load p(r) is illustrated in figure 1. The displayed plate is divided into 4 areas (B). The origin is in the center of the circular plate. Area B-0 describes the center hole, B-I the inner unloaded area next to the area B-0, B-II the loaded and B-III the outer unload area. The plate is fixed by a simple support in z-direction at the outer circle (r=a). In the following, the radius is replaced by a scaled radius:
U
r . a
(9)
The described problem can be solved by using the following analytic approaches for each area: wI ( U )
wII ( U )
CI ,1 U 2 ln U CI , 2 U 2 CI ,3 ln U CI , 4 ,
a 4 U 4 ( p2 r1 p1r2 ) a 5 U 5 ( p1 p2 ) CII ,1 U 64 K (r1 r2 ) 225 K (r1 r2 ) 2
(10) 2
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1· § C II ,3 U 2 ¨ ln U ¸ 2¹ © C II , 2 ln U C II , 4 , 2 wIII ( U )
,
CIII ,1 U 2 ln U CIII , 2 U 2 C III ,3 ln U CIII , 4 .
(11)
(12)
The approaches of the unload areas (B-I and B-III) have only a homogeneous solution function wh,i presented by the integration constants Ci,j. Index i is the number of the area and index j the number of the integration constants in the area i. The approaches for the homogeneous solution wh,i are listed in ‘Girkmann [4]’ and ‘Márkus [6]’. The particular solution wp,i is obtained by integrating the Eq. (1) by consideration of the load function p(r). Each displacement function (Eq. 10 to 12) contains four integration constants Ci,j. The integration constants are determined by the boundary and transition conditions. The individual areas are linked via 4 transition conditions.
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Analytical Solutions for Detail Problems in Structural Glazing
Between area B-I and B-II, for instance, the utilised transition conditions are:
wI
wII ,
w wI wr
w wII , wr
(13)
(15)
mr , I
mr , II ,
(14)
qr , I
qr , II .
(16)
For this case the boundary conditions at the hole edge are:
mr , I
0,
(17)
qr , I
0 ,
(18)
wIII
0.
(20)
and two BC’s at the outer edge given by:
mr , III
0,
(19)
The 12 unknown integration constants Ci,j are calculated from linear equation system with 12 equations. The 12 equation are based on the 4 boundary and 8 transition conditions. Due to the size of the constants, they are not listed here.
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With the known constants it is possible to calculate the displacement and stresses at every point of the plate according to equations presented in section 2.1. The course of principal stress and displacement are illustrated in figure 2 for example 1.
a: principal stress H
b: displacement w()
Figure 2: Solution for a circular plate with center hole and rotationally symmetric load p(r) (see fig. 1)
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2.3. Circular plates with center hole and rotationally antisymmetric load A circular plate with center hole under a rotationally antisymmetric load is pictured in figure 3. This load case presents a moment. A moment is transferred by mechanical and glued point fixings. The plate is separated into four areas (see section 2.2.). In contrast to a circular plate with a rotationally symmetric load the displacement and internal forces are not constant over the angle for a rotationally antisymmetric load. The load varies along an arc according to a cosine function. Because of the cosine load-function the system behavior of the circular plate will change as cosinusoidal.
Figure 3: Circular plate with center hole and rotationally antisymmetric load p(r,) (‘Seel [3]’)
The following analytic approaches with a cosine function are used to solve Eq. (1) for this problem: wI ( U , M )
C · § ¨¨ C I ,1 U ln U C I , 2 U 3 I ,3 C I ,4 U ¸¸ cos M , U ¹ ©
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Analytical Solutions for Detail Problems in Structural Glazing
wII ( U , M )
§ a4U 4 § r p 2 p1 · a 4 U 5 ( p 2 p1 ) ·¸ ¨ ¸¸ ¨¨ p1 1 ¨ 45 K © a r2 a r1 a ¹ 192 K r2 a r1 a ¸ ¸ cos M ¨ C II , 4 ¸ ¨ 3 ¸ ¨ C II ,1 U C II , 2 U C II ,3 U ln U U ¹ ©
(22)
wIII ( U , M )
C · § ¨¨ C III ,1 U ln U C III , 2 U 3 III ,3 C III , 4 U ¸¸ cos M . U ¹ ©
(23)
The boundary and transition conditions for the problem pictured in figure 3 are the same as in section 2.2 with one exception. At the edge there are three boundary conditions (shear force, bending and twisting moment), but the plate theory of Kirchhoff requires only two boundary conditions. The twisting moment mr, and the shear force qr have to be combined to an equivalent shear force q*r at the free edges: q*r
§ 1 GmrM r¨¨ q r r GM ©
· ¸ ¸ ¹
0.
(24)
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The three BC’s are reduced to two BC’s with the help of Eq. (24). The integration constants Ci,j are obtained by solving a set of 12 equations, which consider all boundary and transition conditions. The integration constants are not listed here because of their huge size. The internal forces, stresses and displacement can be calculated by using the integrations constants, analytic approaches and equations in section 2.1.
a: principal stress H1
b: displacement w(,)
Figure 4: Solution for a circular plate with center hole and rotationally antisymmetric load p(r,) (see fig. 3)
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2.4. Circular plates under rotationally symmetric load and antisymmetric load Eq. (1) can be solved for circular plates without a center hole. The solution approaches and transition conditions for rotationally symmetric/rotationally antisymmetric load are the same as in section 2.2/2.3. Only the boundary conditions in area B-I are different. The boundary conditions in the middle ( =0) of the circular plate are: wwI zf, wU
(25)
wI z f .
(26)
From these equations the integration constants can be obtained as:
CI ,1 CI ,3
0 .
(27)
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The remaining integration constants Ci,j can be determined in the same way as described in section 2.2 and 2.3. The analytical solutions for these cases are described in detail in ‘Seel [3]’.
Figure 5: Circular plate without center hole and rotationally symmetric load p(r,) (‘Seel [3]’)
3. Comparison of Results
3.1. Introduction In this chapter calculations are carried out to compare the results of the analytic approaches with the Finite Element Analysis (FEA) results.
The material data from table 1 are the same for all examples. The geometry data for the circular plate with center hole (example 1) are listed in table 2. The used FEA-model for the comparison consists of thin 4-node shell elements with 128 approximately square elements around the center hole. This FEA-model is in accordance with the requirements of ‘Siebert [2]’ for an adequate mesh around a center hole. ‘Siebert [2]’ showed that the mesh quality around the center hole has an important influence on stress value. 330
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Solutions for Detail Problems in Structural Glazing Table 1: Circular plate with and without center hole – material data Parameter
Symbol
Unit
Value
Young’s moduls
E
[N/mm²]
70000
Poisson’s ratio
[-]
0.23
Material behavior
-
-
linear elastic (Hook)
Table 2: Circular plate with center hole (example 1) – geometry data Parameter
Symbol
Unit
Value
thickness
h
[mm]
10
radius of center hole
r0
[mm]
10
radius of p1
r1
[mm]
15.2
radius of p2
r2
[mm]
30
support radius
a
[mm]
60
3.2. Circular plates with center hole and rotationally symmetric load The load values for example 1-sym. are given in table 3. Figure 1 shows the static system of this example.
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Table 3: Example 1-sym. - rotationally symmetric load Load-parameter
Symbol
Unit
Value
load at r1
p1
[N/mm]
2
load at r2
p2
[N/mm]
1
The analytic results (principal stress and displacement) for this example are shown in figure 2. The results (maximum values) for the two calculation methods are listed in table 4. The maximum deviation between the two methods is 0.05% at the hole. Figure 6 shows the course of the principal stress deviation over the radius r. The minimal deviations can based on rounding and numerical errors. The results show that the two approaches provide approximately the same results. Table 4: results - rotationally symmetric load Parameter
Symbol
Unit
FEA
Analytic Solution
Analytic Solution
FEA /
Principal stress, max.
H1
[N/mm²]
46.297
46.318
99.95 %
Displacement, max.
w
[mm]
0.0841
0.0841
100 %
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Figure 6: Comparison FEA with analytic solution for a circular plate with center hole and symmetric load
3.3. Circular plates with center hole and rotationally antisymmetric load The rotationally antisymmetric load data for the circular plate center hole (see figure 3) are listed in table 5.
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Table 5: Example 1-anti-sym. - rotationally antisymmetric load Load-parameter
Symbol
Unit
Value
load at r1 and =0°
p1
[N/mm]
5
load at r2 and =0°
p2
[N/mm]
10
The maximum displacements and principal stresses of each method are presented in table 6 and figure 7. A stress difference of 0.25% at the center hole is the maximum deviation between FEA and analytic solution according to section 2.3. Also here can be shown, that both methods lead to the same results. Table 6: results - rotationally anti-symmetric load Parameter
Symbol
Unit
FEA
Analytic Solution
Analytic Solution
FEA /
Principal stress, max.
H1
[N/mm²]
43.375
43.385
99.98 %
Displacement, max.
w
[mm]
0.0334
0.0334
100 %
332 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Solutions for Detail Problems in Structural Glazing
Figure 7: Comparison FEA with analytic solution for a circular plate with center hole and antisymmetric load (=0°)
4. Conclusion Due to the technical progress and claims in the field of architecture the structures become more and more complex. The determination of the structural behavior is usually done by FEA. It seems to be simple to produce results via the user-friendly FEA software, but there can be a big difference in the quality of these results.
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The reasons for the differences are usually based on inadequate FEA software and actual modeling done by the user. It is always necessary to exclude inadequate FEA results. In this paper, analytical solutions for detail problems (e.g. punctual support glass panes with bore holes) in the field of structural glazing are derived and presented. Due to the extensive equations required for solving these problems a software tool for stress and displacement calculations was developed. The tool can be downloaded from www.unibw.de/glasbau/Download. In the new German DIN standard DIN 18008-3 ‘Glass in Building-Design and constructions rules-Part 3: Point fixed glazing [9]’ there is a simplified method - called SLG-method ‘Beyer [6]’- for stress and displacement calculations of point fixed glass. The analysis of two stress components of the SLG-method is done by the solutions presented in sections 2.2 and 2.3. The results are listed in ‘AIF-Forschungsbericht 16320N [10]’. The developed solutions ‘Seel [3]’for circular plates with and without center hole under symmetrically and anti-symmetrically load can be used for a validation process of point fixing systems (mechanical and glued).
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5. References Beyer J., Ein Beitrag zum Bemessungskonzept für punktgestützte Glastafeln, Dissertation, Darmstadt, 2007 [2] Siebert B., Beitrag zur Berechnung punktgestützter Gläser, Dissertation, Technische Universität München, 2004 [3] Seel, M.: Beitrag zur Bemessung von punktförmig gelagerter Verglasung, Dissertation in Vorbereitung, Professur für Bauphysik und Baukonstruktion an der Universität der Bundeswehr München, Neubiberg, 2012 [4] Girkmann, K., Flächentragwerke, Band 6, Springer Verlag, Wien, 1963. [5] Timoshenko S.; Woinowsky-Krieger S, Theory of Plates and Shells, Second Edition, McGraw-Hill, Tokyo, 1959. [6] Márkus G., Theorie und Berechnung rotationssymmetrischer Bauwerke, 3. Auflage, Werner Verlag, Düsseldorf, 1978. [7] Márkus G., Kreis- und Kreisringplatten unter antimetrischer Belastung, 1. Auflage, Ernst und Sohn Verlag, Berlin, 1973. [8] Márkus G., Kreis- und Kreisringplatten unter periodischer Belastung, 1. Auflage, Werner Verlag, Düsseldorf, 1985. [9] E DIN 18008-3, Glass in Building –Design and construction rules Part3: Point fixed glazing, DIN Deutsches Institut für Normung e. V., Berlin, 2011 [10] AIF-Forschungsbericht 16320N, Standardlösungen für punktförmig gelagerte Verglasungen Ermittlung der Standsicherheit und Gebrauchstauglichkeits, Deutscher Stahlbauverband, Düsseldorf, 2012
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[1]
334 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-335
Glazing with Countersunk Point Fittings Geralt Siebert Universität der Bundeswehr München, Germany, [email protected], www.unibw.de/glasbau Tobias Herrmann Ingenieurbüro Dr. Siebert, Germany, [email protected], www.ing-siebert.de In contrast to raised head point fittings the countersunk alternatives enable a flat and even surface. But there is an uncertainty amongst many engineers regarding the correct structural design of those systems. Present paper collects and arrays design influencing parameters. A lot of them are incorporated in an automated calculation tool using the programming interface of a multipurpose FEA software. Extensive calculations enable an estimation of sensitivity to respective parameters. Further material behavior of synthetic intermediate layers is described with remarks on hyperelasticity and viscoelasticity. Finally effects of the bolting torque are presented.
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Keywords: Glass, Countersunk, Point Fixing, FEA, Elastomer
1. Motivation Plenty of authentic structural calculations treating point fixed glass elements showed a high uncertainty (or unconcern) regarding correct solution of such a design task. It is obvious that missing treatment of structural glass design during academic education in the past is only one reason for this problem. Particularly the high complexity of these comparatively small structural elements is often underestimated. E.g. it is not uncommon that software developed for plates made of reinforced concrete is used, as special glass software is unavailable or general FEA software is unaffordable. Following design task (see Fig. 1) is solved by means of different FE – models of rising complexity. That is to say, that the author intentionally started with a simple plate model with nodal supports (Type 1) and subsequently developed various types (2 – 6) of models implementing substitute springs, adapting the mesh around the bore, introducing 3D-elements and finally considering contact mechanism. The goal is to demonstrate the great bandwidth of results (see Fig. 2) that can be generated on the basis of just one structural task, without adequate knowledge about the appropriate translation into a computational model. The example further confirms that stress around the glass bore is subjected to a larger uncertainty than at homogenous area of mid span. Authors’ research findings shall serve to reduce uncertainties and hence improve the quality of structural design of glazing with countersunk point fittings.
335 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 1: Definition of design task (extract)
Figure 2: Stress results calculated by means of different types of numerical models with raising complexity
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2. Influencing Parameters A large number of parameters effect final results of stress and deformation. They can be assigned more or less clearly to the following classes [1]: x Functional factors x Structural characteristics x Geometric parameters x Material properties x Load bearing mechanisms x Boundary conditions x FEA specifics Functional factors comprise the purpose of the glazing, the associated type of load, the type of load-bearing structure and special requirements (i.e. residual load bearing capacity). Most of these parameters are obvious and often given by the architects draft and common technical rules. Structural characteristics stand for the translation of above requirements to a basic design that is to say choosing the type of glass and support bearing in mind the substructure. Dimensions of the glass plate, its (countersunk) drillings, the point fitting’s components and respective tolerances make up the class of geometric parameters. While mechanic properties of glass and metal are well-known, plastic interlayer as part of laminated glass or as part of the point fittings in particular present the sophisticated section of the material properties (see Chap. 4). A point fixed glazing consists of several detachable components. Loads are transferred by means of contact and friction between these parts. Simple design software usually does not offer these kinds of load bearing mechanisms. Shear transfer in laminated glass is another part of this category. The class of boundary conditions comprises all loads and supports that define the margin of the structural system. Eccentricities, flexibility of bearings and the bolting torque (see Chap. 5) are important parameters in this context. 336 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Glazing with Countersunk Point Fittings
Finally all parameters concerning the translation of above mentioned into a computational model and the computation itself are collected in the group of FEA specifics. Basically by means of the parameters of the first 6 classes an exact and complete description of every structure is possible. But the following problems lead to a wide scope of results: x x x
Lack of knowledge about the parameters Misinterpretation or neglect of the parameters Wrong or incomplete translation into computational model
3. Development of parameterized FEM model To get an impression in what extend above parameters effect the resulting stress a parameterized FEM model is developed [1]. It enables a quick examination of various parameters by means of two systems: x x
double symmetric glazing with four countersunk point fittings all sides line supported glazing with centric countersunk point fitting
The considered parameters of the former are given in Table 1.
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Table 1: Parameters considered in automated calculation Functional
Structural
Geometric
Material
Load bearing
Boundary conditions
FEA specifics
Plate with four point fittings
Countersunk fitting
Glass plate:
Linear elastic
Two-sided contact:
Loads
Diameter of radial mesh
Support:
Width of transition to rectangular mesh
Height Width
Washer
Thickness
Bushing
Load type:
Glass type:
Bore:
Distributed load
Monolithic
Location Diameter
Center load
Young’s Modulus of all components
Countersunk Fixing type: Rigid Hinged
Clamping disc, Washer: Diameter
Poison ratio of all components
Friction in contact areas:
Degrees of freedom
Various coefficients
Substitute springs Preload of bolt
Mesh density bore: Radial Tangential
Thickness
Transversal Mesh density:
Bushing, Countersunk head:
Point fitting components
Thickness
Geometric nonlinear computation
Eccentricities of pin joint and substructure
337 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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3.1. Programming Two approaches are pursued: x x
Parametric study Single Model analysis
The former shall enable an easy way to cover a large bandwidth of respective parameter with tabular output for further manipulation to diagrams. The second one shall allow a quick and user friendly calculation of one configuration.
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The multipurpose FEA-software MSC.MarcMentat® provides a programming interface (program language Python) to generate input files and handle the post-processing. Besides it is possible to extend graphical user interface with own menus and input fields. Figure 3 shows the procedures of both approaches. Examples are given in the next section.
Figure 3: Procedures of parameterized calculation
338 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Glazing with Countersunk Point Fittings
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3.2. Examples The first example investigates the influence of the countersunk angle on glass stress. A squared glass plate with one rigid point fitting is loaded by a transversal force V and normal force N. The countersunk angle (and thereby the angle of the countersunk head) varies between 60° and 120°. The diagram in Fig. 4 points out that maximum glass stress at bore rises considerably under transversal loading with increasing angle , while under normal loading almost no change is recognized.
Figure 4: Example 1 - Influence of countersunk angle on glass stress
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The second example (see Fig. 5) examines sensitivity of glass stress and deformation of point fitting to the stiffness of washer and countersunk bushing. Results show that at least for the configuration of this example lower Young’s moduli of the bushing lead to lower stress and higher deformations. The influence of washer’s stiffness becomes higher if a stiff bushing (i.e. aluminum) is chosen.
Figure 5: Example 2 - Influence of intermediate layer stiffness on stress
340 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Glazing with Countersunk Point Fittings
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Final example is a squared plate with four point fittings under distributed load. The eccentricity e of the pin joint is varied with influence on glass stress. Calculations are performed for compression and tension load. Besides sensitivity to Young’s modulus of washer Et is examined. The diagram (see Fig. 6) shows that a stiff washer increases stress’ sensitivity to eccentricity of the pin joint.
Figure 6: Example 3 - Influence of pin joint’s eccentricity on stress
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4. Polymer interlayer of point fixings 4.1. General The washer and the countersunk bushing nearly represent the smallest components of the whole glazing. Nevertheless their influence on the load bearing behavior is huge. Their basic function is to prevent direct contact between fitting’s metal components and glass. Therefore they must resist UV radiation and detergents. Machinability, stability against changes in temperature and last but not least costs are further criteria. Common materials are polymers like ethylene propylene diene monomere rubbers (EPDM, not for bushings), polyoxymethylenes (POM), silicones and polyamides whose compounds are chosen in a way that above requirements are satisfied. EPDM is an elastomer. Elastomers are nearly incompressible and by comparison to other polymers soft. Large imposed strains generate large transverse strains. If these are inhibited a tremendous increase of stiffness results. This effect should not be neglected during design. POM or other stiffer materials do not show this behavior because strains and Poisson’s ratios are usually smaller.
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4.2. Hyperelasticity of elastomers As strains of soft materials like elastomers are large, Hooke’s law is not longer valid. Special approaches for large strain material use the strain energy density W to define a material law. W is calculated by means of the stretch ratios i (see Fig. 7).
Figure 7: Definition of stretch ratios i
342 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Glazing with Countersunk Point Fittings
For incompressible materials like elastomers Mooney [2] proposed
C1
W
§
O O O C ¨¨ 1 2
2
2
1
2
3
2
© O1
2
1
O
2
2
· 3¸ O 3 ¸¹ . 1
2
(1)
The stress tensor is derived by derivation of W with respect to . In the simple case of uniaxial load principal stress becomes
V
11
ª § § 1 ·¸ 1 ·º C2 ¨1 3 ¸» . 2 «C1 ¨ O 1 «¬ ¨© O1 ¸¹ ¨© O1 ¸¹»¼
(2)
Above equation shows the strong nonlinear relation between stress and stretch. The coefficients must be determined by testing. High performance FEA codes manage hyperelastic material models, but computing time rises considerably. Therefore stiffness of point fitting’s elastomer washer is approximated by Hooke’s law. Two cases (see Fig. 8) are distinguished that take into account the limit states of friction: x
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x
Free transverse movability at interfaces between elastomer / clamp disc and elastomer / glass (free) Transversal strains set to zero at interfaces (blocked)
Figure 8: Section through elastomer washer – limit states ‘free’ and ‘blocked’
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Beginning with the free boundary an equivalent Young’s modulus Efree can be determined by comparison of a Hooke’s spring with a Mooney’s spring [1]:
E
free
2 · § ¨ 3 3 w §¨ w ·¸ ¸ ¨ t © t ¹ ¸¹ § w · 2 © ¨ C1 C1 C2 ¸ . 3 t © ¹ § w· ¨1 ¸ t ¹ ©
(3)
The remarkable effect of blocking transversal strain at the interfaces is approximated by equation (4) [1]. It is based on a parametric FEA study and only valid for hollow cylinders with a ratio between inner radius ri and thickness t bigger than 2.5 and compressive strains smaller than 10 % (see Fig. 9).
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E
blocked
§¨ 0,345 ©
f
2 Form
1,44 ·¸ E free . ¹
(4)
Figure 9: Effect of blocking transversal movement at interfaces of elastomer washer on compressing stiffness
4.3. Visco-elasticity Beyond nonlinearity towards static strains the strain rate dependence of polymers causes further efforts for the exact simulation of material behavior. Relaxation and creep are the keywords regarding long-term loads. Fig. 10 shows corresponding courses of strain and stress towards time.
344 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Glazing with Countersunk Point Fittings
Figure 10: Characteristic time-dependent behavior of visco-elastic material
In case of horizontal glazing creep of polymer interlayer (inside point fitting and laminated glass structure) leads to additional deflections under dead load. Relaxation of the point fitting generated by the bolting torque occurs as the compressive stress of the elastomer washer is partially dissipated (see Chap. 5). As mathematical description for a material model considering time-dependent behavior following equations can be applied. For small strains (Hooke’s law) relaxation may be expressed by means of a series function:
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V (t )
t n · § ¨ ¦ W H 0 © E f i 1 E i e i ¸¹ .
(5)
E, Ei and i can be interpreted as properties of a rheological model (Generalized Maxwell model):
Figure 11: Generalized Maxwell model
345 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Large strain material models need other formulations. The FE-code of MSC.Marc® [3] applies
W (t )
t m § § ·· ¨ 1 1 ¨ ¦ O W 0 ¨© j 1G j © e j ¸¹ ¸¸¹
(6)
which again makes use of strain energy density function W apposite to (1) and a series function similar to (5). Constants must be determined by curve fitting of relaxation test results (example see [1]). Consideration of further nonlinearities like temperature-dependent behavior, aging or wear might be necessary to improve simulation of real structural behavior. 5. Effects of bolting torque The bolt of the point fitting is fastened to clamp the glass pane between countersunk head and inner clamping disk. The contraction causes a compression of the intermediate layers (bushing and washer) and a tangential tensile stress around the bore hole, because the countersunk head tends to expand the corresponding drilling. As shown in Chapter 4.3 and in [4] compression of polymer interlayers decreases over time and hence preload force of the bolt decreases, too. The example in Fig. 12 displays effects on glass stress and stiffness of the fitting by means of a single point fitting under eccentric (bending!) transverse load V with different levels of preload force F.
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A higher preload causes a larger contact area for bending. Hence deflection w decreases and (rotary-) stiffness rises. Example further confirms the incurrence of tensile stresses around the bore due to bolting torque. Preload forces exceeding a certain value (here 1 kN) have negative influence on overall stress F + V.
346 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 12: Structure of parameterized calculation
6. Conclusions The two explained aspects of material behavior and bolting torque show already the strong sensitivity of glass panes with countersunk fitting to changes in small areas. Due to numerous dependencies between the individual parameters general statements are difficult to give. Further details on this will be published in [1], which also contains entire information about presented examples. The material behavior of the polymer components in particular will supply enough work for future research. The aim has to be to define further limit cases that cover material properties on the safe side and reduce design effort.
