A study of stability of axially compressed plates reinforced by edge angles

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PURDUE UNIVERSITY LIBRARIES R e g u la tio n s f o r th e Use o f M anuscript Theses

The r e s u l t s obtained, and th e t h e s i s p re p a re d i n co n n ec tio n w ith th e r e g u la r ly a ssig n e d t h e s i s s u b je c t a r e th e p ro p e rty o f th e U n iv e rs ity and no p a r t o f th e same may be rep ro d u ced o r p u b lish e d w ith o u t th e w r itt e n consent o f th e P r e s id e n t o f th e U n iv e rs ity o r h is d e s ig n e e . U nless o th e rw ise named, th e head o f th e dep artm en t s u p e rv is in g th e work s h a l l a c t f o r th e P r e s id e n t. T his t h e s i s by . . I*evp.s. Bjro.vw\ ifcC^mno/i su b m itted in p a r t i a l f u l f i l l m e n t o f th e re q u ire m e n ts f o r th e d eg ree o f . .Pfr*P*. . . . has been used by th e fo llo w in g p e rs o n s , whose s ig n a tu r e s a t t e s t t h e i r acc e p ta n c e o f th e above r e s t r i c t i o n s . A l i b r a r y which borrow s t h i s t h e s i s f o r u se by i t s r e a d e rs i s expected to secu re th e s ig n a tu r e o f each u s e r .

NAME AND ADDRESS OF USER

BORROWING LIBRARY

DATE OF USE

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PURDUE UNIVERSITY

T H IS IS TO C E R T IF Y T H A T T H E T H E S IS P R E P A R E D U N D E R MY S U P E R V IS IO N

by

Lewis Brown MeGammon

e n title d

A STUDY OF STABILITY OF AXIALLY COhiPriKSSED PLilTfiS

_______________________KiflNFuiCED BY EDGE ANGLES______________

C O M P L IE S W IT H T H E U N IV E R S IT Y R E G U L A T IO N S O N G R A D U A T IO N T H E S E S

A ND IS A P P R O V E D BY M E A S F U L F IL L IN G T H IS P A R T O F T H E R E Q U IR E M E N T S

FOR THE DEGREE OF

D octor o f P hilosophy

P

r o f e sso r in

Charge

Th

of

e s is

H ead o f S c h o o l o n D epa r tm en t

TO T H E L IB R A R IA N :---XEEK T H IS T H E S IS IS N O T T O B E R E G A R D E D A S C O N F ID E N T IA L .

X._/ '

__

F B o n s s a o iy m

o h a bo b

G l tA D . S C H O O L F O R M 0

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A STUDY OF STABILITY OF AXIALLY COMPRESSED PLATES REINFORCED BY EDGE ANGLES

A T h esis S ubm itted t o th e F a c u lty of Purdue U n iv e rs ity by Lewis Brown McCammon, J r . I n P a r t i a l F u lf illm e n t o f th e R equirem ents f o r th e Degree of D octor o f P h ilo so p h y

A ugust, 1951

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ACKNOWLEDGMENTS

The w r ite r i s e s p e c i a ll y in d e b te d to P ro fe s s o r L. T. Wyly, Head, Department o f S tr u c t u r a l E n g in eerin g , Purdue U n iv e r s ity , d i r e c t l y su p erv ised th e work o f t h i s i n v e s t i g a t i o n .

who has

P ro fe s s o r Wyly

o r i g i n a l l y proposed th e program and t e s t e d tw en ty -fo u r specim ens G ra n ite C ity , I l l i n o i s , d u rin g 1940.

at

He a ls o te s t e d 34 a d d itio n a l

specim ens in 1946 a t N o rthw estern U n iv e r s ity .

F in a n c ia l support f o r

t h i s e a r ly work came from th e A m erican I n s t i t u t e o f S te e l C o n stru c tio n and N orthw estern U n iv e rs ity and was a rra n g e d by th e e f f o r t s o f P ro fe s s o r Wyly. For th e work in 1940, t h e American S te e l F oundries f o r two months k in d ly lo a n e d th e use o f t h e i r 1 ,0 0 0 ,0 0 0 pound te s t i n g machine and th e s e r v ic e s o f Mr. Henry C over, who o p e ra te d th e m achine. The f i n a l phase o f th e re se a rc h program was fin a n c e d by th e Purdue R esearch F oundation through an X-R F ellow ship w hich ra n f o r two y e a rs and th ro u g h an a d d itio n a l g r a n t o f $2,500. A ll o f th e t e s t specim ens in c lu d in g th e n e c e ss a ry m a te r ia ls , f a b r ic a ti o n and h e a t tre a tm e n t were g e n e ro u sly su p p lie d w ith o u t charge by th e In la n d S te e l C o rp o ra tio n of C h icag o , I l l i n o i s .

T h is su p p ly in g

o f th e t e s t specim ens amounted to o v er 11,000 pounds o f In la n d H i-S te e l and many hours o f la b o r re q u ire d to f a b r i c a t e th e specim ens which a r e a l l d i f f e r e n t and th e r e f o r e r e q u ir e much c a r e f u l s u p e rv is io n and a t t e n ­ tio n .

