EXPERIMENTAL RESEARC OHN THE BUCKLIN'G BEHAVIOUR OF ...
96
EXPERIMENTAL RESEARCH ON THE' BUCKLING BEHAVIOUR OF SLENDER PRESTRESSED CONCRETE COLUMNS by GYORGY LASZLO Diploma of Civil Engineering Jozsef Nador University Budapest A THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN ENGINEERING in the Department of CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1966
Transcript of EXPERIMENTAL RESEARC OHN THE BUCKLIN'G BEHAVIOUR OF ...
EXPERIMENTAL RESEARCH ON THE' BUCKLING BEHAVIOUR OF SLENDER PRESTRESSED
CONCRETE COLUMNS
by
GYORGY LASZLO
D i p l o m a of C i v i l E n g i n e e r i n g
J o z s e f Nador U n i v e r s i t y B u d a p e s t
A THESIS SUBMITTED IN PARTIAL FULFILMENT
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN ENGINEERING
i n t h e D e p a r t m e n t
of
C I V I L ENGINEERING
We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the
r e q u i r e d s t a n d a r d
THE UNIVERSITY OF BRIT I S H COLUMBIA
A p r i l , 1966
I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of
the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y of
B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y
a v a i l a b l e f o r r e f e r e n c e and s t u d y t I f u r t h e r agree t h a t p e r
m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y
purposes may be granted by the Head of my Department or by
h i s r e p r e s e n t a t i v e s . I t i s understood t h a t ; c o p y i n g or p u b l i
c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l , not be a l l o w e d
w i t h o u t my w r i t t e n p e r m i s s i o n *
Department o f C i v i l E n g i n e e r i n g
The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8 5 Canada
Date A p r i l , 1966.
i .
ACKNOWLEDGMENTS
T h i s t e s t was c o n d u c t e d u n d e r t h e s u p e r v i s i o n o f P r o f e s s o r
Samuel L. L i p s o n , D e p a r t m e n t of C i v i l E n g i n e e r i n g . The a b l e
a s s i s t a n c e o f t h e s t a f f of G r a y b a r P r e c a s t L i m i t e d i n t h e
f a b r i c a t i o n o f t h e s p e c i m e n s , and of t h e s t a f f of t h e C i v i l
E n g i n e e r i n g D e p a r t m e n t i n t h e t e s t i n g , i s g r e a t l y a p p r e c i a t e d .
i i .
ABSTRACT
T h i r t y f u l l s c a l e p r e s t r e s s e d c o n c r e t e s t r u t s a l l h a v i n g a
s l e n d e r n e s s r a t i o o f L/D = 40 were t e s t e d w i t h t h r e e d i f f e r e n t
e c c e n t r i c i t i e s . S t r e s s - s t r a i n c u r v e s o f t h e c o r r e s p o n d i n g
t e s t c y l i n d e r s were e s t a b l i s h e d and t h e Young's M o d u l i e v a l u a t e d .
The s p e c i m e n s were f a b r i c a t e d w i t h d i f f e r e n t p e r c e n t a g e s o f
p r e s t r e s s i n g s t e e l r a n g i n g f r o m ,0.23 t o 1.20$. The i n i t i a l
p r e s t r e s s i n g f o r c e s were s e t t o o b t a i n a f i n a l p r e s t r e s s of
140,000 p s i i n a l l s p e c i m e n s . The d i m e n s i o n s o f t h e s t r u t s ,
and t h e q u a l i t y and m a n u f a c t u r i n g p r o c e s s o f t h e c o n c r e t e , were
k e p t c o n s t a n t . S p e c i a l a d j u s t a b l e s u p p o r t i n g d e v i c e s s i m u l a t e d
i d e a l h i n g e d c o n d i t i o n s . The s t r u t s were t e s t e d t o t h e i r
u l t i m a t e c a p a c i t y and t h e i r c r i t i c a l b u c k l i n g l o a d s were
e v a l u a t e d .
The t e s t s p r o v e d t h a t , p r o v i d e d t h e column i s made of h i g h
q u a l i t y c o n c r e t e , t h e c r i t i c a l l o a d v a l u e s can be o b t a i n e d by
u s i n g B u l e r ' s f u n d a m e n t a l f o r m u l a , and t h e s e v a l u e s a r e
i n d e p e n d e n t o f t h e amount o f p r e s t r e s s i n g . F o r e c c e n t r i c a l l y
l o a d e d s t r u t s maximum s t r e s s e s f r o m a m o d i f i e d s e c a n t f o r m u l a ,
i n c o r p o r a t i n g e f f e c t o f p r e s t r e s s i n g , were compared w i t h t h o s e
c a l c u l a t e d on b a s i s o f o b s e r v e d d e f l e c t i o n s .
A c c o r d i n g t o t h e t e s t r e s u l t s t h e s e c a n t modulus- c o r r e s p o n d
i n g t o t h e a v e r a g e c o m p r e s s i v e s t r e s s s h o u l d be u s e d i n E u l e r ' s
f o r m u l a .
i i i .
TABLE 1 OF CONTENTS
PAGE
C h a p t e r I . - I n t r o d u c t i o n , . . 1
C h a p t e r I I . - O b j e c t and Scope of T e s t s 4
C h a p t e r I I I . - D e s c r i p t i o n of t h e S p e c i m e n s ............ 7
C h a p t e r I V . - P r e p a r a t i o n o f t h e S p e c i m e n s
1. M i x i n g of C o n c r e t e 14
2. Bed E q u i p m e n t and S t r e s s i n g 14
3. P l a c i n g the C o n c r e t e .................... 16
4. C u r i n g and D e s t r e s s i n g of t h e S p e c i m e n s . . 18
5. S h i p m e n t o f the S p e c i m e n s 18
Cha p t e r ' V.- T e s t P r o c e d u r e
1 . T e s t i n g M a c h i n e 20
, 2. D e f l e c t i o n Measurement .................. 20
3. Mechanism o f the S t r u t S u p p o r t 21
4. S p e c i a l T e s t s ........................... 24
5. C y l i n d e r T e s t s 27
C h a p t e r V I . - T e s t R e s u l t s
1 . G e n e r a l 28
2. T a b u l a t e d O b s e r v a t i o n s ........ ......... . 32
3. T a b u l a t e d C a l c u l a t i o n s . .
A. C r i t i c a l L o a d s . . . . . . . . . . . . . . 43
B. S t r e s s e s . . . . . . . . . . . . . . . 60
4. C a l c u l a t i o n o f the M o d u l i ............... 61
i v .
•PAGE
C h a p t e r V I I . - D i s c u s s i o n of T e s t R e s u l t s
1 . I n f l u e n c e of S t e e l R a t i o on
t h e C r i t i c a l Load 69
2. A p p l i c a b i l i t y o f the S o u t h w e l l M e t hod... 70
3. The M o d u l u s t o be Used. 71
4. U l t i m a t e Load C a r r y i n g C a p a c i t y 75
C h a p t e r V I I I . - C o n c l u s i o n s 80
R e f e r e n c e s . 81
L I S T OF TABLES
TABLE .PAGE
I . - Types of S p e c i m e n s 6
l l . - M a n u f a c t u r i n g D a t a of t h e S p e c i m e n s . . . . . . . 9
I I I . - T e s t R e s u l t s 33
I V . - C o m p a r i s o n of S t r e s s e s O b t a i n e d f r o m the
T e s t R e s u l t s w i t h Those Computed by
B r e c k e n r i d g e ' s M o d i f i e d S e c a n t F o r m u l a . 62
V. - C o m p a r i s o n of D i f f e r e n t M o d u l i 68
V I , - R e d u c t i o n F a c t o r s ' f o r S t r u t s w i t h Z e r o
E c c e n t r i c i t y . , , , . . . 78
L I S T OF FIGURES
FIGURE PAGE
1 . D e t a i l s o f S p e c i m e n s 8
2. D e t a i l s of t h e End P l a t e and the
F a s t e n i n g D e v i c e 12
3. D e t a i l s o f t h e S t r e s s i n g E q u i p m e n t 15
4. S c h e m a t i c D e s c r i p t i o n o f t h e S t r e s s i n g P r o c e d u r e 17
5. C r i t i c a l L o a d s f o r S p e c i m e n s w i t h Z e r o
and 0.3 i n . E c c e n t r i c i t i e s 29
6. C r i t i c a l L o a d s f o r S p e c i m e n s w i t h Z e r o
E c c e n t r i c i t y O n l y 30
7. C r i t i c a l L oads f o r S p e c i m e n s w i t h 0.3 i n .
' E c c e n t r i c i t y O n l y 31
8/1-8/4. L o a d - d e f l e c t i o n C u r v e s of S p e c i m e n s w i t h
1.5 i n . E c c e n t r i c i t i e s 37-40
9. L o a d - d e f l e c t i o n C u r v e f o r S p e c i m e n No. 29
T e s t e d t o D e s t r u c t i o n 41
10. The Two Types o f Load E c c e n t r i c i t i e s Used 47
1 l / a - 1 l / c . T y p i c a l S o u t h w e l l P l o t s 48-50
1 l / d - 1 l / e . T y p i c a l S o u t h w e l l P l o t s 52-53
1 l / f - 1 l / i . T y p i c a l S o u t h w e l l P l o t s 55-58
12. V a r i a t i o n o f R a t i o P /P w i t h S t e e l u c r
C o n t e n t 59
v i i .
FIGURE PAGE
13/a— 1 3/"b • C u r v e s of t h e S e c a n t F o r m u l a P l o t t e d
f o r t h e S p e c i m e n s "'"765^64
14/a-14/b. T y p i c a l S t r e s s - s ' t r a i n C u r v e s f o r
C y l i n d e r s . ' : 66-67
15. C o n v e r t e d C r i t i c a l L oads V e r s u s V a l u e s
of a 72
16. C o m p a r i s o n of E u l e r C u r v e w i t h the
C o n v e r t e d C r i t i c a l Loads 74
17. C o m p a r i s o n o f Commonly Used C u r v e s o f
Mo d u l u s w i t h T e s t R e s u l t s 76
18. U l t i m a t e Load of S t r u t s w i t h 1.5 i n .
E c c e n t r i c i t y V e r s u s S t e e l R a t i o . . . . . . 79
\ i i i .
L I S T OF PHOTOGRAPHS
PHOTO PAGE
1. The F a s t e n i n g D e v i c e f o r t h e
A d j u s t a b l e P l a t e . 23
2. ' The S t r u t D u r i n g T e s t i n g . 25
3. B u c k l e d S t r u t w i t h Low P r e s t r e s s 36
4. T e n s i o n F a i l u r e of S p e c i m e n No. 2 9 . . . . . . 42
5. C o m p r e s s i o n F a i l u r e o f S p e c i m e n No. 22.. 44
SYMBOLS
( i n . ) O b s e r v e d I n i t i a l C u r v a t u r e
( i n . ) I n i t i a l E c c e n t r i c i t y (due t o t h e co m b i n e d
e f f e c t o f the : i n i t i a l c u r v a t u r e and t h e
l o a d e c c e n t r i c i t y ) 2
A ( i n . ) G r o s s A r e a of 'the C o n c r e t e
a o a1
•c A„ ( i n . * ) A c t u a l A r e a o f t h e S t r a n d s s
c ( i n . ) D e p t h o f N e u t r a l A x i s f r o m E x t r e m e Compress
i o n F i b r e s
C q ( i n . / i n . ) C r e e p C o e f f i c i e n t
C ( i n . / i n . ) S h r i n k a g e C o e f f i c i e n t s
D ( i n . ) D i m e n s i o n o f t h e S t r u t i n t h e D i r e c t i o n o f
B u c k l i n g
e ( i n . ) Load E c c e n t r i c i t y
E ( k s i ) M o d u l u s o f E l a s t i c i t y o f t h e C o n c r e t e
E' ( k s i ) A r b i t r a r y M o d ulus o f E l a s t i c i t y s e t a t
3,320 k s i
E^ ( k s i ) M o d u l u s o f e l a s t i c i t y O b t a i n e d by' the B e n d i n g
T e s t o f S i x S p e c i m e n s E ( k s i ) M o d u l u s o f E l a s t i c i t y as D e t e r m i n e d by Pauw's P
F o r m u l a
E^ ( k s i ) M o d u l u s o f E l a s t i c i t y o f t h e T e s t C y l i n d e r a t
t h e A n t i c i p a t e d A v e r a g e C o m p r e s s i v e S t r e s s
E, . ( k s i ) T a n g e n t Modulus of E l a s t i c i t y a t Z e r o S t r e s s "C 1
E ( k s i ) M o d u l u s o f E l a s t i c i t y o f t h e S t e e l s
f ( p s i ) F i n a l C o n c r e t e S t r e s s a f t e r L o s s e s
f ^ ( p s i ) U l t i m a t e S t r e n g t h o f the T e s t C y l i n d e r
f " c ( p s i ) C o m p r e s s i v e S t r e n g t h of C o n c r e t e i n F l e x u r e
f 1 ( k s i ) L o s s i n P r e s t r e s s
f . SI
( k s i ) I n i t i a l P r e s t r e s s o f t h e S t e e l
f s o
( k s i ) P i n a l P r e s t r e s s a f t e r L o s s e s
f s u
( k s i ) S t r e s s i n t h e S t e e l a t Load P*
F so
( k i p ) S t r e s s i n g F o r c e C o r r e s p o n d i n g t o f = 140,000 p s i so e
F s u
( k i p ) S t r e s s i n g F o r c e C o r r e s p o n d i n g t o f
I ( i n . 4 ) Moment of I n e r t i a o f t h e S t r u t
L ( i n . ) L e n g t h o f t h e S t r u t ( b e t w e e n o u t s i d e f a c e s o f t h e Embedded P l a t e s )
n M o d u l a r R a t i o o f S t e e l t o C o n c r e t e
P R a t i o o f S t e e l A r e a t o C o n c r e t e A r e a
P ( k i p ) A x i a l Load on t h e S t r u t
P' ( k i p ) T e s t Load a t t h e L a s t R e a d i n g I n c r e m e n t b e f o r e B u c k l i n g O c c u r r e d
P c r
( k i p ) C r i t i c a l I^oad D e t e r m i n e d f r o m t h e S o u t h w e l l P c r P l o t s
P 0
( k i p ) S h o r t Column S t r e n g t h = . 8 5 f " ( A c ~ A g )
R R e d u c t i o n F a c t o r P +F /P u su 0
t ( i n . ) W i d t h o f t h e S t r u t i n the N a r r o w D i r e c t i o n
T ( d a y ) E l a p s e d Time between M a n u f a c t u r e and T e s t i n g
w c
( l b . / c u . f t . ) U n i t W e i g h t of C o n c r e t e
X ( i n . ) D i s t a n c e b e t w e e n t h e E x t r e m e F i b r e and t h e C e n t r o i d o f t h e S e c t i o n
oC. R a t i o o f A p p l i e d Load t o C r i t i c a l L o ad oC* R a t i o o f E ' / E t
(3 ( l / i a . ) C r i t i c a l C u r v a t u r e & ( i n . ) O b s e r v e d L a t e r a l D e f l e c t i o n o f t h e M i d - P o i n t
of t h e S t r u t
x i .
C r i t i c a l S t r a i n i n C o n c r e t e a t M i d - P o i n t
due t o t h e Combined E f f e c t of P c"and P su u
A v e r a g e C o n c r e t e S t r e s s a t Load P' I n c o r p o r a t
i n g t h e E f f e c t o f S t r e s s L o s s e s
Maximum C o m p r e s s i o n S t r e s s a t Load P' ,
Maximum T e n s i o n S t r e s s a t Load P'
I. INTRODUCTION
W i t h t h e r e c e n t t r e m endous g r o w t h i n t h e use of p r e s t r e s s e d
c o n c r e t e s t r u c t u r e s t h e d e s i g n e r s a r e t r y i n g t o expand t h e a r e a
o f a p p l i c a t i o n o f t h i s r e l a t i v e l y new m a t e r i a l . I n t h i s way
t h e u se of s l e n d e r p r e s t r e s s e d columns i s g r a d u a l l y i n c r e a s i n g .
I t has become a p p a r e n t t h a t t h e m a n u f a c t u r e o f s l e n d e r columns
by p r e s t r e s s i n g o f f e r s many a d v a n t a g e s . When b u i l d i n g e l e m e n t s
a r e p r e f a b r i c a t e d t h e p r o b l e m o f t r a n s p o r t a t i o n becomes p r e
d o m i n a n t . I n t h e c a s e o f l a r g e s l e n d e r u n i t s , r e g a r d l e s s o f
t h e i r f i n a l u s e , i t i s o f t e n a d v i s a b l e t o d e s i g n i n p r e s t r e s s e d
c o n c r e t e t o a v o i d c r a c k i n g d u r i n g h a n d l i n g and t r a n s p o r t a t i o n .
A l s o , t h e r e i s an i n c r e a s i n g need f o r p r e s t r e s s e d b e a r i n g w a l l
u n i t s whose s l e n d e r n e s s i s d i c t a t e d by a r c h i t e c t u r a l f e a t u r e s .