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7. References [1] [2] [3]
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[4]
Herrmann, T., Untersuchungen zu punktgestützten Verglasungen mit Senkkopfhaltern, PhD thesis, Universität der Bundeswehr München, Germany, in progress Mooney, M., A theory of large elastic deformation, Journal of Applied Physics, 11(9), 1940, pp. 582592. MSC.Software Corporation, Experimental Elastomer Analysis, Training material course MAR 103, Santa Ana, CA, U.S.A.,2010 Herrmann, T., Aspects on Glass Panes with Countersunk Fixings, Proceedings of the 3rd International Symposium on the Application of Architectural Glass (ISAAG 2010), Universität der Bundeswehr München, Germany, 2010
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-349
Reduction of Edge Effect in Adhesive Joints of Glass Details Olena Soroka G.S. Pisarenko Institute for Problems of Strength, Ukraine, [email protected] Yurii Rodichev, G.S. Pisarenko Institute for Problems of Strength, Ukraine, [email protected] Alexander Shabetia Institute of Applied System Analysis of National Technical University of Ukraine “Kiev Politechnical Institute”, Ukraine, [email protected]
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Adhesive joints in load-bearing structures made of glass under tension are characterized by a significant concentration of stresses at the edge. A lack of sufficiently justified solutions on how to reduce the edge effect restrains the development and use of adhesive joints. The edge effect in adhesive joints of glass details is associated with the mechanism of transfer in a mechanical load from one mating part to another through an adhesive layer. Operating conditions require increase rigidity of the adhesive joints. As a result, the stress concentration increases at the edges of the joint. A new technical approach to control the stresses at the edge by directional change of the modulus of elasticity of adhesive layer in the edge zone is justified. As an example of the calculation of model of adhesive joint consisting of elements in the form of strips, joined by an adhesive layer, it is shown that the reduction of stress concentration at the edge of the adhesive contact with simultaneous overall high rigidity of joint can be achieved by reducing the elastic modulus of adhesion layer next to the edge. The law of the elastic modulus variation is proposed as a "mirror image" to the distribution of shear stresses at the joint with a constant elastic modulus of adhesive. Keywords: Architectural glass, Adhesive joints, Shear stress, Edge effect
1. Introduction Nowadays, adhesive joints of load-bearing structures made of glass are widely used in building and transport (Figure 1, 2). The edges of joints for different types of structural elements in such composites are of significant difficulties in the design and production of joints. Under tension these composites are characterized by a significant concentration of stresses at the edge. The effects caused by large stress gradients on the interface of adhesive joint are called the edge effects. High shear stresses at the interface are responsible for delamination under applied loading which is much lower than the ultimate loading for the materials of composite. The test results and analysis of failure of such structures showed that the edge delamination reduces the efficient rigidity of structure and its ultimate strength. However, the information on the investigation of edge effect and, especially, methods to control this effect in adhesive joins is very limited [1, 2]. At the same time operating conditions require increase in rigidity of the adhesive joints. As a result, the stress concentration increases at the edges of the joint.
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Figure 1 presents a scheme of composite load-bearing structural element under tension. It consits of a laminated glass plate with an internal reinforcing part made of strong metal. The stress concentration in the edges of glass-metal adhesive joints should be taken into account in designing this building structure. Cyclic thermal stresses should be regarded as the main cause of fracture for electric heated glazing of the cockpit (Figure 2). This laminated structure of the aircraft glazing consists of the external electric-heated glass layer - 1 joined with an internal load-bearing glass laminated part through thick polymer adhesive interlayer - 2. Stress concentration near the counter of electrically conducted coating and at the edge zone causes fracture of this glazing under extreme operational conditions at low temperature. 1
h 2
1 3
4
2
1 – laminated glass plate; 2 – metal reinforcing part
1 – external electric heated electricglass heated layer; glass 2- layer; $\^ 2- thick ; adhesive layer; 3, 44– `$ , {$ $| `} $ $$^ 3, – load-bearing layers \|^ with thin strong polimer layer
Figure 1: Scheme of composite load-bearing structural element under tension
Figure 2: Scheme of electric heated glazing of the cockpit
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A lack of sufficiently justified solutions to the problem of reduction the edge effect restrains the development and use of these composites. The previous paper describes the possibility of reduction of the edge effect in adhesive joints of glassceramics composite elements [3]. It was shown that the edge effect in adhesive joints is associated with the mechanism of transfer in a mechanical load from one mating part to another through an adhesive layer. The approach that ensures reduction of the edge effect based on the choice of a law of adhesion interlayer elastic modulus variation was proposed. The paper is devoted to investigation of the edge effect and its control with regard to architectural and transport laminated composite structures consist of carrying glass plates and polymer adhesive layer. The influence of constructional parameters and elastic modulus of composite elements on the shear stress concentration was studied. The possibility of more efficient control of stress gradients at the edge without reduction of general rigidity of composite is shown. 2. Problem Statement To determine the edge effect in the adhesive joint a scheme where the uniform tensile load P is applied only at the ends of central element of composite is adopted. The model of adhesive joint is a symmetrical composition consists of elements in the form of strips, joined by an adhesive interlayer (Figure 3). 2H, h and are the the thickness of glass layers and interlayer respectivly. The length of the joint is 2l. The origin of coordinates 350 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Reduction of Edge Effect in Adhesive Joints of Glass Details
is chosen at the middle point as it shown in the Figure 3. The axis z is a longitudial symmetrical axis of the joint. Loading is transferred to the outer strip through an adhesive layer. Shear stresses at the interface of “glass – adhesive layer” are investigated. Due to symmetry the upper part of composition (above z) is considered.
2 P
h 1
2H
z
0 2l Figure 3: Scheme of loaded composite plate
Due to the fact that the elements of the system are in equilibrium and taking into account that shear stresses in the cross section z = 0 are = 0, we obtain [2] a linear differential equation of second order with constant coefficients for w(z) – difference of the axial displacements of the centers of gravity of outer - 2 and inner - 1 glass strips. d 2 w( z ) k 2 w( z ) dz 2
(1)
0
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Here k is the coefficient, which depends on elastic properties (lateral strain coefficient μ; Young’s moduli of strips E1, E2 and adhesive interlayer Eai) and geometrical parameters of composition elements
k
2
§ 1 1 · ¸¸ ¨¨ © E1 H E2 h ¹ ª 2G h Hº » (1 P ) « E E E1 ¼ 2 ¬ ai
(2)
The analitical solution w(z) of the equation and subsequent accounting of the relationship between stear stresses and displacements resulted in the following equation W
P F1
sh kz
E1
(3)
§ 2E § G h · ·¸ ch kl ¸¸ 1 (1 P ) Hk ¨¨ 1 ¨¨ ¸ H E E 2 ¹ © ai ¹ ©
Where F1 is the cross sectional area of the inner element and
V
P (4)
F1
is the nominal stress under tensile conditions. 351 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Using the equations (2) and (3) the correlation between the interface shear stress and the nominal normal stress (hereinafter called relative shear stress / t) taking into account the influence of Young’s modulus of glass and adhesive, as well as the effect of length of plate 2l and thickness of layers (2H, h and ) was analysed. 3. Results and Discussion The formula (3) makes it possible to examine distribution of shear stresses lengthwise interface of adhesive joint. Basic physical and geometrical parameters of the structural members for analyzed joints (Figure 3) of the glass composite details are given in Table 1. Table 1: Physical and geometrical parameters of analyzed joints of glass composite details. Parameters of members
Section Dimensions [mm]
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Thickness of glass layer 1 (2H)
mm
12, 6, 2
Thickness of glass layer 2 (h)
mm
6, 3, 1
Thickness of adhesive layer 1 ()
mm
4, 1, 0.37, 0.1, 0.01
Length of the joint
mm
1000, 400, 200
Young’s modulus of glass layers
GPa
70
Young’s modulus of adhesive layers Eai
GPa
70, 10, 5, 1, 0.1, 0.01,
The examples of calculated distribution for relative shear stress / when H=h=6mm; =0,37mm; Eai =1GPa for different length of joint are presented in Figures 4 and 5. As follows from the analisys of curves 1-3 (Figure 4), the maximum value of relative shear stress for the same modulus of adhesive layer does not depend on the joint length, but mesuare of shear stress localization depends on the length of composition: for short joints zone of considerable shear stresses correlates with the length of the joint, and stress concentration is more localized near the edge in the long joints while their middle part is much less loaded with shear stresses (Figures 4 and 5). This decreases performance of “short” compositions. /t
/t
0,18
0,18 0,16
0,16
3
0,14
0,14 0,12
2
0,12
1
0,1
0,1
0,08
0,08
0,06
0,06
0,04
0,04
0
100
200
300
400
0
500
Figure 4: Distribution of relative shear stresses lengthwise interface for composites with H=h=6mm; =0,37mm; Eai =1GPa and 2l: 1- 1m, 2-0,4m, 3-0,2m
z-l /l
0
z,mm
0 100
3
2
1
0,02
0,02
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Figure 5: Measure of shear stress localisation for composites with different length 2l: 1- 1m, 2- 0,4m, 3- 0,2m
352 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Reduction of Edge Effect in Adhesive Joints of Glass Details
An increasing in joint length for adhesive with higher Young’s modulus makes it possible simultaneous composite structure rigidity and strength. But as a result of the increased stress localization on the edges and high value of the maximum shear stress a special technical approach should be developed to optimize the stress distribution at the edges. Dependence of the shear stress concentration on elastic modulus of adhesive interlayer was studied for a plate of the length 1 m (Figures 6 and 7). The Young’s modulus of the adhesive interlayer varies from 0.01GPa up to 70GPa. As shown in the Figure 6 an increase of the value of Young’s modulus of adhesive layer Eai from 0.01GPa to 1GPa causes higher shear stress up to 8.5 times. Shear stress concentration also increases significantly. The length of the edge effect area decreases up to 100mm. About 80% of adhesive layer is not loaded enough. The use of low rigid elastic adhesives causes more uniform stress distribution. However low strength of these adhesives results in insuffisient mechanical connection of load-bearing structural memebers as well as decrease of strength and rigidity of composite glass detail. An increase in adhesive layer Young’s modulus up to 10GPa causes to edge stress rising in about 1.5 times. But, further increase in Young’s modulus of adhesive leads to obtaining stable values of relative shear stress, which is about 0.27… 0.3 (See Figure 7). Thus, an effecient control of edge stress value in the range of 0.05< / < 0.27 and structural strength of this type of joint in the composite glass details can be realized by the variation of Young’s modulus of adhesive materials in the range of 0,1…10 GPa.
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The results of study of the influence of glass plates thickness on the edge shear stress concentration are shown in Figure 8. The following parameters of joint were adopted in the calculations: Eai = 1G}, =0.37mm, 1-500mm, H= 6mm. The thickness h of glass layer 2 (Figure 3) was 1mm, 3mm and 6mm.The maximum values of shear stress at the edge of the joint were decreased by about 1.5 times whith thickness h of 1 mm. The length of edge stress zone decreased up to 40mm. The decrease of thickness h causes the decrease of shear stress at the edge of the joint.
353 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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/
1
2
3 z,mm
Figure 6: Dependence of the edge shear stress concentration on elastic modulus of the adhesive interlayer for a composite plate with the length 1 m. H = 6mm, h = 6mm, = 0.37mm. 1- Eai = 1GP, 2- Eai =0,1GP}, 3- Eai =0,01GP}.
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m/
Eai,GPa
Figure 7: Correlation between relative shear stress at the edge of composition and Young’s modulus of the adhesive interlayer
The other way to decrease shear stress concentration in the edge of joints in glass composite details by reducing the rigidity of adhesive layer is shown in Figure 9. Simultaneous decrease of Young’s modulus Eai from 1GPa to 0.1GPa and an increase in thickness of the adhesive layer from 0.37mm to 4mm causes a decrease in the stress parameter / up to 0.02.
354 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Reduction of Edge Effect in Adhesive Joints of Glass Details
/
3
2 1
z, mm
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Figure 8: Dependence of the edge stress distribution on the thickness of glass layer 2. Eai = 1GP}, =0.37mm, 1-500mm, H= 6mm. 1-h=1mm, 2-h=3mm, 3-h=6mm
Correlation between the relative shear stress at the edge of composition and thickness of the adhesive interlayer is shown in Figure 10. Stress distribution was calculated for composite plates with a length 2l =1m and H= h=6mm. Young’s modulus of the adhesive layer was Eai = 1 GPa (upper curve) and Eai = 0,1GPa (lower curve). The thickness of the adhesive interlayer varied in the range of 0.01 mm…4 mm. Decrease in the shear stress at the edge when thickness of adhesive interlayer increases up to 4 mm is significant. This effect can be used to optimize the shear stress distribution at the edge zone of joints as well as to increase the bearing capacity of the plates under mechanical and thermal loads. In order to reduce the stress concentration at the edge of the adhesive joint with simultinuous overall high rigidity of the composite, the method of decreasing the elastic modulus in the rigion of edge effect was proposed. As an example a law of the interlayer elastic modulus variation which is the mirror reflection of the law of shear stress variation, when Eai varies from 1GPa to 0,01GP} was cosidered (Figure11).
355 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 /
/
0,3 0,25
1
0,2 0,15 0,1 0,05
2 3
0
z, mm
0
Figure 9: Shear stress control by the change of adhesive layer rigidity: 1- Eai = 1GP}, =0.37mm, 2- Eai = 1GP} =4mm or Eai =0, 1GP}, =0.37mm (Eai / ~const), 3- Eai =0, 1GP}, =4mm
0,5
1
1,5
2
2,5
3
3,5
4
, mm
Figure 10: Correlation between relative shear stress at the edge of composition (1=500mm, H=6mm, h=6mm) and thickness of adhesive interlayer. Upper curve - Eai = 1 GPa , lower curve - Eai = 0,1GPa
Replacement of the constant Eai by functional dependence Eai=f (z) results in the coefficient k (2) is variable. Therefore equation (1) transforms into a differential equation of second order with variable coefficient:
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d 2 w( z ) k 2 ( z ) w( z ) 0 dz 2
(6)
Figure 11: Shear stress control by replacement of the constant Eai modulus by variable Eai
The numerical solution of this equation allows one to obtain w(z) and shear stress distribution in the case of variable elastic modulus of the interlayer. It is demonstrated in Figure11 that the maximum shear stress at the edge of composite with variable elastic modulus of the interlayer decreased by 1.4 times compared with one where elastic modulus of interlayer is 1GPa, while the regidity of composite is retained. 356
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Reduction of Edge Effect in Adhesive Joints of Glass Details
Some other ways for reduction of the edge effect due to variation of elastic modulus of the interlayer can be proposed, particulary it may be chosen as staircase characteristic: from low value next to edge to higher ones in the middle part of the composition. The obtained results provide a basis for design of architectural and transport composite glass structures with an adhesive joints optimized on strength and rigidity parameters. The following tendencies may be useful to ensure appropriate bearing capacity of these structures taking into account shear stress concentration at the joint edge:
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1) The minimum concentration of the edge stress is typical of joints with the lower values of Young’s modulus and increased thickness of adhesive layer. But low strength and rigidity of these joints leads to insufficient load-bearing behavior under mechanical and thermal loading. 2) The compositions with high strength can be obtained using the strong and rigid adhesive materials. However, the excess concentration and high level of the maximum edge stress will cause fracture of these compositions. Inreasing of the length of rigid joints is not efficient way for bearing capacity increasing on this reason. 3) The combined technical approaches with optimisation of the edge stress distribution on strength, rigidity and fracture resistance parameters have to be developed to decrease the maximum value of the edge stress in composite glass load-bearing structures. 4) Decrease in the elastic modulus of the adhesive interlayer at the edge region, which enable to retain enough regidity to ensure bearing capacity of the joint, causes decrease in the shear stress concetration and provides an adhesive strength of composite. Some suggestions how to reduce edge effect in a practical application are stated: 1) Technologically. It was suggested [3] to obtain an adhesion interlayer with modulus, which depends on the distance to the joint edge when an adhesive composition is used as a solution of a polymer in a volatile monomer with additions of cross-linking plasticizer. During hardening of the adhesive in the edge region the monomer volatilizes from the edge region, the dissolved plasticized polymer is formed in the adhesive layer. As a result the elastic modulus of adhesion interlayer decreases to the edge and varies over a wide range due to variation of the amount of the added volatile monomer and plasticizer. 2) Design method. - faired or stepped geometry of joint face leading to increase of the thickness of the adhesive interlayer at the edge; - stepped change of modulus due to application of different adhesive substances. 3) Decrease of elastic modulus of polymer that depends on strain value under conditions of large deformation due to mechanism of viscous flow can be used.
357 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
4. Conclusion. The results of investigation can be used as a basis of design-technological approach for creation of laminated glass composite structures optimized in terms of adhesive strength and rigidity properties. This approach will make possible to control performance of glass joints at the stage of their design and production. 5. References [1] [2]
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[3]
Kiselev, A.G., Stress state at the edge points of diffusion joints of dissimilar materials, in: Collection of Science Papers, Izd. MIFI, Moscow, 2000, pp 131-132. Bedly, M. R.; Ambrico, J.M., Delamination of thin films from two-dimensional interface flaws at corners and edges, International Journal of Fracture, 3/2001, pp. 205-222. Maslov, V.M.; Soroka, O.B.; Lyashenko B.A.; Rodichev Yu.M., Reduction of edge effect in the adhesive joint of pyroceramics, Strength of materials, 6/2005, pp.606-612.
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Challenging Glass 3
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Strength, Stability & Safety
359
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Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-363
Improvement of Quality of Tempered Glass with Numerical Modeling Antti Aronen, Reijo Karvinen Tampere University of Technology, Department of Energy and Process Engineering, Finland,[email protected] Thin glass has increased problems in a tempering process. Thinner glass needs a higher temperature and higher heat transfer coefficient to get tempered glass. At the same time, bending stiffness of glass plate decreases and the possibility of faults in visual quality increases. Numerical modeling is needed to understand how different tempering parameters and support of glass affect tempering and visual quality. In the paper, the reasons for higher temperature and higher heat transfer coefficients for thin glass are shown. The traditional way of supporting glass with rollers is studied and the effect of different parameters on deformations is shown. Keywords: Tempering, Modeling, Quality
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1. Introduction The purpose of the glass tempering process is to improve glass strength. A tempered glass should have the same visual quality as a float glass. The visual quality of tempered glass can suffer during the tempering process due to high temperature or incorrect heat transfer. The need to reduce the material used has created a demand for thin glass. Thinner glass increases problems in the tempering process. Online measuring is difficult and modeling is needed to understand the behavior of glass in the process. Thin glass needs a higher temperature and a higher heat transfer coefficient to get tempered glass. However, due to the high temperature and uneven support by rollers, bending stiffness reduces and visual faults like roller waves and edge bending are difficult to avoid [1,2]. The stress profile is not the only criterion for tempered glass. Visual quality and the flatness of the tempered glass are criteria that are almost as important. Before conducting modeling, the theory of heat transfer and mechanical behavior of glass has to be understood. The theory of heat transfer is based on energy equation and boundary conditions [3] and mechanical behavior based on thermal stresses and viscoelasticity [4,5]. The aim of this paper is to examine why problems increase with thin glass and how they can be avoided. The paper also considers traditional roller support and studies how the change of a support system affects the roller waves in tempered glass.
363 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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2. Theory 2.1. Heat transfer Heat transfer and the temperature field form the basis of the heat treatment process. Heat transfer and temperature range can affect the stress results in the tempering process. Concerning residual stresses, the temperature field during the cooling process is the most important factor. With thin glass, cooling is fast and radiation temperature is low. So, radiation can be ignored and the calculation of temperature distribution is based on the use of energy equation [3]
Uc p
wT wt
w wx i
§ wT · ¨k ¸ ¨ wx ¸ i ¹ ©
(1)
where U is the density, cp is the specific heat, T is the temperature, t is the time and k is the heat conductivity. In order to solve Eq. (1), boundary conditions have to be fixed, which can be easily achieved using the heat transfer coefficient. For the one-dimensional case where the temperature field is calculated over the thickness b, the boundary equation is q
k
wT b 2 , t wz
h T b 2 , t Tf
(2)
for an upper surface and similarly for a lower surface. The temperature difference in glass transition range has to be about 150 °C to get tempered glass.
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In heat transfer calculations, it must be remembered that heat conductivity is linearly dependent on temperature (Appendix A). In addition, the specific heat is time- and temperature-dependent. The specific heat in the transition range is the combination of heat capacity of equilibrium liquid cp,l and heat capacity in glassy state cp,g [6]. T
Tf
T
T0
T0
Tf
³ c p T ´ dT ´
³ c p, l T ´ dT ´ ³ c p, g T ´ dT ´
(3)
The specific heat in a glassy state is linearly temperature-dependent and constant in equilibrium liquid. The fictive temperature Tf is dependent on structural relaxation, which will be presented in Chapter 2.3. The temperature field can be calculated for the one-dimensional case using the finite difference method [3]. 2.2. Stresses and strains At high temperature, above the transition temperature, the effect of viscoelasticity occurs. Viscoelasticity can be presented using the Maxwell model. The bulk and shear moduli, K and G, are time- and temperature-dependent and can be presented using Prony’s series [5,7]. 364
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Improvement of Quality of Tempered Glass with Numerical Modeling
K t
n § t K f K 0 K f ¦ w2i exp¨¨ i 1 © W 2i
G t
n § t G 0 ¦ w1i exp ¨¨ i 1 © W 1i
· ¸ ¸ ¹
(4)
· ¸ ¸ ¹
(5)
When bulk and shear moduli are known the stress-strain relation is presented with a hereditary integral [8] t
V ij t
G ij ³ K t t´ 0
t w eij w H 3H th dt´ 2 ³ G t t´ dt´ wt´ wt´ 0
(6)
where Vij is stress, H is the sum of Hxx, Hyy and Hzz, eij is deviatoric strain eij = Hij -1/3 H and Hth is thermal strain. In the heat treatment process, the temperature field is connected to thermal strain, which governs the stress calculation. The numerical methods for the solution of stresses and strains are shown in references [8,9]. 2.3. Structural relaxation Glass is a thermorheologically simple material. This means that the relaxation time at different temperatures can be calculated using a shift function I. Because the structural relaxation and the change of fictive temperature have to be taken into account, the shift function is also time-dependent. The shift function is
W ref
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I t , T
W
ªH exp « «¬ R
§ 1 x 1 x ·¸º ¨ » ¨ Tref T T f ¸¹» © ¼
(7)
where W is relaxation time, H is activation energy, R is the universal gas constant and x is a ratio of activation energy in the glassy state and a sum of activation energies in the glassy state and for structure x=Hg/(Hg+Hs). [6] When temperature changes during the process, the time should be replaced by a reduced time. The reduced time [ takes the temperature-weighted relaxation time into consideration.
[ t
t
³ I T t´ dt´
(8)
0
The time in Eq. (6) can be replaced with the reduced time. To calculate Eq. (7), the fictive temperature has to be known. The change of properties is dependent on the fictive temperature and it can be described by the response function 365
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Challenging Glass 3
M p t
p t p 2 f
p 2 0 p 2 f
T f t T2
(9)
T1 T2
In the response function Mp above, p is a property, subscript 1 is the state before the temperature change and subscript 2 is the state after the temperature change. The response function of the material property Mp can be expressed by the analogy with the bulk or shear relaxation function M p t
n
¦ Ci e t / O
(10)
i
i 1
where Ci is a weight coefficient for a structural relaxation time Oi. Using Eq. (9), the fictive temperature can be calculated. T f t
t
T t ³ M p t t´ 0
wT t´ dt´ wt´
(11)
The fictive temperature depends on the speed of temperature change. The numerical solution of fictive temperature can be solved with the algorithm by Markovsky et al. [10].
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3. Effect of initial temperature and heat transfer coefficient on tempering 3.1. Effect of heat transfer coefficient on temperature field The heat transfer coefficient needed for tempering depends on glass thickness. The temperature difference between surface and mid-plane should be over 150 °C. By keeping the initial temperature constant and high enough for tempering, the effect of heat transfer coefficient on the temperature field during cooling and on maximum temperature difference between surface and mid-plane can be studied. The results in Fig. 1 show the maximum temperature difference during cooling when the initial temperature is 650 °C and the thicknesses used were 2, 4, 6 and 10 mm. The material properties shown in Appendix A are used in following simulations. With thinner glass, the heat transfer coefficient needed to get 150 °C temperature difference is higher. The heat transfer coefficient needed is inversely proportional to the glass thickness.
366 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Improvement of Quality of Tempered Glass with Numerical Modeling
Figure 1: Maximum temperature difference during cooling with different heat transfer coefficient and different thicknesses. Initial temperature is 650 °C.
3.2. Effect of cooling rate on glass transition temperature Property change is dependent on the speed of the temperature change. In cooling with a faster temperature change, the time for relaxation shortens. Thus, the change speed of fictive temperature decelerates at a higher temperature. The constant value of the fictive temperature after cooling shows the glass transition temperature.
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For thinner glass, a higher heat transfer coefficient is needed to obtain a high enough temperature difference between surface and mid-plane. Then the transition temperature increases, because the maximum temperature difference is meant to form at the glass transition range. So, temperature before cooling should be higher for thinner glass. Fig. 2 shows the effect of the cooling rate on the behavior of fictive temperature and glass transition temperature. Results in Fig. 2 are calculated using Eqs. (10) and (11).