Mr. W. W. Sm ith, fo rm e rly A s s is ta n t V ice P r e s id e n t o f th e In la n d

S te e l C o rp o ratio n ; Mr. L. E. C ham berlin, A s s is ta n t Manager o f S a le s , P la te and Shape D iv is io n ; and Mr. J . M. H a ile y , C h ie f R esearch E n g in eer,

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ii

R esearch and Development D epartm ent a r e In la n d S t e e l C o rp o ratio n o f f i c i a l s who c o o p e ra te d g en ero u sly i n f u r n is h in g th e t o t a l o f n in e ty two t e s t specim ens. Mr. Henry Penn, Chicago D i s t r i c t E n g in eer f o r the American I n s t i t u t e o f S te e l C o n s tru c tio n , gave much v a lu a b le a d v ic e , a s s is ta n c e and encouragem ent th ro u g h o u t th e e n t i r e program. P r o f e s s o r s R. E. Fadum, John E . G oldberg, G. T. M ille r , E. 0 . S t i t z , R. G. Sturm , and R. B. W iley gave v a lu a b le a id and h e lp fu l s u g g e s tio n s i n t h e i r c a p a c ity as members o f th e w r i t e r 's a d v iso ry and exam ining co m m ittees. P h o to g rap h ic work f o r t h i s t h e s i s was done by R. E. P eterso n and R. C. N eff of Purdue U n iv e rs ity . The fo llo w in g s tu d e n ts o f Purdue U n iv e rs ity have made a sub­ s t a n t i a l c o n tr ib u tio n t o th e co m pletion o f th e e x te n s iv e t e s t i n g program: R. G. Hayes

R. K. Wheeler

D an iel Banks

G. W. Mason

A. Y. A ragaki

Max Luming

A. T. Shak

J . N.

Uhl

R. T. Myers

R. F .

Corder

W. E. W itz e ll

T. M. I r v in e

The fo llo w in g s tu d e n ts of N orthw estern U n iv e r s ity have made a s u b s t a n t i a l c o n tr ib u tio n to th e te s t in g program: F. H oblick G. G reenberg A. G. L inow ieki R ichard C u lte r R ich ard H arza.

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TABLE OF CONTENTS

Page ACKNOWLEDGMENTS .......................................................................................................

i

LIST OF FIGURES .................................................................................................

iii

LIST OF TABLES ...................................................................................................

vi

ABSTRACT.....................................................................................................................

v ii

INTRODUCTION .............................................................................................................

1

DISCUSSION OF PROBLEM............................................................ PURPOSE OF RESEARCH .........................................................................................

10

HISTORY OF THIS INVESTIGATION ...................................................................

10

SCOPE OF THESIS ............................................... ................. . ..............................

11

SUMMARY OF TESTS PERFORMED.............................................................................. 1940 S e r ie s ..............................................- ..................................... 1946 S e r ie s ...................................................................................... . 1950 S e r ie s .............................................................................. TEST PROCEDURES AND EQUIPMENT ....................................................................... G eneral .......... 1940 S e r ie s ......................................................................... 1946 S e r ie s .......................... . ........................................................ 1950 S e r ie s .......................................................................................

12 12 12 12 18 18 23 24 25

MATERIAL TESTS........................................................................................ TEST RESULTS ............................................................................................................ E f f e c t o f Low Y ield P o i n t ................ E f f e c t o f T h in Angle L e g s .......... ........................................... E f f e c t o f R e s tr a i n ts in'! T estin g S e t-U p ............................... E f f e c t o f Using T hree P an els .......... Number o f Naves Between Support P o i n t s ................. S lip o f S u p p o rt Lugs .................................................................... S tr e s s D is tr ib u t io n Across P la t e .......................................... D eterm in atio n o f B uckling Load ....................

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28 32 49 50 51 51 52 52 53 53

TABLE OF CONTENTS (c o n tin u e d ) Page SUMMARY OF TEST RESULTS .....................................................................................

56

COMPARISONS WITHLITERATURE ...............................................................................

59

CONCLUSIONS ................................................................................................................

62

APPENDIX ......................................................................................................................

64

BIBLIOGRAPHY ................................................................................................................

87

VITA ...............................................................................................................................

88

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iii

LIST OF FIGURES Figure 1

Page Model No. 2 of Member A-9 Quebec B rid g e A fte r F a i l u r e ............................................................ . ...................... ..........................................

2 5

2

B u ckling Formulae

3

R e la tio n s h ip o f B uckling V a ria b le s to P la t e T hickness f o r B u ilt Channel S e c tio n .......................

7

4

T e st Column D e ta ils ...................................................................

14

5

N om enclature ...................................................................................

15

6

C r o s s - s e c tio n of T e st S et-u p Showing L a te r a l S upport S y s te m ....................................................................

20

G en eral View o f T e st S et-u p f o r Specimen EO o f th e 1946 S e r i e s ..............................

21

G eneral View Showing In s tru m e n ta tio n f o r 1946 S e r ie s ......................................................................................

21a

A rrangement o f D ials f o r M easuring L a te r a l D e f le c tio n s , 1950 S e r ie s ..............................................

27

10

G eneral View of T e st Set-Up f o r 1950 S e rie s . . . . . . .

29

11

T y p ical T ension S tr e s s - S t r a in Curve f o r M a te ria l Coupon ......................................................................................

31

12

Column D eform ations

o f "A"S e r ie s ....................................

34

13

Column D eform ations

o f "B"S e r ie s .....................................

35

14

Column D eform ations

o f MCMS e r ie s .....................................

36

15

Column D eform ations

o f "D"S e r ie s .....................................

37

16

Column D eform ations

o f "E"S e r ie s .....................................

38

17

Column D eform ations

o f "F1'S e r ie s

..............................

39

18

Column D eform ations

o f "G"S e r ie s ....................................

40

19

Column D eform ations

o f "H"S e r ie s ....................................

41

20

Column D eform ations

o f “J " S e r ie s ................

42

21

Column D eform ations

o f "K"S e r ie s .....................................