E x p e r i e n c e has p r o v e n t h a t t h e s a v i n g i n t r a n s p o r t a t i o n c o s t s
due t o b e t t e r f l e x u r a l p r o p e r t i e s , o f f s e t s t h e l o s s i n com
p r e s s i v e c a p a c i t y . A l s o , t h e r e i s o f t e n a need f o r c r a c k - f r e e
c o n c r e t e e l e m e n t s .
I t i s b e l i e v e d t h a t t h e r e c o g n i t i o n o f t h e s e a d v a n t a g e s
has l e d i n v e s t i g a t o r s t o t u r n t h e i r i n t e r e s t t o w a r d s t h e
s t u d y of the b e h a v i o u r o f p r e s t r e s s e d c o n c r e t e c o l u m n s .
A s e r i e s o f s t u d i e s , i n v e s t i g a t i n g t h e b e h a v i o u r o f p r e -
s t r e s s e d c o l u m n s , was s t a r t e d by R. A. B r e c k e n r i d g e . I n
h i s e x p e r i m e n t a l r e s e a r c h , p u b l i s h e d i n 1953, B r e c k e n r i d g e
p r o v e d t h a t a c o n c e n t r i c a l l y p l a c e d t e n d o n o r p r e t e n s i o n i n g
w i r e has no e f f e c t on t h e c r i t i c a l s u p e r i m p o s e d l o a d w h i c h
t h e c o l u m n s w i l l c a r r y , as l o n g as t h e p r e s t r e s s does n o t
e x c e e d t h e d i f f e r e n c e b e t w e e n t h e c r i t i c a l l o a d and t h e
2.
u l t i m a t e c o m p r e s s i v e s t r e n g t h of the c o n c r e t e .
He a l s o i n c o r p o r a t e d the l o s s of p r e s t r e s s due t o s u p e r
i m p o s e d a x i a l l o a d i n t o a g e n e r a l i z e d e q u a t i o n . F i n a l l y he
m o d i f i e d t h e s e c a n t f o r m u l a i n o r d e r t o compute t h e s t r e s s e s
i n an a x i a l l y p r e s t r e s s e d and e c c e n t r i c a l l y l o a d e d c o l u m n .
To v e r i f y t h e s e e q u a t i o n s he t e s t e d 71 columns of f i v e t y p e s
h a v i n g s l e n d e r n e s s r a t i o s r a n g i n g "between 84 and 155.
O t h e r s t u d i e s have a l s o been p u b l i s h e d s h o w i n g t h a t t h e
u l t i m a t e c a p a c i t y of an e c c e n t r i c a l l y l o a d e d p r e s t r e s s e d c o n
c r e t e c o l u m n does depend on t h e p e r c e n t a g e o f t h e p r e s t r e s s i n g
s t e e l . Some a u t h o r s , f o r e x a m p l e , • P a u l Zung-Teh Z i a i n h i s 20
" U l t i m a t e S t r e n g t h o f S l e n d e r P r e s t r e s s e d C o n c r e t e Columns" p r e s e n t e d g r a p h s s h o w i n g a r e l a t i o n s h i p b etween p e r c e n t a g e of
s t e e l and u l t i m a t e c a p a c i t y of a p r e s t r e s s e d c o n c r e t e s t r u t .
,The maximum s l e n d e r n e s s r a t i o i n h i s e x p e r i m e n t s was L/D = 35.
The a u t h o r s t a t e d t h a t optimum r e s u l t s a r e o b t a i n e d u s i n g 0.5$
to 1.0$ s t e e l . I n 1956, A. M. O z e l l and A. M. J e r n i g a n 1 0
i n v e s t i g a t e d the n e c e s s a r y p r e s t r e s s i n g i n ter m s of the s l e n d e r
n e s s r a t i o . C o m p u t a t i o n method f o r p r e s t r e s s e d columns i s
g i v e n 'by t h e c o m p r e h e n s i v e e x p e r i m e n t a l and t h e o r e t i c a l s t u d y 9
of T. Y. L i n and R. I t a y a p u b l i s h e d i n 1957. R e c e n t l y P r o f . 4
A. E f s e n d e v e l o p e d methods o f c a l c u l a t i o n of e c c e n t r i c a l l y l o a d e d p r e s t r e s s e d c o n c r e t e c o l u m n s , (196 3 ) - A. S. H a l l a l s o
5
' c o n c l u d e d i n h i s e x p e r i m e n t a l r e s e a r c h t h a t t h e l o a d c a r r y i n g
c a p a c i t y of t h e h i g h l y p r e s t r e s s e d c o n c r e t e c o l u m n h a v i n g a
l o a d e c c e n t r i c i t y of L/40 was i n c r e a s e d by 60 p e r c e n t , w hereas
" i n no i n s t a n c e was any b e n e f i c i a l e f f e c t g a i n e d "by a p r e s t r e s s
' 2
l e s s t h a n 0.2 f ", ( 1 9 6 3 ) . Brown, K.I.. , i n h i s comprehen
s i v e p a p e r a b o u t t h e b e h a v i o u r o f p r e s t r e s s e d c o n c r e t e c o l u m n s ,
p u b l i s h e d an i n e l a s t i c a n a l y t i c a l method t o c a l c u l a t e t h e
d e f l e c t i o n o f a s t r u t i n terms of t h e l o a d . He a l s o c o n c l u d e d
t h a t t h e amount o f p r e s t r e s s i n g does n o t i n f l u e n c e t h e s t a b i l
i t y of a s t r u t .
I n t h i s t h e s i s an a t t e m p t . i s made t o c o n t r i b u t e t o t h e
c l a r i f i c a t i o n o f t h e b u c k l i n g b e h a v i o u r of p r e s t r e s s e d c o n c r e t e
c o l u m n s .
The r e s e a r c h m a i n l y c o n c e n t r a t e d on i n v e s t i g a t i n g t h e
r e l a t i o n s h i p b e t ween t he E u l e r l o a d and t h e p e r c e n t a g e o f
s t e e l , and on e s t a b l i s h i n g t h e modulus t o be u s e d i n c a l c u l a t
i n g t h e E u l e r l o a d . Some columns were t e s t e d e c c e n t r i c a l l y i n
o r d e r t o s u p p o r t the v a l i d i t y of B r e c k e n r i d g e ' s m o d i f i e d s e c a n t
• f o r m u l a . A l l t e s t s were made on f u l l s c a l e models h a v i n g
i d e n t i c a l s l e n d e r n e s s r a t i o s of L/D = 40.
II. OBJECT AND SCOPE OF TESTS
The pr imary o b j e c t i v e s of these t e s t s were to study the
f o l l o w i n g :
1) Whether there i s any r e l a t i o n s h i p between the E u l e r
load of a s l ender p r e s t r e s s e d concrete s t r u t and the
percentage of p r e s t r e s s i n g s t e e l .
2) Wheth er E u l e r ' s fundamental formula can be a p p l i e d i n
case of p r e s t r e s s e d s t r u t s .
3) ' Whether the b u c k l i n g load f o r a p r e s t r e s s e d s t r u t can
be p r e d i c t e d from the s t r e s s - s t r a i n curve of s tandard '
t e s t c y l i n d e r s .
In order to answer these quest ions t h i r t y ,(30) f u l l s c a l e
models were t e s t e d . It was dec ided to conf ine the scope of
the re sea r ch to one p a r t i c u l a r s lenderness r a t i o of L/D = 40,
and c e n t r a l p r e s t r e s s .
Wi th in the one va lue of s lenderness r a t i o the f o l l o w i n g
were kept constants
1) . Concrete s t reng th (designed f o r 6000 p s i ) .
2) F i n a l p r e s t r e s s i n the s trands (designed f o r
140,000 p s i ) .
3) Q u a l i t y of i n g r e d i e n t s i n order to ' ob ta in i d e n t i c a l
modulus.
4) Dimensions of the specimens.
and the f o l l o w i n g v a r i a b l e s were used:
1) S t e e l r a t i o (p = 0.23, 0.45, 0 . 6 , *0 .91, 1.20).
2) Load e c c e n t r i c i t y (e / t = 0,' 0. 1 •, 0 .5 ) .
J »
The f i v e v a l u e s of s t e e l r a t i o p r o d u c e d p r e s t r e s s e s a f t e r
l o s s e s r a n g i n g f r o m 328 p s i t o 1680 p s i as shown i n T a b l e I .
The c r o s s s e c t i o n o f a l l t h e s p e c i m e n s was made r e c t a n g u l a r
r a t h e r t h a n s q u a r e . I n t h i s way t h e d i r e c t i o n o f t h e b u c k l i n g
c o u l d be p r e d i c t e d . T h i s a r r a n g e m e n t a l s o made t h e p o s i t i o n
i n g o f the l o a d and t h e . l a t e r a l d e f l e c t i o n measurement as
s i m p l e as p o s s i b l e .
S i n c e t h e p r i n c i p a l s c o p e o f t h e t e s t was. t o s t u d y b u c k l i n g
b e h a v i o u r , an a t t e m p t was made t o s i m u l a t e i d e a l h i n g e d c o n
d i t i o n s a t ' b o t h endso
None of t h e s p e c i m e n s had s t i r r u p r e i n f o r c e m e n t . A l t h o u g h 1 0
O z e l l and J e r n i g a n f o u n d i n t h e i r e x p e r i m e n t a l r e s e a r c h t h a t
t h e u l t i m a t e c a p a c i t y o f an e c c e n t r i c a l l y p r e s t r e s s e d s t r u t
h a v i n g s t i r r u p s i s g r e a t e r t h a n t h e one w i t h o u t s t i r r u p s , i t
was f e l t t h a t t h e use o f s t i r r u p s does n o t i n f l u e n c e t h e
b u c k l i n g c a p a c i t y o f c e n t r a l l y p r e s t r e s s e d s t r u t s .
To e s t a b l i s h t h e c o n c r e t e s t r e n g t h and Young's M o d u l u s o f
the s p e c i m e n a t t h e t i m e o f t e s t i n g , s i x 6" x 12" c y l i n d e r s
were e a s t u n d e r i d e n t i c a l c o n d i t i o n s w i t h t h e s p e c i m e n s - I t
was c o n t e m p l a t e d t o b r e a k two of each s e t a t t h e t i m e of de-
s t r e s s i n g and t h e o t h e r f o u r a t the t i m e o f t e s t i n g .
I t was d e c i d e d t o e s t a b l i s h t h e modulus a t t h e t i m e of
b u c k l i n g u s i n g t h e s t r e s s - s t r a i n c u r v e s o b t a i n e d f r o m t h e
c y l i n d e r s r a t h e r t h a n m e a s u r i n g t h e s t r a i n s on t h e s t r u t s
d u r i n g t e s t i n g .
6.
ITEM
MUAA&E.R-
o r ' S P E C I M E N
S T E b L RATIO
p M
APPLIED INITIAL E X P E C T E D F I N A L STfce-vS IN PTISAN PS
FINAL cONCfc.
6 T R E S 6 S T R A N G ITEM
MUAA&E.R-
o r ' S P E C I M E N
S T E b L RATIO
p M lb . P 4 I .
1 6 0.23 9,038 328 1-5/16"
2 6 0.45 17,588 635 1 -7/1-6"
3 6 0. 60 23,577 140,000 840 1-1/2"
4 6 0.91 18,534 * ) . 1 ,275 2-7/16" 9 18,362
5 6 1 .20 25,454 ft) 1 , 680 2-1/2" I 25,154
* Applied \o the f i r s t s f r a n d
TABLE I . - TYPES OF SPECIMENS
7.
I I I . DESCRIPTION OF THE SPECIMENS
The t e s t s t r u t s were m a n u f a c t u r e d i n the p l a n t o f G r a y b a r
P r e c a s t L i m i t e d , and s h i p p e d t o t h e U n i v e r s i t y , of B r i t i s h
C o l u m b i a a f t e r a l l s t r u t s were c a s t .
The t h i r t y s t r u t s were p r e p a r e d i n f i v e m a j o r g r o u p s ,
e a c h g r o u n c o n t a i n i n g s i x i d e n t i c a l s p e c i m e n s .
F i g u r e 1, shows t h e f i v e t y p e s o f specimen,- and T a b l e I
p r e s e n t s t h e b a s i c d a t a of the s p e c i m e n s u s e d .
The f o l l o w i n g c o n c r e t e mix d e s i g n was u s e d f o r a l l
s p e c i m e n s :
Cement (Type I I I , E l k B r a n d , H i g h - E a r l y ) 180 l b s . Sand 251 3/8" a g g r e g a t e 108 3/4" a g g r e g a t e 374 Water 77
990 l b s . p e r b a t c h
The c o n c r e t e s t r e n g t h was c o n t r o l l e d 'by s t a n d a r d 6" x 12"
c y l i n d e r s , s i x b e i n g t a k e n f r o m e ach day's c a s t . T h r o u g h o u t
t h e t e s t t h e c o n c r e t e m i x , t h e i n i t i a l p r e s t r e s s i n g f o r c e ,
t h e m i x i n g t i m e , and t h e v i b r a t i o n t i m e were k e p t c o n s t a n t .
An a t t e m p t was made t o m a i n t a i n u n i f o r m m a n u f a c t u r i n g p r o c e d
u r e f o r a l l s p e c i m e n s : t h e v a r i a t i o n s a r e shown i n T a b l e I I .
The i n i t i a l p r e s t r e s s was computed so as t o e x p e c t a f i n a l
p r e s t r e s s o f 140,000 p s i .
The f o l l o w i n g a s s u m p t i o n s were made t o p r e d i c t p r e s t r e s s
l o s s e s :
a) To compute e l a s t i c s h o r t e n i n g and c r e e p t h e modulus
of t h e c o n c r e t e was assumed t o be 5,550 k s i and f o r
8.
L I & W T
10"
0 i "o
END b\tMlA& TO T<?P
t 5X1176 * / f
au. ii •'isnMi^»>nwiiM;EB—awn
T Y P E Nc9. I.
* 1 BAR, IO" L0N£,
H£>tE f£>£ *>T&AND
ALT E R - N A T I V E E . N D P L A J E 6
TYPE N0.3.
i |
T Y P E M a 4 .
4> T N D <=> 1
3? * 2
6 e c r i ^ N X -X T Y P I C A L ROB ft>C?TH E.MDS
P i g . 1 - D e t a i l s of Sp e c i m e n s
1. | 3 . 4- 5 . (P. 7 . &. 9 . I I . I -2 . 1 3 . 14- | 5 . \<b. I J'
f\A|6, S T R A N D P A T E
C A S T
T I M E
C A G T
PKESEJ
J I A A E
M i x
' T I M E
DESTfcftS
D A T E
6 T £ A A A
T I M E L O A D
lKJ.TE.KiNd C E L L
R E A D I N G
F l N P v L C E L L R E A D I N G
C Y L I N D E R S Tf^N4> , f\A|6,
S I Z E
P A T E
C A S T
T I M E
C A G T
PKESEJ
J I A A E
M i x
' T I M E
DESTfcftS
D A T E T I A A E - TEAAB T I M E L O A D
lKJ.TE.KiNd C E L L
R E A D I N G
F l N P v L C E L L R E A D I N G AAAfck,
Tf^N4> ,
I M . <£>
t A M M . 1 9 6 5 °F s e c . — "K1 •>
( L b . ) Mr -Sf
( L & . ) ( L B . ) psi-
. 9
1 0. 1 1
2
1 1
7/16
5/16 1/2
2 8/4
28/4 28/4
1 5s00
1 5 s 1 0 1 5 §20
9
9 9
3
3 3
' 2 9/4
2 9/4 29/4
1 2 1 2 1 2
1 38 1 38 1 38
20 20 20
540 540 540 540
3168.2 33 38.8* 1545.0 4030.2
3708.2 3628,8* 2085.0 4570.2
6 9-10-11 4200 4200 4200
I 1 2
1 3 14
- 1. 2
1 -
5/16 7/16
1/2
29/4 29/4
29/4
1 5?40 1 5 s50
1 5 s 55
81 81
81
3* 3
3
30/4 30/4
30/4
1 1 1 1 1 1
1 42 142
1 42
20 20 20
575 575 575 575
1545.0 3168.2 3138.8* 4030.2
2120.0 3743.2 3713.8* 4605.2
6 12-13-14 4500 4500
4500
[ 15 1 6
1 7
. 1 2
1 .
1/2 7/16
5/1 6
30/4 30/4
30/4
1 3 s 30 1 3s30
1 3 s 30
: 1 11 1 1!
111
3
• 3
3
3/5 3/5
•3/5
9 9 ' 9
1 39 1 39 1 39
20 20 20
570 570 570 570
4030.0 3168.2 3138.8* 1545.0
4600.0 3738.2 3708.8* 2115.0
6 15-16-1 7 4500 4500
4500
1 8 1 9
1 2
7/1 6 1/2
4/5 4/5
1 5 ;00 1 5 s00
. 9 9
3 3
3/5 3/5
1 2 1 2
1 42 1 42
20 20
560 560 560
3006.5 4351.7 4299.8*
3566.5 4911 . 7 4859.8*
6 18-19 ' 42 00 4200
20 21
2
1 1 /2 7/1 6
7/5
7/5
1 4 s 30 1 4:30
-
H
10/5
10/5
— 20 20
540
540'
4 3 5 1 . 7 4299.8* 3006.5
4891 .7 4839.8* 3546.5
6 - 20-21 3060
3060
22
23 24
* S ** M
i
2
1 1
econd u 1 1 i p ngs b
1 /2
7/1 6 5/16
S t r a l y Ce y 5«8
11/5
11/5 1 1/5
1 1 Rea 5 l b s .