Figure 2: Effect of cooling rate on fictive temperature and glass transition temperature.
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For a 3 mm glass sheet, the average cooling rate in the glass transition temperature is between 50 - 500 °C/s and with 6 mm glass the cooling rate is between 10 - 100 °C/s depending on the temperature before the cooling and the heat transfer coefficient. 3.3. Effect of initial temperature and heat transfer coefficient on residual stresses In the chapters above, reasons for higher temperature and higher heat transfer coefficients for thinner glass have been presented. The effect of those two tempering parameters can also be studied for one thickness. Residual stresses on the surface for 4 mm glass with modified initial temperature and heat transfer coefficient are shown in Fig. 3. The results show that higher temperature and higher heat transfer coefficient increase the residual stresses.
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In the results, the reference value of heat transfer coefficient hr is the heat transfer coefficient needed to reach 120 MPa surface compressive stress at temperatures above the plateau level for 3 mm glass. The reference value of temperature Tr is the glass transition temperature when the cooling rate is 100 °C/s. This can be calculated using Eq. (11). Temperatures are in degrees Celsius.
Figure 3: Effect of the temperature and the heat transfer coefficient on surface residual stress. Glass thickness is 4 mm.
The temperature should be over 650 °C to get more than 120 MPa compressive stress on the surface. With higher temperatures, the heat transfer coefficient can be decreased.
368 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Improvement of Quality of Tempered Glass with Numerical Modeling
4. Deformations The deformations for a stationary glass plate in viscoelastic case wve can be calculated using deformations in the elastic case we. w ve x , t
J t Ew e
(12)
where J(t) is a creep compliance and E is Young’s modulus. The elastic deformation for glass beam with uniform load q0 is w e x
q0 L4 f x L EI
(13)
For a narrow rectangular beam, the moment of inertia I is I
b 3W 12
(14)
and the uniform load is
q0
UgbW
(15)
In these equations, W is the width and the function f(x/L) depends on the geometry and the support of the beam. Then, the effect of the dimensions of beam on deformations for stationary glass can be found.
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w ve x, t J t
12 UgL4 f x L b2
(16)
The effect of thickness and length for roller-supported glass in the motion on deformations is presented in the sections below.
4.1. Effect of glass thickness on deformations During the tempering process in glass, visual faults like roller waves and edge bending are formed due to the uneven support of rollers and creeping at high temperatures. Visual faults are more common in thin glass due to the high temperature and lower bending stiffness. The result in Fig. 4 compares the displacement of 3 mm and 4 mm thick glasses in the case of the deformation of the rear end of a glass plate that moves on rollers. The results show that ratio is proportional to b-2 ((3/4)-2 = 1.78). Most of the ratios are between 1.7 and 1.8. Some errors are formed due to numerical error during the calculations and rounding errors when displacement is small near the rollers.
369 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Figure 4: Ratio of displacement of rear end of glass plate between two thicknesses (3 mm / 4 mm).
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4.2. Effect of roller distance on deformations The front and rear edges dominate the deformations and when the roller distance changes, the maximum length from the front and the rear end to the nearest roller also changes. The ratio of maximum deflections at two different roller distances (0.12 m and 0.08 m) is presented in Fig. 5.
Figure 5: Ratio of maximum deflections at two different roller distances (0.12 m and 0.08 m)
370 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Improvement of Quality of Tempered Glass with Numerical Modeling
In the case of a stationary glass plate, the ratio is about 5.1. The ratio presented in Fig. 5 is about 6, which is higher than for results in a stationary plate. The change of support should be taken into account, but proportion of length to the fourth power (L4) is a good approximation. 5. Conclusions In glass tempering, both tempering quality and visual quality are important. The quality has to be increased especially for thin glass. The forming of stresses and deformations can be studied with numerical modeling. The modeling gives good results and approximations of glass behavior during the process. Residual stresses can be affected by the temperature level and the heat transfer coefficient. With thinner glass, the heat transfer coefficient should be raised to get sufficiently high thermal strain difference between surface and mid-plane. Due to faster cooling, the glass transition temperature rises, and the temperature level before cooling should be increased. The thickness of glass plate affects the deformations and visual quality of tempered glass. Thinner glass has lower bending stiffness, which increases deformations. More even support of rollers decreases deformations. For thin glass, the higher temperature also increases deformations. 6. Appendix A Material properties for soda-lime-silica glass Table 1: Material properties [11-13] Young’s modulus E = 70 GPa Poisson ratio Q = 0.22
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Thermal expansion coefficient for solid glass Dg = 9·10-6 1/K Thermal expansion coefficient for liquid glass Dl = 32·10-6 1/K Thermal conductivity k = 0.975 + 8.58·10-4 T W/mK ,where T in °C Specific heat of solid glass cp,g = 893 + 0.4 T J/kgK ,where T in K Specific heat of liquid glass cp,l = 1433 J/kgK Ratio H/R = 76200 K Constant x = 0.5 Density = 2530 kg/m3 Environment temperature Tf = 20 °C
371 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 2: Characteristics of shear and bulk relaxation times and response function for structural relaxation (Tref = 869 K) [12] Shear relaxation times w1i
W1i
Bulk relaxation times (K/K0 = 0.18)
W2i
Structural relaxation Ci
Oi
0.0222
5.009·10
-5
0.05523
5.965·10-5
1.197·10-3
0.0224
9.945·10-4
0.08205
1.077·10-2
1.514·10-2
0.0286
2.022·10-3
0.1215
0.1362
0.2137
1.925·10
-2
0.2286
1.505
w2i
0.05523
6.658·10
-5
0.08205 0.1215 0.2286
0.1672
0.2860
0.7497
0.394
0.1199
0.2860
6.747
0.2265
3.292
0.3191
2.033
0.2265
29.63
7. References [1]
[2]
[3] [4] [5] [6] [7] [8]
[9]
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[10] [11] [12] [13]
Henriksen, Thomas; Leosson, Kristján, Anisotropy and Optical Distortion in Architectural Glass, Can It Be Controlled, Proceedings of Glass Performance Days 2009, June 2009, Tampere, Finland, pp. 834-839, 2009. Abbott Mark; Madocks John, Roller Wave Distortion - Definition, Causes and a Novel Approach to Accurate, On-line Measurement, Proceedings of Glass Processing Days 2001, 18-21 June 2001, Tampere, Finland, pp. 226-230, 2001. Bejan, Adrian, Heat Transfer, John Wiley & Sons, Inc., USA, 1993. Boley, Bruno; Weiner, Jerome, Theory of Thermal Stresses, Dover, Mineola (NY), USA, 1997. Flügge, Wilhelm, Viscoelasticity, 2nd ed., Springer-Verlag, Berlin, Germany, 1975. Scherer, George, Relaxation in Glass and Composites, John Wiley & Sons, Inc., USA, 1986. Daudeville, Laurent; Carré, Hélène, Thermal Tempering Simulation of Glass Plates: Inner and Edge Residual Stresses”, Journal of Thermal Stresses, 6/1998, pp. 667-689. Aronen, Antti; Karvinen, Reijo, Modeling of Deformations and Stresses during Glass Tempering, Proceedings of the ASME 2011 International Mechanical Congress & Exposition IMECE 2011, November 2011, Denver, Colorado, USA, 2011. Chambers, Robert, Numerical Integration of the Hereditary Integrals in a Viscoelastic Model for Glass, Journal of American Ceramic Society, 8/1992, pp. 2213-2218. Markovsky, Alex; Soules, Thomas; Boyd, D.C., An Efficient and Stable Algorithm for Calculating Fictive Temperature, Journal of American Ceramic Society, 4/1984, pp. C56-C57. Carré, Hélène; Daudeville, Laurent, Numerical Simulation of Soda-Lime Silicate Glass Tempering, Journal de Physique IV,1/ 1996, pp. 175-185. Carré, Hélène; Daudeville, Laurent., “Load-Bearing Capacity of Tempered Structural Glass”, Journal of Engineering Mechanics, 8/1999, pp. 914-921. Daudeville, Laurent; Bernard, Fabrice; Gy, René, Residual Stresses Near Holes in Tempered Glass Plates, Materials Science Forum, vol. 404-407, 2002, pp. 43-48.
372 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-373
Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Columns and Panels Claudio Amadio, Chiara Bedon University of Trieste, Italy, [email protected], [email protected] Modern and innovative architectural applications are frequently associated to the structural use of glass beams and panels. Such brittle elements are in fact largely adopted to sustain in-plane or out-of-plane loads (e.g. columns, stiffeners, stairs, etc.). However, due to their typical slenderness, they could be affected by stability problems. Because of these reasons, accurate investigations should be dedicated to the analysis of their buckling response. In the paper, simple analytical formulations are proposed to study the load bearing capacity of in-plane loaded 2-layer laminated glass columns and panels. Comparisons with numerical simulations are proposed to validate the analytical models. At last, useful formulations are suggested also for the buckling verification of in-plane compressed 3-layer laminated glass elements.
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Keywords: Buckling Verification, Laminated Glass, Equivalent Thickness, Compressive Loads
1. Introduction Laminated glass (LG) elements, originally used as purely architectural and decorative accessories in buildings, constitute a fundamental structural component in the realization of modern and innovative architectures. However, due to their typical high slenderness, LG elements are frequently affected by stability problems. Because of this reason, several authors investigated the buckled response of glass panels or beams in different loading conditions, providing interesting experimental results and sophisticated numerical validations. In the paper, an analytical approach based on the concept of equivalent thickness is proposed to perform a rational buckling verification of LG panels and columns under compression. The model well applies to 2-layer LG elements, as well as to 3-layer LG elements, which are frequently used in practice. By means of opportunely calibrated correction factors, the model accurately estimates the critical buckling load of these elements and precisely describes the corresponding load N-displacement w relationship. At the same time, it allows to simplify the numerical modeling phase and to reduce the processing time required in simulations. 2. Analytical models for in-plane compressed laminated glass panels 2.1. Buckling verification of 2-layer laminated glass panels In general, the buckling resistance of LG panels under in-plane compression is estimated referring to the common linear elastic theory of sandwich elements [1]. As proposed by Luible [2], the critical buckling load of a flat LG panel (length a, width b), 373
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
simply supported on the four edges (Figure 1), obtained by assembling two monolithic glass sheets (thicknesses t1 and t2, Young’s modulus E, Figure 2) and a middle interlayer (thickness tint, Young’s modulus Eint, shear modulus Gint) subjected to in-pane compression, can be estimated as:
Figure 1: Simply supported flat LG panel subjected to inplane compression. Geometry (a) and deformed configuration (b).
N y ,cr ,lam
Figure 2: 2-layer laminated glass element (cross section).
2 º As b 2 D1 D2 ª§ mb · 2 1 ¸ ¨ » 2 « 2 2 D ¬«© a ¹ a · § mb ¼» S Ds S D , ¸ ¨ mb ¹ b2 ª§ mb · 2 º © a As ¸ 1» 2 «¨ ¬«© a ¹ ¼» S Ds
(1)
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with:
D
D1 Ds D2 ,
Ds
( Et1 z12 Et 2 z 22 ) (1 Q 2 ) ,
(2) (3)
As
Gint ( z1 z 2 ) 2 t int ,
Di
Et i3 12(1 Q 2 ) ,
(4) (5)
i= 1, 2,
z1, z2= distance between the centroidal axis of the interlayer and each glass sheet. Depending on the value of Gint, the value for Ny,cr,lam calculated by means of Eq.(1) is always comprised between the well known limit conditions, which are respectively defined: x
in absence of any shear connection between the glass sheets (layered limit, that is Gint 0)
a · S 2 ( D1 D2 ) § mb ; ¨ ¸ mb ¹ b2 © a 2
N y ,cr ,lam
N y ,cr ,abs
374 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
(6)
Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Beams and Panels
x
in presence of a rigid shear connection between the glass sheets (monolithic limit, that is Gint ) 2
N y ,cr ,lam
N y ,cr , full
a · S 2D § mb . ¨ ¸ mb ¹ b 2 © a
(7)
In this context, numerical and analytical comparisons performed by Luible [2] demonstrated that Eq.(1) can be used to predict the bifurcation load Ny,cr,lam of simply supported LG panels with a good level of accuracy. In particular, the mean ratio between analytical and numerical critical loads of 200 LG panels characterized by various geometrical and mechanical properties resulted equal to 1.05. However, the estimation of the critical buckling load Ny,cr,lam does not constitute a useful criterion to define the ultimate strength of a buckled LG panel, since the post-buckled regime is typically characterized by membrane effects which allow sustaining greater loads. An interesting analytical formulation for the buckling verification of 2-layer LG panels subjected to in-plane compression can be derived from the simplified approach based on the concept of equivalent thickness, originally formulated by Wölfel [3] and recently applied by Bennison to LG elements in several boundary or loading conditions [4]. In accordance with this theoretical model, the effective level of connection offered by the interlayer can be expressed by means of a shear transfer coefficient *, (*= 0: layered limit, *= 1: monolithic limit) defined as:
*
1 EJ s tint 1 9. 6 E Gint t s2 O2
,
(8)
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with:
O
min( a, b) ,
t s ,1
t s t1 (t1 t 2 ) ,
Js
t1t s2, 2 t 2 t s2,1
ts t s,2
0.5(t1 t 2 ) tint ,
t s t 2 (t1 t 2 ) ,
(9) (10) (11) (12) (13)
and E a coefficient depending on the boundary and loading conditions [3]. For the verification of simply supported LG beams in bending, for example, accordingly with the original formulation, the value E= 1 should be taken into account [9]. In these hypotheses, the deformation w of the LG panel can be evaluated referring to an equivalent thickness defined as:
t eq ,w
3
t13 t 23 12*J s .
(14) 375
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Challenging Glass 3
Once teq,w is known, the critical buckling load of a given flat LG panel can be reasonably calculated by means of the classical analytical formulation [5]: 2 2 Etef3 ,w § mb a · S ¨ ¸ 2 2 © a mb ¹ b 12( 1 Q )
N y ,cr ,lam
kV
S2 b2
Def .
(15)
In this context, a series of analytical calculations has been performed to detect if the equivalent thickness approach is sufficiently accurate for the analysis of LG flat panels simply supported along the edges and subjected to in-plane compression. Specifically, a series of critical loads Ny,cr,lam has been evaluated by using the linear elastic sandwich theory (Eq.(1)) and the equivalent thickness approach (Eq.(15), with E= 1). Analytical calculations have been performed taking into account various mechanical and geometrical parameters characterizing a typical LG panel, that is the value of Gint (10-4 N/mm2 < Gint < 104 N/mm2), the aspect ratio D (1 D 5, with b= 1m), the thicknesses of glass sheets and interlayer (6/1.52/6mm, 8/1.52/8mm, 10/1.52/10mm). For the purpose of this work, only the first critical load has been considered (m= 1). The main results are shown in Figure 3 for the 8/1.52/8mm LG panel, as a function of the ratio
N crZenkert . t N cref ,w
RN , panel
(16)
1.40
2.2 D= a/b 1 2 3 4 5
1.35
1.30
8/1.52/8mm b= 1m
m= 1
E coefficient for in-plane compressed 2-layer LG panels
1.8
1.20
E
RN, panel
1.25
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Analytical calibration [6] Fitting curve (Eq.(17))
2.0
1.6
1.15
1.10
1.4
1.05
1.2 1.00 Monolithic limit
Layered limit 0.95
1.0 10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
3
10
10
4
0
2
4
6
8
10
D= a/b
2
Gint [N/mm ]
Figure 4: E coefficient for in-plane compressed LG panels simply supported along the edges. Analytical calibration [6] and fitting curve (Eq.(17)).
Figure 3: Critical buckling load Ny,cr,lam for in-plane compressed LG panels (8/1.52/8mm) simply supported along the edges (m= 1).
As shown in Figure 3, the examined formulations do not agree, and in general the equivalent thickness approach overestimates the critical load Ny,cr,lam. Performed calculations highlighted that RN,panel is independent on the thicknesses of the layers constituting the LG panel. In contrary, the main differences depend on the values of Gint and D. Similar differences between the analytical approaches can be avoided only if in 376
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Beams and Panels
Eq.(8) an appropriate coefficient E, analytically calibrated as a function of D, is assumed (Figure 4). The fitting curve for the so calibrated values of E is [6]:
E
1.09
D2
1.09 .
(17)
In these hypotheses, E can be considered as the correction factor able to give RN,panel = 1. The proposed formulation provides two contemporary advantages, since it allows a suitable calculation of the critical buckling load Ny,cr,lam and at the same time it allows to investigate, for the studied LG panel, the corresponding load N–transversal displacement w relationship. As proposed in a previous effort [6], the load carrying behavior of a generic LG panel, simply supported along the edges, subjected to a uniform in-plane compression Ny, can in fact be investigated by means of Wolmir’s formulation [7]:
Ny
§t· Eb¨ ¸ ©a¹
2
° S 2 S2 ® 2 °¯ 3(1 Q ) 8
2 ª§ w · 2 § w ·§ w0 · § w0 · º ½° w , 3 2 ¨ ¸¨ ¸ ¨ ¸ » ¾ «¨ ¸ © t ¹© t ¹ © t ¹ »¼ °¿ w w0 «¬© t ¹
(18)
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with w0 the maximum amplitude of the possible initial sinusoidal imperfection affecting the LG panel. In [6], comparisons with experimental and numerical results have been proposed to validate this analytical formulation. In this context, according to the Limit State design approach, the buckling verification of a flat LG panel under in-plane compression, simply supported along the four edges, could be reasonably developed by simultaneously considering two different conditions, referred to requisites of deformability and durability. The maximum transversal displacement wmax (Eq.(18), for example, should satisfy the condition:
wmax d
a , k
(19)
with a the length of the LG panel and k an appropriate coefficient, calibrated for each type of glass. For this purpose, the check of deformability should take into account a reasonable amplitude w0 of initial sinusoidal imperfection, representative of possible geometrical imperfections, eccentricities of load or boundaries, residual stresses. At the same time, the design compressive load Ny,Ed should be opportunely limited:
N y , Ed d N y ,b, Rd
N y ,cr ,lam
J M1
,
(20)
with Ny,cr,lam given by Eq.(15) and JM1 an appropriate safety coefficient depending on the mechanical properties of glass.
377 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
2.2. Buckling verification of 3-layer laminated glass panels Further analytical calculations have been performed to extend the validity of the proposed approach to the analysis of 3-layer LG panels (Figure 5).
Figure 5: 3-layer laminated glass element (cross section).
In particular, the performed comparisons showed that the critical buckling load of a 3layer in-plane compressed LG panel, simply supported along the four edges, can be still precisely estimated by means of Eq.(15), by assuming for the equivalent thickness the expression:
teq ,w
3
2t13 t 23 12*J s ,
(21)
whit * and O respectively given by Eq.(8) and Eq.(9). In this specific circumstance, also the following expression should be considered:
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ts
Js
t1 t 2 2tint ,
2t1t s2,1 ,
t s ,1
E
0.5t1 0.5t 2 tint ,
2.18
D2
2.18 .
(22) (23)
(24) (25)
Eq.(25), specifically, represents the fitting curve for the corrective coefficient E able to provide sufficiently accurate results. At the same time, the load N–transversal displacement w relationship of the compressed LG panel can be accurately described by means of Eq.(18). Consequently, the buckling verification can be rationally carried out by contemporarily satisfying the conditions given by Eqs.(19) and Eq.(20).
378 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Beams and Panels
2.3. Numerical validation To validate the proposed analytical approach, several numerical analyses have been performed on 3-layer in-plane compressed LG panels simply supported along the edges, having different geometrical or mechanical characteristics. Three different FE-models have been carried out with the commercial non linear code ABAQUS [8], to calibrate the coefficient E (Eq.(25)) and to check the accuracy of each FE-model. In all the performed simulations, glass was described as an isotropic linear-elastic material (E = 70000N/mm2, Q= 0.23), whereas to characterize the PVB-interlayer, some experimental data available in literature have been taken into account [9].
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In the first and more accurate three-dimensional FE-model (3D+shell), the external glass sheets (thickness t1) have been modeled by means of shell elements (S4R). At the same time, the middle glass sheet (thickness t2) and the layers of PVB-film (tint) have been described through 3D-8 node elements (C3D8H, hybrid formulation, incompatible modes). 3D elements and shell elements were connected together using the same nodes. Moreover, a section offset toffset= t1/2 from the centroidal axis of each glass sheet was applied to the external shell elements. In-plane compression was introduced in the FEmodel in the form of uniformly distributed compressive pressures acting on the upper and lower surface of 3D elements. To avoid possible eccentricities, boundaries have been applied to the central nodes of the middle glass sheet. In the second FE-model (Mshell), the 3-layer composite section was described by means of multilayer composite shell elements (S4R), by taking into account the real thickness of each layer. The third FE-model (TEQshell), finally, consists in a monolithic glass shell (S4R) having an equivalent thickness estimated by means of Eq.(21).
379 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
2500
2000
a= 1m x b= 1m 6/1.52/6/1.52/6mm FULL Analytical (Eq.(15)) ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell) ABS
1500
a= 1m x b= 1m 6/0.76/6/0.76/6mm
1600
Ny,cr,lam [kN]
Ny,cr,lam [kN]
2000
1000
500
1200
800 FULL Analytical (Eq.(15)) ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell) ABS
400
0
0 -2
10
-1
10
10
0
1
Gint
10 [N/mm2]
10
2
3
4
10
10
10
Figure 6: Critical buckling load Ny,cr,lam for in-plane compressed LG panels simply supported along the edges (6/1.52/6/1.52/6mm).
-2
10
-1
10
0
1
10 Gint [N/mm2]
10
2
10
3
4
10
Figure 7: Critical buckling load Ny,cr,lam for in-plane compressed LG panels simply supported along the edges (6/0.76/6/0.76/6mm).
1800
1500
1600 a= 1m x b= 1m 6/0.38/6/0.38/6mm
1250
a= 1m x b= 1m 6/1.52/6/1.52/6mm w0= a/500 Gint= 8.06N/mm2
1400
1000
800
600
200
750
500
FULL Analytical (Eq.(15)) ABAQUS (Mshell) ABAQUS (TEQshell) ABS
400
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Ny,cr,lam= 903kN
1000
N [kN]
Ny,cr,lam [kN]
1200
Analytical (Eq.(18)) Analytical (Eq.(18)), w0= 0
250
ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell)
0
0 -2
10
-1
10
10
0
1
Gint
10 [N/mm2]
10
2
3
4
10
10
Figure 8: Critical buckling load Ny,cr,lam for in-plane compressed LG panels simply supported along the edges (6/0.38/6/0.38/6mm).
0.0
2.5
5.0
7.5
10.0 w [mm]
12.5
15.0
17.5
20.0
Figure 9: Load N-transversal displacement w relationship for in-plane compressed LG panels simply supported along the edges (6/1.52/6/1.52/6mm).
At first, buckling analyses were performed with the three FE-models to predict the critical buckling load Ny,cr,lam of 3-layer LG panels and to validate the analytical procedure (Eq.(15), with E given by Eq.(25)). The main results are proposed for 6/1.52/6/1.52/6mm, 6/0.76/6/0.76/6mm and 6/0.38/6/0.38/6mm LG panels (1m x 1m). Apparently, the 3D+shell FE-model is the more accurate, but the modeling of the LG panel and the performance of the buckling analyses require rather long processing time. Furthermore, the 3D+shell FE-model tends to lightly overestimate the real critical buckling load Ny,cr,lam in presence of soft thermoplastic films (Figures 6-7) and generally has convergence problems if used in presence of extremely thin layers (Figure 8). In contrast, the Mshell FE-model can be quickly implemented and buckling analyses can 380
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Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Beams and Panels
be performed in a very short time, but the accuracy of results is very poor and the model does not converge if the material characterizing the interlayer is very soft (Figures 6-8). This aspect should not be ignored, especially in the verification of LG panels assembled with PVB-films. In this context, the TEQshell FE-model constitutes a major simplification, both in the modeling of the LG panel and in the performance of the buckling analyses. Moreover, the TEQshell has no convergence problems associated with the presence of extremely thin layers or very soft films. In Figure 7, also a comparison between some load N–transversal displacement w curves are proposed for a 6/1.52/6mm LG panel (a=1m x b=1m), having assumed Gint= 8.06N/mm2 and w0= a/500 [6]. Numerical results obtained by performing static incremental analyses are compared with the analytical curve given by Eq.(18), with teq,w= 15.48mm (Eq.(21)). In this circumstance, the 3D+shell FE-model overestimates the effective buckling resistance of the LG panel and the Mshell FE-model strongly underestimates it (Figure 9); in addition the analysis stops for convergence problems when N Ny,cr,lam. In contrast, the N-w relationship obtained with the TEQshell FE-model and the analytical approach (Eq.(18)) are in good agreement.