43

7 8 9

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iv

LIST OF FIGURES (c o n tin u ed ) F ig u re

Page

22

Column D eform ations o f "L" S e r ie s

......................................

^

23

Column D eform ations o f

"M"S e r ie s

......................................

45

24

Column D eform ations o f

"P"S e r ie s

. . . » .............................

46

25

Column Defar c a t io n s o f

"0" S e r ie s

......................................

47

26

Column D eform ations of

"R"S e r ie s

......................................

48

27

E f f e c t o f T e s tin g R e s tr a i n ts on Columns W ithout A ngles ........................................................................................

51a

28

S tr e s s D is tr ib u t io n i n Specimen R-3 . . . . . . . . . . . . . . . .

54

29

S tr e s s D is tr ib u tio n i n Specimen K - l

............................

55

30

Summary o f T est R e su lts .................................................................

57

31

R e la tio n s h ip betw een C r i t i c a l S t r e s s , b / t and R fo r a B u il t Channel w ith L /b = 2 .............................

58

32

Views o f T e ste d Specimens

...................................

65

33

Views o f T ested Specimens

........................................................

66

34

Views of T ested Specim ens

........................................................

67

35

Views o f T e s te d Specimens

................................................

36

Views o f T ested Specimens

37

Views of T e s te d Specimens

...........................................

38

Views o f T e s te d Specimens

........................................................

39

Views o f T ested Specimens

..........................................

40

Views of T e s te d Specimens

........................................................

73

41

Views o f T e s te d Specim ens

........................................................

74

42

Views o f T ested Specimens

............................................

43

Views o f T e ste d Specimens

..........................................................

44

Views o f T e s te d S p e c im e n s

45

Views o f T ested Specimens

...............

68 69 70 71 72

75 76

..............................................

77

.............................................

78

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V

LIST OF FIGURES (c o n tin u e d ) F ig u re

Page

46

Views o f T ested Specimens ...........................................................

79

47

Views o f T ested Specimens

.............................................

80

48

N e u tra l A xis T e st o f Specimen L2

..................................

81

49

N e u tra l Axis T e st o f Specimen D7

.........................

82

50

T est S e t-u p , 1950 S e r ie s

51

View o f Specimen Ml a f t e r F a il u r e

52

View o f Specimen K1 a f t e r F a ilu r e

53

View o f Specimen F4 a f t e r F a ilu r e .................................

........................................

83

............................... ......................................

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84 85 86

Vi

LIST OF TABLES T a b le

Page

1

P r o p e r tie s

o f 1940 S e r ie s o f T est Columns ................................... 13

2

P r o p e r tie s

o f 1946 S e r ie s o f T est Columns ...........................

3

P r o p e r tie s

o f 1950 S e r ie s of T est Columns ....................................18

4

Lengths and S upport D ista n c e s f c r Column S e r ie s ....................... 20

5

Comparison of O bserved and P re d ic te d B uckling

S t r e s s e s . . 61

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17

vii

ABSTRACT Tho purpose o f t h i s re s e a rc h was to d eterm in e th e r e l a t i v e p ro p o rtio n s o f th e fla n g e a n g le s n e c e s s a ry t o make an a x i a l l y com­ p re sse d p l a t e re a c h any bu ck lin g s tr e n g th up t o 60,000 p s i . The p r in c i p a l v a r ia b le s which w ere in v e s tig a te d were th e L/b r a t i o f o r th e p l a t e , th e b / t r a t i o f o r th e p l a t e , and th e s iz e o f edge a n g le s .

S te e l o f v a r io u s y i e l d p o in t s was u s e d , w ith th e maximum

b e irg about 75,000 p s i .

The range o f th e v a r ia b le s was so chosen a s

to c o v e r th e c u r r e n t p r a c t ic e and ex ten d c o n s id e ra b ly above th e v a lu e s now bein g g e n e r a lly used. E ig h ty column specim ens have been t e s t e d under a x i a l compres­ s io n w ith l a t e r a l su p p o rt so arran g ed a s to s im u la te th e e f f e c t o f la c in g b a rs a s used i n column d e sig n .

The specim ens were b u i l t up

c h an n e ls each c o n s is tin g o f a web p l a t e w ith edge a n g le s on one fa c e , The t e s t columns a r e a rra n g e d i n f i f t e e n s e r i e s such th a t th e o n ly v a r ia b le f o r a g iv e n s e r i e s i s th e s iz e o f edge a n g le s u s e d . SR-4 s t r a i n gages were u sed t o d e te rm in e th e s t r e s s d i s t r i b u t i o n th ro u g h o u t th e member and to m easure th e s t r e s s e s d u rin g b u c k lin g . M echanical d i a l i n d i c a t o r s were u sed to d eterm in e th e o v e r a ll change in le n g th o f th e specim en and th e l a t e r a l d e f le c tio n s due t o th e a x ia l lo a d in g . L a te r a l su p p o rt fo r th e specim ens was p ro v id e d a t th e t h i r d p o in ts a lo n g eac h

edge o f th e p l a t e .

P r in c ip a l r e s u l t s and co n clu sio n s a r e as fo llo w s: 1.

I t i s p o s s ib le to s t i f f e n p la te s w ith edge a n g le s so t h a t

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viii

th e y w i l l c a r r y th e s t r e s s given by the Bryan form ula f o r an a x i a l l y com pressed p la te w ith sim ple su p p o rts along the lo n g itu d in a l edges. 2.

P re s e n t methods o f a n a ly s is do check th e ex p erim en tal r e s u l t s .