1 6 :00 1 6 :00 1 6 ;00
TABI
8
8 8
JE I I .
3 3 3
- MAI
12/5
12/5 1 2/5
lUFACTu
1 0
1 0 1 0
\
RING
143
1 43 143
DATA
20 20 20
OF TH
580
580 580
E S P E
4351.7 4299.8* 3006.5 1545.0
CIMENS
4931 .7 4879.8* 3586.5 2125.0
6
(
?2-23-24
Continue
4600
4600 4600
1)
4 f I S A S i P
N<? |4lZ.B !Kl. 4>
DA1E C A 4 T
1IAA.E
C A V f
PRE^E] M I X TIME- TIME-
e !?ESTI?e# 4TEAM DATE TIME TEMR
VIBK'N
TIME
12
. p e s * LOAD
is_ iNlT£RJ<v! CE1LL
I4 FINAL
O & L L
15 16
MA&I6
17 |KAHS|
25 26
1 ^ 5 MlM- 1^65
5/16 7/16
1 2/5 1 2/5
1 5 : 3 0
1 6 s 30 7 l 71
3
3
13/5 1 3/5
5>E£. (Le>.) (Le>.)
1 2 1 46 1 46
20 20
580 580
1545.0 3006.5
2 1 2 5 . 0
3 5 8 6 . 5
25-26 4300 4300
27
28 29
•1/2
7/16 5/1 6
1 3 / 5
1 3 / 5
1 3 / 5
1 5 :00
1 5 :00 1 5 :00
9
9
3
3
U / 5
1 4 / 5
1 4 / 5
1 0
1 0 1 2
1 40
1 40 1 40
'20
20 20
580
580 580
4 3 5 1 . - 7
4 2 9 9 .
3 0 0 6 . 5 1 5 4 5 . 0
4931 8*4879•
7
8 *
3 5 8 6 . 5
2 1 2 5 . 0
27-28-29 4050
4050 4050
30 31
7/1 6 5/1 6
14/5 14/5
1 6 ;00 1 6 ;00
3
3
1 7/5 17/5
1 2 1 2
1 3 9
1 3 9
20 20
580 580
3006.5 1545.0
3 5 8 6 , 5
2 1 2 5 . 0
3 0 - 3 1 3890 3890
3 2
3 3
2
2
1/2
7/1 6
4/6
4/6
3
3
7 / 6
7 / 6
20
20
580 580 575
4351.7 4299. S*|4879 3168.2 3138.8*371
R 9 3 8 . 7 8*
3743.2 3.8*
32-33 3005
3005
3 4 7/1 6 ,7/6 1 7 : 1 0 8/6 143 20 630 3168.2 3238.
3798.2 8* 8*3768,
3 4 3 ' 5 3 5
3 5 1/2 '8/6 17:20 9 / 6 0 1 48 20 550 4030.2 4580.2 3 5 4440
36
37
38 39
2
2
7/16
1/2
9/6
9/6
8; 30
8:30
3
3
10/6
10/6
1 3
1 3
1 4 7
1 4 7
20
20
585
585
3168.2 3138.2* 4351 . 4299.8*14884
3753.2 3723.8* 4936.7
.8*
1 /2 1 /2
10/6 1 0/6
15:10 15:20
3
3
1 1 /6 1 1 /6
14 1 4
1 3 9
1 3 9
20 20
580 575
4 0 3 0 . 2 4 0 3 0 . 2
4610.2 4605 .2
* S e c o n d S t r a n d • • M u l t i p l y C e l l Read
i n g s by 5.85 l b s .
T A B L E I I J - MANUFACT JURINC J DATA' OF T H E S P E C I M E N S '
3 6 - 3 7 4740
4740
38-39 4280 4280
o
11.
t h e s t e e l 28,,000 k s i ( T e s t s showed t h a t E q a c t u a l l y
a v e r a g e d a b o u t 4,800 k s i and E was 27,800 k s i ) . s
However, no a t t e m p t was made t o a d j u s t t h e assumed
s t r e s s l o s s e s b e c a u s e t h e y a r e m a i n l y g o v e r n e d by t h e
e f f e c t of s h r i n k a g e and t h e r e l a x a t i o n of t h e s t e e l .
The d i f f e r e n c e o f 750 k s i i n t h e v a l u e o f E g i v e s
o n l y an e r r o r o f 3.5$.
b) C r e e p c o e f f i c i e n t was assumed t o be C q = 2.5.
c) A s h r i n k a g e c o e f f i c i e n t o f 0.003 x 60$ .= 0.0018 was
assumed b e c a u s e of the v e r y d r y mix u s e d .
d) R e l a x a t i o n o f t h e s t e e l was assumed a t 4$.
C o r r e c t i o n v a l u e s f o r s t r e s s l o s s e s due t o t h e e l a s t i c
s h o r t e n i n g o f t h e p r e s t r e s s i n g b e d , t o v a r i a t i o n s i n s e t t i n g
t h e hand s c r e w j a c k , and t o t h e u n a v o i d a b l e s l i p p a g e o f the
g r i p s , were o b t a i n e d f r o m p r e v i o u s t e s t s . The maximum v a l u e ,
w h i c h was f o u n d to be 660 l b s . f o r a 1/2 i n . d i a m e t e r s t r a n d ,
was t a k e n i n t o a c c o u n t when t h e r e q u i r e d i n i t i a l s t r e s s i n g
f o r c e s were c a l c u l a t e d .
A l l s t r u t s had a b u i l t - i n s t e e l p l a t e 1/4 i n . t h i c k t o
accommodate t h e a d j u s t a b l e h e a d , as shown i n P i g u r e 2. T h i s
p l a t e was a n c h o r e d i n t o t h e c o n c r e t e by two 1/4 i n . d e f o r m e d
b a r s , The ends of t h e s t r u t s were r e i n f o r c e d w i t h l i g h t mesh
i n o r d e r t o d i s t r i b u t e c r a c k s when t e n s i o n , due t o t h e
e c c e n t r i c l o a d a p p l i c a t i o n , o c c u r r e d . The s t r a n d s were c u t
f l u s h w i t h t h e p l a t e and g r o u n d o f f by a c a r b o r u n d u m g r i n d e r
a f t e r d e t e n s i o n i n g was c o m p l e t e d .
T h r e e s i d e s of, t h e s t r u t s had c o a t e d p l y w o o d f o r m f i n i s h .
L E A D
4 OP S P E C I M E N V
•A" P L A T B
'/4 <j> F A S T E N I N O S C R E W
V& L E A D
V E R T I C A L ADJUSTMENT
,< * if-Vz MACHINED GROOVE
>/&" L E A D IO FT- S P E C I M E N
F i g . 2 - D e t a i l s o f t h e End P l a t e and t h e F a s t e n i n g Device.'
13. One 8 i n . s i d e was s t e e l t r o w e l l e d . A l o n g t h e m i d d l e two
f e e t e x c e p t i o n a l c a r e was t a k e n t o t r o w e l the s u r f a c e t o t h e
r e q u i r e d l e v e l and t o keep t h e t h i c k n e s s of t h e s p e c i m e n
w i t h i n an a c c u r a c y o f 1/32 i n . ( M e a s u r e m e n t s o f t h e a c t u a l
u n i t s p r o v e d t h a t t h e d i m e n s i o n s were k e p t c l o s e l y w i t h i n t h e
s p e c i f i e d t o l e r a n c e s ; h o w e v e r , t h e c u r v a t u r e of t h e s t r u t s i n
t h e w eaker d i r e c t i o n v a r i e d b e t ween z e r o and 1/4 i n . ) .
The s p e c i m e n s were i n d i v i d u a l l y numbered and the c o r r e s
p o n d i n g c y l i n d e r s had marks r e f e r r i n g t o a l l s p e c i m e n s c a s t
f r o m t h e same b a t c h . Of t h e 37 s t r u t s m a n u f a c t u r e d two had t o
be r e c a s t s i n c e i t was s u s p e c t e d t h a t s t r a n d s l i p p a g e had
o c c u r r e d . Seven o f them were d i s c a r d e d b e c a u s e of d i s c r e p
a n c i e s i n d i m e n s i o n s o r e x c e s s i v e c u r v a t u r e .
I V . PREPARATION OF THE SPECIMENS
M i x i n g o f C o n c r e t e
The b a t c h was m i x e d i n a 1 / 3 c u . y d . t u r b i n e m i x e r .
A l l i n g r e d i e n t s were w e i g h b a t c h e d . E l k , Type I I I h i g h
e a r l y s t r e n g t h bagged cement was u s e d . P r i o r t o manu
f a c t u r i n g , t h e e n t i r e q u a n t i t y of t h e cement was p u r c h a s e d
and s t o r e d f o r t h e j o b .
The m i x i n g t i m e and s e q u e n c e of t h e b a t c h i n g were
a l s o k e p t c o n s t a n t t h r o u g h o u t t h e work. The t i m e o f m i x i n
was s e t a t t h r e e m i n u t e s measured f r o m t h e t i m e of a d d i n g
w a t e r t o t h e cement. O n l y one b a t c h was u s e d f o r a d a i l y
p r o d u c t i o n and n o r m a l l y t h r e e s t r u t s were c a s t f r o m t h i s
b a t c h . ( E x c e p t i o n s were made when r e c a s t i n g was n e c e s s a r y
o r when, i n one i n s t a n c e , a s p e c i a l t y p e of s t r a n d was n o t
a v a i l a b l e . y I n t h e s e c a s e s o n l y one or two s t r u t s were
c a s t ) .
Bed E q u i p m e n t and S t r e s s i n g
T h r e e i d e n t i c a l l y made s t e e l s t r e s s i n g beds were u s e d
f o r f a b r i c a t i n g the s p e c i m e n s ( F i g u r e 3 ) . The s t r e s s i n g
was p e r f o r m e d by c o n v e n t i o n a l s t r e s s i n g j a c k s r e s t i n g
a g a i n s t a l o a d c e l l . To a v o i d s t r e s s l o s s e s due t o a n c h o r
s l i p p a g e a s p e c i a l l y d e s i g n e d s c r e w - a n c h o r was s c r e w e d
a g a i n s t a s p l i c i n g g r i p a f t e r s t r e s s i n g had been c o m p l e t e d
I n t h i s way t h e a n c h o r s l i p p a g e was e l i m i n a t e d b e c a u s e t h e
wedges i n t h e s p l i c i n g g r i p s y s t e m were a l r e a d y s e t when
i
FIXED END B
15.
v-|o'-4"
—̂
ST£E65IN4 END K
Y T Y R
3/4" 7^-
P L A N
j A C k 6 i i s t ^ M E A D 6 E E DEJAI L 11 X"
*C
CM o
^ V
S E C T I O N A - A 7 C 17.
7~3*4 TUkN NUT
5 E G T I O N B - B II v .11
TYP.
D E T A I L X
L O N G I T U D I N A L S E C T I O N
OF C U 6 T O M ' A A A O E J A C K I N 6 , M E A D
F i g . 3 - D e t a i l s o f t h e S t r e s s i n g E q u i p m e n t .
16.
the a d j u s t a b l e support of the screwjack was t i g h t e n e d .
F i gu re 4 shows the procedure s c h e m a t i c a l l y .
During the s t r e s s i n g procedure an i n i t i a l p r e - l o a d i n g
was a p p l i e d to e l i m i n a t e g r i p s l i ppage at the f a r end, and
then the j a c k i n g was cont inued to the r equ i red v a l u e . The
converted load c e l l readings are t abu l a ted i n Table II t o
gether with a l l data of the manufactur ing procedure.
Res in coated plywood was used f o r the forms to avo id
b l e e d i n g through the j o i n t s . The s ide forms were b o l t e d
to the s t r e s s i n g bed by a dev ice which ensured the proper
p o s i t i o n of the s ide forms at r e - s e t t i n g . The su r f aces of
the plywood not i n contact with the concrete were a l so
t r e a t e d with s h e l l a c to minimize warping of the forms dur ing
s teaming.
P l a c i n g the Concrete
The s t r e s s i n g bed was p laced by an overhead crane onto
a v i b r a t i o n t a b l e . Two e x c e n t r i c s performed the v i b r a t i o n .
The ampl itude and r e v o l u t i o n of the e x c e n t r i c s were set to
s u i t the load of the po r tab le s t r e s s i n g beds and the u n i t s .
V i b r a t i o n time was kept constant and was d i r e c t e d by a
q u a l i t y c o n t r o l l e r . A f t e r v i b r a t i o n the s t r e s s i n g bed was
removed from the v i b r a t i o n tab le and p laced i n to a steaming
k i l n . Before the hood of the k i l n was p laced the f i n i s h i n g
of the sur face was completed.
A s p e c i a l h o l d i n g dev ice was mounted to the v i b r a t i o n
17.
W O O D E N S O F F I T <t>T £ E I N £f JA6IC
(7) 6,IZIP
F I X E D E N D WOODEN SOFE I J
F i g . 4 - Schematic D e s c r i p t i o n of the S t r e s s i n g Procedure.
18.
t a b l e and a l o n g w i t h one of t h e u n i t s t h e s i x c y l i n d e r s
were v i b r a t e d i n t h e same mode as t h e s p e c i m e n s . T h i s
way a b e t t e r a p p r o a c h t o f i n d i n g t h e t r u e Young's Modulus
of t h e s p e c i m e n was a n t i c i p a t e d .
4) C u r i n g and D e s t r e s s i n g of t h e S p e c i m e n s
The s t r u t s were c a s t i n t h e m o r n i n g b e f o r e c o n c r e t i n g
of p l a n t p r o d u c t i o n b e g a n . A f t e r 9 t o 11 h o u r s p r e s e t t i m e
t h e u n i t s were c u r e d a l o n g w i t h t h e p l a n t p r o d u c t i o n u n d e r
l o w - p r e s s u r e s t e a m , l a s t i n g . a p p r o x i m a t e l y 9 t o 12 h o u r s , a t
an a v e r a g e t e m p e r a t u r e o f 140°F.
Some of t h e u n i t s were n o t s t e a m e d , b u t were l e f t f o r
a few days u n d e r a p o l y e t h y l e n e c o v e r a t room t e m p e r a t u r e .
A f t e r two of t h e s i x c y l i n d e r s were t e s t e d t o d e t e r m i n e
t h a t t h e minimum 3,000 p s i t r a n s f e r s t r e n g t h had been r e a c h e d ,
t h e s p e c i m e n s were d e s t r e s s e d . F i r s t t h e n u t s of t h e s c r e w -
j a c k s were r e l e a s e d , t h e n t h e s l a c k e n e d s t r a n d s were c u t by
a g r i n d e r .
When the s p e c i m e n s were removed f r o m t h e f o r m s , t h e y
were f i r s t t i l t e d upwards and t h e n l i f t e d . A f t e r s t r i p p i n g ,
t h e u n i t s were s t o r e d t o g e t h e r w i t h t h e c y l i n d e r s u n d e r a
r o o f . No f u r t h e r c u r i n g was p e r f o r m e d a f t e r t h e u n i t s were
s t o r e d .
5) S h i p m e n t o f t h e S p e c i m e n s
T h r e e days a f t e r t h e l a s t u n i t s were c a s t , a l l s p e c i m e n s
s e l e c t e d f o r t e s t i n g were s h i p p e d t o t h e l a b o r a t o r y and
19.
s t o r e d t h e r e u n t i l t e s t e d . The s t r u t s a l w a y s r e s t e d ' a t
t h e i r o n e - f i f t h p o i n t s w i t h t h e w i d e r s i d e v e r t i c a l . A t
t h e l a b o r a t o r y t h e u n i t s had t o be t u r n e d o v e r s e v e r a l
t i m e s d u r i n g t h e i r p r e p a r a t i o n f o r t h e t e s t i n g . T h i s was
a c h i e v e d by r o l l i n g .them c a r e f u l l y o v e r a t t h e i r o n e - f i f t h
p o i n t s . By h a n d l i n g them t h i s way none of t h e s t r u t s , r e
g a r d l e s s of t y p e , c o u l d d e v e l o p any c r a c k s . A l l c y l i n d e r s
were i d e n t i c a l l y s t o r e d w i t h t h e s p e c i m e n s .
