Effects of web reinforcing on torsional behavior of prestressed … · 2020. 4. 2. · prestressed by the pretensioning method. The cross section of the member, concrete strength,

Effects of web reinforcing on torsionalbehavior of prestressed concrete memebers

Item Type text; Thesis-Reproduction (electronic)

Authors Buckmaster, Barbara Gail, 1932-

Publisher The University of Arizona.

Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.

Download date 04/01/2021 05:17:46

Link to Item http://hdl.handle.net/10150/347576

http://hdl.handle.net/10150/347576

E F F E C T S O F W EB R EIN F OR C IN G ON TORSIONAL BEHAVIOR

O F P R E S T R E S S E D C O N C R E T E M E M B E R S

by

B a r b a r a G a i l B u c k m a s t e r

A T h e s i s S u b m i t t ed to the F a c u l t y of the

D E P A R T M E N T O F CIVIL EN G IN E ER IN G

In P a r t i a l F u l f i l l m e n t of the R e q u i r e m e n t s F o r th e D e g r e e of

M ASTER O F SC IEN CE

In the G r a d u a t e C o l lege

THE UNIVERSITY O F ARIZONA

1 9 6 6

S T A T E M E N T BY AUTHOR

T his t h e s i s h a s been s u b m i t t e d in p a r t i a l f u l f i l lm e n t of r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t the U n i v e r s i t y of A r i z o n a and i s d e p o s i t e d in the U n i v e r s i t y L i b r a r y to be m a d e a v a i l a b l e to b o r r o w e r s u n d e r r u l e s of the L i b r a r y .

B r i e f q u o ta t io n s f r o m th i s t h e s i s a r e a l lo w ab le w i thout s p e c i a l p e r m i s s i o n , p r o v i d e d tha t a c c u r a t e a c k n o w le d g e m e n t of s o u r c e is m a d e . R e q u e s t s fo r p e r m i s s i o n fo r e x te n d e d q u o ta t io n f r o m o r r e p r o d u c t i o n of th i s m a n u s c r i p t in whole o r in p a r t m a y be g r a n t e d by the h e a d of the m a j o r d e p a r t m e n t o r the Dean of the G r a d u a t e Co l lege when in h i s j u d g m e n t the p r o p o s e d u s e of the m a t e r i a l i s in the i n t e r e s t s of s c h o l a r s h i p . In a l l o t h e r i n s t a n c e s , h o w e v e r , p e r m i s s i o n m u s t be o b ta in e d f r o m the a u th o r .

SIGNED L S i h / f * if.

A P P R O V A L BY THESIS D IR E C T O R

This t h e s i s h a s b e e n a p p r o v e d on the da te shown below:

<M o r r i s W. Se lf "/T DateA s s o c i a t e P r o f e s s o r of Civ il E n g i n e e r i n g

A C K N O W L E D G E M E N T S

T he a u t h o r e x te n d s th a n k s to h e r t h e s i s a d v i s o r , M o r r i s W. Self , and to the o t h e r m e m b e r s of h e r c o m m i t t e e , J a m e s D. K r iegh , and H o w a r d P . H a r r e n s t i e n .

S p e c ia l g r a t i t u d e is due John S. S tum, J r . , of J o h n s o n C o n s t r u c t i o n C o m p an y f o r h i s m o s t g e n e r o u s c o n t r ib u t io n s of t im e and e n e r g y in the p ro d u c t io n of the t e s t b e a m s an d h i s a id t h r o u g h out th e p r o j e c t .

E n c o u r a g e m e n t w a s r e c e i v e d f r o m s e v e r a l c o l l e a g u e s in th e A m e r i c a n C o n c r e t e In s t i tu te . A m ong t h e m w e r e T h o m a s T. C. Hsu , E m o r y L. Kemp, Jo h n A. S b a ro u n i s , R o b e r t A. Shoo lb red , and P a u l Zia.

The a u t h o r i s d e ep ly g r a t e f u l to h e r e d i to r , C yn th ia S. Hall , f o r e x c e l l e n t a s s i s t a n c e an d i n s t r u c t i o n . The m a n u s c r i p t w a s t y p e d by K a th e r in e H u r le y .

None of th e a f o r e m e n t i o n e d shou ld be h e ld in an y w ay r e s p o n s ib le f o r s h o r t c o m i n g s , e r r o r s , o r i n a c c u r a c i e s w h ich m a y be p r e s e n t in th i s t h e s i s .

T A B L E OF C O N T E N T S

LIST O F ILLU ST RA T IO N S vi

LIST O F T A B L E S v i i i

A B S TR A C T ix

INTRODUCTION 1

I. I m p o r t a n c e of the Study 1II. O b je c t iv e s of th e Study 4III. S u rv ey of D es ig n R e c o m m e n d a t i o n s 6

A. R e i n f o r c e d C o n c r e t e 6B. P r e s t r e s s e d C o n c r e t e 7

R EV IE W O F E X P E R I M E N T A L R ES E A R C H 11

I. P l a i n and R e i n f o r c e d C o n c r e t e 11II. P r e s t r e s s e d C o n c r e t e 12

TE ST PR O G R AM 18

I. T e s t B e a m s 18II. T e s t A r r a n g e m e n t 33

T E ST R ESU L T S 39

I. N u m e r i c a l Data 39II. L o a d - D e f o r m a t i o n R e la t i o n s h ip 42

A. T o r q u e - T w i s t C u r v e s 42B. T o u g h n e s s 46C. M odu lus of R ig id i ty 47

III. U l t im a te S t r en g th 49IV. N o n - n u m e r i c B e h a v io r 54V. R ev iew of R e in fo rc in g 59.

V

T A B L E OF C O NT EN TS Con t inued

CONCLUSIONS 62

I. D es ign A p p l i c a t io n s 62II. I m p r o v e m e n t of T e s t D es ig n 63III. R e c o m m e n d a t i o n s f o r F u r t h e r