3»

With p ro p e r ca re th e c u r r e n t l i m i t o f b / t fo r web p l a t e s may be c o n s id e ra b ly exceeded.

Edge a n g le s o f s u f f i c i e n t

s iz e must be u s e d . 4*

A s e t o f t e n t a t i v e u ltim a te s tr e n g th cu rv es a r e g iv en show­ in g th e s iz e o f edge a n g le s r e q u ir e d to make a p l a t e o f giv en b / t s a fe a g a in s t b u ck lin g f o r any s t r e s s up to 60,000 p s i.

This cu rv e a p p lie s t o p la te s where th e L /b r a t i o i s 2 .

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A STUDY OF STABILITY OF AXIALLY COMPRESSED PLATES REINFORCED BY EDGE ANGLES

INTRODUCTION Need f o r R esearch A su rv ey of t e s t s o f b u ilt- u p la c e d columns w ill show a g r e a t number o f l o c a l f a i l u r e s a s c o n tr a s te d w ith i n t e g r a l f a i l u r e s .

See f o r

exam ple, T able 1 i n "A B r ie f Review o f S te e l Column T e s ts '1 by L. T. 1 /* Wyly . Such lo c a l f a i l u r e p r e c i p i t a t e s c o lla p s e a t a s t r e s s w e ll below th e y ie ld p o in t of th e m a te r ia l. ty p e d e s c rib e d above.

F ig u re 1 shows a f a i l u r e o f th e

T h is i s th e second model o f th e c r i t i c a l member

o f th e i l l - f a t e d Quebec b rid g e , having ad eq u a te la c in g , i t f a i l e d a t a s t r e s s ab o u t 25 p e r c e n t below th e y ie ld p o in t o f th e m a te r ia l,

in view

o f th e f a c t t h a t th e f a i l i n g lo a d of th e second Quebec model was about th e same a s th e d e sig n lo a d , i t seems h ig h ly p ro b ab le t h a t i f f a i l u r e had n o t o c c u rre d d u rin g c o n s tru c tio n due to f a u l t y la c in g , i t would have o c c u rre d due to d e f i c i e n t bu ck lin g s tr e n g th o f th e main m a te r ia l when 2 /*

th e l i v e lo a d was added i n s e r v ic e .

Column No. 1 o f B u lle tin No. 44

o f th e I l l i n o i s E n g in eerin g Experim ent S ta t io n , r e p o r te d by T a lb o t and

2/*

Moore

, f a i l e d by b u c k lin g o f web and f la n g e a n g le s betw een la c in g

Numbers r e f e r to th e b ib lio g ra p h y a t th e end of t h i s r e p o r t.

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o

y iniiwiim %M a , ,/J 'U L -

t*

-v - ' V’fcft ' , S i > k 4 „

li;v _ fi!

•H

f*4 fc< l> V-l

«5

•ri • /- I. _ fi 0~\ » to 4J to XS c j rJ O H H

«

gj

i-3 M a, c> o

H W ) •H fr*

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co n n ec tio n s a t an average u n it s t r e s s o f ab o u t 23*500 p s i .

The y ie ld

s tr e n g th fo r th e m a te r ia l in th e column was 43*300 p s i and th e p l a t e b / t was 53*3 which c o rresp o n d s to a Bryan s t r e s s o f 37*200 p s i f o r K = 4 -0 .

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4

DISCUSSION OF THE PROBLEM U nit s tr e s s e a used i n d e sig n in g s t e e l columns r e s t s q u a re ly on th e assum ption t h a t th e column elem ents a re s a f e a g a in s t b u c k lin g . The p ro p o rtio n s o f th e web p l a t e s and o u ts ta n d in g le g s o f th e a n g le s a re k/> i /> y based upon th e Bryan form ula . T his form ula i s shown in F ig u re 2 .

The most common c a s e , (shown a s p a r t B o f F ig u re 2 ) where

th e edges o f th e p la te a r e su p p o rted a g a in s t l a t e r a l d is p la c e m e n t, b u t no t a g a i n s t r o t a t i o n , and where th e p l a t e le n g th i s s e v e r a l tim e s th e w id th , u ses a K v a lu e o f 4 -

When the edges a re clam ped, so th e r o t a ­

tio n a s w ell a s d isp lacem en t i s p re v e n te d , K = 7* For th e o u ts ta n d in g le g s of edge a n g le s , (shown a s p a r t D o f F ig u re 2 ) , where one edge of th e p l a t e i s f r e e w h ile th e o th e r i s su p p o rted a g a in s t l a t e r a l d isp lacem en t b u t not a g a in s t r o t a t i o n , KOne of th e m ost commonly u sed s e c tio n s i s composed of two b u i l t chan n els la c e d to g e th e r .

In th i s c o n s tr u c tio n th e s id e s o f th e web

p la te a r e s u p p o rte d a g a in s t l a t e r a l disp lacem en t by th e a n g le s which span between la c in g i n t e r s e c t i o n s and which m ust be s t i f f enough to su p p o rt th e p l a t e in a d d itio n to c a rry in g t h e i r own com pressive lo a d . Where th e a n g le s a r e la r g e enough to do t h i s , th e b u ck lin g s tr e n g th o f th e web p l a t e w i l l be g iv e n by th e Bryan fo rm u la , a s d is c u s s e d above, w ith a v alu e o f K - 4-

I f no a n g le s a t a l l were u sed , th e

s tr e n g th o f th e web p l a t e m ight be assumed to be g iv e n by th e E u ler form ula (see F ig u re 2 ) . I t i s re a s o n a b le to assum e, th e n , t h a t a s th e s iz e o f th e edge