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3. Analytical models for compressed laminated glass columns 3.1. Buckling verification of 2-layer laminated glass columns Concerning laminated glass columns subjected to compressive loads, several analytical formulations are available in literature. Luible [2], for example, proposed for compressed LG beams the classical theory of sandwich columns. Blaauwendraad [10] recently compared some of the existing analytical models for buckling of LG columns, highlighting the similarities of these sandwich-based theoretical approaches and deriving a new approximate formulation able to control the transition between the layered and the monolithic limits. In a previous effort [11], the authors presented a new analytical model developed on the basis of the elastic theory originally proposed by Newmark et al. [12] for the analysis of the flexural behavior of composite elements with deformable connections. According to this exact theoretical model, let us consider a LG beam (width b, buckling length L0) obtained by assembling two external glass sheets (thicknesses t1, t2, Young’s modulus E, Figure 2) and a middle interlayer (thickness tint, Young’s modulus Eint, shear modulus Gint), pinned at the ends of its buckling length L0. The transversal displacement w(z) due to a compressive load N can be evaluated as:
wmax
§ · (D 2 EJ abs L20 EJ full S 2 )L20 N ¸, w0 ¨1 2 ¨ D EJ L2 ( EJ S 2 NL2 ) EJ S 2 ( EJ S 2 NL2 ) ¸ 0 0 ¹ abs 0 full full abs ©
(26)
with:
D2
EA*
K EJ full , EA* EJ abs
( EA1 )( EA2 ) EA1 EA2
K
Ebt1t 2 , t1 t 2
Gint b , t int
EJ abs
Eb 3 3 (t1 t 2 ) , 12 381
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
(27) (28)
(29) (30)
Challenging Glass 3 2 ª § t t ·2 t · º §t EJ abs Eb «t1 ¨ 1 int ¸ t 2 ¨ 2 int ¸ » , © 2 2 ¹ ¼» ¬« © 2 2 ¹
EJ full
A1
bt1 ,
A2
bt 2 ,
(31)
(32)
and w0 the maximum amplitude of the initial sinusoidal imperfection. In these hypotheses, the critical buckling load Ncr of the compressed LG beam is:
N cr
· D 2 L20 S 2 ¸. ¨ ¨ D 2 EJ L2 EJ S 2 ¸ abs 0 full ¹ ©
S 2 EJ abs EJ full § L20
(33)
A rational buckling verification should be performed by limiting the maximum deflection wmax of the LG beam (Eq.(26)) and the maximum design compressive load NEd, as suggested in Ed.(19) and (20) for the verification of LG panels. In [11], the validity of this exact theoretical model has been largely checked. However, the analytical model applies only to 2-layer LG beams and to simple structural systems. Furthermore, according to the verification approach proposed in the previous sections, it might be interesting to propose a univocal formulation for the analysis of LG columns and panels in different loading and boundary conditions. For this purpose, let us consider the expression for the equivalent thickness proposed in Eq.(14). The critical buckling load Ncr could be estimated, once tef,w is known, as:
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N cr
3 S 2 Ebt ef ,w
S2
L20
L20
12
EJ ef .
(34)
In these hypotheses, analytical comparisons have been performed by evaluating Ncr with Eq.(33) and Eq.(34), with E= 1. Calculations were carried out by taking into account for LG columns a series of mechanical and geometrical parameters, that is the value of Gint (10-4 N/mm2 < Gint < 104 N/mm2), the ratio J = b/L0 (0.01 J 0.5, with 100 b 500), the thicknesses of glass sheets and interlayer (6/0.38/6mm, 6/0.76/6mm, 6/1.52/6mm). The main results are shown in Figures 10-11 for the 6/0.38/6mm and the 6/1.52/6mm LG columns (with b= 0.1m), as a function of the ratio
RN ,beam
N crNewmark . t N cref ,w
(35)
382 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Beams and Panels 6.0
6.0 6/0.38/6mm J= b/L0 0.01 b= 0.1m 0.05 0.10 0.20 0.30 0.40 0.50
5.5 5.0 4.5
5.0 4.5 4.0
3.5
RN, beam
RN, beam
4.0
6/1.52/6mm J= b/L0 0.01 b= 0.1m 0.05 0.10 0.20 0.30 0.40 0.50
5.5
3.0
3.5 3.0
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0 Layered limit
Monolithic limit
Layered limit
0.5
Monolithic limit
0.5 10
-4
10
-3
10
-2
-1
10
0
10
1
10
2
10
3
10
4
10
Gint [N/mm2]
10
-4
10
-3
10
-2
-1
10
0
10
1
10
2
10
3
10
Figure 11: Critical buckling load Ncr for compressed LG columns (6/1.52/6mm, b= 0.1m).
Figure 10: Critical buckling load Ncr for compressed LG columns (6/0.38/6mm, b= 0.1m).
As shown in the proposed figures, the equivalent thickness approach does not agree with the theoretical exact model for compressed LG columns. Moreover, the ratio RN,beam depends on the thicknesses of the 3 layers constituting the LG beam, as well as on the aspect ratio J= b/L0. In general, for a fixed aspect ratio J, RN,beam increases as the thickness tint of the interlayer increases. At the same time, for fixed thicknesses of the glass sheets and the interlayer, the maximum value obtained for RN,beam increases as the aspect ratio J increases However, analytical calculations allowed to notice that the fitting curve representing the values E able to give RN,beam= 1 is: 2
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E
§b · 1.03¨¨ ¸¸ . © L0 ¹
(36)
As a result, Ncr can be accurately evaluated by means of Eq.(34) and the load-carrying behavior of the compressed LG beam can be described by taking into account the classical theory of bending for monolithic columns:
wmax
w0 , 1 N N cr
(37)
with w0 the maximum amplitude of the initial sinusoidal imperfection affecting the beam. In these hypotheses, the verification can be still carried out by contemporarily satisfying the conditions expressed by Eqs.(19) and (20).
383 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
4
10
Gint [N/mm2]
Challenging Glass 3
3.2. Buckling verification of 3-layer laminated glass columns The equivalent thickness approach proposed for the analysis of 2-layer LG beams under compression can be also easily extended to 3-layer composite columns. In the specific circumstance, tef,w can be estimated by means of Eq.(21), with: 2
E
§b · 2.06¨¨ ¸¸ , © L0 ¹
(38)
and the buckling verification can be performed by taking into account the Eqs.(19), (20).
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3.3. Numerical validation Also in this circumstance, to validate the proposed approach, three different FE-models have been realized with the code ABAQUS. 3D+shell, Mshell, TEQshell models were used to describe the flexural behavior of 3-layer LG columns having different geometrical and mechanical properties. Numerical results obtained by buckling analyses were compared with analytical predictions (Eq.(34)). The curves proposed in the Figures 12-14, for example, are referred to 0.1m x 1m LG columns (6/1.52/6/1.52/6mm, 6/0.76/6/0.76/6mm, 6/0.38/6/0.38/6mm). In general, in presence of soft thermoplastic films, the 3D+shell FE-model overestimates the exact critical load Ncr (Figures 12, 13), although very thin layers compromise the accuracy of results (Figure 14). The Mshell FE-model provides sufficiently accurate results only for stiff interlayers, whereas it tends to underestimate the critical load Ncr for LG columns with soft interlayers (0.5 N/mm2 < Gint < 10N/mm2) and it does not converge for Gint < 0.5N/mm2. In contrast, the TEQshell FE-model always provides precise results. In the Figure 15, a comparison between some load Ndeflection w curves are shown to confirm the accuracy of the equivalent thickness approach.
384 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Analytical Approaches for Buckling Verification of In-Plane Loaded Laminated Glass Beams and Panels
50
60
b= 0.1m x L0= 1m 6/0.76/6/0.76/6mm b= 0.1m x L0= 1m 6/1.52/6/1.52/6mm
50
40
Ny,cr,lam [kN]
Ny,cr,lam [kN]
40
30
20
FULL Analytical (Eq.(34)) ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell) ABS
10
30
20 FULL Analytical (Eq.(34)) ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell) ABS
10
0
0 -2
10
10
-1
10
0
1
Gint
10 [N/mm2]
10
2
3
10
4
-2
10
10
Figure 12: Critical buckling load Ncr for 3-layer LG columns (6/1.52/6/1.52/6mm, 0.1m x 1m).
10
-1
10
0
1
10 Gint [N/mm2]
2
10
3
4
10
10
Figure 13: Critical buckling load Ncr for 3-layer LG columns (6/0.76/6/0.76/6mm, 0.1m x 1m).
40
40 b= 0.1m x L0= 1m 6/0.38/6/0.38/6mm
b= 0.1m x L0= 1m 6/1.52/6/1.52/6mm w0= L0/500 Gint= 8.06N/mm2
35
30
Ncr= 32kN
30
N [kN]
Ny,cr,lam [kN]
25
20
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15
FULL Analytical (Eq.(34)) ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell) ABS
10
20
10 Analytical (Eq.(37)) ABAQUS (3D+shell) ABAQUS (Mshell) ABAQUS (TEQshell)
5
0
0 -2
10
10
-1
10
0
1
Gint
10 [N/mm2]
10
2
3
10
4
10
Figure 14: Critical buckling load Ncr for 3-layer LG columns (6/0.38/6/0.38/6mm, 0.1m x 1m).
0
5
10
15
20
25 30 w [mm]
35
40
45
Figure 15: Load N-transversal displacement w relationship for 3-layer LG columns (6/1.52/6/1.52/6mm, 0.1m x 1m).
385 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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4. Conclusions Because of their high slenderness, LG elements can be frequently affected by stability problems. In literature, several analytical models derived from the theory of sandwich panels are available, but in general they are applied only to 2-layer LG elements, as well as in specific loading or boundary conditions. In the paper, a simple and accurate analytical model based on the concept of equivalent thickness is proposed to evaluate the critical buckling load and the corresponding load N-deflection w relationship of LG panels and columns under in-plane compression. By means of appropriate correction factors, the analytical model can be easily applied to 2 or 3-layer LG panels under inplane compression as well as to 2 or 3-layer compressed LG columns. Numerical comparisons are proposed to highlight the accuracy and the potentiality of the approach. 5. References Zenkert, D, The handbook of sandwich construction, UK: Eng. Mat. Advisory Service Ltd., 1997. Luible, A., Stabilität von Tragelementen aus Glas, Thése EPFL 3014, Ecole Polytechnique Fédérale de Lausanne (free download: http://icom.epfl.ch/publications), Lausanne, 2004. [3] Wölfel, E., Nachgiebiger Verbund eine Näherungslösung und deren anwendungsmöglichkeiten, Stahlbau 6/1987, 1987, p. 173-180. [4] Bennison, S.J., Quin, M.H.X., Davies, P.S., High-performance laminated glass for structurally efficient glazing, Innovative light-weight structures and sustainable façades, Hong Kong, 2008. [5] Timoshenko, S., Theory of Plates and Shells, McGraw-Hill Book Company, 1989. [6] Bedon, C., Amadio, C., Buckling of flat laminated glass panels under in-plane compression or shear, Engineering Structures, 36 (2012), p.185-197. [7] Wolmir, A.S., Biegsame platen und schalen, VEB Verlag für Bauwesen, Berlin, 1962. [8] ABAQUS® version 6.9, Simulia, Pawtucket, R.I. 02860 USA, 2009. [9] Bennison, S.J., Jagota, A., Smith, C.A., Fracture of glassy/poly(vinyl butyral) (Butacite®) laminates in biaxial flexure. J. Am. Ceram. Soc. 1999; 82(7); 1761-1770. [10] Blaauwendraad, J., Buckling of laminated glass columns, Heron, 52(1-2), 2007. [11] Amadio, C., Bedon, C., Buckling of Laminated Glass Elements in Compression, Journal of Structural Engineering, Vol.137, No. 8, August 1, 2011. [12] Newmark, N.M., Siess, C.P., and Viest, I.M., Tests and analysis of composite beams with incomplete interaction, Proc. Soc. Exp. Stress Anal., 9(1), 75-92, 1951. Copyright © 2012. IOS Press, Incorporated. All rights reserved.
[1] [2]
386 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-387
Contact Damage Near the Supporting Pillars in Vacuum Glazing Units Minxi Bao, JianYang, University of Birmingham, UK, [email protected] Xiaogen Liu, Yiwang Bao China Building Materials Academy, P.R.China, [email protected] The contact damage caused by the supporting pillar on the glass surface in vacuum glazing units is investigated. XFEM numerical modeling is employed to simulate the cone crack initiation and propagation. The critical indentation loads in localized uniform pressure and that for a cylindrical indenter are calculated and compared. The stress distributions due to the indenters of different geometries are investigated. In light of the numerical results, an improved design of supporting pillar is recommended, which is able to mitigate the severe concentration at the contact rim.
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Keywords: Indentation, crack, contact stress, vacuum glazing units, XFEM
1. Introduction Significant progress has been made on the development of vacuum glazing units after this type of glass structure was first invented in 1913[1]. However, the high fracture occurrence due to the construction features of vacuum glazing units is still a predominant challenge in engineering application. As the test carried out in a previous study, the strength of vacuum glazing unit is only 40% or 50% of that of normal monolithic glass sheet [2]. This is because the barometric pressure induces severe stress concentration at the contact area between the glass sheets and supporting pillars. Consequently, the contact damage caused by the indentation of pillars would result in the breakage under low wind or snow loads. The stress concentration at a pillar of the vacuum glazing units was observed by polariscope, as shown in Figure 1. As is well known, a cone cracks will occur due to the excessive indentation forces, as shown in Figure 2a and b. This contact damage depends on the indenter geometry, but it is still unclear of which type of indenter is better, i.e. causing minimum contact damage. In the present paper, an XFEM numerical method is introduced to simulate the crack initiation and propagation due to the indentation load. The contact stress resulted from indenters are examined. In order to optimize the pillar geometry, the stress fields at the contact area with uniform, cylindrical and spherical indentation loading conditions are investigated, respectively.
387 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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(a) Cylindrical indenter Figure 1: The stress concentration near the pillar
(b) Spherical indenter
Figure 2: The cone cracks caused by the cylindrical and spherical indenters respectively [3, 4].
2. The Mean Strength Theory Hertz[5] first published a research on indentation fracture in 1881. An elastic linear analysis conducted by him indicated that the surface principle stress 1 at the edge of contact circle was the maximum radial tensile stress. Hertz demonstrated that when the applied indentation load was sufficient, the initiation of the cone crack beneath the indenter would occur at wherever the principle stress 1 was greatest. Frank and Lawn [6] pointed out that the crack path should start at the circumference of the contact circle and follow the trajectory of the third principle stress outside the contact zone.
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In indentation tests, a peculiar phenomenon is discovered in a great number of tests, which contradicts the traditional strength theories mentioned above: a brittle material does not always fracture in a high stress concentration areas even where the peak stress is greater than the critical strength. Bao [7] proposed a Mean Strength Criterion (MSC) in 1993 to address the problems. He stated that instead of a point stress on the surface of the specimen, it is the maximum mean stress near the contact circle that determines the crack initiation. The crack will not take place until the mean stress over a small process zone in thickness direction reaches a critical value. The mean stress is calculated by equation 1.
V
1 ' ³ V dz ' 0 1
(1)
Where is the mean stress, 1 is the first principle stress near the contact circle; ' is the integral thickness, which can be obtained by equation 2. '
2 / S ( K IC / V 0 ) 2
(2)
where, 0 is the localized bending strength, KIc is known as the plain strain fracture toughness, and can be readily measured. An empirical equation deduced from the experiments is introduced [7] to calculate the critical indentation load.
388 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Contact Damage Near the Support Pillars in Vacuum Glazing
Pc
V 0Sa 2 [0.1373a 2 0.2862a 0.0236]
(3)
where Pc is the critical indentation load in N, a is the radius of contact area caused by a spherical indenter. In previous research [2-4], MSC has been used to determine the critical load of brittle material, and good agreement has been discovered with experimental data. In this study, it will be adopted to validate the numerical modeling. 3. Simulation of Crack Initiation and Growth with XFEM
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3.1. Introduction of XFEM In order to further study the indentation damage for vacuum glazing, numerical method is employed. Many documented FEA simulations do not involve the crack initiation, so it is difficult to predict the critical indentation load for crack initiation. In traditional discrete cracking modeling methods, possible crack boundaries requires to be predefined to avoid splitting elements, as cracks cannot appear within elements. Nevertheless, it is difficult to precisely predefine the dimension and the location of the cone crack unless sufficient experimental data are provided. In this study, the XFEM module integrated in the ABAQUS is utilized to simulate the crack initiation and propagation. XFEM is termed for “extended finite element method”, which extends the piecewise polynomial function space of conventional finite element methods with extra enrichment terms. Different from conventional crack simulations, it allows arbitrary cracks independent of the mesh, and the discontinuous elements separated by the crack. The incorporated Heaviside enrichment term enables the displacement to jump cross crack. Therefore, two discontinuous elements can be deemed as a superposition of two continuous elements with “phantom nodes”. Detailed introduction of the methodology on XFEM simulation can be referred in the ABAQUS/CAE user's manual [8]. 3.2. The indentation modeling with uniform load A flat glass disk with the radius 30mm and the thickness 4 mm is established as an asymmetrical model. The indentation load is assumed to be uniform in this model. The schematic diagram is depicted in Figure 3.
Figure 3: The schematic diagram of the axisymmetric model
389 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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The linear elastic material properties of tempered glass are assigned to the model; i.e. Young’s modulus E= 70000MPa, Poison ratio = 0.24. In the XFEM simulation, the initial crack will pass through an element in which the maximum principle stress reaches a critical value. This critical maximum principle stress is defined as the localized strength based on the MSC, and the element thickness is selected as the integral thickness. The model is simply supported, and a uniform pressure is applied on the central circular area, representing the indentation load. The indenter radiuses modeled are 0.1mm, 0.15mm, 0.2mm, 0.25mm and 0.3mm respectively. The element type CAX4R is a four-node bilinear quadrilateral with reduced integration. Figure 4 present an image showing a cone crack caused by a spherical indenter. The crack simulated in the XFEM analysis is shown in Figure 5 with a large scale factor. The simulated crack is propagating in a cone-shape, which is in good accordance with the experiment result.
Figure 4: The cone crack caused by spherical indenter[4]
Figure 5: The cone crack section simulated by the XFEM in axial symmetric mode.
It is noted in the simulation results that the crack always initiates at a circle larger than the loading area, as presented in Figure 6. surface stress Mean stress
V p m
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1.0
1.1
1.2
1.3 r0 / a
1.4
1.5
Figure 6: The crack circle larger than the loading area
Figure 7: The surface stress and the mean stress outside the contact area [4]
The large crack circle has also been observed and mentioned in the previous laboratory work [9]. In theory, the crack is supposed to take place at the edge of the loading circle, where 1 is calculated to be the maximum. The MSC is used to explain the contradiction. As it is stated above, the crack initiation is determined by the maximum mean stress. The distribution of the surface stress and the mean stress starting from the edge of contact circle is depicted in Figure 7. The maximum surface stress is at 1.0a,, i.e., at the 390
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Contact Damage Near the Support Pillars in Vacuum Glazing
edge of the loading area, while the maximum mean stress is found to be at about 1.1a, where the crack initiation is likely to occur. The history of the maximum local principle stress 1 versus the indentation pressure for different loading radiuses are captured at the origin of crack, as shown in Figure 8. The stress will drop immediately once the crack is formed, and experience a re-bounce within a narrow range before completely drop to the zero value. The maximum value of 1 is always located at the tip of the crack to stimulate crack propagation, and the previously formed crack does no longer carry any load. An interesting result is found that the critical pressures for different loading radiuses remain almost consistent, independent of loading radiuses.
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Figure 8: The critical indentation pressure of different radiuses
The critical force can be obtained by integrating the critical pressure in the contact area. The results of analytical approach and XFEM modeling are listed in Table 1, and the curves are presented in Figure 9. It is found that the modeling results are in excellent agreement with the MSC and the applicability of XFEM numerical approach is validated. It is noted that the empirical equation developed by Bao [7] is based on the spherical indentation tests. Therefore, the uniform indentation loading simulation is proved to be very similar to the spherical indenter. Table 1: The critical indentation loads derived from analytical method and XFEM simulation. Calculated critical indentation load (N) Radius(mm) Mean strength equation
XFEM modeling
0.1
185.64
186.14
0.15
419.73
418.56
0.2
747.45
743.66
0.25
1169.85
1161.27
0.3
1699.29
1671.21
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Figure 9: The critical indentation load of different radii.
3.3. The crack simulation considering the contact stress The support pillars adopted in vacuum glazing units are usually treated as cylindrical indenter. Instead of the uniform loading applied in the previous modeling process, the contact stress distribution induced by the cylindrical indenter is non-uniform. It is difficult to derive analytical equations of real contact stress due to the complexity of contact problems. So the numerical method is employed to explore the indentation damage caused by real contact stress. The cylindrical indenters are modeled with the radius 0.1mm, 0.15mm, 0.2mm, 0.25mm and 0.3mm. The material properties of steel with E =175000 N/mm2, = 0.3 is assigned to the pillars. A uniform pressure is applied on the top of the pillar. As for the contact interface, the pillar surface is deemed as the master face and the contact glass is set as the slave surface. To enhance the convergence of the simulation, the contact interface is assumed to be frictionless. Figure 10 shows the critical indentation loads yielded by the uniform forces and cylindrical indenters. The critical indentation loads of cylindrical indenters are reduced significantly. When the contact stress is considered, the indentation pressure is no longer a constant, but influenced by the size of indenters.
392 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Contact Damage Near the Support Pillars in Vacuum Glazing
Figure 10:The critical loads comparison between uniform load and cylindrical indenter
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Since the contact stress of cylindrical indenter is found to have an important impact on the critical indentation load, it implies that the load bearing capacity of the vacuum glazing is also affected by the geometry of indenters. Therefore, the stress distributions in the glass resulted from three different loading conditions i.e. uniform pressure, cylindrical indenter and spherical indenter are now further compared. Assuming the same contact radius of three models, the maximum principle stress distributions at the critical state are presented in Figure 12. Where, the horizantal axis represents the distance from the centre of the indenter on the path indicated in Figure 11. Symbol “a” denotes the radius of loading area, and the normalized stress for vertical axis is expressed as V n V / V max .
Figure 11: The schematic diagram of the indentation
Figure 12: The maximum principle stress distribution of uniform pressure, cylindrical indenter and spherical indenter at critical state
393 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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As shown in Figure 12, the stress distribution of uniform pressure and spherical indenter outside the contact area are very similar and both decreasing slowly. Underneath the indenter, the spherical indenter exhibits a smoothly increasing curve, wherease severe stress concentration takes place at the contact edge of the cylindrical indenter, and results in a sudden peak stress outside contact circle. The integration of the maximum principle stress beneath the cylindrical indenter reaches only one third of that under the spherical indenter or uniform pressure. As the stress integration beneath the indenters at critical state reflects the critical indentation pressure, it can be concluded that the adoption of cylindrical pillars in vacuum glazing will lead to an earlier occurrence of contact damage due to the intensive stress concentration near the edge of contact ring. A novel pillar design is therefore introduced (see Figure 13). Instead of the conventional flat surface, the contact section of the improved pillar is produced to be a curved surface in order to reduce the stress concentration. The radius of the curve surface is determined by the equivalent spherical indenter.
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Figure 13: A novel pillar design with curved contact surface.
4. Conclusions The contact damage triggered by the support pillar is studied. The XFEM numerical method is employed and the applicability is validated by an analytical method using MSC. It is demonstrated that the ring crack appears outside of the contact area, rather than at the edge of the contact area where the surface stress is in the maximum. The critical indentation loads with uniform pressure, the cylindrical indenter and spherical indenter are compared. It is found that the uniform pressure model can be used to represent the spherical indenter in determining the critical indentation load. The critical indentation pressure applied on the pillar becomes dependent of the value of contact radius when the real contact stress distribution is considered. The stress distribution within and outside the contact zone under the uniform pressure, a cylindrical indenter and a spherical indenter are presented. The results show that the stress concentration due to a cylindrical indenter is more severe than that from the sphere indenter or uniform pressure. So the critical load for indentation damage is much lower than the latter. Based on the obtained conclusions, an improved pillar design is proposed, which can be adopted in the engineering practice for the future manufacturing.