R e s e a r c h 64

S E L E C T E D READINGS 65

LIST O F ILLU ST RA T IO N S

F i g u r e P a g e

1 L o ad - D e f o r m a t i o n C u r v e s 4

2 Z i a ' s C o m p a r i s o n of F a i l u r e T h e o r i e s 15

3 Z ia ' s . T o r q u e - T w i s t C u r v e s f o r R e c t a n g u l a r S e r i e s 17

4 T e s t B e a m s « 18

5 B e a m D r a w in g s 20

6 S t i r r u p Spac ings 21

7 The P r e s t r e s s i n g B ench 23

8 P r e s t r e s s i n g Bench D e ta i l s 25

9 T e n s io n in g th e S t r a n d 27

10 R e i n f o r c in g and F o r m w o r k 28

11 C o n c r e t e C y l in d e r T e s t s 29

12 P l a c i n g C o n c r e t e 31

13 Cut t ing S t r a n d and T r a n s p o r t i n g th e B e a m s 32

14 T e s t S tand 34

15 T e s t S tand wi th B5 35

16 M e a s u r i n g A p p a r a t u s 36

17 R e c o r d i n g of D a ta 37

18 L eng th of M o m e n t A r m 42

19 A ngle o f R o ta t io n 43

vi

LIST O F ILLU STRA TIO N S C on t inued

T o r q u e - T w i s t C u r v e s fo r B4, B2, and B3

T o r q u e - T w i s t C u r v e s fo r B5 and B6

P o r t i o n of C u r v e s in E l a s t i c Range

C o n s ta n t R e l a t i n g T o r q u e and T w is t

F a i l u r e S u r f a c e s

D iagonal T e n s io n C r a c k s

B5 C o m p r e s s i o n Side and B5 T e n s io n Side

S -S h ap ed C o m p r e s s i o n F a i l u r e s

T e s t S p e c im e n s B l , B3, B2, B4, and B6

M eth o d s of E x p r e s s i n g A m o u n t of Web R e i n f o r c in g

LIST O F T A B L E S

T a b le P a g e

1 T e s t Da ta 40, 41

2 R e la t iv e T o u g h n e s s of S p e c im e n s 46

3 P r e d i c t e d T o r q u e R e s i s t e d by S t i r r u p s 51

4 P r e d i c t e d T o r q u e R e s i s t e d by C o n c r e t e 52

5 T e s t V a lu e s and P r e d i c t e d U l t im a te T o r q u e 53

6 A m o u n ts of Web R e i n fo rc in g 60

v i i i

A B S T R A C T

The p r o b l e m w a s to i n v e s t i g a t e the e f fe c t s of web r e i n

f o r c in g on th e b e h a v i o r of p r e s t r e s s e d c o n c r e t e m e m b e r s s u b j e c

t e d to t o r s i o n . P h a s e s of b e h a v io r s tu d ie d w e r e l o a d - d e f o r m a t i o n

r e l a t i o n s h i p , c o n f ig u r a t io n of f a i l u r e s u r f a c e , t o r s i o n a l t o u g h n e s s ,

and u l t i m a t e t o r s i o n a l c a p a c i ty .

R e c t a n g u l a r b e a m s , s ix i n c h e s by s ix t e e n i n c h e s in c r o s s

s ec t io n , h ad an a x ia l p r e s t r e s s i n g f o r c e a p p l i e d b y the p r e t e n s i o n

ing m e th o d . The c r o s s s e c t i o n of the m e m b e r , c o n c r e t e s t r e n g th ,

p r e s t r e s s i n g fo r c e , an d long i tud ina l r e i n f o r c i n g w e r e t r e a t e d a s

c o n s t a n t s . The only v a r i a b l e w a s th e a m o u n t of web r e i n f o r c i n g

in the f o r m of c l o s e d s t i r r u p s . Six s p e c i m e n s w e r e t e s t e d to f a i l u r e

in p u r e t o r s io n .

The t e s t r e s u l t s d e m o n s t r a t e th a t the sudden f a i l u r e gen-I '-.

e r a l l y a s s o c i a t e d with c o n c r e t e in t o r s i o n m a y be a v o id ed and th a t

t o r s i o n a l t o u g h n e s s c a n be o b ta in e d in p r e s t r e s s e d c o n c r e t e m e m

b e r s by the u s e of a su f f ic ien t a m o u n t of web r e in f o r c in g .

INTRO D U CTIO N

I. I m p o r t a n c e of the Study

P r e s t r e s s i n g r e q u i r e s c o u r a g e an d im a g i n a t i o n on th e p a r t of

th e d e s i g n e r . "Happi ly , one c an bu ild , w i thou t knowing e v e r y th in g , at

t h e p r i c e of an e x a g g e r a t i o n of m a r g i n s of s a fe ty . Th is s t a t e m e n t

w a s m a d e by E u g e n e F r e y s s i n e t in h i s f o r e w o r d to G u y o n ' s w o r k on

p r e s t r e s s e d c o n c r e t e p u b l i s h e d in P a r i s in 1951. E v e n today , f i f t een

y e a r s l a t e r , p r e s t r e s s i n g i s a t e c h n o l o g y s t i l l in i t s in fancy .

F r e y s s i n e t ’s s t a t e m e n t i m p l i e s th a t i f a l l g u e s s w o r k i s m a d e

t o w a r d the c o n s e r v a t i v e , a d e q u a te s a f e ty w i l l be i n s u r e d . If th i s w e r e

so, on ly e c o n o m y would be lo s t . U n fo r tu n a te ly , w hen k n ow ledge is

in su f f i c i e n t , m o r e th a n e c o n o m y m a y su f fe r .