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20

:4 p

60

I

$0

;

b

p Wldtb - ThickneBej Ratio BRTAMS BUCKLING FORMULA: : ' ' '

; 2 _

|

1tV

| ~

| C ritical Stress * K

TT B

| . ■; : ' '

S 1 !■■-•! "

. .2

a nort* irw^ ft\ -. 0,0905JETT

1■■■ :

■t

i Where: K " Constant determined by] the boundary conditions ~j ; E ]■ Modulus of e la s tic ity ((taken as 30,000,000 p s i,) ! :MT Ratio (taken as 0,3) I .' ; I ’ .; j EDLSl’ S COLUMN FORMULA, fo r I* • b: 2

! C ritic a l Stress - ^ T T 2 E f | \ FIGURE 2 ;

I i '

! I

-

i

2

0.0835 TT2 E

Buakling Formulae i

:

■(

R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.

I , I

100

6

a n g le s in c r e a s e s th e b u ck lin g s tr e n g th o f th e web p l a t e w ill in c re a s e t 2 from th e E u le r v alu e (no edge a n g le s ) o f 0.0835 E ( £ ) t o th e Bryan v alu e o f 0.090 5 K 7r^( ^ ) ^ .

T h e re fo re , by u sin g a n g le s o f th e

p ro p e r s i z e , so th a t th e y a d e q u a te ly s u p p o rt th e edges o f th e p la te a g a in s t l a t e r a l d is p la c e m e n t, t h e s tr e n g th of th e web p la te may be in c re a s e d f o u r f o ld .

By in c re a s in g th e s iz e o f th e a n g le s s t i l l f u r t h e r ,

so t h a t th e edges o f th e p l a t e cannot e i t h e r d is p la c e o r r o t a t e , th e s tr e n g th of th e p l a t e may be in c re a s e d s e v e n fo ld .

T his l a t t e r in c re a s e

w i l l be very d i f f i c u l t and r e q u ir e v e ry la r g e a n g le s b u t th e f o u r f o ld in c r e a s e i s w e ll w ith in th e ra n g e o f p r a c t i c a l p o s s i b i l i t y . C u rren t d e sig n s p e c if i c a t io n s assume th a t p l a t e s w i l l reac h th e Bryan s t r e s s w ith K = 4*

The d e s ig n e r m ust th e r e f o r e u se la r g e

enough a n g le s to g iv e th e sim ple edge su p p o rt re q u ir e d . P re s e n t d e sig n s p e c i f i c a t i o n s a r e g e n e r a lly in a d eq u ate w ith re g a rd to th e d e s ig n of t h e s e c tio n between th e la c in g i n t e r s e c t i o n s . S p e c if ic a tio n s assume th a t th e e n t i r e s e c tio n , p l a t e p lu s a n g le s , w i l l a c t as a r i g i d u n i t .

T his i s n o t th e a c tio n which o c c u rs, s in c e

th e p l a t e and a n g le s w i l l each te n d to b u ck le in d iv id u a lly .

The

v a r i a t i o n o f " r" f o r th e t o t a l s e c tio n , as th e p la te in c r e a s e s , i s shown i n F ig u re 3 f o r a s p e c if i c c a s e .

I t w i l l be seen t h a t as th e

p l a t e th ic k n e s s in c re a s e s from 3 / 8 in c h to 1 in c h th e " r" f o r th e t o t a l s e c tio n becomes sm aller and th e " L /r" g r e a t e r .

P re se n t p r a c t ic e would

th u s r e q u ir e th e la c in g c o n n ec tio n s t o be moved c l o s e r to g e th e r f o r th e same assumed s tr e n g th , alth o u g h we have good re a so n to b e lie v e t h a t th e p la te i s s tre n g th e n e d in s te a d of w eakened.

More im p o rta n t, i t w i l l

be n o te d t h a t th ro u g h th e e n t i r e ran g e o f p l a t e th ic k n e s s s tu d ie d ,

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7

Column Section

800

Angles x 4 x 1/2

700

Length between l a t e r a l supports taken ■ bn

600

Euler stre ss fo r en tire section

Web p late width ■ 24inchea thickness; variable 500

40

400

Bryan stre ss fo r p late K - 4.0 300

1.0

5 0 .8 u

0 ..

.

t

FIGUREi 3,

1.0 ' 2.0 ; tp » Plate thickness!, inches .1

. . . .

.

.....

. . .

I

...

; .

.!

3.0 j

tpj • Plate thickness,

. . . . . .

Relationship of Buckling Variabjl,es to P late Thickness fo r a B uilt Channel Section

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8

from 3 /8 to 3 in c h e s , th e change in " r" i s very sm all and can have l i t t l e e f f e c t , a s su ch , on th e " L /r" v a lu e . i s n o t th e t r u e s t a t e o f a f f a i r s .

Again we know th a t t h i s

The r e l a t i v e s t i f f n e s s o f th e an g les

r e q u ir e d to a t t a i n a g iv e n s tr e n g th v a i l v ary m arkedly a s th e p la te th ic k n e s s i s changed. Any ex p erim en tal approach to th e problem o f p ro p o rtio n in g th e edge s t i f f e n e r s f o r a p la te w ill en co u n ter s e v e ra l q u e s tio n s which r e q u ir e th e u se o f c a r e f u l l y made assu m p tio n s.

These m ight be b r i e f l y

l i s t e d a s fo llo w s : 1.

What v a lu e o f p l a t e w idth s h a l l be used f o r com puting th e Bryan s tr e s s e s ? C u rren t s p e c if i c a t io n s u se th e d is ta n c e betw een l i n e s o f r i v e t s , a lth o u g h th e r e i s good e x p e rim e n ta l reaso n f o r u sin g th e o v e r a ll w idth o f th e p l a t e .