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Contact Damage Near the Support Pillars in Vacuum Glazing
5. Acknowledgements This work is supported by the international collaboration project (S2011ZR0397). 6. References [1] [2] [3]
[4] [5] [6] [7]
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[8] [9]
Collins, R.E, Simko, T. M, Current status of the science and technology of vacuum glazing, Solar Energy 62 (3), 1998, pp189-213. Liu, Xiaogen; Safety evaluation and failure detection of glass curtain wall, PhD Thesis, China Building Material Academy, Beijing, China, 2005. Liu, Xiaogen; Bao, Yiwang; Xu, Haifeng; Wang, Xiufang; Propagation mechanism and control criterion of fracture indentation in vacuum glazing, Materials Science and Technology, 6/2010,pp878882 Bao, Y.W; Gao, S.J., Local strength evaluation and proof test of glass components via spherical indentation, Journal of Non-Crystalline Solids, 2008, pp1278-1381 Hertz, Heinrich, Hertz’s Miscellaneous papers, Nature 55, 11/1896, pp.6-9. Frank, C.K,; Lawn, B.R.; On the Theory of Hertzian fracture, Proceedings of the Royal Society, Cambridge, Britain, 1967. Bao.Y; Jin, Z; Size effects and a mean-strength criterion for ceramics, Engineering Structure and Materials, 8/1993, pp829-935. Hibbitt; Karlsson; Sorensen, Abaqus/CAE User's Manual, Pennsylvania State, USA, 2010 Mouginot, R., Crack formation beneath sliding spherical punches, Journal of Materials Science, 22/1987, 989-1000
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-397
Towards a European Structural Glass network: COST Action TU0905 Jan Belis Ghent University - LMO, Belgium, [email protected], www.glassnetwork.org Jürgen Neugebauer FH Joanneum, Austria, [email protected] Jens Schneider TU Darmstadt, Germany, [email protected] Mauro Overend University of Cambridge, UK, [email protected] Danijel Mocibob RI ISA (Permasteelisa Group), Croatia, [email protected] COST Action TU0905 “Structural Glass: novel design methods and next generation products” provides a platform for European scientists to cooperate and exchange expertise in the research area of Structural Glass. The main objective of this Action is to provide a strong contribution to the ongoing development of innovative high performance structural glass products mainly in architectural and solar applications, and to European standards and education in this field. This contribution intends to give an overview of the context, organization, objectives and activities of this successful network, which currently is about mid-term.
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Keywords: COST, Action TU0905, Structural Glass, European Network, Education Pack, Short Term Scientific Mission, Training School.
1. Introduction Prior to zooming in to the European Structural Glass network provided by COST Action TU0905, it is important to know the context of the COST framework, which is consequently explained in this introduction. The information in the following subsections is largely taken from the COST website [1]. 1.1. About COST COST is an intergovernmental framework for European Cooperation in Science and Technology, allowing the coordination of nationally-funded research on a European level. COST has a very specific mission and goal. It contributes to reducing the fragmentation in European research investments and opening the European Research Area to cooperation worldwide. As a precursor of advanced multidisciplinary research, COST plays a very important role in building a European Research Area (ERA). It anticipates and complements the activities of the EU Framework Programmes, constituting a “bridge” towards the scientific communities of emerging countries. It also increases the mobility of 397
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Challenging Glass 3
researchers across Europe and fosters the establishment of scientific excellence in nine key domains, among which “Transportation and Urban Development” (TUD). 1.2. About COST Actions COST does not fund research itself but provides a platform for European scientists to cooperate on a particular project and exchange expertise. These projects are called "Actions". Each COST Action is a network centred around nationally-funded research projects in fields that are of interest to at least five COST countries. COST provides the COST Actions with financial support for joint activities such as conferences, short-term scientific exchanges and publications. Each COST Action has an objective, defined goals and clear deliverables. COST Actions have located their topic into one of COST’s scientific Domains. One of COST's main characteristics is its flexibility, allowing for an easy implementation and light management of the research initiatives. Activities are launched following a "bottom-up" approach, meaning that the initiative of launching a COST Action comes from the European researchers themselves. After a competitive selection procedure and peer review process, a number of successful proposals are awarded with COST support.
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A Memorandum of Understanding (MoU) provides the formal basis of an Action. The member countries participate on an "à la carte" principle, in that only countries interested in the Action participate. An Action is launched when at least five COST member states have agreed the MoU and starts with the first Management Committee meeting of the Action. It runs for an average of four years. 2. COST Action TU0905 “Structural glass: novel design methods and next generation products” This section summarises the objectives of the Action and explains its origin. In addition, it gives an overview of its organisational structure and responsibilities at the time of writing. Additional information on the COST Action on Structural Glass can be found on the Action’s website [2]. 2.1. Objectives of the Action The main objective of this Action is to provide a strong contribution to the ongoing development of innovative high performance structural glass products mainly in architectural and solar applications, and to European standards in this field. The Action will identify and share the outcomes of existing fragmented activities within the European research community. In addition, the Action will establish a diverse multidisciplinary network that will encourage new research and collaborations. Finally, the Action will strengthen the current and future generations of European glass designers by developing a structural glass education pack for university curricula across Europe. 2.2. Origin of the Action The initiative of this Action on Structural Glass was taken by the five authors of this article, involving already right from the start international involvement of five European countries (Austria, Belgium, Croatia, Germany, United Kingdom). Several of the 398 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Towards a European Structural Glass network: COST Action TU0905
initiators had priory been involved in WG3 “Structural Glass” of COST Action C13 “Glass and interactive building envelopes”, which ended in 2005. Action TU0905 “Structural glass: novel design methods and next generation products” was launched on January 21, 2010 and started with the kick-off meeting in Brussels on April 7, 2010. Consequently, the expected end date of the Action currently is April 6, 2014, although COST foresees the possibility to apply for an extension of the Action duration. 2.3. Structure and members of the Action During the kick-off meeting in Brussels, the Chair, Vice Chair and Grant Holder were elected by the Management Committee (MC) members. Furthermore, the Domain Committee Rapporteur, the COST Science Officer and the Administrative Officer play an important role in the evaluation and/or support of the Action. Chair, Vice Chair, Rapporteur and WG Chairs together form the so-called Core Group (CG) of the Action, see Table 1. Table 1: Overview of Core Group (CG) and COST Officers of COST Action TU0905. NB: WG = Working Group
Core Group
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COST Officers
Name
Function
Prof Jürgen Neugebauer (AT)
MC Chair
Prof Jan Belis (BE)
MC Vice Chair
Prof Jens Schneider (DE)
Grant Holder WG2 Chair
Prof Nina Penkova (BG)
WG1 Chair
Dr Mauro Overend (UK)
WG3 Chair
Dr Christian Louter (CH)
WG4 Chair
Prof Kiril Gramatikov (MK)
Domain Committee Rapporteur
Dr Thierry Goger
COST Science Officer
Ms Carmencita Malimban
COST Administrative Officer
Four Working Groups (WG) are defined in the Memorandum of Understanding (MoU), based on four priority areas detected to be critical for the further development of European Structural Glass research. An overview of the WG’s and their respective Chairs is given in Table 2. Although not described in the original MoU, 13 Task Groups (TG) have been installed as further subgroups of the WG’s during later MC meetings in Madrid and Sofia. The main objective of installing the TG’s was to assess and further break down specific tasks more easily in relatively small groups of experts. An overview of the TG’s and their respective leaders is also listed in Table 2. Finally, the 25 members states listed in Table 3 have joined the Action at the date of writing, corresponding to 91 contributing members (WG and MC). More details are available on the COST Action website [2].
399 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 2: Overview of Working Groups (WG) and Task Groups (TG) of COST Action TU0905 (status on April, 2012). WG
TG
1
Name
TG Leader
Predicting complex loads on glass structures 1
Thermal Fracture
Mr Marc Vandebroek (BE)
2
Insulating Glass Units
Prof Jürgen Neugebauer (AT)
3
Dynamic Load Combinations
Dr Olga Río (ES)
2
Material characterisation and material improvement 4
Thermal Tempering
Prof Reijo Karvinen (FI)
5
Glass Strength
Ms Maria Lindqvist (CH)
6
Interlayers
Dr Gérard Savineau (FR)
3
Post-Failure Performance 7
Numerical Know –how and validation
Mr Martin Larcher (DE)
8
Structural Design Philosophy
Dr Mauro Overend (UK)
9
Learning from Failure
Mr Daniel Honfi (HU)
4
Novel Glass Assemblies 10
Connections
Prof Frank Wellershoff (DE)
11
Architectural Geometries
Dr Ognen Marina (MK)
12
Stability
Prof Jan Belis (BE)
13
Hybrid Components
Dr Christian Louter (CH)
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Table 3: Overview of member states which joined COST Action TU0905 (in alphabetical order; status on April, 2012). Nr
Member State
Nr
Member State
1
Austria
14
Lithuania
2
Belgium
15
Luxembourg
3
Bulgaria
16
Malta
4
Croatia
17
Netherlands
5
Czech Republic
18
Portugal
6
Denmark
19
Serbia
7
Finland
20
Slovenia
8
France
21
Spain
9
Germany
22
Switzerland
10
Greece
23
The Former Yugoslav Republic of Macedonia
11
Hungary
24
Turkey
12
Israel
25
United Kingdom
13
Italy
400 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Towards a European Structural Glass network: COST Action TU0905
3. Activities In this section, a short summary is presented of the activities of the Structural Glass COST Action up till the submitting deadline of this article. 3.1. Meetings Typically, minimum two Action meetings are organized every year, one of which is (partly) devoted to a MC meeting, whereas the other usually is a WG or TG meeting. Since the kick-off meeting in Brussels, six meetings have been organized up till the date of writing this article, including two MC+WG meetings (in Düsseldorf and Sofia, respectively), one WG meeting (in Madrid), one Core Group meeting (in Copenhagen) and two TG meetings (in Cambridge and Graz, respectively). 3.2. Short Term Scientific Missions Specifically to stimulate and help early stage Structural Glass researchers, the latter can apply for so-called Short Term Scientific Missions (STSM) within the Action. The main purpose of STSM’s is to provide financial support to young researchers for a stay at a research institute in another member state, devoted to research which contributes to the global objectives of the COST Action. Up to date, six STSM’s have been approved within the Action, e.g. to the University of Cambridge, Ghent University (UGent), Technical University of Denmark (DTU) and Ecole polytechnique fédérale de Lausanne (EPFL). STSM topics included the improvement of methods for numerical modeling of adhesively bonded joints, reinforced glass beams, strength of monolithic glass beams in bending, hybrid glass beams, and the Education Pack.
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Several completed STSM’s have resulted in successful publications of research papers, some of which have been listed at the end of this paper [3-6]. 3.3. Education Pack In contrast to more traditional building materials such as concrete or steel, structural analysis courses related to glass usually are not (yet) part of structural, architectural or civil engineering educational programs. However, high-level education obviously is essential to further develop structural glass research and its further implementation in practice by qualified engineers. Consequently, one of the major objectives of this Action is to develop an Education Pack based on the wide expertise and know-how available in a large variety of very specialized subdomains in the area of Structural Glass. The final version of the Education Pack is intended for academic education at universities throughout all participating member states. In general, the Education Pack is subdivided in three large parts, being A) Materials and glass products, B) Components and connections, and C) Structural glass systems. In addition, a fourth part is foreseen, called D) “Glossary of terms”. Each part is coordinated by a responsible, but the content is basically produced and delivered at TG level by small groups of specialists.
401 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Given the availability of certain existing textbooks, e.g. [7] and the short-term need of readily usable educational support for new courses triggered by and originating during the COST Action, it was a MC decision to give the highest priority to a series of elaborated lecture presentations. Currently a first draft of presentations on a large variety of subtopics has already been produced, according to a uniform template created especially for the Education Pack. The presentations are intended as an extensive database (currently still subject to further development and changes) from which teachers can select specific sections according to the specific target audience and aims of their own custom made course. However, even if this is already a huge and very useful step forward, it is a real challenge not to lose essential information during transferring the presentations from the authors towards other users. Consequently, in the longer run the Action has the ambition to produce a new textbook which supports the final version of the presentations. As such, an integrated Education Pack will hopefully be ready to be released by the end of the Action. 3.4. Training School Closely after the deadline of the current article, a first international Training School on Structural Glass is scheduled which will be organized by and at Ghent University, Belgium. The target audience of the Training School consists of beginning researchers at early PhD or advanced Master level. Participants of over 20 countries are expected, and during a full week (April 2-6, 2012) they will be submerged in the domain of Structural Glass by lectures coming from all over Europe, but also by a student colloquium, company visits, laboratory demonstrations, a workshop, and technical excursions.
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A more elaborated information report on the Training School is intended to be released in a future mini-symposium on Structural Glass initiated by COST Action TU0905 in cooperation with IABSE, which will be held in Portugal [8]. 4. Conclusions and outlook COST Action TU0905 “Structural glass: novel design methods and next generation products” wants to help avoiding fragmentation in research efforts, to build a strong professional network and to ensure the leading position of Europe in Structural Glass research and education. The Action is currently ongoing and has an expected end date in April, 2014. The Action has a clear organizational structure now and currently counts over 90 individual members coming from 25 member states. Up till now the Action has organized a number of successful activities, ranging from Action meetings over Short Term Scientific Missions to a Training School (expected April 2012). One of the major deliverables will be an Education Pack on Structural Glass, which will be made available to universities of participating member states after the end of the Action and which is expected to boost academic education in this young and challenging research domain.
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Towards a European Structural Glass network: COST Action TU0905
5. Acknowledgements The authors would like to acknowledge COST Action TU0905 “Structural glass – novel design methods and next generation products”, which provides excellent networking and feedback opportunities in the field of Structural Glass and which is of great value for the efficient further development of this challenging research domain. They would also like to thank all members of COST Action TU0905 for their continuous efforts to make this Action a success. 6. References [1] [2] [3]
[4]
[5] [6] [7]
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[8]
http://www.cost.eu http://www.glassnetwork.org Louter, Christian; Belis, Jan; Veer, Fred; Lebet, Jean-Paul, Structural response of SG-laminated reinforced glass beams; experimental investigations on the effects of glass type, reinforcement percentage and beam size, Engineering Structures, Vol 36, March 2012, p. 292-301. Louter, Christian; Belis, Jan; Veer, Fred; Lebet, Jean-Paul, Durability of SG-laminated reinforced glass beams: effects of temperature, thermal cycling, humidity and load-duration, Construction and Building Materials, Vol 27, Issue 1, February 2012, p. 280–292. Vandebroek, Marc; Lindqvist, Maria; Belis, Jan; Louter, Christian, Edge strength of cut and polished glass beams, Proceedings of Glass Performance Days, Finland, 2011, p. 476-479. Lindqvist, Maria; Vandebroek, Marc; Louter, Christian; Belis, Jan, Influence of edge flaws on failure strength of glass, Proceedings of Glass Performance Days, Finland, 2011, p. 126-129. Haldimann, Matthias; Luible, Andreas; Overend, Mauro, Structural Use of Glass. Structural Engineering Documents 10, IABSE, Zürich:2008. http://www.icsa2013.arquitectura.uminho.pt/
403 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-405
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
Fabrice Bernard Université Européenne de Bretagne, Institut National des Sciences Appliquées de Rennes, France, [email protected] Bouazza Fahsi, Baghdad Krour Université de Sidi Bel Abbes, Algérie Glass is a material that has been used for a long time in windows as a filling material and has much to offer in this regard due to its possibility to carry high compressive stresses. For several years, there has been a trend in architecture to use glass not only as a part of the building envelope, but also as material for loadbearing elements. This represents a special challenge because of the glass brittleness. Knowing how to model the failure of such structures is then a very important challenge and can contribute to a decrease of the partial safety coefficients used in the design. Most of time, such a modeling needs to be based on a statistical approach. This is the case for glass beams in current zones. The present contribution focuses, in a first part, on the modeling of failure in annealed glass single panes using Weibull model extended to take into account the subcritical cracking. Then, in a second part, the modeling of laminated glass beams with a SGP interlayer is presented. This modeling is performed with the FE software Abaqus and takes into account the mechanical contribution of the interlayer thanks to a Mooney-Rivlin model. The special challenge is here to reproduce the post-peak behavior of the laminated glass beam and then the remaining load carrying capacity of the structure. The third part of the paper deals with the failure in connection area. Thanks to a combination of FE modeling, experimental campaigns and microscopy observations (with optical and electronic microscopes) the deterministic aspect of the failure in these special zones is put into evidence. This important result enables to simplify the modeling of the mechanical behavior of such area Keywords: Glass, load-bearing elements, connections, failure
1. Introduction Glass is a material that has been used for a long time in windows as a filling material and has much to offer in this regard due to its possibility to carry high compressive stresses. For several years, there has been a trend in architecture to use glass not only as a part of the building envelope but also as a material for load-bearing elements, i.e. beams, columns or shear walls… This represents a special challenge because of the glass brittleness. Indeed, new applications of glass in such structural parts need a good knowledge of the load-bearing capacity, of its post-breakage behaviour and the lifetime of the structural glass components. 405
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Thus, knowing how to model the failure of such structures is a very important challenge and can contribute to a decrease of the partial safety coefficients used in the structural design process. This communication investigates this point through the full study of three different glass elements: a single-pane glass beam, a laminated glass beam and the connection area in glass structures. Only the failure modes by overstresses are considered here. 2. Study of a single-pane glass beam 2.1. Statistical model Glass does not possess an inherent ductility and disintegrates after failure. Moreover, the sensitivity of the material to the damage of its surface (weak toughness) leads to statistical and size-dependent failure behaviour. For example, the failure stress of a macroscopic annealed glass element under tension is between 30 and 100 MPa whereas the tensile stress of a glass fiber is more than 10 GPa. Griffith [1] explained this by the presence of microcracks. Their origins are located on the machined edges. Failure is then governed on one hand by their propagation and on the other hand by their random distribution. The Weibull model [2] is a statistical approach for the failure analysis of brittle materials with random flaws. The failure probability Pf of a single glass plate is given by:
Pf
ª 1 1 exp « «¬ S 0
§V Vu ³S ¨¨© V 0
m º · ¸¸ dS » »¼ ¹
(1)
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where S0 is the unit area, S is the surface with flaws, V is the threshold stress (for Pf =0) and m and V0 are the parameters of the Weibull law. For a glass plate under bending, S is the polished surface under tension. It is well known, so the integration of the law is explicit. The Weibull model accounts for the size effect and the stress concentration effect. Weibull parameters depend not only on the material but also on the loading rate. Indeed glass is subjected to a subcritical crack growth phenomenon, especially when annealed glass is considered. 2.2. Subcritical crack growth and how to take into account? In classical Linear Elastic Fracture Mechanics (LEFM), failure due to the propagation of cracks from the edge can be modeled by means of the stress intensity factor. As glass is a brittle material, its fracture mode can be considered as a pure mode I. Instantaneous failure occurs when KI reaches and exceeds the critical stress intensity factor, also called the material toughness.
406 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations
This condition is called Irwin’s fracture criterion and is expressed as follows:
K I t K Ic
(2)
A typical value for KIc for silica-soda -lime glass is 0.75 MPam. However, in glass, a crack propagation occurs even if K I d K Ic . This subcritical crack growth phenomenon under static loads, originally called “static fatigue” was discovered by Grenet [3]. As revealed after by [4], this phenomenon is not observed in vacuum conditions and is due to the effect of moisture at the crack tips. This phenomenon explains also the dependence of glass on the rate and the duration of the loading. Figure 1 illustrates the subcritical crack growth and presents the cracking velocity according to the stress intensity factor. v (m/s) Kcb KIth
10 3
KIc
III 1
II Water 10 -3
Air 50 % R.H.
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Air 25 % R.H.
I
10 -6
Vacuum 10 -9 10 -12 0
0,5
1,0
1,5
2,0
2,5
3,0
KI (MPa.m ) 1/2
Figure 1: Cracking velocity according stress intensity factor ([5], after [4])
407 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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The presence of the stress corrosion threshold KIth has not been clearly demonstrated or put into evidence until now. A conservative (=safe) assumption would be to neglect it. Evans [6] proposed a model including the dependence of the cracking velocity with the stress intensity factor (region I, figure 1):
v
da dt
AK In
(3)
with A and n the parameters of the law (A=0.124 and m=12.76) [5] for silica-soda-lime glass, KI the stress intensity and a the flaw size. The association of the Weibull and Evans models enables then to account for the subcritical crack growth in the statistical analysis. The apparent Weibull parameters (m and V0) depend on both the loading rate and the environment for a given edge finishing. Intrinsic parameters m* and V0* can be defined for the strength in inert media. These intrinsic parameters are independent of the loading conditions. For a bending test, the stress intensity factor is equal to:
KI
VY a
(4)
where a is the flaw size, Y the shape factor and V the applied stress. The Evans law leads to:
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da dt
A VY a
n
(5)
=constant leading to V V t f (where tf denotes Assuming (1) a constant loading rate V the service life), (2) that the initial flaw length is small compared to the final crack length ( a(t 0) a(t t f ) ), and (3) that KIth=0 as previously explained, and integrating in time the previous equation, the failure probability can be expressed in function of the Weibull intrinsic parameters and the Evans ones [5]:
ª § V ·m º Pf 1 exp « ³ ¨¨ ¸¸ dS » »¼ «¬ S © V 0 ¹ m* nm* m* ª º n2 § t · n2 § · V 1 · n2 » § f « ¸¸ ¨¨ ¸¸ ¨ 1 exp ³ ¨¨ ¸ dS » « V * t n 1 © ¹ 0 0 © ¹ © ¹ «¬ S »¼
408 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
(6)
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations
with m, V0 the Weibull apparent parameters, m* and V0* the intrinsic parameters, A and n the Evans law parameters, tf the service life, V the applied stress, Y the shape factor and
t0
2 2 1 V 0* . 2 n2 n 2 AY K Ic
Consequently, the Weibull apparent parameters are:
m
n 1 m * n2
1
and V 0
V 0 *
n2 n 1
ª ºn 2 n 1 V « 2 n2 » ¬ n 2 AY K Ic ¼
(7)
It can be noted that only the Weibull apparent stress V0 depends on the stress rate. Considering two loading rates, v1 and v2, V 0 v and V 0 v are linked through the 1
2
following relation: 1
V 0 v
1
§ ·n V 0 v2 .¨¨ v1 ¸¸ © v2 ¹
(8)
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2.3. Application to a given problem Carré and Daudeville [5] performed 4 points-bending tests under displacement control on small annealed glass beams (L=230mm, h=37.5mm, e=19mm) with polished edges and with different loading rates (0.5 and 0.05 m/s), see figure 2.
Figure 2: Four points bending test. Specimen tested in the experimental campaign led by Carré and Daudeville [5].
409 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Figure 3 presents the results of the large experimental database in terms of failure probability vs. failure stress.
Figure 3: Experimental results obtained by [5]. Predictions with the Weibull model.
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Apparent Weibull parameters, m and V0, for the loading rate of 0.5 m/s were firstly identified with these previous tests results (continuous line in figure 3). For a loading rate of 0.05 m/s, the failure prediction thanks to equations 6, 7 and 8 is given by a dashed line in figure 3. The correct prediction validates the association of the subcritical crack growth model with the Weibull theory. Such developments can be easily included in a design code, as it was done in the standard concerning glass tensile strength. Only the quality of the polishing should be precisely evaluated since it governs directly the value of the Weibull parameters. 3. Modelling of the behaviour of laminated glass beams Single conventional glass panes cannot be used as safety glass because of their brittleness. The basic construction of laminated glass involves two pieces of float glass together with an interlayer. To achieve that, Polyvinyl Butyral (PVB) interlayers have been used for a long time. During the two last decades, some companies have put considerable efforts into the development of new interlayer materials with increased structural properties. One of these products is SentryGlassPlus (SGP) which is about 100 times siffer and 5 times stronger compared to conventional PVB. With such laminated glass panes, brittle failure of an individual element may occur, but the structure is able to redistribute loads to other elements, thereby providing redundancy.