In the 1956 A m e r i c a n C o n c r e t e In s t i tu te code t h e r e a p p e a r e d

a m o r e s t r i n g e n t r e q u i r e m e n t f o r s t i r r u p s p a c in g s in co n t in u o u s m e m

b e r s t h a n h a d p r e v i o u s l y b e e n in e f fec t . ^ S e v e r a l s t r u c t u r e s d e s ig n e d

by the 1951 code h a d b e h a v e d b ad ly in s h e a r . B e s t known a r e th e r i g i d

1. " F o r t h e u r e u s e m e n t , on peu t c o n s t r u i r e , s a n s tou t con- n a l t r e , au p r i x d 'u n e e x a g e r a t i o n d e s m a r g e s de se 'cu r i te . " F r e y s s i n e t , E u g e n e in Yves Guyon, Beton P r e c o n t r a i n t ( P a r i s , E y r o l l e s , 1951),p. v i i i .

2. ACT C o m m i t t e e 318, Build ing Code R e q u i r e m e n t s f o r R e i n f o r c e d C o n c r e t e , ACI 3 1 8-56 ( D e t ro i t , A m e r i c a n C o n c r e t e I n s t i tute^ 1956), p. 946.

1

f r a m e f a i l u r e s w hich o c c u r r e d a t the A i r M a t e r i e l C o m m a n d W a r e h o u s e

in Shelby, Ohio. T h e y a r e ab ly d e s c r i b e d in th a t a b s o r b i n g m o n o g r a p h ,

3L e s s o n s f r o m F a i l u r e s of C o n c r e t e S t r u c t u r e s . L a b o r a t o r y t e s t s c o n

f i r m e d the n e e d to r e v i s e the code.

The co n cep t of s a f e ty of a p a r t i c u l a r m e m b e r o r s t r u c t u r e is

c o m p le x . The f a c t o r of s a f e ty in u l t i m a t e s t r e n g t h d e s ig n is u s u a l l y

de f in ed m e r e l y a s the r a t i o of c o l l a p s e o r f a i l u r e load to the s e r v i c e

load. In w o rk in g s t r e s s d e s ig n the f a c t o r of s a f e ty i s the r a t i o of the

load a t which the m e m b e r b e g in s to y ie ld to the d e s ig n load. F a c t o r

of s a f e ty i s an i m p o r t a n t index but i s in s u f f i c i e n t by i t s e l f . One m u s t

a l s o d e s c r i b e the p r e d i c t e d m o d e of f a i l u r e and th e a s s u m e d load p a t t e r n

f r o m w hich it r e s u l t s . Then , w i th th i s p a r t i c u l a r lo ad p a t t e r n , i t i s

n e c e s s a r y to d e t e r m i n e the s a f e ty f a c t o r on a n o t h e r k ind of f a i l u r e if

the p r e d i c t e d f a i l u r e could be p r e v e n te d . One should a l s o c o n s i d e r the

l ik e l ih o o d of o t h e r a r r a n g e m e n t s of l ive load which cou ld c a u s e d i f f e r

ent k in d s of f a i l u r e .

It i s of ten i m p o r t a n t to know how m u c h d e f o r m a t i o n t a k e s

p la c e b e f o r e c o m p le t e c o l l a p s e o c c u r s . Any k ind of b r i t t l e o r sudden

f a i l u r e is p o t e n t i a l l y m o r e d a n g e r o u s th a n a g r a d u a l f a i l u r e which g iv e s

a w a rn in g . One m i g h t a l s o be i n t e r e s t e d in such p r o p e r t i e s a s ' d u c t i l

i ty and to u g h n e s s . $>

3. F e ld , J a c o b , L e s s o n s f r o m F a i l u r e s of C o n c r e t e St ru e - t u r e s (D e t ro i t , A m e r i c a n C o n c r e t e In s t i tu te , and A m e s , Iowa Sta te U n i v e r s i t y P r e s s , 1964), p. 25.

The u n d e r s t a n d i n g of t h i n a t u r e of one type of b e h a v io r l a g s

b eh ind th a t of a n o th e r . A s H o g n e s ta d p o in te d out, ’/ R e s e a r c h r e s u l t s

t o d a y a r e be ing t r a n s l a t e d in to p r a c t i c e a t a r a t e u n e q u a l l e d in the

h i s t o r y of s t r u c t u r a l c o n c r e t e . When th e a s p e c t s of s t r u c t u r a l

d e s ig n th a t a r e u n d e r s t o o d a r e r e f in e d , o t h e r p h e n o m e n a m a y s u d d e n

ly m a k e t h e i r d a n g e r known by c a u s in g f a i l u r e s u n e x p e c t e d and a t

f i r s t no t u n d e r s to o d .

S t r u c t u r a l d e s ig n in g e n e r a l i s b e co m in g m o r e s o p h i s t i

c a ted . T h e r e i s an i n c r e a s i n g d e s i r e on the p a r t of d e s i g n e r s , a s

w e l l a s t h e o r i s t s , to l e a r n the t r u e b e h a v i o r of m a t e r i a l s , m e m b e r s ,

and s y s t e m s . In r e i n f o r c e d c o n c r e t e and in p r e s t r e s s e d c o n c r e t e ,

t h i s t r e n d i s e s p e c i a l l y m a n i f e s t e d in u l t i m a t e s t r e n g t h d e s i g n and

in l i m i t d e s ig n . T h e r e is i n c r e a s i n g i n t e r e s t in the t r u e f a c t o r of

s a f e t y on th e l ive load. M o r e r a t i o n a l m e t h o d s of d e s ig n a r e being

d e v e lo p e d fo r b l a s t f o r c e s , w ind lo a d s , and e a r t h q u a k e .