2.

I s i t p o s s ib le to assume a c e r t a i n a x is f o r com puting th e p r o p e r ti e s o f th e com posite s e c tio n ?

G e n e ra lly sp e a k in g , th e

c e n tr o id a l a x is o f a b u i l t ch an n el l i e s f a i r l y c lo s e to th e p la n e o f c o n ta c t between th e an g les and th e p l a t e , and i t would g r e a t l y s im p lify th e d e s ig n e r 's c a l c u la tio n s i f he co u ld s a f e ly make a sim ple assu m p tio n o f t h i s k in d . 3.

How many p a n e ls should th e b u d d in g model c o n ta in ? A l a r g e number o f p a n e ls would g iv e a b e t t e r ap p ro x im atio n o f what m ight happen n e a r th e c e n te r o f a la c e d column, b u t economic re a s o n s r e q u ir e a lim ite d number.

4*

When can a specim en be s a id to have buckled? For th e t h e o r e t i c a l l y s t r a i g h t column th e r e would be no

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9

l a t e r a l d e f le c ti o n u n t i l th e c r i t i c a l o r bu ck lin g s t r e s s was reac h ed , th e n a sudden l a t e r a l d e f le c tio n would c l e a r l y mark th e b u ck lin g s t r e s s . The a c t u a l t e s t colum ns, how ever, would have c e r t a i n in e sc a p a b le i n i t i a l d e f le c ti o n s .

These i n i t i a l d e f le c tio n s g iv e r i s e to d e f le c tio n s which

in c re a s e s t e a d i l y as th e lo a d i s a p p lie d , and th e r e i s no sh arp b u ck lin g p o in t a s would be found i n th e t h e o r e t i c a l l y s t r a i g h t co lu m n .• A stu d y o f th e t e s t r e s u l t s w i l l a llo w a more d e ta ile d d is c u s s io n o f th e s e q u e s tio n s l a t e r i n t h i s t h e s i s . The p r in c i p a l v a r ia b le s i n t h i s problem a r e : b / t f o r th e p l a t e L/b f o r th e p l a t e , w ith L being th e d is ta n c e between l a t e r a l sup­ p o rts . R = I aA p , which i s a measure o f th e s iz e o f th e a n g le w ith r e f e r ­ ence t o th e s iz e o f th e p l a t e . For t h i s s tu d y , a range o f b / t v a lu e s from 16 to 64 was u se d .

The

range b ra c k e ts th e v alu e of 40 which i s th e maximum c u r r e n t ly allow ed by s p e c i f i c a t i o n s .

The 16 i s g e n e r a lly sm a lle r th a n commonly u sed and

the 64 i s g e n e r a lly h ig h e r th a n commonly u se d . The ra n g e o f L /b was from 1 .0 to 2 .0 .

For an L /b o f l e s s th an

1 .0 o nly v ery sm all a n g le s would be needed to reach v ery high s t r e s s e s , -L/b « 2 .0 i s g r e a te r th a n would be g e n e r a lly used i n p r a c t i c e . The range f o r R was chosen t o f i t th e p a r t i c u l a r s e r i e s o f colum ns, an e f f o r t b ein g made to e x ten d th e R v a lu e s u n t i l th e s e r i e s reac h ed th e y ie ld p o in t o f th e m a te r ia l or th e Bryan s t r e s s f o r K = 4* Another v a r ia b le i s th e y ie ld p o in t of th e m a te r ia l.

H ere, a

s u c c e s s fu l e f f o r t was made t o b rirg th e m a te r ia l y i e l d p o in t to 75,000

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10

p s i.

This v a lu e i s c o n s id e ra b ly above th e y ie ld p o in ts f o r m a te r ia ls

commonly used i n modern s t r u c t u r e s , and should cover improvements i n m a te r ia ls fo r sane tim e t o come. Thus an e f f o r t has been made to choose ran g es f o r th e v a r ia b le s which in c lu d e c u r r e n t p r a c t i c e and e x te n d somewhat above and below th e p re s e n t v a lu e s u sed . PURPOSE OF RESEARCH The p u rp o se o f t l i s r e s e a r c h i s to d eterm in e th e r e l a t i v e p ro p o r­ tio n s o f th e f la n g e a n g le s n e c e s s a ry to make th e column web s a fe a g a in s t lo c a l b u d d in g in a b u i l t c h an n e l la c e d column s e c tio n .

A f u r th e r p u r­

pose i s t o p re s e n t ex p erim en tal d a ta to be u sed as a g u id e f o r th e p ro p o rtio n in g o f any p l a t e s t i f f e n e d by edge a n g le s , f o r a x i a l s t r e s s up to 60,000 p s i . HISTORY OF THIS INVESTIGATION In F ebruary o f 1940, P r o f e s s o r L. T. Wyly, th e n of N o rthw estern U n iv e rs ity , i n t e r e s t e d Mr. Henry Penn, D i s t r i c t E n g in eer of th e Ameri­ can I n s t i t u t e of S te e l C o n s tru c tio n , I n c . , a t C hicago, and Mr. W. W. S m ith, S a le s E ngineer o f th e In la n d S te e l Company, i n t h i s problem . At t h a t tim e , N o rth w estern U n iv e rs ity d id n o t have a l a r g e t e s t i n g machine and th e American S te e l F oundries k in d ly ag reed to a s s i s t i n th e t e s t i n g work a t t h e i r G ra n ite C ity la b o ra to r y where th ey have a o n e -m illio n pound t e s t i n g m achine. fu lfille d

Both o f th e se agreem ents were

and in J u ly and August of 1940 P ro fe s s o r Wyly t e s t e d 22

specim ens to f a i l u r e .