V. TEST PROCEDURE
T e s t i n g M a c h i n e
The s p e c i m e n s were t e s t e d i n a T i n i u s O l s o n , 200,000
l b . e l e c t r o - m e c h a n i c a l u n i v e r s a l t e s t i n g m achine h a v i n g a
minimum r e a d i n g i n c r e m e n t o f 200 l b . T h i s m achine p r o v i d e
a c o n s t a n t r a t e o f s h o r t e n i n g b e t w e e n i t s l o a d i n g h e a d s ,
and m e a s u res t h e l o a d d e v e l o p e d i n t h e s p e c i m e n due t o
t h i s s h o r t e n i n g . The l o a d a p p l i c a t i o n on t h e s p e c i m e n was
u n i n t e r r u p t e d f r o m s t a r t t o f a i l u r e and t o o k a p p r o x i m a t e l y
20 m i n u t e s . L a t e r a l d e f l e c t i o n r e a d i n g s were t a k e n a t
l o a d i n c r e m e n t s o f :
2.5 k i p s f o r c e n t r a l l y l o a d e d s t r u t s
1 .5 k i p s f o r e c c e n t r i c i t y o f e / t = 0.1
1.0 k i p f o r e c c e n t r i c i t y o f e / t = 0.5
As soon as t h e d i a l n e e d l e s t o p p e d , i n d i c a t i n g t h a t
t h e s p e c i m e n c o u l d n ot c a r r y more l o a d , t h e machine was
s t o p p e d . A t t h i s u l t i m a t e l o a d ( d e s i g n a t e d P ), a l t h o u g h u
no f u r t h e r p r e s s u r e was a p p l i e d , t h e l a t e r a l d e f l e c t i o n
s t i l l i n c r e a s e d and t h e mode of f a i l u r e was r e c o r d e d .
On some s p e c i m e n s , a f t e r t h e u l t i m a t e l o a d had been
r e c o r d e d , t h e l o a d i n g was c o n t i n u e d i n o r d e r t o i n v e s t i
g a t e t h e b e h a v i o u r o f t h e s t r u t s a f t e r b u c k l i n g had
o c c u r r e d . D e f l e c t i o n Measurement
The l a t e r a l d e f l e c t i o n was r e a d by two t r a n s i t i n
s t r u m e n t s , p l a c e d 20' f r o m e a c h s h o r t f a c e of t h e s t r u t .
21 .
A s c a l e w i t h g r a d u a t i o n s of 0.1 i n . was mounted at- t h e
c e n t r e of t h e s t r u t . R e a d i n g s t o 0.01 i n . were e s t i m a t e d .
I n f i v e i n s t a n c e s the l a t e r a l d e f l e c t i o n of t h e head of t h e
m a c h i n e was measured u s i n g a n o t h e r two t r a n s i t s . A l l f i v e
c a s e s p r o v e d t h a t t h e b o t t o m head d i d n o t move a t a l l ; and
t h e t o p head moved a maximum of 0.03 i n . and t h i s movement
t o o k p l a c e a t t h e b e g i n n i n g of t h e l o a d i n g . As s o o n as
t h e l o a d i n g r e a c h e d 5 t o 10 k i p s no f u r t h e r movement of
t h e t o p head c o u l d be o b s e r v e d . I t was assumed t h a t i n
a l l c a s e s t h e l a t e r a l d e f l e c t i o n o f t h e head of t h e machine
was no g r e a t e r t h a n t h e f i v e c a s e s o b s e r v e d .
M e c h a n i s m of t h e S t r u t S u p p o r t s
An a t t e m p t was made t o p r o v i d e a s u p p o r t w h i c h
( a ) s i m u l a t e d an i d e a l h i n g e d s u p p o r t and (b) l o c a t e d t h e
l o a d as a c c u r a t e l y as p o s s i b l e . I n o r d e r t o do t h i s an
a d j u s t a b l e 3/4 i n . t h i c k s t e e l p l a t e was a t t a c h e d t o t h e
1/4 i n . t h i c k s t e e l p l a t e embedded i n t h e end of t h e s t r u t
as shown i n F i g u r e 2. T h i s p l a t e was p r o v i d e d w i t h two
g r o o v e s each h a v i n g a s e m i - c i r c u l a r c r o s s s e c t i o n m a c h i n e d
t o an a c c u r a c y of 0.001 i n . S i m i l a r p l a t e s were mounted
a t t h e t o p and b o t t o m heads of t h e t e s t i n g m a c h i n e , and
l u b r i c a t e d r o l l e r s 1/2 i n . i n d i a m e t e r were u s e d i n t h e
m a t i n g g r o o v e s .
I t was assumed t h a t t h i s a r r a n g e m e n t k e p t t h e f r i c t i o n
c o e f f i c i e n t a t an a v e r a g e of 0.025. Thus t h e e c c e n t r i c i t y
due t o f r i c t i o n o f t h e h i n g e a t maximum l o a d was l e s s t h a n
22.
0.01 i n . , and c o u l d be n e g l e c t e d .
Lead shims were l a i d b e t w een t h e two p l a t e s t o t a k e up
p o s s i b l e d i s c r e p a n c i e s i n the embedded s t e e l p l a t e s .
I n o r d e r t o l o c a t e the l o a d as a c c u r a t e l y as p o s s i b l e
t h e a d j u s t a b l e p l a t e was m a n u f a c t u r e d as f o l l o w s :
One g r o o v e was l o c a t e d a t t h e c e n t r e of t h e a d j u s t a b l e
p l a t e and t h e o t h e r e x a c t l y 1.5 i n . away. T h e r e f o r e by
l o c a t i n g t h e c e n t r e g r o o v e a t t h e r e q u i r e d p o s i t i o n ( a l o n g
t h e e s t a b l i s h e d a x i s of t h e s t r u t ) t h e 1.5 i n . e c c e n t r i c i t y
was a u t o m a t i c a l l y o b t a i n e d . F o r t h e 0.3 i n . e c c e n t r i c i t y
the e n t i r e a d j u s t a b l e p l a t e was s e t by t h e thumb s c r e w s so
t h a t t h e m i d d l e g r o o v e was o f f s e t 0.3 i n . f r o m t h e a x i s of
the s t r u t ( F i g u r e 2 ) .
I n o r d e r t o e s t a b l i s h t h i s a x i s a t r a n s i t was s e t up
o v e r t h e c e n t r e p o i n t of t h e s h o r t f a c e . A f t e r e n s u r i n g
t h a t t h e s t r u t was r e s t i n g plumb a s t r a i g h t l i n e was e s t a b
l i s h e d , by means of t h e t r a n s i t , t h r o u g h t h i s p o i n t p a r a l l e l
t o a l i n e j o i n i n g t h e m i d - p o i n t s of t h e two ends o f t h e
member. The measured e c c e n t r i c i t y of l o a d i n g was w i t h
r e s p e c t t o t h e c e n t r e s e c t i o n .
The d i s t a n c e b e t w e e n t h e c e n t r e s of t h e end s e c t i o n s
and t h e s t r a i g h t l i n e wa.s t h e measure of the c u r v a t u r e of
t h e s t r u t s , and was r e c o r d e d i n T a b l e I I I i n Column 11.
When l a r g e (1.5 i n . ) e c c e n t r i c i t y was u s e d t h e a d j u s t
a b l e p l a t e s were a l s o t i e d t o t h e s i d e o f t h e column ( s e e
P h o t o 1) . The f o r c e , r e q u i r e d t o d e v e l o p a d e q u a t e f r i c t i o n
23.
PHOTO 1 The F a s t e n i n g D e v i c e f o r t h e A d j u s t a b l e P l a t e .
24.
b e t w e e n the c l a m p s and the s i d e of the s t r u t , was c r e a t e d
by t i g h t e n i n g t h e b o l t s c o n n e c t i n g t h e two a n g l e i r o n s
t o g e t h e r ( F i g u r e 2 ) . T h i s a r r a n g e m e n t was b e l i e v e d t o be
n e c e s s a r y b e c a u s e i t was f e a r e d t h a t the embedded p l a t e
w o u l d n o t t r a n s m i t t h e moment i n t o t h e s t r u t . A f t e r t h e
a l i g n m e n t was e s t a b l i s h e d as a c c u r a t e l y as p o s s i b l e , t h e
l o c k i n g s c r e w s were t i g h t e n e d and t h e s t r u t was l i f t e d i n t o
i t s f i n a l p o s i t i o n ( s e e P h o t o 2 ) .
W i t h t h i s a r r a n g e m e n t no f u r t h e r a d j u s t m e n t , c h e c k i n g ,
o r o t h e r work was n e c e s s a r y w h i l e t h e s p e c i m e n s were p l a c e d .
A f t e r the s t r u t s were p l a c e d i n t o t h e m achine an i n i t i a l
300 l b . l o a d was k e p t on them u n t i l t h e l i f t i n g c l a m p s
were removed and d e f l e c t i o n t a r g e t s mounted. U s i n g the l o a d
i n c r e m e n t s p r e v i o u s l y m e n t i o n e d , t h e t e s t l a s t e d a p p r o x i
m a t e l y 20 t o 25 m i n u t e s . An a v e r a g e o f t h r e e t e s t s was
p e r f o r m e d e a c h day. The c r i t i c a l v a l u e s of two s p e c i m e n s
(No. 10 and No. 13) seemed t o be o u t of l i n e , and i n o r d e r
t o e n s u r e r e l i a b l e a v e r a g e s , t e s t s of a d d i t i o n a l s p e c i m e n s
were d e s i r e d . S i n c e no s p a r e s t r u t s were c a s t t h e s e add-'
i t i o n a l s p e c i m e n s were t a k e n f r o m t h o s e a l r e a d y t e s t e d w i t h
l a r g e e c c e n t r i c i t y (No. 36 and No. 3 7 ) . I n t h e s e c a s e s
c a r e was t a k e n t o e n s u r e t h a t t h e e x p e c t e d t e n s i o n w o u l d
o c c u r on t h e s i d e p r e v i o u s l y u n d e r c o m p r e s s i o n .
S p e c i a l T e s t s
Two c o n t r o l t e s t s were a l s o c a r r i e d out as f o l l o w s :
a) A t e s t t o e s t a b l i s h t h e i n f l u e n c e of p o s s i b l e s m a l l
PHOTO 2. The Strut During Testing.
26.
e c c e n t r i c i t y i n t h e d i r e c t i o n p e r p e n d i c u l a r t o
b u c k l i n g . S t r u t No. 36 was so t e s t e d , once w i t h
1 / 8 i n . and once w i t h 1 1 / 8 i n . e c c e n t r i c i t i e s .
These were o b t a i n e d by t i l t i n g t h e s p e c i m e n r e l a t i v e
t o t h e b e a r i n g p l a t e (by means of t h e h o l d i n g s c r e w s )
u n t i l the r e q u i r e d e c c e n t r i c i t y was o b t a i n e d a t the
t o p . The t e s t f o r b o t h e c c e n t r i c i t i e s was c a r r i e d t o
u l t i m a t e l o a d , t h i s b e i n g p o s s i b l e b e c a u s e t he s t r u t
r e m a i n e d u n c r a c k e d ( b e i n g h i g h l y p r e s t r e s s e d ) . The
u l t i m a t e l o a d s f o r t h e s e two c o n d i t i o n s were 54.2 k i p s
and 57.2 k i p s . S i n c e t h e s e a r e w i t h i n a b o u t s i x p e r
c e n t , of e a c h o t h e r , no c o r r e c t i o n f o r p o s s i b l e
e c c e n t r i c i t y i n t h i s d i r e c t i o n was made.
F l e x u r a l modulus of f i v e s p e c i m e n s was a l s o e s t a b
l i s h e d by c a r r y i n g out b e n d i n g t e s t s f o r c o m p a r i s o n
w i t h t h e v a l u e s o b t a i n e d f r o m the c y l i n d e r t e s t s .
S t r u t s Nos. 34, 36, 3 7 , 3 8 and 39 were so t e s t e d . The
s p e c i m e n s were s u p p o r t e d on t h e i r w i d e r s i d e 15 i n .
f r o m t h e i r ends and l o a d e d w i t h one c o n c e n t r a t e d l o a d
a t t h e m i d s p a n . Two i n d i c a t o r d i a l s were p l a c e d on
b o t h s i d e s o f t h e s t r u t s a t t h e l o c a t i o n o f t h e l o a d ,
and t h e a v e r a g e of t h e two r e a d i n g s was t a k e n as a
measure o f the d e f l e c t i o n . I n o r d e r t o a v o i d c r a c k i n g
of t h e s p e c i m e n s t he l o a d i n g was c a r r i e d o n l y t o a
v a l u e w h i c h p r o d u c e d a maximum t e n s i o n s t r e s s o f
200 p s i . The c o n c e n t r a t e d l o a d was a p p l i e d i n 250 l b .
27.
i n c r e m e n t and l o a d d e f l e c t i o n c u r v e s were drawn. The
p l o t s f e l l a l o n g a s t r a i g h t l i n e i n d i c a t i n g t h a t t h e
s e c t i o n s d i d n o t c r a c k d u r i n g t e s t i n g . From the
o b s e r v e d l o a d and c o r r e s p o n d i n g d e f l e c t i o n r e a d i n g s
t h e modulus was c a l c u l a t e d . O n l y f i v e t e s t s were so
c a r r i e d o u t .
C y l i n d e r T e s t s
A B a l d w i n H y d r a u l i c T e s t i n g M a c h i n e t e s t e d t h e c y l i n d e r s
a t t h e t i m e of l o a d i n g . F o r each c y l i n d e r a s t r e s s - s t r a i n
c u r v e was e s t a b l i s h e d , b u t the c o m p r e s s o m e t e r ( s t r a i n -
gauge) was always- removed when t h e c o n c r e t e s t r e n g t h a p p r o a c h
ed i t s e x p e c t e d u l t i m a t e v a l u e , so t h a t t h e u l t i m a t e s t r a i n
was n o t o b t a i n e d .
V I . TEST RESULTS
Gene r a l
• Tb/e" r e s u l t s o f the^'te'Sts .are' g i v e n 1 an' T a b l e , Li?r, and
g r a p h s o f t h e c r i t i c a l l o a d s o b t a i n e d by t h e S o u t h w e l l 15 16
method, ' d i s c u s s e d i n C h a p t e r V I - 3 , a r e p l o t t e d
i n F i g u r e s . 5 , 6 and 7. I t i s n o t i c e a b l e t h a t i n s p i t e
o f t h e c a r e t o s i m u l a t e i d e a l l a b o r a t o r y c o n d i t i o n s
t h e v a l u e s have c o n s i d e r a b l e s p r e a d . F o r z e r o e c c e n
t r i c i t y t h e y v a r y b e t w e e n 5 8 . 2 k i p s and 7 8 . 0 k i p s , and
f o r 0 . 3 i n . l o a d e c c e n t r i c i t y b e t ween 4 6 . 0 k i p s and
6 2 . 3 k i p s . I n o r d e r t o e l i m i n a t e the e f f e c t o f d i f f e r e n t
m o d u l i on t h e c r i t i c a l l o a d a l l v a l u e s o b t a i n e d f r o m t h e
S o u t h w e l l P l o t s were c o n v e r t e d t o v a l u e s c o r r e s p o n d i n g
t o an i d e n t i c a l m o d u l u s , a r b i t r a r i l y c h o s e n . T h i s
a r b i t r a r i l y c h o s e n v a l u e was s e t a t E' = 3 .320 k s i , a
v a l u e 5$ l e s s t h a n t h e one o b t a i n e d f r o m t h e ' l o w e s t
c y l i n d e r t e s t r e s u l t , i n o r d e r t o a r r i v e a t a c o n v e r s i o n
f a c t o r a l w a y s l e s s t h a n one. The c o n v e r s i o n was made
l i n e a r by m u l t i p l y i n g t h e c r i t i c a l l o a d s , o b t a i n e d f r o m
t h e S o u t h w e l l P l o t s , by t h e r a t i o o f E' = 3 ,320 k s i t o
th e m o d u l i o b t a i n e d f r o m the c o r r e s p o n d i n g s t r e s s - s t r a i n
c u r v e s o f t h e c y l i n d e r t e s t s ( s e e C h a p t e r V I - 4 ) . T h i s
r a t i o i s d e n o t e d i n T a b l e I I I as oc' . The c o n v e r t e d
c r i t i c a l l o a d v a l u e s a l s o show a s p r e a d b e t w e e n 43.7 k i p s
and 58.7 k i p s f o r t h e c e n t r a l l y l o a d e d s t r u t s , and be
tween 38 .2 k i p s and 56.7 k i p s f o r t h o s e w i t h 0 . 3 i n .
o < O _)
<
d o
70
A C T U A L CRITICAL LOADS V*. p % F<9K A L L 6PECI/WEM^ TESTED WITH O i O.*? ECCENTRICITIES CONVERTED CRITICAL LOADS » 11 11
AVEieA^E.'.4>.9
A 2 0.4 1.0 F i g . 5 C r i t i c a l Loads f o r Specimens w i t h Z e r o and 0.3 i n , .-2 |.T
E c c e n t r i c i t i e s . P 7 ° IV)
< 0 _ l
< 0
A C T U A L CRITICAL L O A D S V*. p & FOfc < ? P E C I A A E N 6 T E S T E D C O N C E N T R I C A L L Y C O N V E ^ T E P CRITICAL LOAE?4> n « » n . n
AV E K,A4 £ i 6 5 , £8
AVEfcAqe.: 48.2.
o.2 OA o.b o.e> \.o \.t py* F i g . 6 C r i t i c a l Loads f o r Specimens w i t h Z e r o E c c e n t r i c i t y O n l y .