G lenn M u rp h y , in P r o p e r t i e s of E n g i n e e r i n g M a t e r i a l s ,

d e f in e s to u g h n e s s a s the c a p a c i t y of a m a t e r i a l f o r r e s i s t i n g f r a c t u r e

/ 5u n d e r d y n a m ic load ing . M odu lus of t o u g h n e s s i s d e f in e d a s th e

4. H o g n e s ta d , E. , " E f f e c t s of R e s e a r c h on M o d e r n A m e r i c an S t r u c t u r a l C o n c r e t e D es ign , " J o u r n a l of th e S t r u c t u r a l D iv is ion , P r o c e e d i n g s of the A m e r i c a n So c ie ty of C iv i l E n g i n e e r s , P r o c e e d i n g s P a p e r 2034, LXXXV, ST 5 (M ay 1959), 7.

5. M u rp h y , Glenn, P r o p e r t i e s of E n g i n e e r i n g M a t e r i a l s (S c ran to n , I n t e r n a t i o n a l T ex tbook C o m p an y , 1957), pp. 4 4 -4 7 .

m a x i m u m a m o u n t of e n e r g y which a un i t v o lu m e of the m a t e r i a l w i l l

a b s o r b . As such, i t s un i t s a r e in c h -p o u n d s p e r cub ic inch , and i t i s

a p p r o x i m a t e l y equa l to the a r e a u n d e r th e s t r e s s - s t r a i n c u r v e f o r

a x ia l loading . The m o d u lu s of t o u g h n e s s m a y be e x te n d e d to m e m b e r s

o r s t r u c t u r e s a s w e l l a s m a t e r i a l s . A r e a s u n d e r l o a d - d e f o r m a t i o n

c u r v e s m a y be u s e d to c o m p a r e t o u g h n e s s .

D u c t i l i ty and u l t i m a t e s t r e n g t h both c o n t r ib u t e to the m o d u lu s

of t o u g h n e s s . An i n c r e a s e in d u c t i l i ty a lone , u l t i m a t e s t r e n g t h r e m a i n

ing a p p r o x i m a t e l y the s a m e , is enough to i n c r e a s e the t o u g h n e s s c o n

s id e r a b ly . See F i g u r e 1.

Q<o_1

L o a d - D e f o r m a t i o n C u r v e s F i g u r e 1

II. O b je c t iv e s of th e Study

The p r o b l e m w a s to i n v e s t i g a t e the b e h a v i o r of p r e s t r e s s e d

c o n c r e t e m e m b e r s in t o r s i o n . T o r s i o n f a i l u r e s a r e e s p e c i a l l y sudden

in p l a in an d r e i n f o r c e d c o n c r e t e . P r e s t r e s s i n g i n c r e a s e s the t o r s

iona l s t r e n g t h of a m e m b e r . But f a i l u r e s in p r e s t r e s s e d c o n c r e t e

a r e a l s o d e s c r i b e d a s " s u d d e n " a n d v io l e n t " . S o m e t i m e s a p a r t i c

u l a r a m o u n t of duc t i l i ty , the a m o u n t depend ing on th e fu n c t io n of the

m e m b e r , i s sought. M o n o r a i l b e a m s p r o v i d e an e x a m p l e . The b e a m s

on the c u r v e d p o r t i o n of th e m o n o r a i l a r e s u b jec t to l a r g e t o r s i o n a l

f o r c e s an d a h igh d e g r e e of d u c t i l i ty an d e n e r g y a b s o r p t i o n i s r e q u i r e d .

The h y p o t h e s i s th a t p r o m p t e d th i s s tudy i s th a t an i n c r e a s e in w eb

r e i n f o r c i n g i n c r e a s e s d u c t i l i ty and to u g h n e s s of a m e m b e r .

The s tu d y is an e x p e r i m e n t a l in v e s t ig a t i o n of the e f f e c t s of

w eb r e i n f o r c i n g in th e f o r m of c l o s e d s t i r r u p s on the b e h a v i o r of p r e

s t r e s s e d c o n c r e t e m e m b e r s s u b j e c t e d to t o r s i o n . P h a s e s of b e h a v io r

s tu d ie d inc lude i n i t i a l c r a c k i n g p a t t e r n , l o a d - d e f o r m a t i o n r e l a t i o n

ship , c o n f ig u ra t io n of f a i l u r e p lan e , a n d u l t i m a t e s t r e n g t h . The p r i m

a r y p u r p o s e of the s tudy w a s to d e t e r m i n e th e e f fec t of web r e i n f o r c i n g

on the to u g h n e s s an d t o r s i o n a l c a p a c i t y of a m e m b e r .

The in v e s t ig a t i o n w a s l i m i t e d to r e c t a n g u l a r b e a m s with a

d e p t h - t o - w i d t h r a t i o of a p p r o x i m a t e l y 3 to 1. The beam 's w e r e a x i a l l y

p r e s t r e s s e d by th e p r e t e n s i o n i n g m e th o d . The c r o s s s e c t io n of the

m e m b e r , c o n c r e t e s t r e n g th , p r e s t r e s s i n g f o r c e , and lo n g i tu d in a l r e i n

f o r c in g w e r e t r e a t e d a s c o n s t a n t s . The only v a r i a b l e w a s the a m o u n t ’

6. Zia , P a u l , " T o r s i o n a l S t r e n g th of P r e s t r e s s e d C o n c r e t e M e m b e r s , " Ph . D. d i s s e r t a t i o n ( U n i v e r s i t y of F l o r i d a , I960) , p. 1; Kemp,E . L. J r . , "An A n a ly t i c a l and E x p e r i m e n t a l Study of T o r s i o n in R e i n f o r c e d C o n c r e t e B e a m s , " P h . D. d i s s e r t a t i o n ( U n i v e r s i t y of I l l in o i s , 1962), p. 31.

7. Z ia ( I960) , p. 106.

of web r e i n f o r c i n g . A u n i f o r m s t i r r u p s i z e w a s e m p lo y e d ; v a r i a t i o n

w a s a c h i e v e d by v a r y i n g th e s t i r r u p sp ac in g .