410 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations
The following of this section will concern the modelling of the post-breakage performance of a glass beam composed of 2 panes through a Finite Element Analysis with the FE package ABAQUS. 3.1. Assumptions of the modelling: constitutive materials behaviour Glass is assumed to be brittle in tension; A smeared crack model, Hillerborg-type [7] is used to represent this tensile behaviour. Cracking is thus assumed to be the most important aspect of the behaviour and it dominates its modelling. The model does not track individual “macro” cracks. Rather constitutive calculations are performed independently at each integration point of the FE model and the presence of cracks enters into these calculations by the way that cracks affect the stress and material stiffness associated with the integration point. A Rankine criterion is used to detect crack initiation: this criterion states that “cracking” occurs when the maximum principal stress reaches and exceeds the tensile strength of the material. Thus crack detection is based only on mode I facture considerations. ABAQUS then assumes that “cracks” are fixed and orthogonal to the direction of the maximum principal stress. The specification of the post-failure behaviour needs to enter the post-failure stress as a tabular function of the displacement across the crack (instead of strain which can introduce mesh I
I
sensitivity) or, in an equivalent way, the value of the fracture energy G F . G F represents the energy required to form a unit area of crack surface. This material property can be obtained thanks to the following LEFM formula:
G
K Ic2 E
I F
(9)
where KIc is the glass toughness (0.75 MPam) and E is the Young’s modulus (70 GPa). I
Consequently, G F
8 N/m for silica-soda-lime glass.
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Moreover, the following assumptions are made: x
In a first simulation, two different values around the 5% fractile of figure 3 ( f t 30 and 40 MPa) are used for the two considered glass panes;
x x
the compression behaviour of glass is assumed to be always linear elastic; in order to avoid any problems of convergence due to excessive distortion of elements which can no longer carry stress, a brittle failure criterion called “kill element method” is used. Thus, when the local cracking displacement in an element reaches a critical value ( u ck
2G FI f t ), all the stress components
are set to zero and the corresponding element is removed from the mesh. Besides, the obvious advantage for the computational convergence, this technique allows also to visualize crack patterns in the beam. The interlayer, whatever is its nature (PVB or SGP), exhibits a hyperelastic behaviour. A material is called hyperelastic if the stress can be derived from an energy function W that is uniquely related to the current state of deformation. The strain energy depends solely on the deformation gradient. 411
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There are several forms of strain energy potentials available in ABAQUS to model such incompressible isotropic elastomers. The Mooney-Rivlin form has already shown its capacity to reproduce accurately interlayer materials behaviours in laminated glass structures [8]. This form is thus used in the present study; the strain energy potential is given by:
c01 I 1 3 c10 I 2 3
W
(10)
where: - c01 and c10 are material parameters to be identified; -
I 1 and I 2 are the first and second deviatoric strain invariants defined as:
I1
2
2
O1 O2 O3
2
and
O1
I2
2
O2
2
O3
2
with
Oi
the
deviatoric stretches. ABAQUS enables an automatic identification of the material parameters c01 and c10 by providing the results of an uniaxial test. In this study SGP is considered as the interlayer materials and the schematic stress-strain curve of uniaxial tensile tests for a reference loading rate of 5mm/min is given in figure below [9]. 35 30
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stress (MPa)
25 20 15 10 5 0 0
0.5
1
1.5
2
2.5
3
3.5
4
strain
Figure 4: Schematic stress-strain curve used in this modelling work for SGP.
3.2. Assumptions of the modelling: studied case A beam composed of two annealed glass panes with a SGP interlayer subjected to a 3 points bending test is investigated in this numerical analysis. Each individual glass component is 3000 mm length and 150 mm height. Their nominal thickness is 6 mm. The interlayer thickness is 1.52 mm. 412
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations
Solid brick linear Finite Elements are considered for all parts of the model. The mesh is refined enough for the interlayer so that elements are not degenerated. Between all parts of the model (glass 1-interlayer and interlayer-glass 2), the contact is supposed to be perfect (“tie” contact). In a first approximation this assumption can be considered as correct since [9] concludes that SGP beams do not show important local delaminations. 3.3. First results and future work Figure 5 presents the load-deflection curve obtained by the modelling. Compared to a single pane –glass beam, the laminated beam exhibits a small post-peak safety. This first modelling aims only to show the feasibility of the numerical approach. In a future work it is proposed to quantify this post-failure safety by evaluating an “equivalent” fracture energy for the laminated glass beam. The methodology proposed by the RILEM network (international union of laboratories and experts in construction materials, systems and structures) is envisaged to achieve this purpose [10]. Such an equivalent fracture energy could be drawn in function of the failure stress or in function of the associated failure probabilities of the two glass panes. This new result might be of importance for structural engineers. 3
2.5
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Load (kN)
2
1.5
1
0.5
0 0
1
2
3
4
5
Deflection at mid span (mm)
Figure 5: Load-deflection curve for laminated SGP beam. A first modelling result.
413 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
6
Challenging Glass 3
4. Study of the failure in connection area In the past decade, an important and considerable effort has been performed on the study of connection area in glass structures [11-14]. Indeed these particular zones cannot be avoided, especially when large spans of high stiffness beams are considered. Point bearings in holes are investigated in this study and more particularly countersunk point fixtures with conical drillings. In [14] an exhaustive experimental campaign has been presented. Push out tests adapted for glass structures have been performed. Besides cylindrical holes, three geometries of conical holes have been considered (namely holes b1, b2 and c1, see figure 6 and table 1). Both annealed and fully tempered 19 mm thick glass plates have been tested.
Figure 6: Cross section of conical holes.
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Table 1: The 3 different conical geometries Designation
)int (mm)
)ext (mm)
b1
24
40
b2
40
56
c1
30
40
More details concerning not only the connection (and particularly on the interlayer washer enabling to avoid any contact between steel and glass) but also on the experimental campaign itself, can be found in [14] or [15]. For conical holes, almost 60 samples have been tested until failure (40 on annealed glass and 18 on tempered one more precisely). A special attention has been paid on the initial torque applied to the bolt: indeed various values have been used. This initial prestressing has been applied thanks to a torque wrench. Tables 2 a and b present all the experimental results for respectively annealed and tempered glass. The number of experiments as well as the standard deviation (if it is pertinent) are also given.
414 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations Table 2: Results of the experimental campaign on annealed glass. Ultimate loads according to initial torque and standard deviations. Hole geometry
Initial torque (daN.m)
Ultimate load (kN)
Exp. number (stand. deviation kN)
Hole b1
0
12.7
1
1
23.3
5 (2.3)
2
22.7
4 (4.3)
>2.5
0
3
1
21.8
3 (2.1)
2
22
9 (2.5)
5
11.9
1
Hole b2
Hole c1
>5
0
2
2
24.4
2 (2.4)
2.5
16.8
3 (3.3)
3
20.5
5 (4.6)
5
26
2 (4.7)
One of the main conclusions is that the deviation is quite low although glass is sensitive to surface flaws. Overall, the deviation is smaller than the deviation obtained during 4 points bending tests (see figure 3).
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Table 3: Results of the experimental campaign on tempered glass. Ultimate loads according to initial torque and standard deviations. Hole geometry
Initial torque (daN.m)
Ultimate load (kN)
Exp. number (stand. deviation kN)
Hole b1
1
107
4 (7.1)
7.5
118.5
1
10
115.7
1
2
112
4 (6.1)
4
109
1
10
85
1
Hole b2
Hole c1
1
86.5
2 (9.2)
2.5
94.2
1
7.5
89
1
10
62
2 (2.9)
415 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Fractography analyses, i.e. post mortem analyses of the failure origin, coupled with SEM observations, have also shown that: x -
x -
for annealed glass: failure has been most of time initiated on the conical part of the hole chamfer even if the cylindrical parts are less carefully machined; the interaction between aluminium interlayer and glass excites a flaw on the glass surface: this contact is at the origin of the failure; mode accurately, the failure starts from a flaw located on the bottom of the conical chamfer (see figure 6) near to the cylindrical part, where the tensile stresses due to in-plane loading are the most important or, a few times, located on the top of the chamfer where the contact is the most intensive. for tempered glass: failure is always located on the bottom of the chamfer; the FE modelling of the thermal tempering, presented in [16] has shown that the decrease of the residual compressive stresses from the bottom to the top of the chamfer is less important than the decrease of the applied tensile stress. Thus during the push-out tests performed on tempered glass, the top of the chamfer is never decompressed and failure cannot occur from this location That explains why standard deviations are relatively less important for tempered glass than for annealed one.
All these remarks tend to prove that a deterministic approach of the resistance of the connection is sufficient and effective. Of course, such an approach is easier to perform for structural engineers.
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5. Summary and conclusions In this paper a discussion concerning failure in glass structures is proposed. This discussion compiles experimental, analytical and numerical considerations. Single glass panes, laminated ones and connections are studied. Several conclusions have been pointed out: x
x x
the probabilistic model of Weibull is used in association with a subcritical crack growth model. For a given surface finish, the model can take into account the effects of the specimen size, of the stress distribution and of the rate of loading; the use of a smeared crack model (for glass) and a hyperelastic one (for interlayer) in a Finite Element Analysis can lead to a quantification of the postfailure safety of a laminated beam; the failure in connections is quite different from the one observed in current zones: indeed the cracks origins have always been found in a small area of the chamfer leading to low deviations in experimental results. A deterministic approach of the failure seems thus to be possible.
416 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
How to Model Failure in Load-bearing Glass Elements? A Discussion Based on Analytical, Numerical and Experimental Considerations
6. References
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[1] Griffith, A. The phenomena of rupture and flow in solids, Philosophical Trans. Royal Soc., London, A221/1920, pp. 163–198. [2] Weibull, W. A. (1951). A statistical distribution function of wide applicability, J. Appl. Mech., 18/1951, pp. 293–297. [3] Grenet, L., Mechanical strength of glass, Bull. Soc. Enc. Nat., Paris, 5/1899, pp. 838–848. [4] Michalske, T. A., and Frieman, S. W. (1983) A molecular mechanism for stress corrosion in vitreous silica, J. Am. Ceramic Soc., 66/1983, pp. 284–288. [5] Carré H.; Daudeville L., Load bearing capacity of tempered structural glass, ASCE Journal of Engineering Mechanics, 125/1999, pp. 914-921. [6] Evans, A. G., Slow crack growth in brittle materials under dynamic loading conditions, International Journal of Fracture, 10/1974, pp.251-259. [7] Hillerborg, A.; Modeer, M.; Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cem. and Concrete Research, 6/1976, pp. 773–782. [8] Timmel, M.; Kolling, S.; Osterrieder, P.; Du Bois,P.., A finite element model for impact simultion with laminated glass, Int. Journal of Impact Engineering, 34/2007, pp. 1465-1478. [9] Belis, J.; Depauw, J.; Callewaert, D.; Delincé, D.; Van Impe, R.; Failure mechanisms and residual capacity of annealed glass/SGP laminated beams at room temperature, Engineering Failure Analysis, 16/2009, pp. 1866-1875. [10] RILEM Committee FM C50, Determination of the fracture energy of mortar and concrete by means of 3 points bending tests on notched beams, 1985. [11] Laufs, W.; Sedlacek, G., Stress distribution in thermally tempered glass panes near the edges, corners and hole, Glass Science and Technology, 72/1999, pp.1-14. [12] Maniatis, I., Numerical and Experimental Investigation on the Stress Distribution of Bolted Connection under In-Plane Load, Ph-D thesis, Technische Universität München, 2006. [13] Schneider, J., Glass Strength in the Borehole Area of Annealed Float Glass and tempered Float Glass, Research in Architectural Engineering Series, 1/2007, pp.157-167. [14] Bernard, F., Daudeville, L., Point fixings in annealed and tempered glass structures: modeling and optimization of bolted connections, Engineering Structures, 31/2009, pp. 946-955. [15] Bernard, F., Sur le dimensionnement des structures en verre trempé: étude des zones de connexion, Ph-D thesis, ENS Cachan, 2001. [16] Daudeville, L.; Bernard, F.; Gy, R., Residual stresses near holes in tempered glass plates, Material Science Forum, 404-407/2002, pp.43-48
417 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-419
New Expressions for the Effective Thickness of Laminated Glass Laura Galuppi, Gianni Royer-Carfagni Department of Civil-Environmental Engineering and Architecture, University of Parma, Italy, [email protected] The deformability of the interlayer does not provide a perfect shear transfer between the glass plies, so that flexural response of laminated glass is somehow intermediate between that of a monolith and that of free-sliding plies. In the design practice, this effect is usually taken into account through the definition of the Effective Thickness (ET), i.e., the thickness of a monolith with equivalent bending properties. Classical formulas for the ET have been proposed by Bennison et al. [1], based on the original analysis by Wölfel [2]. Here, we propose new expressions for the ET based upon strain energy minimization. Practical formulas are derived which apply to the one-dimensional case of beams, as well as to the twodimensional case of laminated plates. The better efficiency of the proposed method with respect to others is proved by the comparison with accurate three-dimensional numerical simulations. Keywords: Laminated glass, plate design, effective thickness, laminated plate, composite structures, sandwich structure.
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1. Mechanical behavior of laminated glass An effective technique to enhance the post-glass-breakage performance of architectural glazing consists in bonding glass plies together with polymeric interlayers via lamination in autoclave at high temperature and pressure. In such a way a laminated glass acquires safety properties because, after breakage, shards remain attached to the polymer and the system maintains a small but significant load bearing capacity, avoiding injuries due to catastrophic collapse. But the interlayer affects also the preglass-breakage response because it allows the transfer of shear stresses among glass plies, at the price of a relative sliding due to the deformation of the polymer. Laminated glass is thus a sandwich structure, whose stiffness and strength may be considerably less than those of a monolithic glass with the same total thickness, because, due to the shear deformability of the polymer there is not a perfectly coupling between any two consecutive glass plies. The behavior of the structure will be intermediate between two limit cases: x the monolithic limit for which the relative sliding is null (fig. 1a); this limit corresponds to ܩ՜ λ; x the layered limit (frictionless relative sliding of the plies), attempted for ܩ՜ Ͳ (fig. 1b).
419 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
a)
b)
c)
Figure 1: Laminated glass composed of two plies and one interlayer under flexure. The two limit cases of a) monolithic limit and b) layered limit; c) the intermediate real configuration.
In the design practice, the problem is simplified and reduced to a case in which all the materials, including the viscoelastic interlayer, are considered linear elastic. In numerical computations, the response of laminated glass could be modeled by a layered shell element that takes into account the competing stiffness between glass and interlayer, but most of the commercial numerical codes do not have such elements in their library. On the other hand, a full 3D analysis is complicated and time consuming. This is why, in the design practice and especially in the preliminary design, it is very useful to consider approximate methods for the calculation of laminated glass. 1.1. The approach by Wölfel-Bennison (W-B) Currently, the most used approach is probably the one proposed by Bennison [1] based upon the theory for composed sandwich beams proposed by Wölfel [2]. To illustrate, consider the laminated beam of length l and width b shown in Figure 2, composed of two glass plies of Young’s modulus E, connected by a polymeric interlayer of shear modulus G.
E, A1,I 1
y
p(x) Copyright © 2012. IOS Press, Incorporated. All rights reserved.
h1 x
t
G
H
h2 l b
E, A2,I 2
Figure 2: Beam composed of two glass plies bonded by a polymeric interlayer. Longitudinal and cross sectional view (not in the same scale).
420 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
New expressions for the effective thickness of laminated glass
Let
ܣଵ ൌ ܾ݄ଵ , ܣଶ ൌ ܾ݄ଶ , ܪൌ ݐ
భ ାమ ଶ
, ܫଵ ൌ
భయ ଵଶ
, ܫଶ ൌ
మయ ଵଶ
Ǥ
(1)
When the layered limit is attained, the moment of inertia of the laminated beam equals the sum ܫଵ ܫଶ . In the monolithic limit, the moment of inertia reads ܫ௧௧ ൌ ܫଵ ܫଶ
ܣଵ ܣଶ ܪǤ ܣଵ ܣଶ
(2)
For intermediate cases, Wölfel [2] proposed a strong approximation according to which the effective moment of inertia is of the form ܫ ൌ ܫଵ ܫଶ Ȟ
ܣଵ ܣଶ ܪଶ ǡ ܣଵ ܣଶ
(3)
where the parameter accounts for the capability of the interlayer to transfer shear stress between the glass plies. Hypothesis (3) is equivalent to assume that the bending stiffness of the external layers has no influence on the coupling offered by the central layer: the less the bending stiffness of the external layers, the more accurate is this hypothesis. Wölfel proposed for the expression Ȟൌ
ͳ ǡ ܣ ܧݐଵ ܣଶ ͳߚ ଶ ܾ݈ ܣଵ ܣଶ
(4)
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where depends upon the loading and boundary condition. Bennison [1] has adopted Wölfel’s approach for the case of laminated glass, suggesting to using in (4) the value ߚ ൌ ͻǤ although in Wölfel’s theory this is a particular case associated with simply supported beams under uniformly distributed load. From (3), one can calculate the stress- and the deflection-effective thickness, i.e., the (constant) thickness of the homogeneous plate that, under the same boundary and load conditions of the considered problem, has the same maximal stress or maximal deflection, respectively. Introducing, as per [1], the quantities ݄௦Ǣଵ ൌ
ுభ భ ାమ
ǡ ݄௦Ǣଶ ൌ
ுమ భ ାమ
ଶ ଶ ǡ ܫ௦ ൌ ݄ଵ ݄௦Ǣଶ ݄ଶ ݄௦Ǣଵ ǡ
the deflection-effective thicknesses turns out to be: య ݄Ǣ௪ ൌ ඥ݄ଵଷ ݄ଶଷ ͳʹȞܫ௦ ,
(5)
(6)
whereas the stress-effective thickness for glass plies number 1 and 2 is given by ݄ଵǢǢఙ ൌ ඨ
య Ǣೢ
భ ାଶೞǢమ
ǡ ݄ଶǢǢఙ ൌ ඨ
య Ǣೢ
మ ାଶೞǢభ
Ǥ
421 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
(7)
Challenging Glass 3
Although these expressions (referred to in the sequel as the Wölfel-Bennison approach) refer to a very particular static scheme, they are commonly used in numerical computations with models of monolithic plates with constant thickness. 1.2. The Enhanced Effective Thickness (EET) approach An alternative formulation has been very recently proposed in [3]. This procedure, called Enhanced Effective Thickness (EET) method, is based upon a variational approach and consists in finding the best approximation for the response of laminated glass among a restricted class of shape functions for the deflection surface through the minimization of the strain energy functional. The main hypotheses for this model are: x x x x
the interlayer has no axial or bending stiffness, but only shear stiffness; shear deformation of glass is neglected; all materials are linear elastic; geometric non-linearities are not considered.
Remarkably, not only the method applies to the one-dimensional case of beams under bending, but it can be naturally extended to the two-dimensional case of plates [4] under the most various load and boundary conditions. Tables for the calculation of the relevant coefficients in the most common cases have been presented in [5] for ease of reference and to facilitate the practical use. The efficiency of the EET formulation is confirmed by comparison with the results of precise numerical simulations on paradigmatic examples. 2. Enhanced Effective Thickness: the one-dimensional case 2.1. Theoretical model The enhanced effective thickness (EET) method is manly based upon two assumptions: Copyright © 2012. IOS Press, Incorporated. All rights reserved.
x
the equivalent moment of inertia moments of inertia
IR
is the weighted harmonic mean of the
I tot (associated with the monolithic limit) and I1 I 2
(layered limit), that is: ͳ ߟ ͳെߟ ൌ ǡ ܫோ ܫ௧௧ ܫଵ ܫଶ
x
(8)
where the non-dimensional weight parameter ߟ plays a role analogous to that of in (3), because it tunes the response from the layered limit (ߟ ൌ Ͳ) to the monolithic limit (ߟ ൌ ͳ); the deformed shape of the laminated glass beam has the form of the elastic curve ݃ሺݔሻ of a monolithic beam with constant cross section under the same loading and boundary conditions of the problem at hand.
422 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
New expressions for the effective thickness of laminated glass
The parameter K is of the form ߟൌ
ͳ ǡ ܫ ݐܧଵ ܫଶ ܣଵ ܣଶ Ȳ ͳ ܫ ܾܩ௧௧ ܣଵ ܣଶ
(9)
where , as illustrated in [3], is a parameter that is calculated from minimization of the strain energy. In particular, denoting with the one-dimensional domain representative of the reference configuration of the beam, the quantity is defined as Ȳൌ
ஐ ሺݔሻ݃ሺݔሻ݀ݔ ஐ ݃Ԣሺݔሻଶ ݀ݔ
Ǥ
(10)
Such a parameter depends upon the boundary and load conditions and its values are recorded in [5] for the cases of most practical relevance. Notice as well that depends upon the mechanical and geometrical properties of the laminated beam. From (8), the deflection-effective thickness hˆw then turns out to be ݄௪ ൌ
ͳ Ǥ ߟ ͳെߟ ඩ ଷ ଷ ଷ ଷ ݄ଵ ݄ଶ ͳʹܫ௦ ݄ଵ ݄ଶ
Recalling the definitions (5) of hs;1 and h for the stress-effective thickness:
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݄ଵǢɐ ൌ ඨ
s;2
(11)
, one also finds the following expressions
ଷ ଷ ݄ଵଷ ݄ଶଷ ͳʹܫ௦ ݄௪ ݄ଵଷ ݄ଶଷ ͳʹܫ௦ ݄௪ ǡ ݄ଶǢɐ ൌ ඨ Ǥ ʹߟ݄௦Ǣଶ ݄ଵ ʹߟ݄௦Ǣଵ ݄ଶ
(12)
The EET approach presents no additional difficulty with respect to the Wölfel-Bennison formulations, giving the compact formulas (11) and (12) for laminated glass design. Moreover, it can be readily extended to the two-dimensional case. 2.2. Examples The results obtainable with the EET approach are now compared with those proposed by Bennison [1] and with the numerical experiments performed by means of the finite element software SJ-Mepla, specifically conceived of for laminated glass [6]. For the sake of comparison, in the present section, three paradigmatic cases are analyzed in detail. With the same notation of Figure 2, assumed geometrical and structural parameters are l = 3150 mm, b = 1000 mm, h1 = h2 = 10 mm, t = 0.76 mm, E = 70 GPa, while the shear modulus G of the polymeric interlayer is varied to evaluate its influence on the shear-coupling of the glass plies. The distributed load per unit length becomes p = 0.75 N/m. 423
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
Three constraint conditions for a uniformly loaded beam are here considered: x x x
simply supported beam (Figure 3.a) beam with three supports (Figure 3.b); double clamped beam (Figure 3.c).
In the following graphs, the stress- and deflection-effective thicknesses, calculated through (11) and (12), are plotted as function of G with a continuous line, whereas the effective thicknesses calculated with the Wölfel-Bennison’s approach is represented with a dashed curve. Results of numerical experiments are indicated with dots.
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In the case of simply supported beams under uniform load the models give results that in practice coincide, a finding that is not surprising because this is the simplest case upon which the W-B approach is calibrated. Numerical results confirm the good approximation that is achieved. In the cases of beams with three supports and of clamped beams, there is a substantial deviation between the EET and W-B approaches especially for the lowest values of G, but the numerical experiments are clearly in favor of the EET approach. Observe that W-B is not on the side of safeness, because it predicts effective thicknesses greater than in reality and, consequently, underestimates deflection and stress.
424 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
New expressions for the effective thickness of laminated glass
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Figure 3: Beam with different constraint condition under distributed load. Comparison of the effective thicknesses obtained with: Wölfel-Bennison (WB) approach; the enhanced effective thickness (EET) approach; the numerical simulations.
425 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenging Glass 3
3. Enhanced Effective Thickness: the two-dimensional case 3.1. Theoretical model Consider now a laminated glass plate identified by the xy domain under distributed load p(x,y), composed of two glass plies of thickness h1 and h2 and Young’s modulus E and Poisson’s ratio , connected by a polymeric interlayer of thickness t and shear modulus G. Defining the flexural rigidity of the i-th glass ply as ܦ ൌ
ாయ
ଵଶሺଵିɋమ ሻ
, it can be
demonstrated (see [4]) that the flexural rigidity for the monolithic limit reads ܦ௧௧ ൌ ܦଵ ܦଶ ͳʹ
ܦଵ ܦଶ ܪଶ ǡ ܦଵ ݄ଶଶ ܦଶ ݄ଵଶ
(13)
In analogy to the one-dimensional case, the deformed shape of the plate can be selected as the elastic deformed surface ݃ሺݔǡ ݕሻ of a monolithic plate with constant thickness under the same loading and boundary conditions. Moreover, the equivalent rigidity DR, in analogy with (8), can be assumed to be ߟ 1-ߟ ͳ ൌ . ܦோ ܦ௧௧ ܦଵ ܦଶ
(14)
The minimization of the strain energy of the sandwich plate allows to determine the counter part of (10) for the two dimensional case in the form ߟ=
ͳ
ͳ
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where Ȳൌ
ܦ ݐଵ ܦଶ ͳʹܦଵ ܦଶ Ȳ ܦ ܩ௧௧ ܦଵ ݄ଶଶ ܦଶ ݄ଵଶ
,
ஐ ሺݔǡ ݕሻ݃ሺݔǡ ݕሻ݀ݕ݀ ݔ ଶ ሺݔǡ ݕሻ ஐ ሾ݃ǡ௫
ଶ ሺݔǡ ݕሻሿ݀ݕ݀ݔ ݃ǡ௬
(15)
ǡ
(16)
depends upon the plate shape, the load distribution ሺݔǡ ݕሻ and the boundary conditions. The stress- and deflection-effective thicknesses may be readily calculated and take expressions analogous to (11) and (12), respectively. It is important to note that the only “difficulty” of the proposed method consists in calculating from (16), because all the other formulas are simple analytical expressions. Values of that refer to the most common cases of the design practice (plate under various boundary condition, under distributed and concentrated load) are reported in [5]. 3.2. Examples In the sequel, we compare the deflection- and stress-effective thickness for rectangular plates under a uniformly distributed load with various constrain conditions, calculated according to the proposed EET approach through equations (11) and (12), with the ones calculated with the W-B formulas (6) and (7). Results are also validated by means of 426
Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
New expressions for the effective thickness of laminated glass
numerical analysis performed with the finite element software SJ-Mepla. Assumed structural parameters are the size of the plate 3000 mm x 2000 mm; the thicknesses of the glass plies h1 = h2 = 10 mm; the thickness of the interlayer t = 0.76 mm; the elastic parameters for glass E = 70 GPa and = 0.22. The shear elastic modulus G of the polymeric interlayer is again varied between 0.01MPa and 10MPa. The distributed pressure on the plate is taken equal to 0.75 10-3 N/mm2.