< A C T U A L CRITICAL L O A D S fO$L S p E C I A A E N T E S T E " O W I T H O.h E C C E N T R I C I T Y
-J C O N V E R T E D CRITICAL L<9AD€» » " •• n
P i g . 7 C r i t i c a l Loads f o r S p e c i m e n s w i t h 0 . 3 i n . E c c e n t r i c i t y O n l y .
32. e c c e n t r i c i t y .
Table I I I shows the t e s t specimens d i v i d e d i n t o f i v e
main groups a c c o r d i n g to t h e i r s t e e l r a t i o s , and w i t h i n
these groups s e p a r a t e d a c c o r d i n g to the l o a d e c c e n t r i c i t i e s
used under the heading Test Data. There i s a l s o r e f e r e n c e
to the amount of s t e e l and the c o r r e s p o n d i n g i n i t i a l s t r e s s ,
and Column 6 shows the time i n days which e l a p s e d between
c a s t i n g and t e s t i n g .
T a b u l a t e d O b s e r v a t i o n s
Two c h a r a c t e r i s t i c l o a d r e a d i n g s are shown i n Table I I I .
Under Column 8 l o a d s c o r r e s p o n d i n g to the l a s t r e a d i n g at
which l a t e r a l d e f l e c t i o n c o u l d be observed are shown as
P ' . The l a t e r a l d e f l e c t i o n c o r r e s p o n d i n g to P ' i s r e c o r d e d
as S under Column 9. The u l t i m a t e l o a d , as r e c o r d e d by the
machine d i a l , d e s i g n a t e d P ^ , i s i n Column 7. I n v a r i a b l y t h i s
l o a d i s l e s s than a f u l l increment g r e a t e r than P ' .
In a l l cases of specimens w i t h zero and 0.3 i n .
e c c e n t r i c i t i e s , when the l o a d approached i t s u l t i m a t e P
v a l u e , the r a t e of the l a t e r a l movement of the c e n t r e of the
s t r u t suddenly i n c r e a s e d , and at t h i s p o i n t no f u r t h e r
d e f l e c t i o n r e a d i n g s were p o s s i b l e . Meanwhile the d i a l
i n d i c a t o r reached the maximum r e a d i n g and then the l o a d
dropped to a v a l u e at which the l a t e r a l movement a l s o
stopped. The s t r u t s kept r e s i s t i n g t h i s reduced l o a d and
the c o r r e s p o n d i n g d e f l e c t i o n s v a r i e d *;between 0.6 i n . and
3.5 i n . depending on the nat u r e of the b u c k l i n g .
Most of the s t r u t s w i t h s m a l l percentage of s t e e l
T A. O e. P V A T I c?K<5 C A- t . CU L As T 1 <S> SJ S> 1. 3. 4-. 5. 7. \o. II . VL. 13. I4- 15. 16. 17- \e>. 1 19. 'LO.
MIC P i i "co T Pu p' S
r l
\- ao <3| Per r c - ) 1
OC oc'fcr — % IN. psi. IN. IN. IN- ICS I. PSI. psi- —
,1 0 0 .23 1-5/16 328 86 66.0 62 . 5 . 11 ^8973 .094 .01 5 72.0 4833 124 3048 3698 . 2398 .69 49.7 1 2 75 54.2 52.5 .58 8770 .063 . 1 27 63.O 4683 1 24 2555 561 5 -T545 .71 44.7
67.5 47.2 1 7 0.1 77 32.9 31 .5 .47 7652 .280 .212 46.0 401 7 1 31 1 684 3479 -.111 .83 38.2 24 97 37.4 36.0 .57 6509- -.117 .290 54.0 3638 1 28 1 681 4271 -'909 .91 49. 1 24 37.4
50 ;o 43.7 25 0.5 96 12.1 12.0 .65 7087' -. 1 25 - - 4093 1 37 789 2609 -1 0,31 -29 96 10.7 10.0 .43 6448 . 1 32 - - 3685 1 37 748 2348 - 852 - -31 100 11.6 11.0 .48 - .000 - - - 1 37 789 2609 -1 031 - -
1 8 0 .45 1-7/6 635 76 58.9 57.5 .20 8328 .063 .036 69.0 4595 1 25 3020 41 70 1 870 .73 50.4 1-7/6 76 48.4 47.5 .29 7290 .01 6 .067 58.2 4407 1 26 2540 3980 1 280 .75 43.7 76 48.4 47.5 .29
63.6 47. 1 1 5 0.1 77 32.9 32.5 .62 7652 .074 .31 2 50.0 401 7 1 31 1 964 4484 ' - 556 .83 41 .5 35 68 41 .0 40.5 .65 7397 . 1 02 . 200 54.0 41 1 3 1 29 2293 5153 - .567 .81 43. 7 35 41 .0 40.5 .65 7397
52.0 -1 461
42 . 6 28 0.5 96 12.5 12.5 .70 6448 . 1 40 - - 3685 1 36 839 31 39 -1 461 - -30 1C0 12.5 12.0 .53 - . 1 25 - - - 1 37 830 2860 -1 200 — -1 1 0 .60 1 -1/2 . 840 86 65.0 62 . 5 .22 8973 .055 .020 67.5 4833 1 24 3460 4730 21 90 .69 46.6 1 4 75 ' 57.5 55.0 .70 8770 .063 .060 62.5 4683 1 26 31 50 6610 - 3 1 0 .71 44.4 1 4 75 ' 57.5 55.0 .70 8770 .063
65.0 45.5 23 0.1 97 37.4 36.0 .55 6509 .047 .260 52.9 3638 1 28 2330 4750 - 90 .92 48.7 26 96 49'. 0 •49.0 .51 7087 . 1 88 .092 50.0 4093 1 27 2807 5257 - 357 .82 41 .0 26 96 49'. 0 •49.0 .51 7087 .092
51 .5 44.8 38 0.5 64 13.9 13.0 .65 7228 .110 - - 3972 136 • 871 3210 -1 469 - -39 65 14.3 14.0 ..75 7228 . 1 25 - - 3972 136 91 3 3533 -1 707 — —
TABLE I I I ' . - TEST RESULTS ' ( C o n t i n u e d ) ^
D A. • T A U U A T I O N S 1.. '2. 3 . 4-- 5 . (o. 7. 8. IC II • 13. I4-- 15. \<o. 17- 10. \o>- io .
MK r ( ) 'co T Pu p' 5 o Qo Per Et "su (To <*fcr
— % I KJ - P6I. DAY I4IPS KIPS IN- psi. IN. iN- KIPS KSI. Psi. PSI- psi . — KIPS 9 0 .91 2-7/6 1 275 86 62 „ 5 6 0 . 0 .34 8973 . 0 0 0 .040 6 7 . 3 4833 1 25 3320 L 5200 1 440 .69 4 6 . 4
1 3 1D9 72,5 7 0 . 0 . 1 0 8973 .055 .01 2 7 8 . 0 4683 1 22 41 35 4790 3480 .71 55 .4 34 64 57 . 2 5 5 . 0 . 3 8 721 3 .079 ,030 6 0 . 0 4523 1 25 3450 5330 1 570 .74 4 4 . 4 36 61 54 . 2 52.5 .32 7388 . 1 25 . 1 02 6 8 . 2 3861 1 24 3495 5455 .2045 .86 5 8 . 7
68 .4 5 1 . 2 1 6 0 . 1 77 4 0 . 1 39.0 .70 7652 .440 .310 5 8 . 2 401 7 1 28 2840- 6090 - 410 .83 48.. 3 33 53 34 .3 3 4 . 0 .44 6627 -.226 .225 47 .5 3730 129 2600 4720 - 480 .89 4 2 . 3
52 .9 4 5 . 3 36 0 .5 62 15 .2 1 5 . 0 .89 7388 .01 7 - - 3861 1 36 2990 3945 -2035 - -1 9 20 37
0 1 . 2 0 2 - 1/2" 1680 104 65 61
60 ,0 57 .9 43.6
60 .0 57.5 42 ,5
.06
.39
.43
8328 7290 7^,88
.118
. 0 0 0
.250
.025
.01 9
.1 94
6 2 . 8 6 0 . 9 5 9 . 0
4595 4407 3861
1 24 123 1 28
4070 3880 3365
5205 581 0 5995
2935 1 950
735
.73
.75
. 86
45 . 8 4 5 . 7 50 ,7
1 9 20 37
104 65 61
60 ,0 57 .9 43.6
60 .0 57.5 42 ,5
.06
.39
.43
.025
.01 9
.1 94 6 0 . 9
4595 4407 3861
47 .4 32 27
0 . 1 53 96
3 7 . 8 46 .0
36 . 0 4 5 . 0
.47
.70 6627 64.4R
.210
.070 . 1 62 .278
4 9 . 3 6 2 . 3
3730 3685
1 28 1 26
31 1 5 3430
5875 7220
- 355 - 360
.89
.91 4 3 . 9 56 .7 32
27 53 96
3 7 . 8 46 .0
36 . 0 4 5 . 0
.47
.70 . 1 62 .278
5 5 . 8
3730 3685
5 0 . 3 22 37
0 . 5 97 6S
18,0 17.3
18 .0 17 .0
. 8 8 1.06
6509 7388
.090
. 320 3638 3861
134 1 36
1 075 998
4655 41 1 e
-2505 -2122
TABLE I I I ' , - TEST RESULTS
3 5 .
c r a c k e d a f t e r t h e l o a d a p p r o a c h e d i t s u l t i m a t e v a l u e . As
a c o n s e q u e n c e of t h e c r a c k i n g t h e s e s t r u t s s u d d e n l y de
f l e c t e d 2 i n . t o 3.5 i n . ( s e e an example i n P h o t o 3 ) .
Whereas s t r u t s w i t h l a r g e p e r c e n t a g e of s t e e l d i d n o t c r a c k
and s t o p p e d m o v i n g l a t e r a l l y a t 0.6 i n . t o 1.2 i n . These
were a l l s t r u t s p r e s t r e s s e d w i t h a t l e a s t 1 - 1/2 i n . d i a .
s t r a n d f o r no e c c e n t r i c i t y , and 2 - 7/16 i n . d i a . s t r a n d s
f o r 0.3 i n . e c c e n t r i c i t y . The l o a d d r o p p e d t o a p p r o x i m a t e
l y o n e - t h i r d o f i t s u l t i m a t e v a l u e f o r t h e low p r e s t r e s s e d
s t r u t s w h i c h c r a c k e d , and t o 80 - 90$ of i t s u l t i m a t e v a l u e
f o r t h e h i g h p r e s t r e s s e d ones w h i c h d i d n o t c r a c k . A l l
t h e s e o b s e r v a t i o n s t o o k p l a c e w h i l e t h e machine was n o t i n
m o t i o n .
The s t r u t s w i t h 1.5 i n . e c c e n t r i c i t y b e h a v e d d i f f e r e n t
l y t h a n t h e ones i n t h e f i r s t two g r o u p s . L a t e r a l d e f l e c
t i o n s were l a r g e r t h a n i n t h e o t h e r s p e c i m e n s a t a l l v a l u e s
of l o a d , and when t h e u l t i m a t e l o a d was r e a c h e d , and t h e
l o a d i n g s t o p p e d ;then no f u r t h e r d e f l e c t i o n t o o k p l a c e . I n
most c a s e s t h e l o a d was n o t c o n t i n u e d i n o r d e r t o s a v e t h e
s p e c i m e n s .
F i g u r e s 8/1 t o 8/4 show t h e l o a d d e f l e c t i o n c u r v e s o f
s p e c i m e n s l o a d e d w i t h 1.5 i n . e c c e n t r i c i t y , and F i g u r e 9
shows t h i s g r a p h f o r s t r u t No. 2-9 ( 3 2 8 p s i p r e s t r e s s )
w h i c h was t e s t e d t o d e s t r u c t i o n and f a i l e d i n t e n s i o n
when 3.0 i n . d e f l e c t i o n was r e a c h e d (Photo' 4 ) . S t r u t
No. 22 was a l s o t e s t e d t o d e s t r u c t i o n ; h owever, t h i s
s t r u t w h i c h was h i g h l y p r e s t r e s s e d (1 ,680 p s i ) f a i l e d i n
36.
PHOTO 3. B u c k l e d S t r u t w i t h Low P r e s t r e s s .
•co
IB
•4
<
4
G
•
.«5 .U> .7 1.0
F i g . 8/ L o a d - d e f l e c t i o n C u r v e s of S p e c i m e n s w i t h 1 .5 i n . E c c e n t r i c i t i e s .
io
18
\o>
14
t - 10
- 8 d
< 0
1
o 0
STR UT ".
-e—« *
.2 .2) -4 -5 .6 -7 DEFLECTION "5" (IN.)
38.
p1 * 1-2.5^
eo
ie
a. 14
10
G e l
4
(9
STR: UT"? »<?»
I ~ %
^
.1 .'L .3 .4 .5 .7 D fc F U E-d-T IC>M " § " ( I N . )
F i g . 8/2 L o a d - d e f l e c t i o n C u r v e s o f S p e c i m e n s w i t h 1.5 i n . E c c e n t r i c i t i e s .
P 1 • l^.O
to
CL \0
_»
4
2
F i g ,
.4 .5 -7 .e> P & P L - £CJ\OM e> ( IN.)
8/3 L o a d - d e f l e c t i o n C u r v e s o f Sp e c i m e n s w i t h 1.5 i n . E c c e n t r i c i t i e s .
_ lo
< /
4
-2
-2"
-
'•2. .?> .4 .5 .7 P E F L E - C T I ^ N "c5 11 (IN-)
-6 .<T*
Pu *
p1 * \e>.o£-
F i g . 8/4 L o a d - d e f l e c t i o n C u r v e s o f S p e c i m e n s w i t h 1.5 i n . E c c e n t r i c i t i e s .
" p " ST&vj N£ # 9 (e * l .£ I M . )
PHOTO 4. T e n s i o n F a i l u r e o f S p e c i m e n No. 2 9 ,
c o m p r e s s i o n a t 1.7 i n . d e f l e c t i o n ( s e e P h o t o 5 ) . T h i s
i n d i c a t e d t h a t t h e c o m p r e s s i v e f i b r e s t r e s s had r e a c h e d
i t s u l t i m a t e v a l u e due t o the c o m b i n a t i o n of t h e b e n d i n g
moment, e x t e r n a l l o a d and t h e p r e s t r e s s i n g f o r c e .
I t was o b s e r v e d t h a t s t r u t s No. 28 and No. 29 c r a c k e d
d u r i n g t e s t i n g a t t h e t e n s i o n s i d e , 6 i n . f r o m t h e b o t t o m
and t h e t o p , a t t h e l o c a t i o n where the f a s t e n i n g a n g l e
i r o n o f t h e h o l d i n g d e v i c e was s e t . No s u c h v i s i b l e
c r a c k s c o u l d be o b s e r v e d f o r t h e r e s t o f t h e s p e c i m e n s .
Column 10 shows t h e a v e r a g e u l t i m a t e s t r e n g t h o f t h e
c o r r e s p o n d i n g f o u r c y l i n d e r s . I n s p i t e o f t h e h i g h l y
c o n t r o l l e d o p e r a t i o n t h e s e v a l u e s v a r i e d b e t w e e n 6,509
p s i • a n d 8,973 p s i .
I n Column 11 t h e o b s e r v e d i n i t i a l c u r v a t u r e of the
s p e c i m e n s a r e shown, d e n o t e d by t h e s y m b o l a Q . These
v a l u e s a r e t h e a v e r a g e s o f t h e f o u r d i s t a n c e s b e t w e e n t h e
e s t a b l i s h e d a x e s and t h e c e n t r e s of t h e s e c t i o n s measured
a t t h e ends of t h e s t r u t s ( s e e C h a p t e r V - 3 ) .
T a b u l a t e d C a l c u l a t i o n s
A) C r i t i c a l L o a d s . - I n Columns 12 t o 20 of T a b l e
I I I a r e shown c a l c u l a t e d v a l u e s as f o l l o w s . The c r i t i c a l
l o a d s were o b t a i n e d by the S o u t h w e l l Method ' . T h i s
method e l i m i n a t e s t h e e f f e c t of t h e i n i t i a l c u r v a t u r e and
th e d i s c r e p a n c i e s of p l a c i n g t h e l o a d s , p r o v i d e d t h a t :
a) t h e d e f l e c t i o n s a r e s m a l l enough t o j u s t i f y t h e
44.
PHOTO 5. C o m p r e s s i o n F a i l u r e o f S p e c i m e n No. 22.
a p p r o x i m a t i o n i n t h e e x p r e s s i o n f o r t h e c u r v a t u r e ,
w h i c h i s u s e d t o d e r i v e t h e d i f f e r e n t i a l e q u a t i o n
of a c u r v e d b a r ( i n c o r p o r a t i n g a s m a l l i n i t i a l
c u r v a t u r e o f t h e b a r ) ;
b) t h e d e f l e c t i o n s a r e s m a l l enough t o p r e v e n t
i m p a i r m e n t of the m a t e r i a l d u r i n g t e s t i n g
( c r a c k i n g , y i e l d i n g ) ;
c ) b o t h the d e f l e c t i o n and l o a d a r e l a r g e enough t o
make t h e d e t e r m i n a t i o n o f the r a t i o of t h e
d e f l e c t i o n t o t h e l o a d p o s s i b l e w i t h s u f f i c i e n t
a c c u r a c y ;
d) t h e d i s t a n c e o f t h e i n i t i a l d e f l e c t i o n of t h e
c e n t r a l l i n e f r o m t h e l i n e o f t h r u s t s h o u l d
v a n i s h a t e i t h e r end of t h e s t r u t , o r a t l e a s t be
as s m a l l as p o s s i b l e .