- HI. S u r v e y of D es ig n R e c o m m e n d a t i o n s

A. R e i n f o r c e d C o n c r e t e .

A th o ro u g h d i s c u s s i o n of the d e s ig n f o r t o r s i o n in r e i n f o r c e d

c o n c r e t e m e m b e r s s p e c i f i e d in v a r i o u s n a t io n a l c o d e s h a s b een p r e -g

s e n t e d by G o rd o n F i s h e r and P a u l Z ia . The ACI code b a r e l y m e n t i o n s

t o r s i o n , s t a t in g only th a t c l o s e d s t i r r u p s an d lo n g i tu d in a l r e i n f o r c i n g

9shou ld be u s e d in s p a n d r e l b e a m s . F r a n c e , G e r m a n y , A u s t r a l i a ,

P o la n d , H u n g a ry , and R u s s i a a r e am o n g c o u n t r i e s w h o se co d es g ive

e x p l i c i t r e q u i r e m e n t s f o r m e t h o d of c a l c u l a t i n g s t r e s s e s , f o r p e r m i s

s ib le s t r e s s e s , an d fo r p r o p o r t i o n i n g of t o r s i o n a l r e i n f o r c e m e n t .

C o d es in s e v e r a l o t h e r c o u n t r i e s m e r e l y de f ine p e r m i s s i b l e s t r e s s e s .

C o d es in m a n y c o u n t r i e s m a k e no m e n t i o n of d e s ig n f o r t o r s i o n .

A s h o r t but c o m p r e h e n s i v e t r e a t m e n t of th e a n a l y s i s and

d e s ig n of b e a m s f o r t o r s i o n m a y be found in th e r e i n f o r c e d c o n c r e t e

d e s ig n te x t by W in te r , U r q u h a r t , O 'R o u r k e , and N i lson . ^ T hey

8. F i s h e r , G o rd o n P . and P a u l Zia , "R ev iew of Code R e q u i r e m e n t s f o r T o r s i o n D e s i g n , " J o u r n a l of the A m e r i c a n C o n c r e t e In s t i tu t e , P r o c e e d i n g s LXI, 1 ( J a n u a r y 1964), 1 -44 .

9. ACI C o m m i t t e e 318, Build ing Code R e q u i r e m e n t s f o r . R e i n f o r c e d C o n c r e t e , ACI 318-63 (D e t ro i t , A m e r i c a n C o n c r e t e I n s t i tu te , 1963) , p . 47.

10. W in te r , G. , L. C. U r q u h a r t , C. E. O 'R o u r k e , and A. H. N i lson , D e s ig n of C o n c r e t e S t r u c t u r e s , 7th ed. (New York , M c G r a w - Hil l , 1964), pp. 647 -652 .

r e c o m m e n d th a t th e c a l c u l a t i o n of t o r s i o n a l s t r e s s e s be b a s e d on the

c l a s s i c a l t h e o r y of Sa in t V enan t , ^ th a t p e r m i s s i b l e t o r s i o n a l s h e a r

s t r e s s e s be th e s a m e a s v a l u e s p r e s e n t l y p r e s c r i b e d f o r f l e x u r a l s h e a r ,

and th a t s t i r r u p sp ac in g and lo n g i tu d in a l r e i n f o r c i n g be d e t e r m i n e d a st

i t i s by the A u s t r a l i a n code.

B. P r e s t r e s s e d C o n c r e t e

In d e t e r m i n i n g web r e i n f o r c i n g r e q u i r e m e n t s , t o r s i o n a l

s t r e s s e s m a y be c o n s i d e r e d q u a l i t a t i v e ly i d e n t i c a l w i th o t h e r ty p e s

of s h e a r i n g s t r e s s e s . In t o r s i o n , d ia g o n a l t e n s i o n c r a c k s open on

one s ide of th e b e a m b e f o r e c o m p r e s s i o n f a i l u r e o c c u r s on th e o th e r .

D i s c u s s i n g web r e i n f o r c i n g , m o s t t e x t s a g r e e th a t i t i s c u s

t o m a r y to p r o v id e n o m i n a l s h e a r o r w eb r e i n f o r c i n g even w hen su ch

r e i n f o r c i n g is no t r e q u i r e d t h e o r e t i c a l l y . The B u r e a u of P u b l i c R o a d s '

C r i t e r i a f o r P r e s t r e s s e d C o n c r e t e r e q u i r e s th a t the m i n i m u m web

r e i n f o r c i n g be 0. 0008 of the c r o s s - s e c t i o n a l a r e a of the b e a m , s p a c e d

12a t t h r e e - q u a r t e r s of the dep th of the b e a m . The A C I-A S C E J o in t

C o m m i t t e e 323 r e c o m m e n d e d 0. 0025 b ' s w h e r e b ‘ i s th e width of the

13web and s i s the s t i r r u p sp ac in g .

11. See T i m o sh e n k o , S. and J . N. G o o d ie r , T h e o r y of E l a s t i c i ty , 2nd ed. (New York , M c G r a w - H i l l , 1951), pp. 258-315 .

12. B u r e a u of P u b l i c Roads in J a m e s R. L ibby , P r e s t r e s s e d C o n c r e t e (New Y ork , Ronald P r e s s , 1961), p. 71.

13. A C I-A S C E J o in t C o m m i t t e e 323, " T e n ta t i v e R e c o m m e n - . d a t io n s f o r P r e s t r e s s e d C o n c r e t e , " J o u r n a l of th e A m e r i c a n C o n c r e t e In s t i t u t e XXIX, 7 ( J a n u a r y 1958), 545-578 .