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The considered case are: x simply supported plate on four sides (Figure 4.a): in this case the two formulations give different results at the qualitative level. Again W-B is not on the side of safeness, because it underestimates deflection and stress; x point-wise supported plate at the corners (applying to frameless glazing, Figure 4.b): in this case the EET and W-B give similar results, in agreement to numerical outcomes; x plate with two opposite edges simply supported and one edge built-in (for example, glass banisters, Figure 4.c): it is evident that the EET model and W-B approach give substantially different results and that numerical experiments are in favor of EET.
427 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
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Figure 4: Rectangular plate with different constrained condition, under distributed load. Comparison of the effective thicknesses obtained with: Wölfel-Bennison (WB) approach; the enhanced effective thickness (EET) approach; the numerical simulations.
428 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
New expressions for the effective thickness of laminated glass
4. Conclusions One of the currently most-used simplified approaches for the structural design of laminated glass is that due to Bennison [1], which is based upon the original work by Wölfel [2]. However, Wölfel’s model was primarily conceived of for a sandwich beam with external plies with considerable axial stiffness but negligible bending stiffness and an intermediate layer that can only bear shear stress, with zero axial and flexural strength. Whenever the external layers present considerable bending stiffness, as in the case of laminated glass, Wölfel proposed a very approximate solution that in any case, as we have verified here, gives results in agreement with more accurate (numerical) methods of analysis for the only case in which the load is uniformly distributed and the deformed shape tends to be cylindrical. In the other cases, the standard Wölfel-Bennison approach gives results that are not on the side of safeness. Better approximations can be achieved with the Enhanced Effective Thickness approach, which presents no additional difficulty with respect to the more traditional formulation. Such an approach can be easily extended to the two-dimensional (plate) case, for which it gives results that fit more closely the real situation both for the deflection and the stress calculation. The EET method furnishes compact formulas for both the beam case and the plate case and, remarkably, the most relevant expression (11) and (12) are analogous to those corresponding to the one dimensional case. The coupling offered by the interlayer can be readily evaluated by using the values of that have been tabulated in [5] for all those cases that are relevant for the design practice. However, using (16), the value of can be calculated with no difficulty for any laminated plate under any load condition. The enhanced effective-thickness approach thus seems to represent an accurate and powerful tool for the practical calculation of laminated glass.
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5. Acknowledgements The autors acknowledge the Italian MURST for its partial support under the PRIN2008 program. 6. References [1] [2] [3] [4]
[5] [6]
Bennison, S. J., Stelzer, I., Structural properties of laminated glass, Short Course, Proceedings Glass Processing Days, Tampere, Finland, 2009. Wölfel, E., Nachgiebiger Verbund Eine Näherungslösung und deren Anwendungsmöglichkeiten, Stahlbau, 6/1987, pp. 173-180. Galuppi, L., Royer-Carfagni, G., Effective Thickness of Laminated Glass Beams. New Expression via a Variational Approach, Engineering Structures, 38/2012, pp. 53-67. Galuppi, L., Royer-Carfagni, G., The effective thickness of laminated glass plates, Journal of Mechanics of Materials and Structures, accepted for publication. Available on line at http://dspaceunipr.cilea.it/handle/1889/1703. Galuppi, L., Manara, G., Royer-Carfagni, G., Practical expressions for the design of laminated glass, submitted. Available on line at http://dspace-unipr.cilea.it/handle/1889/1720. SJ MEPLA, User’s manual, version 3.5, 2012.
429 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-431
A Study of Polishing Performance of Glass Using Fluid Jet Polishing Anders Jönsson, Pia Lindahl, Johan Fredin Blekinge Institute of Technology, Sweden, [email protected],www.bth.se Christina Stålhandske Glafo – the Glass Research Institute, Sweden, [email protected], www.glafo.se The strength of glass designs are relying on good surfaces. Complex shapes and small holes calls for new polishing methods. Polishing of glass using fluid jet polishing is well known as a suitable method for acquiring high quality surfaces. In this study the combination of higher pressure and aluminum oxide as polishing material is tested in terms of higher polishing performance. A design of experiment study is done where important process parameters are varied. The results are compared to fluid jet polishing using cerium oxide. The polishing effect on the float glass is evaluated using visual grading and by using optical profilometry. In addition an analysis of sustainability aspects are done comparing the two different polishing materials. It is clearly shown that aluminum oxide is increasing the polishing performance.
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Keywords: Glass, Optical Profiler, Fluid Jet Polishing, Surface Analysis, Abrasive
1. Introduction Polishing of glass is becoming more and more important for different glass products. Traditionally, the polishing of glass in the art and design sector is a well established process. Different polishing processes like acid polishing, mechanical and chemical/mechanical polishing are well recognized. Due to complicated geometries and ecological aspects, alternative polishing processes are developed and under evaluation. Within the float glass industry more and more attention is given to the fact that the making of holes is introducing defects in the glass. These defects are a disadvantage for the strength of the glass product and therefore ways to reduce or remove these defects are searched for. Fluid Jet Polishing (FJP) has a potential of being well suitable for removing these defects. The principle of FJP is conceptually described as the process of flowing a slurry that contains a mix of a fluid and polishing abrasives. This process can be described as a combination of the suspension jet technology [1] used for effective water jet cutting of materials and bowl feed polishing used for reaching very fine surface qualities, down to 0.1 nm RMS, [2]. In FJP the pressure is typically quite low compared to traditional suspension jets for cutting of materials, often the pressure is in the range of 0.5-2 MPa. The FJP process is also unique in the sense that it both polishes and shapes the surface in the same process step. This opens up for a wide range of potential areas of usage besides the polishing of glass. 431
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Compared to mechanical polishing, where the tool is in contact with the glass surface, FJP has no mechanical contact between the “tool” and the surface to be polished. This enables the jet to reach and polish arbitrary geometries. This also includes nonsymmetrical holes and small radii in corners for example which are extremely difficult to polish with traditional mechanical polishing methods. This also implies that the automation potential of FJP is high, since the accuracy needed of the tool path to follow is decreased due to the flexible “tool”. Compared to acid polishing, there are distinct environmental advantages both in terms of ecological and social aspects if the suitable polishing abrasive is chosen. Earlier work on FJP has shown that the process is capable of producing good surface qualities. Several types of abrasives have been tested and evaluated. To the author’s knowledge no earlier studies have been done, comparing cerium oxide and aluminum oxide when using FJP with higher pressures. This work presents initial results on the influence of the abrasives during FJP at higher pressures than traditionally used for polishing. In addition an introductory study of environmental aspects is done in order to compare the abrasives regarding other perspectives than pure technical.
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2. Experimental 2.1. FJP setup The experimental setup used in this work is a traditional FJP set-up shown in Figure 1. It consists of a container, slurry buffer, where the slurry made of water and polishing abrasives are buffered. From this container the pump is sucking the slurry and increasing the pressure. The pressure is controlled by regulating the speed of the pump and measured via an analogue pressure transducer. The pump speed is set manually to provide the correct pressure for the test. After the pump the slurry is transported through pipes to a nozzle where the potential energy due to the pressure of the slurry is converted to kinetic energy in the form of jet velocity. The pressure before the nozzle, the flow through the nozzle and the velocity of the jet after the nozzle are strongly depending of the jet nozzle geometry. The relative position of the nozzle to the work piece to be polished is controlled by a CNC-controller. The slurry in this work is a mixture of tap water and commercial cerium oxide under the brand name Regipol with an average particle diameter of 6.4 Pm or an aluminum oxide with average particle size of 10.1 Pm. No measurements of pH-values of the slurry have been done in this test. The temperature of the slurry is varying slightly between 20 and 30 degrees Celsius during the test run.
432 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
A Study of Polishing Performance of Glass Using Fluid Jet Polishing
Figure 1: Schematic overview of the experimental setup for FJP.
Copyright © 2012. IOS Press, Incorporated. All rights reserved.
An example of test-set-up is shown in Figure 2 where the polishing nozzle is adapted to a 5-axis water jet cutting machine utilizing the 3D motion control possibilities.
Figure 2: 5-axis manipulator used in the experimental setup for FJP.
433 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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During the tests the following parameters are varied: x x x x
velocity between nozzle and work piece in mm/s angle between work piece and jet in degrees stand-off distance between work piece and nozzle exit in mm pressure at pressure gauge just before the nozzle in bar
The parameters are varied between a high and a low value. The total test series is consisting of 16 parameter sets. The nozzle is run forward and back once over the work piece surface. This gives two passages of the jet for every set of parameters. In both test series the same type of nozzle with a diameter of 1.3mm has been used. The work pieces to be polished are made of 110 by 150 mm float glass and prepared by grinding using 25μm abrasives.
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2.2. Surface analysis The polished surface is judged visually in order to have a subjective judgment of the surface quality. The visual examination is performed in an enclosed area with black background and light coming from above. Six categories are used where 0 is hardly any impact and 5 is a bright surface corresponding to an acid polished surface. The judgment is done by experienced glass professionals, but it is still difficult to provide an objective judgment mainly due to the small surface analysed. In addition to the visual inspection, an optical profiler, a Bruker NPFLEX is used for measurements of the surfaces. The main parameters measured are the mean roughness of the surface, Sa, the root mean square surface slope of the surface, Sdq, and the developed interfacial area ratio Sdr. [3]. The measurements are made with a magnification of 2.7 times magnification in VSI mode and the measured area is 1.7 x 2.3 mm. In addition a planar fit is done. 3. Results and Discussion The results reported in this work are based on two equal test series except for the polishing abrasive used. In the first test cerium oxide is used and in the second test aluminum oxide is used. In addition a brief analysis of sustainability aspects for the two different abrasives are done. 3.1. Polishing In general it is found that Sdq and Sdr parameters correlate better to the naked eye evaluation than Sa values. It is the very fine cracks that should be removed and they scatter light giving rise to a less bright appearance of the surface. Smooth structures as polished grinding tracks and water cut structure remain even after small cracks are removed and will influence the Sa value but not scatter light. In Table 1 the results for the test series with 20 weight percent cerium oxide is shown.
434 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
A Study of Polishing Performance of Glass Using Fluid Jet Polishing
Table 1: Test series using 20% cerium oxide, 1.3mm nozzle Velocity [mm/s]
Pressure [MPa]
Stand-off distance
Angle
Visual
Sa [nm]
Sdq [deg]
Sdr [%]
[deg]
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[mm] 2
2
6
45
1
313
8.1
0.93
8
2
6
45
0
312
8.4
0.99
2
4.8
6
45
3
179
3.7
0.21
8
4.8
6
45
2
202
5.3
0.42
2
2
50
45
2
197
5.4
0.43
8
2
50
45
1
220
6.6
0.62
2
4.8
50
45
3
165
3.4
0.17
8
4.8
50
45
2
290
6.3
0.57
2
2
6
90
0
339
8.2
0.95
8
2
6
90
0
262
7.2
0.73
2
4.8
6
90
3
202
4.4
0.31
8
4.8
6
90
1
218
5.6
0.47
2
2
50
90
2
255
6.2
0.56
8
2
50
90
1-
342
8.9
1.14
2
4.8
50
90
2+
281
5.0
0.36
8
4.8
50
90
2
305
6.9
0.68
It is clear from the table that the parameters that give the best results are low velocity and high pressure. The other parameters seem to have less influence. The best values reached are Sa 165 nm, Sdq 3.4 deg and Sdr 0.17when the velocity is low, the pressure high, high stand-off distance and 45 degrees angle between the jet and the work piece surface.
Figure 3: a) 20% cerium oxide 2mm/s, 4.8 MPa, distance 50mm and angle 45 degrees b): 20% aluminum oxide 2mm/s, 4.4 MPa, distance 6mm and angle 90 degrees
435 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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The surface is shown in Figure 3a and the grooves from the grinding process are visible but not clear. In Figure 3b, the corresponding aluminum oxide surface except that the smaller distance is used. In Table 2 the results for the test series with 20 weight percent aluminum oxide is shown. It is here clear that a low velocity will increase the surface quality. It should be noticed that the strong positive effect of a higher pressure is not evident in this test. Instead the stand-off distance has remarkable higher influence on the surface quality. It is also noticeable that the values for Sdq and Sdr are significantly lower than for the cerium test series, (approximately 3 respectively 9 times better) even though the Sa values are in the same order. The Sdq and Sdr are clearly better correlated to the visual judgment then the Sa values [3]. Table 2: Test series using 20% aluminum oxide, 1.3mm nozzle Velocity [mm/s]
Pressure [Mpa]
Stand-off distance
Angle
Visual
Sa [nm]
Sdq [deg]
Sdr [%]
[deg]
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[mm] 2
20
6
45
3
301
2.6
0.11
8
20
6
45
2
173
3.7
0.20
2
20
50
45
2
220
1.7
0.05
8
20
50
45
2
144
3.1
0.14
2
20
6
90
4
587
1.4
0.03
8
20
6
90
4-
189
2.8
0.12
2
20
50
90
2
267
2.0
0.06
8
20
50
90
2
155
3.5
0.18
2
44
6
45
3
564
2.1
0.08
8
44
6
45
3
278
2.0
0.06
2
44
50
45
2
1437
3.6
0.19
8
44
50
45
2
336
2.6
0.10
2
44
6
90
4
387
1.3
0.02
8
44
6
90
4-
314
1.7
0.04
2
44
50
90
2
700
3.3
0.16
8
44
50
90
2
249
3.4
0.18
In Figure 4a an area is measured that includes none polished and polished sub-areas, where the polished are is clearly visible as a furrow. The groves origin from the grinding preparation of the glass surface is still remaining and clearly visible. This is a typical look from a cerium oxide polished surface. In this specific figure the concentration of cerium oxide is 50%. In figure 4b a similar 3D picture of an aluminum oxide polished surface with a similar furrow. Here the grinding grooves are not easily seen. 436
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A Study of Polishing Performance of Glass Using Fluid Jet Polishing
Figure 4: a) Surface for cerium oxide, 0.5mm nozzle, 2mm/s, 3MPa, 6mm, 45 degrees and visual 4 [3] b): Surface for aluminum oxide, 1.3mm nozzle, 2mm/s, 4.5MPa, 6mm, 90 degrees and visual 5
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Figure 5 gives a complementary view of the surface by displaying the profiles at specific X and Y coordinates of the surface through the furrow. The X profile is showing the surface profile along the furrow bottom and the Y profile is representing a cross section of the furrow.
Figure 5: Additional surface analysis performed using surface profiles.
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3.2. Sustainability evaluation In this work the cerium oxide and the aluminum oxide have been compared from a sustainability perspective [4,5] while assuming that the material flows are linear, i.e. the materials are not reused after the polishing process but will be emitted to water. The evaluation is qualitative comprehensive and do not consider how assimilation to natural systems will be affected by shape or size of the emitted substances. However, even though neither cerium oxide nor aluminum oxide are listed in national databases related to toxicity –since the work is dealing with small particles of the materials, working environment precautions should be committed to avoid exposure – specifically through inhalation. Lack of data regarding the mining of the materials affects the ability to evaluate the extraction process. Information from suppliers has indicated that both substances could be extracted in China, why similar working conditions could be assumed but not confirmed.
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In Table 3, criteria are shown that are used for comparing the substances. From the evaluation of the criteria it is clear that aluminum oxide should be the preferable alternative. This is based on the facts that aluminum is very common in the earth crust, that the anthropogenic flows for cerium oxide is already larger than the natural flows and that Cerium is a rare substance that should not be used in a dissipative way to secure future generations availability of the material. Cerium is also listed on the EU list of critical metals in the group of rare earths. In addition, and due to the reasons given above, the price for cerium has been raised dramatically the last years, while the price for aluminum is more stable.
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Table 3: Comparing cerium oxide and aluminum oxide from a sustainability point of view. Comparison of two materials
Cerium oxide
Aluminum oxide
Comments
A. Avoiding systematic increasing concentrations in nature due to exchanges of basic elements with other systems
-
+
B. Avoiding systematic increasing concentrations in nature due to transformation of substances within the system
-
+
The anthropogenic dominance of the mobilization flows of the element are larger for Cerium than for Aluminum why there is a greater risk that emissions of Cerium will contribute to increasing concentrations in nature [6] Both Cerium oxide and Aluminum oxide are naturally occurring substances; however, the natural availability of Aluminum oxide in water is greater than the availability of Cerium oxide [7].
C. Avoiding systematic physical degradation of ecological systems due to land-use change
Information is lacking regarding implications on land-use change why further information is needed.
D. Avoiding systematic physical degradation of ecological systems due to land-cover change
Information is lacking regarding implications on land-cover change why further information is needed.
E. Avoiding systematic physical degradation of ecological systems due to depletion of renewable resources
Information is lacking regarding implications on renewable resources why further information is needed.
F. Avoiding systematic physical degradation of ecological systems due to degradation of non-renewable resources
-
+
G. Avoiding systematic violations of economical, social and cultural rights
-
-
H. Avoiding systematic violations of civil and political rights
-
-
The natural availability in Earth’s Crust of Aluminum is larger than the availability of Cerium [7]. Furthermore, even if Cerium is one of the most common Rare Earths metals, the availability of the substance for future generations are seen as critical [8]. The major extractions of both Aluminum and Cerium are conducted in China, why we assume that possible contributions to degradations of social systems are comparable for Aluminum and Cerium.
Information is lacking regarding implications regarding associated flows why further information is needed.
I. Avoiding systematic violations of any of the above criteria due to associated flows
Green color means that the positive advantages is clear, grey color means that there is a need for more information, yellow color indicates an obvious negative effect.
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4. Summary and Future Work Two test series have been done in order to qualitatively compare the polishing performance of fluid jet polishing using cerium oxide and aluminum oxide. The polishing results are evaluated by visual examination and measured with an optical profiler. The Sdq and Sdr values are correlated to the visual examination. Both visual examination and Sdq and Sdr show clearly that aluminum oxide give significantly better polishing results on the glass surfaces. An introductory study for sustainability aspects of the materials are performed and indicates that most likely aluminum oxide is a better choice from a strategic sustainable point of view. Further tests should be done in order to statistically verify the results. The influence of temperature and pH value is also of interest for investigation in future work. With more test results the correlation between Sdq and Sdr values and visual examination can be consolidated. A more thorough sustainability study is also suggested also including alternative abrasive materials and including the recycling of the materials. 5. Acknowledgements Funding’s have been provided by EU structural funds, Region Blekinge and Kalmar Regionförbund. Orrefors Kosta Boda, Glasteknik i Emmaboda, Water Jet Sweden, KMT Robotic Solutions have all contributed to the success of the project. 6. References [1] [2] [3] [4] [5]
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[6] [7] [8]
Michele Monno, Massimiliano Annoni, Chiara Ravasio, Water jet, a flexible technology, Polipress Politecnico di Milano, ISBN 97888-7398-030-9, 2007. Booij, S.M., Fluid Jet Polishing - possiblites and limiations of a new fabrication technique, Technische Universiteti Delft, 2003. Stålhandske, C. and M. Lang, Flexible glass polishing with a cerium oxide containin fluid jet, in Proceedings of Glass Performance Days 2011: Tampere, Finland. p. 446-448, 2011. K-H Robèrt et al., Strategic Leadership Towards Sustainability, Psilanders grafiska, Karlskrona, Sweden, 2004. H. Ny et al., Sustainability Constraints as System Boundaries: An Approach to Making Life-cycle Management Strategic, Journal of Industrial Ecology 10, no. 1–2 , 61–77, 2006. Klee, RJ, Graedel TE. 2004. Elemental cycles: A status report on human or natural dominance. Annual Review Of Environment And Resources. 29:69-107. Emsley, J.,Web Site: Chemical Case Studies. Angewandte Chemie International Edition, 42: 4425. doi: 10.1002/anie.200390584, 2003. Critical raw materials for the EU, European Commision, 30 July 2010.
440 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-441
Design of Arches Strengthened with Cables for Glass Roofs Wim Kamerling Delft University of Technology, Faculty of Architecture, The Netherlands, [email protected] Arches are structurally very efficient. Nevertheless the dimensions of an arch can be reduced further by strengthening with cables. For arches of glass the efficiency of strengthened arches will be showed. To prevent the cables to be subjected to compression it is advisable to post-tension the cables. This paper focuses on the design and structural analysis of arches composed of glass elements, strengthened with post-tensioned cables to support transparent roofs. Keywords: Glass, Arches, Cables, Post-Tensioning, Grid Shell,
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1. Introduction The transparency of glass roofs will be optimal in case the supporting structure is made of glass and the dimensions of the glass elements are minimal. Generally form-active structures [2] such as funicular arches are structurally very efficient. Arches are constructed for at least two thousands years. However the dimensions of the Roman arches of masonry were quite substantial. Later, thanks to Hook, Poleni and other scientists and engineers arches could be designed less massive.
15,0 m
Figure 1: The roof of the GUM department store is supported by half circular arches, strengthened with cables to reduce the bending moments acting on the arch [1].
Arches, subjected to normal forces only, can be dimensioned much smaller than sectionactive structures, subjected to bending moments. However it is difficult to optimize the dimensions of an arch, especially in case the structure is subjected to several load combinations. To minimize the dimensions, the line of the system has to approach the varying lines of thrust of the load combinations. For an arch, subjected to several load combinations, the bending moments can be reduced considerately by strengthening the arch with cables. At the beginning of the 20th century the Russian engineer V.G. Shukhov designed half circular arches for the GUM department store in Moscow, see figure 1. Post-tensioning the guy rods provided the arch with six additional bearings, 441
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capable of working both in compression and tension [1]. The analysis of a cable strengthened arch is complex. Nowadays an engineer can analyze these structures with a finite element program [3], but probably Shukhov designed these arches with just a slide rule. To understand these remarkable structures this paper focuses on the analysis of the load transfer. Recommendations are given to design these arches with minimal dimensions, to optimize the transparency of the glass roof. 2. Three hinged arch of glass A structure of glass fails if the structure is exposed to a tensile stress exceeding the ultimate tensile stress [5]. Due to their form, arches are mainly subjected to normal compressive forces. Mostly these normal forces will compensate, entirely or partly, the tensile bending stresses. So arches are very suitable for structures of glass, masonry and concrete. To show the potentials at first an example of a three hinged arch of glass is described. For form-active structures of glass subjected by bending and normal forces the stresses are validated with equation (1) based on the Theory of Elasticity, provided the effect of second order is small and can be neglected:
J g .N g A. f t
f
J g .M g W . ft
f
J e .N e A. f t
0
J e .M e d1 W . ft 0
(1)
With: Load factor permanent load:
Jg = 1,2
Load factor live load:
Je = 1,5
Area:
A [mm2]
Modulus of the section:
W [mm3]
Bending moment due to the permanent load:
Mg [Nmm]
Normal force due to the permanent load:
Ng [N]
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Bending moment due to the live load:
Me [Nmm]
Normal force due to the live load:
Ne [N]
Ultimate tensile stress for permanent loads, t = f :
f t =f 6,0 [MPa]
Ultimate tensile stress for instantaneous loads, t = 0:
f t=0 14,4 [MPa]
2.1. Example 1: Three hinged arch of glass Assume a roof is supported by arches of glass with a radius of 3,6 m and a span of 7,2 m. The roof is composed of glass panes, thickness 3*8 mm, spanning 1,2 m, supported by glass purlins, section 30*180 mm2 , spanning 2,0 m. The purlins are supported by beams, section 50* 360 mm2 with a span of 3,6 m. The beams are supported by the arches and prevent the arches of buckling perpendicular to the main axis. The length of sheets of glass is limited [4] so the arches, section 125 * 500 mm2, are composed of stepwise glued plates with a thickness of t = 25 mm. At a joint three sheets are continuously, consequently the area A and modulus of the section W are reduced with a factor 0,6. The half circular arches are subjected to five concentrated loads, see figure 2 and 3. The wind and permanent load acting at the nodes of the arches are described in table 1. 442
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Design of Arches Strengthened with Cables for Glass Roofs Table 1: Loads acting at a node of the arch: Load
Number
Weight
Length
Fep
Roof glass panes
3*
0,024 * 1,2 * 25
* 2,0 =
4,32 kN
Purlins
3*
0,03 * 0,18 * 25
* 2,0 =
0,81 kN
Beam
0,05 * 0,36 * 25
* 3,6 =
1,62 kN
Arch
0,125 * 0,5 * 25
* 1,9 =
2,97 kN
Force due to the permanent load
9,72 kN
Force due to the wind load
1,0 * 3,6
* 2,0 =
7,2 kN
4 3
4
5
3 2
5
6
2 I 1 r
6
1
7
7 I
Figure 2: Arch subjected to concentrated loads due to the permanent load.
r
Figure 3: Arch subjected to an anti-metric radial load.