I n th e summer o f 1942, th e tw e n ty -th ir d specimen

was t e s t e d a t N orthw estern U n iv e rs ity in th e new o n e -m illio n pound

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t e s t i n g m achine.

The m a te r ia l f o r th e s e specim ens had a y ie ld p o in t

o f ab o u t 57»OQQ p s i . At v a rio u s tim e s d u rin g 1945> P ro fe s so r Wyly t e s t e d th r e e a d d i­ ti o n a l specim ens, none of w hich had edge a n g le s . H irin g th e summer months o f 1946, P ro fe s s o r Wyly t e s t e d t h i r t y one specim ens, many o f which had been h e a t - t r e a t e d in o rd e r t o r a i s e th e y i e l d p o in t o f th e m a te r ia l above 65,000 p s i . I n June o f 1948, th e w r i t e r was g ra n te d an XE F ello w sh ip by th e Purdue R esearch F o u n d atio n and a stu d y was und ertak en t o d eterm in e what f u r t h e r t e s t i n g sh o u ld be done to com plete th e i n v e s t ig a t io n .

Study

of th e d a ta re v e a le d t h a t th e h e a t tre a tm e n t o f th e specim ens had v a r ie d c o n s id e ra b ly and i t was th e r e f o r e d e s ir a b le to cu t coupons from undamaged p o rtio n s o f th e t e s t specim ens o f th e 1946 s e r i e s and p erfo rm te n s io n t e s t s upon them to d e te rm in e th e p h y s ic a l p r o p e r ti e s o f th e m a te r ia l in each t e s t specim en.

W ith t h i s in fo rm a tio n , i t was th en p o s s ib le to

re q u e s t an a d d itio n a l t h i r t y - f o u r specim ens from th e In la n d S te e l Company. These t e s t specim ens a r r iv e d du rin g th e summer o f 1950 and t e s t i n g was im m ediately begun.

At t h e p re s e n t tim e , a l l specimens have been t e s t e d

w ith t h e e x c e p tio n o f eleven p ie c e s mhich w i l l have s tr e n g th s exceeding th e c a p a c ity o f th e m achines c u r r e n tly a v a ila b le . SCOPE OF THIS THESIS T h is t h e s i s re c o rd s th e ex p erim en tal r e s u l t s an d e x p la in s th e m ethods o f teajbing used i n th e in v e s tig a tio n .

An a tte m p t i s made to

show th e c o r r e l a ti o n betw een ex p e rim e n ta l d a ta and r a t i o n a l methods used t o a r r i v e a t th e c r i t i c a l s t r e s s f o r such a b u il t- u p s e c tio n . e x p erim en tal d a ta a r e p re s e n te d in th e form o f c u rv e s, w hich, i t

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The

12

i s hoped, w ill be o f v a lu e t o th e d e s ig i e n g in e e r. SUMMARY OF SPECIMENS TESTED 1940 S e r ie s The 1940 s e r i e s c o n s is te d o f tw e n ty -th re e specim ens th e dim ensions o f which a r e shown i n Table 1 .

G eneral la y o u t o f th e t e s t specim ens i s

shov/n in F ig u re 4 , and an e x p la n a tio n o f th e no m en clatu re used i s shown in F ig u re 5* The web p l a t e s and a n g le s u sed f o r t h i s s e r i e s were In la n d H i-S te e l w ith a y ie ld s tr e n g th o f 57,000. o rd in a ry m ild carbon s t r u c t u r a l s t e e l . d ia m e te r, d riv e n h o t.

The d e t a i l s were made o f

R iv e ts were o n e -h a lf in c h in

Both ends o f th e columns were m ille d a t 90 d eg rees

w ith th e a x is of th e specim en, both ways.

S p e c if ic a tio n s c a l l e d fo r

s t r a i g h t m a te r ia l and f a b r ic a te d columns w ith o u t k in k s o r cam ber. 1946 S e r ie s The 1946 s e r i e s c o n s is te d o f t h i r t y - f o u r specim ens, th e dim ensions o f TAhich a re shown i n T able 2 .

A ll main m a te r ia l i n th e s e specim ens

was to be In la n d H i- S te e l and c e r t a i n o f th e t e s t members were to be h e a t t r e a t e d to r a i s e t h e y ie ld p o in t o f th e m a te r ia l.

G eneral form o f

th e 1946 specim ens was th e same a s f o r the 1940 s e r i e s (See F ig u re 4)* 1950 S e r ie s The 1950 s e r i e s c o n s is te d o f t h i r t y - f o u r specim ens, th e dim ensions o f which a re shown in TahLe 3*

A ll main m a te r ia l i n th e s e specim ens was

to be I n la n d H i- S te e l and a l l members were t o be h e a t t r e a t e d to a s s u re a y ie ld s tr e n g th o f 75,000 p s i minimum.

G en eral form o f th e 1950 s p e c i­

mens was th e same a s f o r th e 1940 an d 1946 s e r i e s ( See F ig u re 4)* Cou­ pons of th e m a te r ia l, h e a t t r e a t e d a t t h e same tim e a s th e f a b r ic a te d specim ens,w ere s u p p lie d f o r a l l o f the 1950 s e r i e s .

R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.

Mark

Web P la te (in ch es)

Angle S iz e (inches.)