I f t h e s e c o n d i t i o n s a r e met t h e r e l a t i o n s h i p b e t w e e n t h e
l o a d , i n i t i a l c u r v a t u r e and the d e f l e c t i o n c o r r e s p o n d i n g
t o t h e l o a d c a n he e x p r e s s e d by the e q u a t i o n
O = a o ............ a.) P /P -1
c r
The v a l u e s o f S c a n be p l o t t e d a g a i n s t t h e r a t i o h/?
g i v i n g a s t r a i g h t l i n e w h i c h i n t e r s e c t s t h e c o o r d i n a t e
e>/p = 0 a t t h e d i s t a n c e a f r o m t h e o r i g i n . Then t he o
i n v e r s e s l o p e o f t h i s l i n e g i v e s t h e c r i t i c a l l o a d and
t h e d i s t a n c e r e p r e s e n t s the i n i t i a l c u r v a t u r e .
46.
.Timoshenko, i n h i s " T h e o r y of E l a s t i c S t a b i l i t y " ,
C h a p t e r 4.1, p. 141, f u r t h e r d e v e l o p s t h e S o u t h w e l l P l o t
method f o r use when s m a l l l o a d e c c e n t r i c i t y i s c o m b i n e d
w i t h i n i t i a l c u r v a t u r e . Then t h e e q u a t i o n a.) may b e '
w r i t t e n as S - - ( a + 4e / l t ) 1 . . . . . . . . . . . b . ) 0 P /P-1 c r
T h e r e f o r e , an a t t e m p t was made t o use t h e S o u t h w e l l
Method f o r f i n d i n g t h e c r i t i c a l l o a d s f o r a l l s p e c i m e n s
h a v i n g z e r o and 0.3 i n . l o a d e c c e n t r i c i t i e s . The c o m b i n e d
e f f e c t o f t h e i n i t i a l l o a d e c c e n t r i c i t y and t h e i n i t i a l
c u r v a t u r e ( i n c o r p o r a t i n g a l l m a n u f a c t u r i n g i m p e r f e c t i o n s ) ,
d e n o t e d by the l e t t e r a^ and t a b u l a t e d i n Column 12, a r e
t h e v a l u e s t a k e n f r o m t h e s e S o u t h w e l l P l o t s drawn f o r e a c h
s p e c i m e n . V a l u e s o f a^ i n Column 12 s h o u l d be e q u a l t o
t h e measured v a l u e s a Q i n Column 11 p l u s 4e/TC .
T h e r e were t h r e e s p e c i m e n s (No. 24, No. 25, and No.
33) w h i c h b u c k l e d o p p o s i t e to t h e i r c u r v a t u r e . Two of them
were l o a d e d w i t h 0.3 i n . e c c e n t r i c i t y and t h e t h i r d w i t h
1.5 i n . e c c e n t r i c i t y . The d i f f e r e n c e s b e t w e e n t h e v a l u e s
a.| and (a + 4,e/fC ) must be a t t r i b u t e d t o t h e e x p e r i m e n t a l
e r r o r i n p l a c i n g t h e l o a d , m e a s u r i n g a , and t o t h e f a c t
t h a t t h e e c c e n t r i c i t y e may be of same or o p p o s i t e s i g n t o
t h e v a l u e o f a ( s e e P i g u r e 1 0 ) . 0 Some c h a r a c t e r i s t i c S o u t h w e l l P l o t s a r e shown i n
P i g u r e 11. F i g u r e s 11 / a , 1 l / b , and 1 l / c show e x a m p l e s of the
S o u t h w e l l P l o t done f o r s t r u t s Nos. 10, 20 and 17 h a v i n g
47.
P I P P ^ ^ M T U0ADIN4 C<9ND!TI0N^ P0K. eaU/SsL ZCC£tilZ\C\V&>. (LATELY EXA^ESLA-TEp)
P. ,p
fclGHTlU^ M O M E N T
0.3 I M .
C E N T R O I P A L A X I 6
£ I 4 H T I M 4 AAOMEKJT D I A C j & A M
* IN.
.SPECIMEN
L -ESTASLIMMED AX|£
LOADING OPNPITI^K 2
F i g . 10. The two Types of Load E c c e n t r i c i t i e s u s e d .
48.
S T R U T 10.
o.oob
5(114.) F i g . 11/a. T y p i c a l S o u t h w e l l P l o t s ,
STieUT 20.
F i g . 11/b. T y p i c a l S o u t h w e l l P l o t s .
. 0 0 4
o
50.
S T R U T 17
Per * °>'^ s 4(r> ^ .00S = =
a{ * 0.112 (IN.)
, 3 - 4 - .5.
S ( l M )
F i g . 1l/c. T y p i c a l S o u t h w e l l P l o t s .
51 .
e c c e n t r i c i t i e s .015 i n . , .019 i n . and .212 i n C r e s p e c t
i v e l y . The p l o t t e d v a l u e s f o l l o w q u i t e a c c u r a t e l y t h e
s t r a i g h t l i n e i n the v i c i n i t y of t h e h i g h e r P v a l u e s .
F i g u r e 11/d ( s t r u t No. 32) i s a s i m i l a r example where,
t h o u g h t h e p l o t s show a s t r a i g h t l i n e p a t t e r n , t h e l a s t
two p l o t s , one of w h i c h i s t h e P , t e n d t o d e v i a t e f r o m u
t h e s t r a i g h t l i n e . F i g u r e 11/e i s an example where o n l y
t h e u l t i m a t e P v a l u e f a l l s above t h e s t r a i g h t l i n e , - an u i n d i c a t i o n t h a t t h e b u c k l i n g a l r e a d y t o o k p l a c e . I t i s
a l s o n o t e w o r t h y t h a t a t t h e b e g i n n i n g of t h e l o a d i n g t h e
p l o t t e d p o i n t s a r e s c a t t e r e d , b e c a u s e a t t h i s r a n g e t h e
a s s u m p t i o n s on w h i c h t h e S o u t h w e l l method i s b a s e d a r e
n o t s a t i s f i e d . A good example i s t h e p l o t of s t r u t
No. 17 i n F i g u r e 1 1 /c .. F u r t h e r m o r e , a c c o r d i n g t o t h e
e x a c t a n a l y s i s t h e s t r u t may f i r s ' t d e f l e c t i n one d i r e c
t i o n and l a t e r on s u d d e n l y b u c k l e i n t h e o p p o s i t e d i r e c
t i o n . (See T i moshenko "Theory of E l a s t i c S t a b i l i t y " C h a p t e r
4, Page 191, and C h a p t e r 1, Page 1 4 ) . A good example of t h i s
was t h e t e s t of s t r u t No. 13 w h i c h f i r s t d e f l e c t e d e a s t
u n t i l 45 k i p s l o a d was r e a c h e d , t h e n s u d d e n l y d e f l e c t e d
w e s t and f a i l e d a t 72.5 k i p s l o a d .
A f t e r t h e l o a d was removed a r e s i d u a l d e f l e c t i o n of
0.3 i n . e a s t was m e a s u r e d . W i t h t h i s i n i t i a l c u r v a t u r e t h e
s t r u t was r e l o a d e d and f a i l u r e o c c u r r e d a t 49.0 k i p s
l o a d . The S o u t h w e l l P l o t was drawn f o r b o t h c a s e s and
t h e c r i t i c a l v a l u e s 78 k i p s and 76 k i p s o b t a i n e d r e s p e c t
i v e l y . T h i s d o u b l e t e s t i s good e v i d e n c e t h a t t h e
F i g . 1 1 / d . T y p i c a l S o u t h w e l l P l o t s .
6_ o - (%
0\(o
.014
.012
.010
.006
.OOlo
.004
j u O
6 T£UT 12 53.
1 — - 0
r
U t 0 q
• 3 i e —
r * CO 5
a, <• 7 ( NO
.2 . 3 •4 5 ( INCHED
.7 ,6
F i g . 11/e. T y p i c a l S o u t h w e l l P l o t s
54.
S o u t h w e l l P l o t i s u s e f u l t o e s t i m a t e t h e c r i t i c a l l o a d
v a l u e .for s t r u t s w i t h any i n i t i a l c u r v a t u r e p r o v i d e d
t h a t t h i s c u r v a t u r e i s s m a l l .
A n o t h e r r e a s o n f o r t h i s e r r a t i c p l o t was t h a t a t t h e
b e g i n n i n g t h e s t r u t s moved u n t i l t h e y f o u n d t h e i r f i n a l
p o s i t i o n i n t h e m a c h i n e . As a l r e a d y m e n t i o n e d i n
C h a p t e r V-2, t h e t o p head moved a p p r o x i m a t e l y 0.02 t o
0.03 i n . a t t h e b e g i n n i n g o f t h e l o a d i n g w h i c h l e a d s t o
f a l s e d e f l e c t i o n m e a s u r e m e n t s. B u t t o w a r d s t he end o f
t h e l o a d i n g t h e movement d i d n o t o c c u r and t h u s d i d n o t
a f f e c t t h e v a l i d i t y o f t h e r e a d i n g s .
P l o t s o f f i v e s p e c i m e n s f r o m t h e f i r s t two g r o u p s ,
h o w e v e r , d i d n o t show c l e a r s t r a i g h t l i n e p a t t e r n ( s t r u t s
Nos. 13, 19, 26, 27 and 3 3 ) . I n t h e s e c a s e s two o r more
l i n e s c o u l d be drawn w i t h e q u a l j u s t i f i c a t i o n . P i g u r e
1 l / f shows t h e S o u t h w e l l P l o t o f No. 33 as an 'example.
A l t h o u g h i t was d o u b t f u l t h a t t h e c r i t i c a l l o a d s ob
t a i n e d f r o m t h e S o u t h w e l l P l o t s f o r s p e c i m e n s w i t h 1.5 i n .
l o a d e c c e n t r i c i t y w o u l d y i e l d r e l i a b l e r e s u l t s , an a t t e m p t
was made t o draw t h e S o u t h w e l l P l o t s f o r t h e s e s p e c i m e n s as
w e l l . F i g u r e s 11/g, 11/h and 1 l / i show t h r e e e x a m p l e s .
The a v e r a g e r a t i o o f P t o P c r i s 0.83 f o r t h e g r o u p ,
w i t h " z rero7 and 1 0 . 73' t or' t h e gr'oupr w i t h " 0 . 3 'in' , ' " e c c e n t r i c i t y .
The ' r a t i o s * do n o t " a p p e a r 1 t o ̂ depend '.'on t h e " s t e e l ' ' r a t i o as
s h o w h " " i n - F i g u r e 12.
S T K U T 33 '
F i g . 1 1 / f . T y p i c a l S o u t h w e l l P l o t s .
F i g . 11/g. T y p i c a l S o u t h w e l l P l o t s .
F i g . 1 1 / i . T y p i c a l S o u t h w e l l P l o t s .
F i g . 12. V a r i a t i o n of R a t i o P /P w i t h S t e e l C o n t e n t . u c r
Under the main h e a d i n g o f " c a l c u l a t i o n s " i n T a b l e I I I
a r e shown t h e v a l u e s of the t a n g e n t m o d u l i o b t a i n e d a t
t h e a n t i c i p a t e d c o m p r e s s i v e s t r e s s l e v e l , g r a p h i c a l l y
e s t a b l i s h e d f r o m t h e s t r e s s - s t r a i n c u r v e s ( s e e C h a p t e r
' V I - 4 ) . They a r e a v e r a g e s o f t h e c o r r e s p o n d i n g f o u r
c y l i n d e r t e s t r e s u l t s and t h e i r v a l u e s v a r y b e t w e e n
3,832 k s i and 4,833 k s i .
B) S t r e s s e s . - I n T a b l e I I I Columns 16, 17, and 18
show t h e c a l c u l a t e d s t r e s s e s c o r r e s p o n d i n g t o t h e P '
v a l u e s . The P v a l u e s c o u l d n o t be u s e d f o r t h e s e u c a l c u l a t i o n s b e c a u s e t h e c o r r e s p o n d i n g d e f l e c t i o n
measurements were n o t a v a i l a b l e , as a l r e a d y n o t e d . I n
Column 16 t h e a v e r a g e c o m p r e s s i v e s t r e s s e s , d e n o t e d by
(3c due t o t h e p r e s t r e s s i n g f o r c e and P ' a r e t a b u l a t e d .
The p r e s t r e s s i n g f o r c e s d e c r e a s e due t o t h e s u p e r i m p o s e d
P ' l o a d s and t h e i r v a l u e s , d e n o t e d by t h e l e t t e r s f , J su
a r e shown i n Column 15. I n o r d e r t o c a l c u l a t e t h e
e x t r e m e f i b r e s t r e s s e s , d e n o t e d by C 3 { ^ + ' on t h e c o m p r e s s
i o n s i d e and (j on the t e n s i o n s i d e , t h e moment due to'
th e l o a d P ' a c t i n g a t t h e l e v e r arm (& + oxt) was s u p e r
i m p o s e d on (j & and t h e r e s u l t s t a b u l a t e d i n Columns 17
and 18 r e - s p e c t i v e l y . When s t r e s s l o s s e s were c a l c u l a t e d
t h e c o r r e s p o n d i n g E^ v a l u e s were t a k e n i n t o a c c o u n t and
the v a l u e E g was t a k e n t o be 27,800 k s i f r o m t h e a c t u a l
m i l l c e r t i f i c a t e s . Thus t h e e f f e c t o f the v a r i a t i o n i n n
i s a l s o i n c o r p o r a t e d i n t h e s e v a l u e s . The c a l c u l a t i o n s
assumed an u n c r a c k e d s e c t i o n , u s i n g t h e g r o s s s e c t i o n of
61 .
t h e s t r u t i n s t e a d of t h e t r a n s f o r m e d s e c t i o n . T h i s
a p p r o x i m a t i o n g i v e s an e r r o r o f l e s s t h a n 1$. The e f f e c t
o f t h e f r i c t i o n o f t h e h i n g e s was a l s o i g n o r e d .
F i b r e s t r e s s e s of s t r u t s w i t h 1.5 i n . e c c e n t r i c i t y -
were a l s o c a l c u l a t e d u s i n g e l a s t i c a n a l y s i s f o r v a l u e s of
P u/2 a t w h i c h t h e s p e c i m e n s s t i l l b e h a v e d e l a s t i c a l l y .
The v a l u e s a r e compared i n T a b l e i v / a w i t h s t r e s s e s
c a l c u l a t e d by a m o d i f i e d S e c a n t f o r m u l a
A c + A c [ > p + 1/ \^TJ r \4E^r) j
3
d e v e l o p e d f o r p r e s t r e s s e d c o n c r e t e s t r u t s by B r e c k e n r i d g e .
I n u s i n g t h e m o d i f i e d s e c a n t f o r m u l a t h e v a l u e s were t a k e n
f r o m T a b l e I I I .
The e l a s t i c a n a l y s i s o f s t r e s s e s c o r r e s p o n d i n g t o t h e
u l t i m a t e l o a d ( T a b l e i v / b ) i n d i c a t e s t h a t a l l s p e c i m e n s i n
t h i s g r o u p c r a c k e d , and the b e h a v i o u r of the s t r u t s must
be a n a l y s e d i n e l a s t i c a l l y .
F i g u r e s 13/a and 13/b show t h e c u r v e s of t h e m o d i f i e d
s e c a n t f o r m u l a p l o t t e d f o r t h e t e s t s p e c i m e n s c o r r e s p o n d i n g
t o t h e s m a l l e s t and l a r g e s t p e r c e n t a g e of s t e e l and 4 , 3 0 0
k s i f o r t h e modulus o f c o n c r e t e .
C a l c u l a t i o n o f t h e M o d u l i
F i n a l l y , T a b l e I I I shows the m o d u l i , d e n o t e d by t h e
l e t t e r o b t a i n e d f r o m the s t r e s s - s t r a i n c u r v e s of the
t e s t c y l i n d e r s a t t h e a n t i c i p a t e d a v e r a g e c o m p r e s s i v e
s t r e s s o f 3,285 p s i , as a l r e a d y n o t e d . I n e a c h c a s e , t h e
v a l u e of t h e modulus i s t h e s l o p e o f t h e c h o r d b e tween
62.
a) S T R E S S E S D U E TO Pu/z
AAK,. P' S T R E S S CALCULATED F R O M OBSERVATION
STRESS C A L C U L A T E D * U S I N G E f i
S T R E S S CALCULATED* U S I N G Ef
AAK,. P' COMPRESSION TENSION COMPRESSION T E N S I O N WMpRESS IOM T E N D O N
AAK,.
% p 6 i . p s i . p e i . p6>i.