L ib b y r e c o m m e n d s web r e i n f o r c i n g " as a m e a n s of p r o t e c t i o n

a g a i n s t h o r i z o n t a l c r a c k s which s o m e t i m e s o c c u r in the w e b s of I-

s h a p e d b e a m s a s a r e s u l t of c o n c r e t e s h r in k a g e , f o r m ex p an s io n , o r

t h e r m a l s t r a i n s , a s w e l l a s a g a i n s t h o r i z o n t a l c r a c k s w h ich s o m e t i m e s

o c c u r in th e w e b s of b e a m s which a r e l o a d e d n e a r u l t i m a t e . " If the

top f lange b e c o m e s s e p a r a t e d f r o m th e r e s t of th e b e a m it i s p o s s i b l e

14fo r th e top f lange to f a i l p r e m a t u r e l y by buck l ing .

Some a u t h o r s u n q u a l i f i e d ly r e c o m m e n d the u s e of a n o m in a l

a m o u n t of web r e i n f o r c i n g . ^ O th e r s q u e s t i o n th e m e r i t of th i s

16p r a c t i c e .

The A u s t r a l i a n p r e s t r e s s e d c o n c r e t e code p r o v i d e s f o r the

u l t i m a t e s t r e n g t h d e s ig n of m e m b e r s s u b je c t e d to t o r s i o n . " T o r s

io n a l - s h e a r s t r e s s e s s h a l l be c a l c u l a t e d by a s s u m i n g fu ll p l a s t i c d i s -

17t r i b u t i o n of s t r e s s in the c r o s s s e c t i o n . " When t o r s i o n i s not a

d o m in a n t d e s ig n f a c t o r t o r s i o n a l - s h e a r r e i n f o r c e m e n t i s p r o v i d e d

f o r th a t p a r t of th e u l t i m a t e tw i s t in g m o m e n t w h ich p r o d u c e s p r i n c i

pa l t e n s i l e s t r e s s in e x c e s s of 4 ^ £ ' ^ "When t o r s i o n i s the d o m in a n t

14. L ibby, p. 71.

15. Lin , T. Y. , D es ig n 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 , 2nd ed. (New York , Jo h n Wiley, 1955), p. 224.

16. Chi, M. and F . A. B i b e r s t e i n , T h e o r y of P r e s t r e s s e d C o n c r e t e (E ng lew ood Cl i f f s , New J e r s e y , P r e n t i c e - H a l l , 1963), pp. 144-t u t :

17. Cowan, H. J . , R e i n f o r c e d and P r e s t r e s s e d C o n c r e t e in T o r s i o n (L ondon , E. A rn o ld , 1965), p. 128.

f a c t o r in a d e s ig n , a c a t a s t r o p h i c f a i l u r e m a y o c c u r i m m e d i a t e l y

a f t e r the f o r m a t i o n of the f i r s t t e n s i o n c r a c k . In th i s c a s e th e c a l c u

l a t e d u l t i m a t e t e n s i l e s t r e s s s h a l l no t e x c e e d 4][ f ' i r r e s p e c t i v e of

18the a m o u n t of n o n - p r e s t r e s s e d s h e a r r e i n f o r c e m e n t . n The u p p e r

l i m i t on the p r i n c i p a l t e n s i l e s t r e s s f o r w o rk in g lo a d s i s 3 l j f 8 i r

r e s p e c t i v e of the a m o u n t of u n t e n s i o n e d r e i n f o r c e m e n t .

The fo llowing f o r m u l a e a r e g iv e n f o r c a lc u l a t i n g t o r s i o n a l

r e i n f o r c e m e n t .

A r e a of two l e g s of t r a n s v e r s e c l o s e d h o o p s :

8 MtsA.

sv 0. 8 x , y . f1 ' 1 s y

T o ta l a r e a of long i tu d in a l b a r s :

x i + nA s - A sv

s

w h e r e s i s the p i t c h of the h o ops , and «y a r e the s m a l l e r and l a r g e r

d i m e n s i o n s of the h o o p s r e s p e c t i v e l y , m e a s u r e d c e n t r e to c e n t r e ,

is th e tw i s t in g m o m e n t to be r e s i s t e d by i n s e r t i o n of the h o o p s and a

19c o r r e s p o n d i n g a m o u n t of lo n g i tu d in a l s t e e l .

The only o t h e r code with p r o v i s i o n s f o r p r e s t r e s s e d c o n c r e t e

i s the G e r m a n code , DIN 4227, which g iv e s m a x i m u m a l lo w ab le

s t r e s s e s f o r th e c o n c r e t e . ^

18. C ow an (1965), p. 128.19. Cowan (1965), p. 38.20. F i s h e r a n d Zia , p. 29 -31 .

H e n r y J . C ow an b a s e s h i s t h e o r y on the M a x im u m S t r e s s

C r i t e r i o n of f a i l u r e . F o r an a x i a l l y p r e s t r e s s e d m e m b e r s u b j e c t e d

to t o r s i o n the c r i t i c a l s t r e s s i s the m i n o r p r i n c i p a l s t r e s s . Cowan,

in R e i n f o r c e d C o n c r e t e and P r e s t r e s s e d C o n c r e t e in T o r s i o n , p r e

s e n t e d fo u r e x a m p l e s of d e s i g n of p r e s t r e s s e d m e m b e r s w i thou t

21w eb r e i n f o r c i n g . In a s e p a r a t e s e c t io n e n t i t l e d " N o n - p r e s t r e s s e d

s h e a r r e i n f o r c e m e n t " Cowan r e f e r r e d to tl>e w o r k of P a u l Z ia a s the

on ly r e c o r d e d in v e s t ig a t i o n in wh ich t o r s i o n a l - s h e a r r e i n f o r c e m e n t

22h a s b e e n u s e d . He quo ted Z i a ' s c o n c lu s io n s . Cow an th en p r o v id e d

a d e s ig n e x a m p l e i l l u s t r a t i n g the c o m p u ta t io n of r e q u i r e d web r e i n

f o r c in g f o r a g iven p r e s t r e s s e d b e a m to r e s i s t a g iven t o r s i o n a l

m o m e n t .