AO Al A2 A3

12 x 3 /4 tl tl It

None 2 x lj x i 2 x l£ x I 2 x 1 -3 /4 x £

3.5 3.5 3.5 3.5

B1 B2 B3 B4

12 x 3 /8 it it it

2 2 2 2

x x x x

1 -1 /8 x 3/16 l£ x 1 /8 1 - 3 /4 x 1/8 2 x 3 /16

3.5 3.5 3.5 3.5

Cl C2 C3 C4

12 x £ n if it

2 2 2 2

x x x x

1 x 1 /8 l £ x 1 /8 l j x 1 /8 1 - 3 /4 x 3/16

3.5 3.5 3.5 3.5

Dl D2 D3 D3

12 x 3/4 ii ii it

2 2 2 2

x x x x

1^ x 5/16 2 x £ 2£ x i 3 x £

5.0 5.0 5.0 5.0

El E2 E3

12 x 3/8 11 It

2 x 1 -3 /8 x 3 /1 6 2 x 1-7/8 x 3 /1 6 2 x 2 i x 3 /16

5.0 5.0 5.0

FI F2 F3 F4

12 x £ It It II

2 2 2 2

5.0 5.0 5.0 5.0

x x x x

l£ x £ 1 -5 /8 x 3/16 2 -1 /8 x 1 /8 2 - 3 /4 x 3 /1 6

O v e ra ll Length (fe e t)

R e p ro d u c e d with perm ission of th e copyright owner. Further reproduction prohibited without permission.

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

T ab le 1 Angles

P la te b /t

J j. u X m.

16 16 16 16

1.69 1.69 1.69 1.69

32 32 32 32

I in . *

b /t

P r o p e r tie s of 1940 S e r ie s o f T e st C R . i/ Ia /Ip

T o tal S ectio n 2/ r X I 4 in . (in ch es)

4.5 0 5 .5 0 6. 50

0 .344 0.580 0.911

0 0 .203 0.343 0.533

0.375 0.476 0.494 0.516

0.422 1.244 1.571 2.012

0 .2 ] 0.32 0.36 0.4(

0.211 0.211 0.211 0.211

5.50 11.50 13.50 10.16

0.186 0.283 0.443 1.008

0.880 1 .3 4 2 .1 3 4-78

0.283 0.276 0.294 0.370

0.345 0 .4 5 2 0 .6 2 0 1.249

0.22 0.2'0 . 3; 0.4!

48 48 48 48

0 .0 6 3 0.0625 0.0625 0.0625

7 .5 0 9 .5 0 11.50 8 .8 3

0.085 0.165 0.283 0.678

0.190 0.210 0.234 0.310

0.135 0.227 0.357 0.6 2 4

0.1' 0.2, 0 .3 0 .4

16 16 16 16

1.69 1.69 1.69 1.69

4 .3 0 7.50 9 .5 0 11.50

0.737 1.351 2.614 4. 520

0.437 0.800 1.547 2.6 8

0.523 0.542 0.597 0.661

1.860 2.565 4.060 6.106

0.4 0 .4 0.6 0.7

32 32 32

0.211 0.211 0.211

6 .8 3 9.5 0 11.50

0.334 0.832 1.430

1.59 3.95 6.78

0.301 0.354 0.402

0.515 1.055 1.630

0 .; 0.2. 0 .!

48 48 48 48

0.0625 0.0625 0.0625 0.0625

4.50 8.16 1 6 .5 0 14.16

0 .344 0.531 0.797 2. 608

5. 51 8.50 12.76 4 1 .70

0.278 0.289 0.306 0.482

0.404 0.602 0.850 2.418

o .; o .: 0.2 0/

—

MM

1.3 6 2 .6 4 4 .5 3 10.87

1/

About c o n ta c t p la n e betw een p la te and a n g le s . See F ig . 4 f o r d e t a i l s of specim ens.

2

/

About cen tred .d al a x i s .

5

I 1 I

6

R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

D S e rie s o f T e st Columns T o ta l S ectio n 2/ r I 4 ) in .

. :

Area Sq. i n . Wtd. Mom.

Y .P. Asked k si

A ctu al Y .P. M a te ria l P la te Angles k si k si

Observi S' 1

L /r

0.422 1.244 1.571 2.012

0.216 0.345 0.385 0.432

56 35 31 28

9 .0 0 10.50 10.62 10.74

-8 .8 0 10.40 10.51 10.67

57 57 57 57

-— --

0.345 0 .452 0 .6 2 0 1.249

0.248 0.291 0.339 0 .4 5 9

48 41 35 26

5-60 5.34 5.40 5.92

5.45 5.25 5.25 5.89

57 57 57 57

--63 56

0 .135 0.227 0.357 0 .624

0.190 0.245 0.305 0.408

63 49 39 29

3.72 3.78 3 .8 4 4.3 2

3 .6 6 3. 72 3.7 6 4*28

57 57 57 57

— 63 — 58

1.860 2.56$ 4.060 6.106

0.412 0.486 0.604 0.732

44 37 30 25

11.00 1 0.88 1 1 .12 11.38

11.06 10.90 11.12 11.38

57 57 57 57

—-— —

0.515 1.055 1.630

0.301 0.424 0.520

60 42 35

5.69 5.87 6 .0 2

5.61 5.82 5.99

57 57 57

0 .404 0.602 0.850 2.418

0.299 0.377 0.462 0 .716

60 48 39 25

4.50 4 .2 4 4 .0 0 4 .7 1

4 .4 5 4 .1 7 4.02 4 .8 0

57 57 57 57

■ -

_

— — —■ —

4

— 58 57

Y

— 55 ~ 59

< r