"25 29 31
.23 + 771 + 704 + 663
+ 401 + 404 + 4 8 9
+ 797 + 727 + 670
+ 369 + 379 + 472
+ 806 + 731 + 674
+ 360 + 377 + 464
28 30
. 4 5 + 1 061 + 851
+ 713 + 513
+ 1 078 + 1076
+ 678 + 679
+ 1 083 + 1082
+ 673 + 674
38 39
.60 + 1 341 + 1325
+ 933 + 905
+ 1 347 + 1 360
+ 8 6 8 + 866
+ 1 348 + 1365
+ 865 + 861
36 .91 + 1 692 + 1440 + 1 770 + 1325 4 1774 + 1 320
22 37
1 . 2 0 + -2 2 99 + 2472
+ 1715 + 1512
+ 2 3 4 5 + 2571
+ 1 625 + 1 404
+ 2368 + 2599
+ 1 602 + 1379 I
b) S T R . E S > S E S D I JB TO Pa I
25 29 31
• 23 + 2609 + 2348 + 2609
- 1031 - 852 - 1031
+ 2 9 9 5 + 1838 + 2618
- 1 333 - 1006 - 1042
+ -3084 + 2571 + 2700
- 1 41 9 - 1 079 - 1 1 20
28 30
. 4 5 , + - 3 139 + 2860
- 1461 - 1 200
+ 3509 + 3349
- 1233 - 1 1 09
+ 3648 + 3640
- 1372 - 1210
38 39
.60 + 321 0 + 3533
- 1469 - 1 707
+ 3797 + 4109
- 1072 - 1313
+ 3889 + 4245
- 1 1 71 - 1455
36 .91 + 3945 - 2035 + 4729 - 91 9 + 4820 - 1110
22 37
1 .20 + 4 6 5 5 + 4118
- 2 5 0 5 - 2 1 2 2
+ 6730 + 6675
- 2000 - 1 995
+ 7960 + 7835
~ 3240 - 3165
F H O M S E C A . N J T F O R - M U L A
TABLE I V . - COMPARISON OF STRESSES OBTAINED FROM THE TEST RESULTS WITH THOSE COMPUTED BY BRECKENRIDGE'S MODIFIED SECANT FORMULA
e * o. i (M ^j- S * OA I N .
e * 0.3 IN.
— e «• 0 . 0 I N . , ,
Sooo 5ooo
6
\oooo psi
(+)
F i g . 1 3/a. C u r v e s o f t h e S e c a n t F o r m u l a P l o t t e d f o r t h e S p e c i m e n s . cn
P i g . C u r v e s of t h e S e c a n t F o r m u l a P l o t t e d f o r t h e S p e c i m e n s .
t h e two p o i n t s on t h e c u r v e 855 p s i above and b e l o w t h e
v a l u e o f 3,285 p s i . T h i s i s t h e r a n g e o f a n t i c i p a t e d
s t r e s s e s u n d e r t e s t . A l t h o u g h t h e t e s t r e s u l t s i n
Column 16 showed t h a t t h e a c t u a l a v e r a g e c o m p r e s s i v e
s t r e s s i s 2,960 p s i i n s t e a d o f t h e a n t i c i p a t e d 3,285
p s i t h e r e - e v a l u a t i o n of t h e t e s t r e s u l t s was i g n o r e d .
The m o d u l i so o b t a i n e d a r e shown i n Column 14.
F i g u r e s 14/a and 14/b d e m o n s t r a t e two e x a m p l e s s h o w i n g
t h e above c h o r d as w e l l as t a n g e n t s a t z e r o s t r e s s and
a t 5,700 p s i , w h i c h i s t h e v a l u e of t h e h i g h e s t c o m p r e s s
i v e s t r e s s . F i g u r e 14/a i s a r e p r e s e n t a t i v e c y l i n d e r o f
a h i g h q u a l i t y c o n c r e t e w h i l e 14/b i s a r e p r e s e n t a t i v e o f
a l o w e r q u a l i t y .
T a b l e V shows t h e d i f f e r e n t m o d u l i . I n Column 4 a r e
t h e i n i t i a l t a n g e n t m o d u l i w h i c h were e s t a b l i s h e d by
v i s u a l l y f i t t i n g a l i n e a t t h e i n t e r s e c t i o n p o i n t o f t h e
s t r e s s - s t r a i n c u r v e and the a b s c i s s a . S i n c e t h e r e c o r d
i n g n e e d l e e x h i b i t e d many i r r e g u l a r i t i e s when the t e s t i n g
s t a r t e d t h e s l o p e of t h e t a n g e n t r e f l e c t s t h e s e u n c e r t a i n
t i e s .
Column 1 shows t h e age of t h e c y l i n d e r s . The f i g u r e s
i n t h e p a r e n t h e s i s d e n o t e t h e days of two c y l i n d e r s b r o k e n
a t a d i f f e r e n t t i m e c o r r e s p o n d i n g t o s p e c i m e n s t e s t e d
s e v e r a l d a y s a p a r t . Under t h e h e a d i n g E^, Column 6,
v a l u e s c a l c u l a t e d f r o m t h e b e n d i n g t e s t s a r e t a b u l a t e d .
Column 6 shows t h e v a l u e s - o b t a i n e d f r o m Pauw's 13 i 2r—
e q u a t i o n , E= 33w Jfr now recommended by
F i g . 14/a. T y p i c a l S t r e s s - s t r a i n C u r v e s f o r C y l i n d e r s .
fcfcpL-ICA Of T H £ * > T K ^ ^ - ^ T ^ A I M Of
Y
F i g . 14/b. T y p i c a l S t r e s s - s t r a i n C u r v e s f o r C y l i n d e r s .
68.
I 1 3 4 6 7
T fc Ec MARK- w . IC6I. M. 9-10-11 86 8973 4833' 5256 - 5625 4906
1 2-13-14 1 5-16-17 (104)
77
8777
7652
4683
4017
4953
4480
— 5567
5198
4886
4757 T8-T9 20-21
till) 65
8328 7290
4595 4407
4480 51 50
— 5422
5073 4838 4708
22-23-24 97 6509 3638 4300 : 3960 4794 4590 25-26 96 7087, 4093 4600 4740 5002 4670
27-28-29 96 6448 3685 4202 5100 4771 4579 30-31 - - - - — _
32-33 53 6677 3730 4576 4855 4617 34 64 721 3 4523 4980 5300 5046 4697 35 62 7397 41 1 3 4400 - 5093 4716
36-3^ 38-39 <P>
64
7388 7328
3861 3972
4230 4360
4890 • 4570
5107 5057
4722 4700
TABLE "V... -COMPARISON OF DIFFERENT MODULI
t h e A m e r i c a n and C a n a d i a n Codes, c o r r e s p o n d i n g t o a c t u a l
f ^ ' v a l u e s t a b u l a t e d i n Column 2. A c t u a l d e n s i t y m e a s ure-c ments showed t h a t t h e tpst c y l i n d e r s a v e r a g e d 148 l b s . / c u .
f t . and t h i s v a l u e was u s e d i n t h e c a l c u l a t i o n s .
F o r c o m p a r i s o n p u r p o s e s modulus c a l c u l a t e d f r o m 1 3
J e n s e n ' s f o r m u l a 6x106
J 1 + 2 0 0 0 / f c
a r e shown i n Column 7.
V I I . DISCUSSION OF TEST RESULTS
I n f l u e n c e o f S t e e l R a t i o on t h e C r i t i c a l Load
The f i r s t q u e s t i o n t o be a n s w e r e d i s w h e t h e r o r n o t
t h e c r i t i c a l l o a d of a p r e s t r e s s e d c o n c r e t e s t r u t depends
on t h e amount o f p r e s t r e s s i n g . F i g u r e 5 shows t h e t e s t
r e s u l t s i n a g r a p h where c r i t i c a l l o a d s , o b t a i n e d f r o m
t h e S o u t h w e l l P l o t s , a r e drawn a g a i n s t the p e r c e n t a g e of
s t e e l . These v a l u e s a r e t h e a v e r a g e s of a l l t e s t r e s u l t s
o b t a i n e d f r o m the s t r u t s w i t h z e r o and 0.3 i n . e c c e n t r i c i
t i e s , f o r e a c h s t e e l c o n t e n t . These t e s t r e s u l t s show no
t e n d e n c y o t h e r t h a n t h a t t h e c r i t i c a l ' l o a d does n o t
depend on t h e m a g n i t u d e of p r e s t r e s s i n g . F i g u r e 5 a l s o
shows t h e c o n v e r t e d c r i t i c a l l o a d s w h i c h e l i m i n a t e the
e f f e c t o f t h e v a r i a t i o n i n t h e m o d u l i ( s e e C h a p t e r VI-1 ) .
The p l o t s o f t h e c o n v e r t e d c r i t i c a l l o a d s a l s o l i e a l o n g
a h o r i z o n t a l s t r a i g h t l i n e . I n F i g u r e s 6 and 7 t h e
c r i t i c a l l o a d s ( b o t h t h e a c t u a l and the c o n v e r t e d ) a r e
p l o t t e d s e p a r a t e l y fo.r t h e s t r u t s l o a d e d w i t h z e r o and
0.3 i n . e c c e n t r i c i t i e s . N ote t h a t t h e a v e r a g e of t h e
a c t u a l c r i t i c a l l o a d s f o r t h e c e n t r a l l y l o a d e d s t r u t s
( F i g u r e 6) i s a p p r o x i m a t e l y 23$ h i g h e r t h a n t h a t f o r
s t r u t s w i t h s m a l l e c c e n t r i c i t i e s ( i n F i g u r e 7 ) . C o n v e r t e d
c r i t i c a l v a l u e s i n F i g u r e 6 l i e a l o n g a h o r i z o n t a l l i n e
w h e reas c o n v e r t e d v a l u e s i n F i g u r e 7 a p p e a r t o l i e on a
s l o p i n g l i n e marked A. I f , h o w e v e r , s p e c i m e n No. 27 i s
o m i t t e d f r o m t h i s t a b u l a t i o n p o i n t Y w i l l f a l l a t p o i n t X,
70.
and t h e n t h e a v e r a g e v a l u e f o r a l l s t r u t s w i l l change
f r o m 45.34 k i p s t o 43.9 k i p s . F o r t h i s c a s e t h e v a l u e s
w i l l come c l o s e r t o a h o r i z o n t a l l i n e . I t i s p o s s i b l e
t h a t s p e c i m e n No. 27 had a h i g h e r v a l u e of t h e m o d u l u s ,
o r h i g h e r p r e s t r e s s , or b o t h , t h a n a n t i c i p a t e d , g i v i n g
an i n o r d i n a t e l y h i g h v a l u e of c r i t i c a l l o a d .
I n C h a p t e r V I - 3 i t was m e n t i o n e d t h a t s o m e t i m e s t h e
l a s t p l o t s f a l l above t h e s t r a i g h t l i n e , an i n d i c a t i o n
t h a t t h e s p e c i m e n a l r e a d y s t a r t e d t o f a i l i n b e n d i n g .
N o t i c e t h e h i g h C J c ^ - ^ t e n s i l e s t r e s s e s of s t r u t s Nos.
24, 15, and 35 i n T a b l e I I I . These t e n s i o n s t r e s s e s a r e
i n t h e r a n g e of the c r a c k i n g l i m i t of t h e c o n c r e t e .
C o n s e q u e n t l y t h e s e s p e c i m e n s m i g h t have c r a c k e d s h o r t l y
b e f o r e t h e i r u l t i m a t e c a p a c i t y was r e a c h e d , and t h e l a s t
p l o t s f e l l a l o n g a h a r d l y n o t i c e a b l e c o n v e x c u r v e r a t h e r
t h a n a l o n g t h e s t r a i g h t l i n e . Thus a p o s s i b l e - e r r o r i n
f i t t i n g t h e s t r a i g h t l i n e may l e a d t o a f a l s e , somewhat
s t e e p e r l i n e g i v i n g a r e s u l t on the low s i d e . The h i g h
v a l u e of s p e c i m e n No. 27 and the l o w e r v a l u e s of s p e c i m e n s
w i t h low . p r e s t r e s s must be c o n s i d e r e d as e x p e r i m e n t a l
e r r o r s , a nd have no b e a r i n g on t h e c o n c l u s i o n t h a t t h e
m a g n i t u d e of t h e E u l e r l o a d o f a p r e s t r e s s e d c o n c r e t e
s t r u t i s i n d e p e n d e n t of t h e amount of p r e s t r e s s .
A p p l i c a b i l i t y of t h e S o u t h w e l l Method
F i g u r e s 1 l / a t o 1 l / f f o r z e r o and 0.3 i n . e c c e n t r i c i t y
show t h a t t h e S o u t h w e l l method of e s t i m a t i n g t h e c r i t i c a l
l o a d s i s r e a s o n a b l y r e l i a b l e f o r p r e s t r e s s e d c o n c r e t e s t r u t s .
71 .
F i g u r e s 11/g t o 1 1 / i , however i n d i c a t e t h a t f o r
e c c e n t r i c i t i e s o f 1.5 i n . t h e S o u t h w e l l method does n o t
a p p e a r t o he r e l i a b l e .
Of t h e o b s e r v e d v a l u e s , "those g r e a t e r t h a n 7 k i p s f o r
low p r e s t r e s s , and a b o u t 10 k i p s f o r h i g h p r e s t r e s s w i l l
e x c e e d t h e p r o p o r t i o n a l l i m i t , and t h e r e f o r e a r e n o t
u s a b l e . S i m i l a r l y , o b s e r v e d v a l u e s b e l o w a b o u t 4 k i p s
may not have s u f f i c i e n t a c c u r a c y . Thus o n l y a few r e a d
i n g s , b e t ween t h e s e l i m i t s , a r e a v a i l a b l e f o r p l o t t i n g ,
and t h e s e do not g i v e a s u f f i c i e n t l y l o n g l i n e t o e s t i m a t e
t h e t r u e c r i t i c a l l o a d .
V a l u e s o f c r i t i c a l l o a d f o r a l l s t r u t s l o a d e d w i t h
z e r o or 0.3 i n . e c c e n t r i c i t y a r e p l o t t e d a g a i n s t v a l u e s
o f a^ w h i c h were o b t a i n e d f r o m t h e S o u t h w e l l P l o t s , i n
F i g u r e 15. T h e r e does n o t a p p e a r t o be any d i s t i n c t
i n d i c a t i o n o f d i f f e r e n c e s i n r e l i a b i l i t y o f t h e method
f o r d i f f e r e n t m a g n i t u d e s of e c c e n t r i c i t y up t o a b o u t
0.3 i n .
The M o d ulus t o be Used
I n o r d e r t o be a b l e t o c a l c u l a t e t h e E u l e r l o a d of
a p r e s t r e s s e d c o n c r e t e s t r u t i t i s n e c e s s a r y t o use t h e
p r o p e r e l a s t i c modulus i n t h e E u l e r f o r m u l a . B e c a u s e t h e
c o n c r e t e m a t e r i a l e x h i b i t s a t l e a s t a s l i g h t c u r v i l i n e a r
r e l a t i o n o f s t r e s s and s t r a i n , e ven a t low v a l u e s , and
i t s p r o p o r t i o n a l l i m i t i s u n d e f i n e d , t h e modulus c o r r e s
p o n d i n g t o t h e E u l e r or c r i t i c a l l o a d must be d e f i n e d .
CONVE&TE.P CRITICAL L0AP£ vs. V A L U E S OF Q \
80
TO
6.0
20
40
1 H 1
0 1
i
;
—1
—1
1
1
C|E AL b>E
k-
it
-® Hp — . \
r _ - i — .
»- -*
-
—
T*~
1 1 |
!
1
MAKxlC OF
ECXENT&lf-ITY-'
V A L U E S OP : <2.(W.)