21. Cowan (1965), pp. 72 -73 .

22. See be low, Rev iew of E x p e r i m e n t a l R e s e a r c h , pp. 14- 17.

REV IE W O F E X P E R I M E N T A L R E S E A R C H

I. P l a i n and R e i n f o r c e d C o n c r e t e

The f i r s t i n v e s t i g a t i o n s of th e t o r s i o n a l s t r e n g t h of s t r u c t u r

a l c o n c r e t e w e r e r e p o r t e d in 1903. M o r s c h in G e r m a n y an d M e s n a -

g e r in F r a n c e e ac h p e r f o r m e d s i m p l e t e s t s on c i r c u l a r s p e c i m e n s .

A n o th e r i n v e s t ig a t i o n w a s c a r r i e d out a t th e T e c h n i s c h e H o c h sc h u le

S tu t tg a r t by B ach a n d G r a f in 1912. T h e i r e x p e r i m e n t s i n c lu d e d

s q u a r e and r e c t a n g u l a r r e i n f o r c e d s p e c i m e n s a s w e l l a s p la in c o n

c r e t e s p e c i m e n s w i th v a r i o u s c r o s s s e c t i o n s . Cowan d e s c r i b e d

t h e s e i n v e s t i g a t i o n s in h i s p a p e r , " D e s ig n of B e a m s Subjec t to T o r -

23s io n R e l a t e d to th e New A u s t r a l i a n Code. " The, fo l lowing i n v e s t i

g a t io n s a d d ed to the u n d e r s t a n d i n g of r e i n f o r c e d c o n c r e t e in t o r s i o n :

G r a f and M o r s c h , 1922; Young, Sa.gar, and Hughes , 1922; M iy am o to ,

1927; T u r n e r an d D a v ie s , 1934; P a u l A n d e r s e n , 1935; M a r s h a l l and

T e m b e , 1941; N y la n d e r , 1 9 4 5 ; ^ Cowan, 1 9 5 1 . ^

23. Cowan, H. J . , "D es ig n of B e a m s Sub jec t to T o r s i o n R e l a t e d to the A u s t r a l i a n Code, " J o u r n a l of th e A m e r i c a n C o n c r e t e , I n s t i tu te XXXI, 7 ( J a n u a r y I960) , 613 -614 .

24. Cowan ( I960) , pp. 614 -618 .

25. Cowan, H. J . , " T e s t s o f th e T o r s i o n a l S t r e n g th and D e f o r m a t i o n of R e c t a n g u l a r R e i n f o r c e d C o n c r e t e B e a m s , " C o n c r e t e and C o n s t r u c t i o n a l E n g i n e e r i n g XLVI, 2 ( F e b r u a r y 1951), 51-59 .

11

II. P r e s t r e s s e d C o n c r e t e

N y la n d e r in 1945 r e p o r t e d on t e s t s c a r r i e d out on 60 b e a m s

a t Kungl iga T e k n i s k a H og sk o lan , S tockho lm . ^ The b e a m s w e r e

t e s t e d wi th v a r i o u s c o m b in a t io n s of load ing a s w e l l a s in p u r e t o r s i o n .

N y la n d e r c o n c lu d e d th a t i m m e d i a t e l y b e f o r e f a i l u r e th e c o n c r e t e s e c

t io n a c t e d p l a s t i c a l l y ; the s h e a r i n g s t r e s s w a s c o n s t a n t o v e r the

e n t i r e s e c t i o n and e q u a l to th e t e n s i l e s t r e n g t h of the c o n c r e t e . He

r e a s o n e d th a t the a d d i t io n of a c o m p r e s s i v e f o r c e would i n c r e a s e the

t o r s i o n a l s t r e n g t h . N y la n d e r d id no t d i s c u s s t o r s i o n a l - s h e a r r e i n -i

f o r c in g .

Cowan in 1953 and Cowan an d A r m s t r o n g in 1955 and 1957

2 7r e p o r t e d on v a r i o u s e x p e r i m e n t s . Some of t h e s e in c lu d e d c o m

b in e d bend ing a n d t o r s i o n t e s t s on p r e s t r e s s e d c o n c r e t e b e a m s . B e

tw e e n 1953 an d 1957 Cowan f o r m u l a t e d an d s u b s t a n t i a t e d h i s own c r i

t e r i o n of f a i l u r e f o r c o n c r e t e . His c r i t e r i o n c o m b i n e s R a n k i n e 1 s

m a x i m u m s t r e s s t h e o r y and C o u l o m b ' s i n t e r n a l f r i c t i o n t h e o r y . It

c o m p r i s e s the two m o d e s of f a i l u r e of c o n c r e t e : c l e a v a g e and s h e a r

f r a c t u r e .

26. N y la n d e r , H. , V r id n in g och v r idn ing s in sp an n in g v id b e t o n g k o n s t r u k t i o n e r ( T o r s i o n and T o r s i o n a l R e s t r a i n t by C o n c r e t e S t r u c t u r e s ) , B u l le t in No. 3 (S tockho lm , S ta te n s K o m m i t t e b y g g n a d s - f o r s k n in g , 1945).

27. Zia , P a u l , " T o r s i o n a l S t r e n g th of P r e s t r e s s e d C o n c r e t e M e m b e r s , 11 J o u r n a l of th e A m e r i c a n C o n c r e t e In s t i t u t e XXXII, 10 (A p r i l 1961), 1358, R e f e r e n c e s 2 -4 .