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Due to the permanent load the concentrated force is equal to Fg = 9,72 kN. The supports are subjected to the thrust and the vertical reaction force equal to respectively Hrep = 1,134.Fg and Rrep = 2,5.Fg. The arch is subjected to bending, for node 5 and 6 the maximum bending moment is equal to Mg rep = -0,232.Fg.r. Due to the wind load, pe = 1,0 kN/m2 , the structure is subjected to radial nodal loads, acting anti-metric on the arch, equal to Fe = 7,2 kN, see figure 3. Due to this load the supports are subjected to a horizontal force equal to Hrep = 1,366.Fe. The vertical reaction force is nihil, Rrep = 0. For node 5 and 6 the maximum bending moment is equal to Me = Hrep.r.cos S/3. For element S56 the stresses are validated with expression (1), with: Reduced area:
A = 0,6 * 0,125 * 0,5 =
37,5.103 mm2
Reduced modulus of the section:
W = 0,6 * 0,125* 0,52/6 =
3,125.106 mm3
Reaction
R = 2,5 * 9,72 =
24,25 kN
Thrust permanent load:
Hrep = 1,134 * 9,72 =
11 kN
Bending moment due to the permanent load:
Mg = 0,232*9,72* 3,6 =
8,1 kNm
Normal force due to the permanent load, S56:
Ng =
18,1 kN
Thrust live load:
Hrep = 1,366 * 7,2 =
9,9 kN
Bending moment due to the live load:
Me = Hrep .r.cos S/3 =
17,7.kNm
Normal force due to the live load S56:
Ne =
5,1 kN
443 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
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1, 2 * 18 ,1 * 10 3 1, 2 * 8 ,1 * 10 6 1,5 * 5 ,1 * 10 3 1,5 * 17 , 7 * 10 6 |1 37 ,5 * 10 3 * 6 , 0 3,125 * 10 6 * 6 , 0 37 ,5 * 10 3 * 14 , 4 3,125 * 10 6 * 14 , 4
3. Strengthened arch The dimensions can be reduced in case the arch is strengthened with cables running from the supports to the nodes. The form-active structure is changed into a vector-active structure, so the elements are mainly subjected to normal loads.
4 3
4
5
2
3 6
1
2 7
I
5 6
1
r
7 I
Figure 4: Arch composed of hinged bars and 4 cables subjected to concentrated loads acting at the nodes.
r
Figure 5: Arch subjected to an anti-metrical radial load.
Figure 4 and 5 show an arch composed of bars and cables connected with hinges. The statically determinacy of the structure is defined with expression (2):
SD
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With:
S 2 .K R
(2)
SD = statically determinacy S = number of bars K = number of nodes R = number of reactions
Substituting S = 10, K = 7 and R = 4 into (2) gives SD = 0, so the structure is statically determinate. Successively the normal forces acting on the bars are defined from the top to the supports. Table 2 shows, for the right half of the arch, the normal forces acting parallel to the bars, due to concentrated nodal loads. To simplify the calculations the loads acting at the nodes are solved into horizontal and vertical components. For the members the sign is positive if the member is stretched and negative if the member is compressed. A horizontal force or vertical force acting at a node is positive in case this force is acting parallel to the positive X or Y axis.
444 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Design of Arches Strengthened with Cables for Glass Roofs Table 2: Solving horizontal loads and vertical loads acting on the nodes 4, 5 and 6 parallel to the members. Node
Member
Normal force acting on node
horizontal component
vertical component
4
S45 =
- ½ H4 /cos I½ V4 /sin I
H5 = - S45 * cos I
V5 = + S45 * sin I
5
S15 =
+ H5.sin 3Isin 5I V5.sin 3Isin 7I
H5 = - S15 * cos 2I
V5 = - S15 * sin 2I
S56 =
- H5.sin 2Isin 5IV5.sin 4Isin 7I
H6 = - S56 * cos 3I
V6 = + S56 * sin 3I
S16 =
+ H6.cos I V6.sin I
H6 = - S16 * cos I
V6 = - S16 * sin I
S67 =
- H6.sin IV6 cos I
H7 = - S56 * sin I
V7 = + S56 * cos I
6
Table 3 gives the normal forces acting on the members due to the horizontal and vertical nodal loads including the forces from the supported members above. Table 4 gives the normal forces, due to a vertical load acting on the nodes equal to Vi = -1p. Table 3: Member forces due to the horizontal forces Hi and vertical forces Vi acting at the nodes including the supported member forces. Node
Member
Normal force Si due to a horizontal force Hi en vertical Force Vi
4
S45 =
- ½ H4 /cos I ½ V4 /sin I
5
S15 =
+ (+ H5 – S45.cos I . sin 3Isin5I + (+V5 + S45.sin I sin 3Isin7I
S56 =
- ( + H5 – S45.cos I sin 2Isin5I + (+V5 + S45.sin I sin 4Isin7I
6
S16 =
+ (+ H6 – S56.sin 3I.).cos I (+V6 + S56.cos 3I sin I
7
S67 =
- ( + H6 – S56.sin 3I sin I (+V6 + S56.cos 3I cos I
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Table 4: Normal forces due to a symmetrical vertical loading acting at the nodes equal to V4 = V5 = V6 = -1p Node
Member
Due to load V4
Due to load V3, V5
Due to load V2, V6
Normal force due to load 6Vi
4
S45 =
-1,9318517
0
0
-1,9318517
5
S15 =
+1,0
-0,7305080
0
+0,2679492
S56 =
- 1,4142163
- 0,8965755
0
- 2,310789
S16 =
+ 0,7071068
+ 0,4482877
- 0,2588191
+ 0,8965755
S67 =
- 1,2247449
- 0,7764571
- 0,9659258
- 2,9671278
6
Table 4 shows that for the permanent load the members of the arch are compressed and the cables are tensioned, so this vector active structure transfers the vertical loads quite well. Unfortunately some cables are compressed if the structure is subjected to horizontal loads. Table 5 shows the forces due to anti-metrical radial loads. For the right half of the arch the bars and cables are tensioned, but for the left part the bars and cables are compressed. To avoid compressive loads acting on the cables the structure must be post-tensioned or loaded by an extra weight at the top.
445 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 Table 5: Normal forces due to anti metrical radial loads acting at the nodes Node
Member
Normal force due to a radial load Fi = 1
Fi = F
5
S15 =
+ (cos 4I).sin 3Isin 5I (sin 4I . sin 3Isin 7I
+1.F
S56 =
- (cos 4I .sin 2Isin 5I+ (sin 4I . sin 4Isin 7I
+0,5176381.F
S16 =
+ [ - S56 .sin 3I + (+cos 2I)].cos I+ [S56.cos 3I + (+sin 2I)].sin I
+0,7071068.F
S67 =
- [ - S56.sin 3I + (+cos 2I)]..sin I>S56.cos 3I + (+sin 2I)].cos I
+0,7071068.F
6
3.1. Example 2: strengthened arch The arch described in example 1 is strengthened. Due to the permanent load the nodes are subjected to a vertical force Fg = 9,72 kN and due to the live load the nodes are subjected to a radial anti-metric load Fe = 7,2 kN. The cable S15 is subjected to a force: S15 = + 0,268. Jg . Fg r 1,0.Jg . Fe Substituting Jg = 0,9, Fg = 9,72 kN, Jg = 1,5 and Fe = 7,2 kN shows that this cable can be subjected to a compressive load. To prevent the cable of subjected by a compressive load we can decide to increase the vertical load acting at the top. Next the needed extra force dFg acting at the top is calculated with Je = 0,9 and Je = 1,5: S15 = 1,0 * dFg + 0,268 * 0,9 * 9,72 - 1,0 * 1,5 * 7,2 > 0 dFg > 9,4 kN p 4. Post-tensioned Arch Post-tensioning can be helpful to avoid the cables loaded by compression. To posttension the arch two extra cables, S14 and S47, running from the supports to the top, are added and tensioned. Table 6 shows the normal forces due to a vertical force P acting at the top of the ach in case the two cables S14 and S47 are post-tensioned.
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Table 6: Normal forces due to the post tensioning force P acting at the top, node 4 Node
Member
Normal forces due to the force P acting at the top
Force
4
S45 =
- ½ P /sin I
-1,9318517.P
5
S15 =
-S45.cosIsin3Isin5IS45.sinIsin3Isin7I
S56 =
+S45.cosIsin2Isin5IS45.sinIsin4Isin7I
- 1,4142163.P
S16 =
+ (-S56. sin 3I.cos I S56. cos 3I.sinI
+ 0,7071068.P
S67 =
- (-S56. sin 3I. Sin I S56. cos 3IcosI
- 1,2247449.P
6
+1,0.P
446 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Design of Arches Strengthened with Cables for Glass Roofs
4 3
5
2
6
1
7 I
r
Figure 6: Ach loaded at the top due to the post tensioning of the cables S14 and S47.
4.1. Statically indeterminate arch Adding the two cables S14 and S47 increases the statically determinacy of the structure, so the transfer of the loads is effected by the stiffness of the members. To define the load distribution the structure is partitioned into a statically determinate arch strengthened with 4 cables and the triangular structure composed of the two diagonals S14 and S47. The deformation u of both vector active structures is defined with the following expression according to the Theory of Mohr. u
6 in 1 N i . N 'i .l E i . Ai
(4)
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With: u=
Deformation of the structure for a given node
Ni =
normal force acting into element i due to the loading
N’i =
normal force acting into element i due to the virtual load F = 1 acting at the given node parallel to the deformation u
Ei =
Young’s modulus of an element
Ai =
Area of an element
1.1. Deformation of the triangular structure at the top Due to the force F acting at the top both elements S14 en S47 are subjected to a force ½.F2. The length of the bars is equal to r2. The deformation of the triangle formed by S14 en S47 with section Ad and Young’s Modulus Ed is equal to:
u
F .r 2 E d . Ad
(5)
4.2. Deformation of the statically determinate arch at the top The deformation of the statically determinate arch due to a force F acting at the top is calculated with expression 4 and table 7. The vertical deformation of the arch at the top due to the force V4 = F acting at node 4 is equal to:
u
F .r .C p E d . Ad
With: CP = 2 * (3,74359. EdAd/EsAs + 2,69798) 447
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(6)
Challenging Glass 3
Table 7: Deformation of the ach due to a concentrated load acting at the top V4 = - Fp Member
N
N'
Length
N.N'.length/EiAi
S45
-1,9318517.F
-1,9318517
2.r.sin I
EsAs
1,9318517.F.r/(Es.As)
S15
+1,0.F
+1,0
2.r.cos 2I
Ed.Ad
1,7320508.F.r/(Ed.Ad)
S56
- 1,4142163.F
- 1,4142163
2.r.sin I
Es.As
1,0352762.F.r/(Es.As)
S16
+ 0,7071068.F
+ 0,7071068
2.r.cos I
Ed.Ad
0,9659258.F.r/(Ed.Ad)
S67
- 1,2247449.F
- 1,2247449
2.r.sin I
Es.As
0,7764572.F.r/(Es.As)
4.3. Load distribution for a concentrated load acting at the top For the structure subjected to a force F acting at the top, the triangular structure, composed of the cables S14 en S47, will transfer the force DF and the determinate arch will transfer a force (1-D) F. The ratio D follows from the following equation: (1 D 1 ) F .r .C p
u
E d . Ad
D 1 . F .r . 2 E d . Ad
D
Cp 1
Cp
(7)
2
Probably the sections of the cables are smaller than the sections of the bars, so the parameter Cp is much larger than 2 and the ratio D1 is within a range of 0,8 1 2,5 *10 6 *14,4
The stresses do not fulfill the demands. To reduce the bending stresses the structure is post-tensioned. The needed minimal post–tensioning is found for x = ½ a, with expression (14): 1,0 * P * cos D * 10 3 30 *10 3 * 6,0
1,2 *10,8 *103 3
30 *10 * 6,0
1,0 * 1 * P * sin D * 3,6 * 10 6 2 > 2,5 * 10 6 * 6,0
1,2 * ( 3 * 21,6 1 * 5,4 * 7,2 / 4) *106 1,5 * 23,4 *103 1,5 * ( 3 * 46,7 1 *11,7 * 7,2 / 4) *106 4 2 4 2 1 2,5 *106 *14,4 2,5 *106 * 6,0 30 *103 *14,4
The minimum post tensioning force has to be P > 22,5 kN. Next the maximum posttensioning load is defined with expression (15) for x = a:
1,0 * P * 0,97 3
30,0 * 10 .6,0
1,0 * P * 0,2425 * 3600 6
2,5 * 10 * 6,0
0,9 * 10,8 * 10 3 3
30,0 * 10 * 6,0
0,9 * (21,6 5,4 * 7,2 / 4) * 10 6 2,5 * 10 6 * 6,0
d1
P < 33,3 kN.
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For the minimum post-tensioning load P = 22,5 kN the strut is subjected to an upward load 2.P.sin D = 10,9 kN, the beam is subjected to a normal force Np = P.cos D = 21,8 kN and a bending moment Mp = 2.P.sin D(2.a)/4 = 19,6 kNm. 9.3. Beam strengthened with two struts Next the structure is designed with a strengthening composed of two struts center to center a = 2,4 m and two cables running on both sides with a diameter of 20 mm. The beam is constructed of 5 plates with a thickness 15 mm and a height of 300 mm, section 75 * 300 mm2, Eglass = 70 GPa. Both struts, length 0,6 m, are split in two parts which are connected to the sides of the beam: 2 *30*100 mm2, tan D = 6/2,4 = ¼, D = 14,040 , sin D = 0,2425, cos D = 0,97, cables 20, area 2 * 314 m2. E steel = 210 GPa .
q a tan D a
a
a
Figure 7: Beam strengthened with two struts 464 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Design of Cable Strengthened Beams for Glass Structures
Self weight
G=
Second moment of area
0,075 * 0,3 * 25 =
0,56 kN/m
3
Iby =
168,75 *106 mm4
75 * 300 /12 =
The factor C2 is defined with expression (7): C2
7 *104 * 22,5 *103 5
2
1
0,25 *
2
2,1*10 * 628* 0,2425 * 0,97 0,25
7 *104 * 22,5 *103 4
7 *10 * 2 * 30 *100
1 7 *104 * 22,5 *103 /(2,1*105 * 628) 2 * 0,252
C2 = 330. Next the distribution ratio E is defined with expression (10):
E
1 6 1 * 330 *168,75 *106 /( 22,5 *103 * 24002 ) 5
Permanent load
qg =
0,6 + 1,0 * 2,4 =
3,0 kN/m
Pay load
qe =
2,4 * 3,0 =
7,2 kN/m
Permanent load
Mg =
2
19,4 kN/m
2
3,0* 7,2 /8 =
Pay load
Me =
7,2 * 7,2 /8 =
46,7 kNm
Permanent load
EFg =
0,66 * 1,1 * 3,0 * 2,4
5,2 kN
Mg = EF.a =
5,2 * 2,4 =
12,5 kNm
Ng = EF/tan D
1
5,2/( /4) =
20,8 kN
E Fe =
0,66 * 1,1 * 7,2 * 2,4
12,5 kN
Moment upward force Normal force Pay load, upward force
1
Ne =EF/tan D
Normal force:
12,5/( /4) =
50,0 kN
12,5 * 2,4 =
30,0 kNm
/5*75 * 300 =
18,0 * 103 mm2
/5 *75* 3002/6 =
0,9 * 106 mm3
Me = EF*a
Moment upward force
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= 0,66
Reduced section area
Ab =
Moment of resistance
W=
4 4
The tensile bending stresses are checked with the equation (15), halfway the span, for x = 3/2 a:
1, 2 * 20 ,8 .10 3 3
18 * 10 * 6
1, 2 .(19 , 4 12 ,5 ). 10 6 5
9 * 10 * 6
1,5 * 50 ,0 .10 3 3
18 * 10 * 14 , 4
1,5 .( 46 ,7 30 ,0 ). 10 6 9 * 10 5 * 14 , 4
!1
The stresses do not fulfill the demands. To reduce the bending stresses the structure is post-tensioned. According to expression (14) the minimal post-tensioning load follows from: 1,0 * P * cos D *10 3 1,0 * P * sin D * 2,4 *10 6 ! 0,9 *10 6 * 6,0 18 *10 3 * 6,0
1, 2 * 20 ,8 * 10 3 1, 2 * (19 , 4 12 ,5 ) * 10 6 1,5 * 50 ,0 * 10 3 1,5 * ( 46 ,7 30 ,0 ) * 10 6 1 18 * 10 3 * 6 9 * 10 5 * 6 18 * 10 3 * 14 , 4 9 * 10 5 * 14 , 4 465
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Challenging Glass 3
P > 17 kN. According to expression (15) the maximum post-tensioning load follows from:
1,0.P * 0,97 3
18 * 10 .6,0
1,0 * P * 0,2425 * 2400 6
0,9 * 10 * 6,0
0,9 * 20,8 * 10 3 3
18 * 10 * 6,0
0,9 * (19,4 12,5) * 10 6 0,9 * 10 6 * 6,0
d1
P < 23,5 kN. For the minimum post-tensioning load P = 17 kN the strut is subjected to an upward load P.sin D = 4,1 kN. The beam is subjected to a normal force Np = P.cos D = 16,5 kN and a bending moment Mp = P.a.sin D= 9,9 kNm.
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9.4. Evaluation Due to the strengthening the area and self weight of the beam can be reduced considerately. For the not-strengthened beam the required section is 100 * 900 mm2. For the beam strengthened with one strut the required section is 75 * 500 mm2 and for the beam strengthened with two struts the section is only 75 * 300 mm2. 10. Conclusions Strengthening beams of glass with cables and struts is very effective to increase the transparency, to reduce the dimensions, the self weight and the footprint of the structure. Thanks to the statically indeterminacy the safety of the structure is increased too, provided the struts are prevented to turn over perpendicular to the main axis of the beam. Post-tensioning the cables is effective, especially if the stiffness of the truss is small, to reduce the bending moments and tensile stresses. For the given example the height of the beam, strengthened with one strut, was only 5/9 of the height of the not-strengthened beam. Nevertheless it is effective to increase the number of struts. For the given example the height of the beam, strengthened with two struts, was only 1/3 of the height of the not- strengthened beam. Further research is needed to test these structures in practice. 11. Literature [1] [2] [3] [4]
[5]
Belenya E., Prestressed Load-Bearing Metal structures, MiR Publishers, Moscow, 1977; Engel, Heino, Structural systems, Verlag Gert Hatje, Germany, 2th edition 1999; Hollander J.P., Optihalisatie, Constructietypen en ontwerpaspecten voor eenbeukige stalen hallen, Bouwen met Staal, The Netherlands, 2007; Louter, Christan; Belis, Jan; Bos, Freek; Veer, Fred; Hobbelman Gerrie, Reinforced Glass Cantilever Beams, Proceedings of the 9th International Conference of Architectural and Automotive Glass (Glass Processing Days) Tampere, Finland, 2005; Louter, Christian; J.F van Heusden, F.A. Veer, J.N.J.A. Vambersky, H.R. de Boer, J.Versteegen, Posttensioned Glass Beams, TuDelft Library, The Netherlands;
466 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3 – Conference on Architectural and Structural Applications of Glass Bos, Louter, Nijsse, Veer (Eds.), IOS Press, 2012. © 2012 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-061-1-467
The Design of an All Glass Roof to the EN1990 Ron Kruijs Glasimpex Schiedam, Holland, [email protected] Member of TC129WG8, TC250WG3, and the Dutch construction glass workgroup Architects van Mourik designed, in cooperation with Glasimpex Holland, an all glass roof for a cultural centre at Utrecht. The roof is sized 13x17m1, the main beams are 13m length. Because of the low budget the beams are split in four pieces size 3,25m1. Bearing hole connection is used. The design have to meet the EN1990 and national annex of Holland. Meaning the probability of failure and the way the structure fails must meet the requirements of the EN1990. Using the Dutch standard NEN2608, the EN1990 is respected. NEN2608 annex D given method, based on Fine and Kinney, is used to estimate the number of broken plies from the structural member that can be expected during the servility of the structure. The damaged structure must be able to carry a given level of load. Keywords: Glass, EN1990, NEN2608
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1. General The reliability according to EN1990 can be split into the probability (chance of failure) and the way the structure fails. For both parts demands are set. The layout for the way a structure may fail is defined by the basic requirement (EN1990 section 2). For a homogeneous plate of glass it is not possible to meet all requirements. Additions must be made. In this paper the process of design for an all glass roof to the EN1990 is described. This roof is built in March this year. 2. Probability of failure Consequence Class (annex B EN1990) The probability of failure has a function in the consequence of that failure. The glass roof will be built above the lobby of a cultural Centre. Failure would have medium consequence for loss of human life. In consultation with the building inspector the Class of consequence is set at CC2. Meaning chance of failure ( =3,8) 1/10.000. Now we have to investigate what values for glass strength can be used. The EN13474 given values for glass strength but no connection is made with Consequence Class. The Dutch standard NEN2608 given design value for the strength of glass are based on CC2. We will use the NEN2608.
467 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
3. The way the structure fails Demands for the way a structure may fail are given in the basic requirement of the EN1990. A few of these requirements are difficult for glass and need special attention. 3.1. A structure shall be designed and executed in such a way that it will not be damaged by events such as impact and human error to an extent disproportional to the original cause (EN1990 2.1(1)P) When using telescopic boom lift (or so) for cleaning aid there is always the risk of breakage of glass by human error. Using homogeneous glass there is no residual strength. So a small local damage can lead to the complete failure of a homogeneous glass beam. The glass has to be laminated, but how many plies do we need in this laminated glass? The number of plies is depending of the amount of layers that can be broken by that event. 3.2. Potential damage shall be avoided or limited by appropriate choice of the following. Selecting a structural form and design that can survive adequately the accidental removal of an individual member or the occurrence of acceptable local damage. Avoiding as far as possible structural systems that can collapse without a warning. (EN1990 2.1.(5)P) As we know glass has a brittle fracture behavior. So again we need laminated glass or, and way be and, a second load path.
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3.3. Conclusion We need a procedure to estimate the amount of broken plies in the laminated glass member ( the reduction in load capacity). This structure must be able to carry a certain level of load when this level of broken glass is presented. The NEN2608 has a procedure based on “Fine and Kinney”. With this procedure a level of broken glass can be estimated. This procedure is informative, the goal is to oblige the designer to take into account the possibility of breakage of glass. This breakage of glass can occur by accident or vandalism. 3.4. Structural calculation There is a need for at least two different structural calculations. According to the EN1990 those will be. x x
Fundamental combinations. Combinations of actions for accidental design situation, with a described level of broken glass.
This procedure is set in the NEN2608.
468 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
The Design of an All Glass Roof to the EN1990
4. The all glass roof. Now we have to implement the above mentioned demands and procedures.
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Figure 1: Artist impression of the foyer by van Mourik Architects (Klaas van der Molen)
Figure 2: Glass roof plan and sections
469 Challenging Glass 3 : Conference on Architectural and Structural Applications of Glass, edited by F. Bos, et al., IOS Press, Incorporated,
Challenging Glass 3
4.1. Differed glass assembly of the roof The main beam 1060x36mm consisted of a 12mm toughened/1,52mm pvb/12mm toughened/1.52mm pvb/12mm toughened glass (Securipoint). The length of the beam is 13m1 and it is spliced in 4 pieces. Lateral every 1625 mm a secondary beam is placed. This beam is 520x16mm and consisted of 8mm toughened/1,52mm/8mm toughened glass (Securipoint). The glass roof has a plates size 1730x1625mm and consist of a laminated 8mm toughened/ 1,14mm pvb/6mm toughened glass. 4.2. Partial load factors CC2 YG=1,2(National annex EN1990 Holland) en YQ=1,5 4.3. Fine and Kinney procedure according toNEN2608 Fine and Kinney allows to estimate the risk (RD) caused by an event. This is based on the probability of damage, exposure and the effect of that damage. The probability of this risk is than related to the level of damage of that structural member. 4.4. Method used in the NEN2608 based on Fine and Kinney The standard describes three steps to be taken. 1) Determine the attack side of the member (The attack side is the side of damage) 2) Determine the risk of damage pro attack side using formula E1 3) Determine pro attack side the level of damage according to table E2 Formula E1
Rd = Pd x Ed x Effd Rd = risk of damage Ed = exposure to the risk of damage Effd = effect of the damage Table E2:
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Risk of damage
Exposure to risk of damage
Effect of damage
Impossible
0,1
Very rare
0,5
First aid
1,0
Practical impossible
0,2
Few time a year
1,0
Minor injury
3,0
Possible but highly unlikely
0,5
Monthly
2,0
Severe injury
7,0
Only possible on long term
1,0
Weekly
3,0
One dead
15
Possible
6,0
Daily
6,0
Several dead
40
Unavoidable
10
Always
10
Disaster many dead
100
One side lateral damage Rd