•23 27 24 i(b 20 19 10
12> 10 ll 33 9 2.1
O 2& O.h O
\1
O
31
0.3
3>5 3D> 57 17 OWTC-WT'ONAL) p i g . 15. C o n v e r t e d C r i t i c a l Loads V e r s u s V a l u e s o f
To i n v e s t i g a t e t h i s p r o b l e m t h e t h e o r e t i c a l c u r v e 2 2
P = Tt E l / I T was drawn i n P i g u r e 16, on a b a s e o f
modulus E. I n F i g u r e 1 6 ( a ) a r e a l s o shown v a l u e s of
P c r . ( f r o m S o u t h w e l l P l o t s ) on a b a s e of t a n g e n t modulus
E^, w h i l e i n F i g u r e 1 6 ( b ) on a b a s e o f i n i t i a l t a n g e n t
modulus E,.. t i
I t a p p e a r s t h a t t h e i n i t i a l t a n g e n t m o d u l i p r o v i d e a
b e t t e r f i t t o t h e t h e o r e t i c a l c u r v e . However, due t o
t h e d i f f i c u l t y i n f i n d i n g t h e i n i t i a l t a n g e n t m o d u l u s ,
i t w o u l d be d e s i r a b l e t o use t h e more e a s i l y o b t a i n e d
s e c a n t modulus of a s t r e s s - s t r a i n c u r v e . C o n s i d e r i n g
t h a t t h e v a l u e s of t h e a v e r a g e c o m p r e s s i v e s t r e s s
of t h e s p e c i m e n s r a n g e b e t w e e n 1,681 p s i and 4,135 p s i ,
i t c a n r e a d i l y be shown t h a t t h e d e v i a t i o n b e t w e e n t h e
s e c a n t m o d u l i c o r r e s p o n d i n g t o t h e s e s t r e s s e s and t h e
t a n g e n t m o d u l i i s n e g l i g i b l e . E x c e p t f o r c y l i n d e r s
No. 22-23-24 and one o f t h e f o u r s t r e s s - s t r a i n c u r v e s of
c y l i n d e r No. 34, a l l s t r e s s - s t r a i n c u r v e s c o r r e s p o n d i n g
t o t h e s p e c i m e n s t e s t e d f o r b u c k l i n g , e x h i b i t e d a c u r v e
v e r y c l o s e t o a s t r a i g h t l i n e i n t h e l o w e r s t r e s s r a n g e
as d e m o n s t r a t e d i n F i g u r e 14/a. C o n s e q u e n t l y t h e s e c a n t
m o d u l i c o r r e s p o n d i n g to' t h e a v e r a g e c o m p r e s s i v e s t r e s s
l e v e l h a r d l y d e v i a t e s f r o m t h e v a l u e s of t h e i n i t i a l
t a n g e n t m o d u l i as s e e n i n F i g u r e 14/a. T h e r e f o r e , c o n
s i d e r i n g t h e h i g h s t r e n g t h c o n c r e t e u s e d , t h e i n i t i a l
m odulus c o u l d be r e p l a c e d w i t h good a p p r o x i m a t i o n by t h e
s e c a n t m o d u l u s . S i n c e o n l y two s t r e s s - s t r a i n c u r v e s of
7 4 .
\0
'SI
ft
0
J
<
H & O
< y— o <
A * zi
©* 0 :Z0 ZCCtW ,?> I N . II
"&|£ iT>f
A
A
© A
A A
A < D A
© .X* >^ < d
MODULUS i
7 0
6o
5o
4oJ
a) 5tfoo
4ooe> b)
A ^ Z-E © * 0, 5 IN. H
• | & i « T Y A
A
A
©
A
A A A
A /
A A
r
v
©
1 w (!) ©
MODULUS £
F i g . 16, C o m p a r i s o n o f E u l e r C u r v e w i t h t h e C o n v e r t e d C r i t i c a l L o a d s .
c y l i n d e r s Wo. 12-13-14 and one of No. 34 showed a
d i v e r g e n c e of and E^ c u r v e s , f u r t h e r r e s e a r c h i s
n eeded t o p r o v e w h e t h e r t h e use of the s e c a n t modulus i n
t h e E u l e r f o r m u l a i s p r o p e r when the s t r u t s a r e made of
low q u a l i t y c o n c r e t e .
P i g u r e 1? shows two commonly u s e d c u r v e s f o r modulus
on a base of c y l i n d e r s t r e n g t h , as w e l l as t h e v a l u e s of
E, and E,. o b t a i n e d f r o m the t e s t c y l i n d e r s . I t a p p e a r s
t h a t b o t h e q u a t i o n s g i v e v a l u e s somewhat i n e x c e s s of
t h e t e s t v a l u e s . Of t h e s e two e q u a t i o n s t h e J e n s e n
e q u a t i o n comes c l o s e r t o t h e d e s i r e d v a l u e s .
U l t i m a t e Load C a r r y i n g C a p a c i t y
A l t h o u g h t h i s r e s e a r c h c o n c e n t r a t e d p r i m a r i l y on t h e
i n v e s t i g a t i o n o f t h e r e l a t i o n s h i p s between t h e E u l e r l o a d
t h e p e r c e n t a g e of s t e e l , and t h e modulus t o be u s e d i n
E u l e r ' s f o r m u l a , a b r i e f d i s c u s s i o n of t h e u l t i m a t e l o a d
c a r r y i n g c a p a c i t y of t h e s p e c i m e n s w o u l d be a p p r o p r i a t e . 2
R e c e n t l y , f o r s t r u t s s u b j e c t t o a x i a l l o a d i n g Brown
d e v e l o p e d an i n e l a s t i c a n a l y t i c a l method t o p r e d i c t t h e
e x t e r n a l u l t i m a t e l o a d P i n t e r m s of t h e s h o r t c o l u m n u
s t r e n g t h and t h e p r e s t r e s s i n g f o r c e F1 c o r r e s p o n d i n g t o S Ul
P , The a n a l y s i s i s b a s e d on t h e f o l l o w i n g p r i n c i p a l ;
1) t h e c r i t i c a l c o n c r e t e c o m p r e s s i v e s t r a i n a t f a i l u r e
i s 8 C = 180 x 1 0 ~ 5 i n . / i n . 2) t h e s t r e s s - s t r a i n r e l a t i o n s h i p f o r c o n c r e t e i s
it t p a r a b o l i c w i t h maximum s t r e s s f = °85f,, o c c u r r i n g >
0 l\ . ^ 11
76.
F i g . 1 7 . C o m p a r i s o n of Commonly Used C u r v e s of M o dulus w i t h T e s t R e s u l t s .
where £ = 180 x 1 0 - - 5 i n . / i n . ^ c ' 3) t h e t o t a l d e f l e c t i o n due t o p r e s t r e s s and l o a d i n g
u n d e r c r i t i c a l c o n d i t i o n s i s g i v e n hy = L 2 ^ / 5
where ^ i s a f u n c t i o n o f t h e d e p t h o f t h e s t r e s s
"block a t t h e m i d - p o i n t o f t h e s t r u t .
F o r c e n t r a l l y l o a d e d and c e n t r a l l y p r e s t r e s s e d s t r u t s
Brown f o u n d t h a t t h e summation of t h e e x t e r n a l u l t i m a t e
l o a d P^, and t h e c o r r e s p o n d i n g p r e s t r e s s i n g f o r c e P g u >
i s e q u a l t o t h e s h o r t column s t r e n g t h P = 0 . 8 5 f (A -A ) 0 C C S
m u l t i p l i e d "by a r e d u c t i o n f a c t o r R w h i c h depends on t h e
s l e n d e r n e s s r a t i o and w h i c h i s g i v e n i n g r a p h f o r m i n
h i s p a p e r . Thus P = RP - F ............ e. ) u 0 su
F o r s l e n d e r n e s s r a t i o L / r = 1 3 5 , u s e d i n t h i s t e s t ,
Brown's g r a p h i n d i c a t e s a r e d u c t i o n f a c t o r of R = 0 . 4 7 .
The c a l c u l a t e d r e d u c t i o n f a c t o r s f o r s t r u t s t e s t e d w i t h
z e r o e c c e n t r i c i t y a r e shown i n T a b l e VI'.']- They v a r y
b e t w e e n 0 . 3 4 and 0 . 6 3 .
As l o a d e c c e n t r i c i t y i n c r e a s e s t h e u l t i m a t e l o a d
c a r r y i n g c a p a c i t y d e c r e a s e s . However, whereas r e s u l t s o f
th e s t r u t s t e s t e d w i t h s m a l l ( 0 . 3 i n . ) e c c e n t r i c i t y do no
a p p e a r t o depend on the s t e e l r a t i o ( s e e F i g u r e 1 2 ) , t h e
r e s u l t s o f t h e s t r u t s t e s t e d w i t h l a r g e ( 1 . 5 i n . )
e c c e n t r i c i t y show t h a t t h e i r u l t i m a t e c a p a c i t y i n c r e a s e s
w i t h t h e amount of s t e e l . F i g u r e 18 shows t h e u l t i m a t e
l o a d p l o t t e d a g a i n s t t h e p e r c e n t a g e o f s t e e l b e t w e e n
0 . 2 3 and 1 . 2 0 p e r c e n t .
The e v a l u a t i o n o f P f o r t h e 1 . 5 i n . e c c e n t r i c i t y
78 .
1. 3. 4- 5. 6. 7 .
M|i.. P . • 8 5 f t Po Pu Pu+Fsu Po
psi. bps kips kips
1 0 1 2
. 2 3 7630 7460
1 83 179
7 .2 7 .2
66 .0 54 .2
»40 .34
1 8 21
.45 7080 6200
1 69 1 48
13.6 13 .7
58 .9 48 .4
.43
.42 1 1 H
.60 7630 7460
1 82 1 78
17 .9 18.1
65 .0 57 .5
.46
.42
9 1 3 • 34 36
.91 7630 7630 61 40 6280
1 81 1 81 1 46 149
27 .2 26 .6 27 .2 2 7 . 0
62 . 5 72 .5 57 .2 54 .2
.50
.55
.58
.55
1 9 20 37
1 .20 7080 6200 6280
1 68 1 47 1 49
35 .7 35 .4 36.6
60 .0 57 .9 43 .6
.57
.63
.54
TABLE V I . - REDUCTION FACTORS FOR STRUTS
WITH ZERO ECCENTRICITY.
needs i n e l a s t i c a n a l y s i s , which i s beyond the scope of
t h i s t h e s i s . However, at a r b i t r a r i l y chosen loads of
P /2 the behaviour of the s t r u t s i s e l a s t i c . At these u
loads the te s t s show c lo se agreement with the s t r e s s e s
c a l c u l a t e d from the mod i f ied secant formula (as shown i n
Table IV /a ) , i n d i c a t i n g 'the v a l i d i t y of i t s use w i t h i n
the' p r o p o r t i o n a l l i m i t .
ULTIAAATLt Lc9AD (Pu) V4. p %
F i g . 18. U l t i m a t e Load o f S t r u t s w i t h 1 .5 i n . E c c e n t r i c i t y V e r s u s S t e e l R a t i o .
CONCLUSIONS
The E u l e r l o a d of a s l e n d e r p r e s t r e s s e d c o n c r e t e s t r u t
does n o t depend on t h e amount of p r e s t r e s s i n g f o r c e
p r o v i d e d t h a t 1) t h e s t r e s s due t o t h e p r e s t r e s s i n g i s
l e s s t h a n t h e c r i t i c a l s t r e s s and 2) t h e c o n c r e t e i s
of s u c h a q u a l i t y as t o f o l l o w Hooke's Law. Under t h e s e
c o n d i t i o n s t h e b u c k l i n g l o a d c a n be c a l c u l a t e d by E u l e r ' s
f u n d a m e n t a l f o r m u l a .
The method o f t h e S o u t h w e l l P l o t may be u s e d t o f i n d the
c r i t i c a l l o a d f o r p r e s t r e s s e d c o n c r e t e s t r u t s . E c c e n t r i
c i t y r a t i o e / t = .1 does n o t i n t r o d u c e any s u b s t a n t i a l
e r r o r .
S e c a n t m o d u l u s , o b t a i n e d f r o m s t a n d a r d c o n t r o l c y l i n d e r s ,
w i l l y i e l d r e a s o n a b l y good v a l u e s of t h e b u c k l i n g l o a d .
When th e u l t i m a t e c a p a c i t y of a p r e s t r e s s e d c o n c r e t e
s t r u t ( h a v i n g a s t e e l r a t i o l e s s t h a n 1.2%) i s g o v e r n e d
by b e n d i n g r a t h e r t h a n by b u c k l i n g , i t s c a p a c i t y i s
p r o p o r t i o n a l t o t h e m a g n i t u d e of p r e s t r e s s .
I n s p i t e o f t h e c a r e t a k e n i n t h e p r e p a r a t i o n o f t h e
s p e c i m e n s , and i n t h e l o a d i n g p r o c e d u r e s , t h e d i f f e r e n t
t e s t r e s u l t s show c o n s i d e r a b l e s p r e a d .
81 .
REFERENCES
1. B o r o c z , J . ( i n H u n g a r i a n ) P r e s t r e s s e d S t r u c t u r e s ( F e s z i t e t t
S z e r k e z e t e k ) K o z l e k e - d e s i K i a d o , B u d a p e s t 1953.
2. Brown, K. I . , The U l t i m a t e Load C a r r y i n g C a p a c i t y of
P. C. Columns u n d e r D i r e c t and E c c e n t r i c L o a d i n g , C i v i l
E n g i n e e r i n g and P u b l i c Works Re v i e w ( L o n d o n ) V o l . 60,No.705
A p r . 1 965, pp. 539-541} No. 706 May 1965 , pp. 683-687; No.707
June 1965, pp. 841-845.
3. B r e c k e n r i d g e , R. A., A S t u d y o f t h e C h a r a c t e r i s t i c s of
P r e s t r e s s e d C o n c r e t e Columns, R e p o r t No. 18-6, U. S. C i v i l
E n g i n e e r i n g U n i v e r s i t y of S o u t h e r n C a l i f o r n i a , Los A n g e l e s ,
A p r i l 1953.
4. E f s e n , A. P r o f . , E c c e n t r i c a l l y L o a d e d P r e s t r e s s e d C o n c r e t e
Columns ( i n D a n i s h ) by P r o f . E f s e n . F . I . P . P r e s t r e s s e d
C o n c r e t e A b s t r a c t s . Copenhagen, 1963.
5. H a l 1 , A. S., B u c k l i n g o f P r e s t r e s s e d Columns. C o n s t r u c t i o n a l
R e v i e w . June 1963.
6. I t a y a , Raymond, D e s i g n and Uses o f P r e s t r e s s e d C o n c r e t e
Columns, J o u r n a l of t h e P r e s t r e s s e d C o n c r e t e I n s t . V o l . 10,
No. 2 , June 1965.
7. J e n s en, V. P. , The E l a s t i c i t y R a t i o o f C o n c r e t e and i t s
E f f e c t on t h e U l t i m a t e S t r e n g t h o f Beams, A. C. I . J o u r n a l
V. 3 2 No. 6,June 1943,pp. 565-584.
8. L e o n h a r d t , F r i t z , S p a n n b e t o n F u r D i e P r a x i s , W i l h e l m E r n s t
& J o h n , B e r l i n 1955.
82.
9. L i n , T. Y. and I t a y a . R.. A P r e s t r e s s e d C o n c r e t e Column
Under E c c e n t r i c L o a d i n g , J o u r n a l of t h e P r e s t r e s s e d
C o n c r e t e I n s t i t u t e , V o l . 2, No. 3 Dec. 1957.
10. O z e l l . A. M.. and J e r n i g a n . A. M.. Some S t u d i e s on t h e
B e h a v i o u r of P r e s t r e s s e d C o n c r e t e Columns, Techn. P r o g r e s s i
R e p o r t No. 3 , E n g i n e e r i n g P r o g r e s s a t t h e U n i v e r s i t y of
F l o r i d a , V o l . X No. 7. S u p p l e m e n t J u l y 1 956 ;
11. Osgood, ¥. R., The D o u b l e Modulus T h e o r y of Column A c t i o n .
C i v i l E n g i n e e r i n g 5:174-175 March 1935.
12. Peabody, D, J r . , The D e s i g n o f R e i n f o r c e d C o n c r e t e
S t r u c t u r e s . Second E d i t i o n 1957. N. Y. J o h n W i l e y & Sons,
Lond on; Chapman & H a l l .
13. Pauw, A d r i a n , S t a t i c M o d u l u s o f E l a s t i c i t y of C o n c r e t e as
A f f e c t e d by D e n s i t y , J o u r n a l of A m e r i c a n C o n c r e t e I n s t i t u t e ,
V.32, No.' 6 pp. 679-687. 1 960.
14. S h a n l e y , F. R., S t r e n g t h of M a t e r i a l s ; M c G r a w - H i l l Book
Company (New Y o r k , T o r o n t o , London) 1957.
15. S o u t h w e l l , R. V., On t h e A n a l y s i s o f E x p e r i m e n t a l O b s e r v a
t i o n s i n P r o b l e m s o f E l a s t i c S t a b i l i t y ; P r o c . R o y a l S o c i e t y
o f L ondon, S e r i e s A, V o l . 135 pp. 601.
16. T i m o s h e n k o , S. P. and J . M. G e r e , T h e o r y of E l a s t i c S t a b i l
i t y , M c G r a w - H i l l Second E d i t i o n , 1961 New Y o r k , T o r o n t o ,
London.
17. T r o x e l l , G. E. and H. E. D a v i s , C o m p o s i t i o n and P r o p e r t i e s
of C o n c r e t e ; M c G r a w - H i l l Book Company New Y o r k , T o r o n t o ,
London 1956.
83.
18. I n P o l i s h - The d e s i g n of P r e s t r e s s e d C o n c r e t e - by Cement
and C o n c r e t e A s s o c . and P r e s t r e s s e d C o n c r . D e v e l o p m e n t
Group. T r a n s l a t i o n f r o m P o l i s h by T. K o l e k , London,
Cement & C o n c r . A s s c . 1963, pp. 32.
19. Z a s l a v s k y , A r o n , Column B u c k l i n g Loads by C o n j u g a t e Beam
Method, The S t r u c t u r a l E n g i n e e r No. 6 V o l . 43 1965.
pp. 183.
20. Zung-Teh Z i a , P., U l t i m a t e S t r e n g t h of S l e n d e r P r e s t r e s s e d
C o n c r e t e Columns, T e c h n . P a p e r S e r i e s No. 131 Eng. P r o g r e s s
a t t h e U n i v e r s i t y of F l o r i d a V o l . X I No. 7 J u l y 1957.