13

In 1957 H u m p h r e y s r e p o r t e d on an i n v e s t ig a t i o n he co n d u c te d

a t K in g ' s C o l lege , U n i v e r s i t y of D u r h a m . He t e s t e d a to t a l of 94

s q u a r e and r e c t a n g u l a r b e a m s wi th p r e s t r e s s i n g f o r c e s v a r y i n g f r o m

z e r o to 6000 p s i . He c o n c lu d e d th a t the t o r s i o n a l s t r e n g t h of su i t a b ly

p r e s t r e s s e d c o n c r e t e m a y be s a f e ly i n c r e a s e d above th e s t r e n g t h of

p la in c o n c r e t e in th e r a t i o 2. 5:1 w i thou t changing o t h e r p h y s i c a l p r o p -

28e r t i e s of the c o n c r e t e . The t h e o r e t i c a l c u r v e fo r u l t i m a t e t o r s i o n

a l s t r e s s i s Tut=Y ^ + 4% f c w h e r e (Tj i s th e m a x i m u m t e n s i l e s t r e s s

a n d f c i s the a p p l i e d a x i a l co m p ress iv e* ’ s t r e s s . H u m p h r e y s d e r i v e d

a r e g r e s s i o n l ine f r o m h i s t e s t da ta . I ts e q u a t io n i s r (J= 6^ + 0. 3070

f . C o m p a r i n g t h e s e two c u r v e s he found th a t th e r e g r e s s i o n l ine

w a s in c l o s e a g r e e m e n t wi th the t h e o r e t i c a l c u r v e th ro u g h f c = 3500

p s i . H u m p h r e y s s u b s t i t u t e d T = + 0. 3 f c f o r th e m a x i m u m s t r e s s

in to the f o r m u l a d e r i v e d in t h e o r y of e l a s t i c i t y which r e l a t e s s t r e s s

and to r q u e .

The m a x i m u m tw is t in g m o m e n t Tu which m a y be s a f e ly a p p l i e d to a c o n c e n t r i c a l l y p r e s t r e s s e d r e c t a n g u l a r c o n c r e t e s e c t io n i s :

T + 0 . 3 f 2Tu = k 2 " ~ C 2 b (2a )

w h e r e ? i s th e u l t i m a t e t o r s i o n a l s t r e s s of p la in .co n c re te , f c i s the

m a g n i tu d e of the c o n c e n t r i c p r e s t r e s s r e m a i n i n g a f t e r a l l l o s s e s h a v e

28. H u m p h r e y s , R. " T o r s i o n a l S t r en g th of P r e s t r e s s e d C o n c r e t e " , The S t r u c t u r a l E n g i n e e r , London, XXXV, 6 (June 1957). 223.

14

b een ded u c ted , F is the f a c t o r of sa fe ty , 2a is the l e a s t l a t e r a l d i m e n

s ion of the b e am , and 2b is the g r e a t e s t l a t e r a l d im e n s io n of the b e am .

£>.-2-3-----

2 43*SAd<7- n -v h o b / a .

The c o n s t a n t d ep en d s upon the shape of the r e c t a n g l eand fo r p la in c o n c r e t e o r s e c t io n s con ta in ing bonded p r e s t r e s s i n g h a s the va lue g iven in the f ig u r e above . ^

At the U n iv e r s i t y of F l o r i d a in I960, P a u l Zia p r e s e n t e d a

d i s s e r t a t i o n e n t i t l e d T o r s i o n a l S t r en g th of P r e s t r e s s e d C o n c r e t e

M e m b e r s . ^ Z ia t e s t e d 68 p r e s t r e s s e d c o n c r e t e b e a m s wi th r e c

t a n g u l a r , T - and I- s e c t i o n s u n d e r p u r e t o r s i o n . Both a x ia l and e c c e n

t r i c p r e s t r e s s i n g f o r c e s w e r e u sed . F o r the f i r s t t i m e s e c t io n s with

web r e i n f o r c i n g w e r e t e s t e d in ad d i t ion to s e c t io n s withou t .

To a t t a in f u l l e r a g r e e m e n t with H u m p h r e y s ' t e s t d a ta and

to m a k e a s m o o t h e r t r a n s i t i o n b e tw ee n the two m o d e s of f a i l u r e , Zia

m o d i f i e d C o w a n ' s t h e o ry . The m o d i f i ed t h e o r y is v e r y c lo s e to t e s t

r e s u l t s when the p r e s t r e s s i n g f o r c e is not g r e a t e r than a p p r o x i m a t e l y

0. 5 f ' c . P r e s t r e s s i n g f o r c e s u s ed in a c tu a l c o n s t r u c t i o n a r e u s u a l ly

w i th in th is range .

29. H u m p h r e y s , p. 223.30. Zia ( I960) , pp. 1-160.

15

— « —

AVonED CaKM

0 ,'L l.o7

f c / f 'c

31Z i a ' s C o m p a r i s o n of F a i l u r e T h e o r i e s F i g u r e 2

31. Zia (I960) , p. 66.

1

16

Zia s t a t e d th a t the M od if ied Cowan T h e o r y i s , in effec t , a c l o s e a p p -

' 32r o x i m a t i o n of M o h r ' s g e n e r a l i z e d i n t e r n a l f r i c t i o n th e o r y . Z ia

c o n c lu d e d a s fo l lows .

The M od if ied Cowan T h e o r y d ep en d s on two in d e p e n d e n tp r o p e r t i e s of c o n c r e t e ; c o m p r e s s i v e s t r e n g t h and t o r s i o n a ls t r e n g th . The l a t t e r i s a s s u m e d to be e q u a l to t e n s i l es t r e n g t h and i s g iven by a n e m p i r i c a l r e l a t i o n = f ft =0. 68 ( f ,c ) ' . A c c o r d i n g to th i s t h e o r y the o p t i m u m p r e s t r e s si s 70 p e r c e n t of th e c o n c r e t e c o m p r e s s i v e s t r e n g th . With th i sp r e s t r e s s i n g e f f o r t the c o r r e s p o n d i n g t o r s i o n a l s t r e n g t h ofthe c o n c r e t e i s 2 .8 1 t i m e s th a t of p la in c o n c r e t e if the con -

33c r e t e c o m p r e s s i v e s t r e n g t h is 6000 p s i .

Z ia a l s o a s s e r t e d th a t u l t i m a t e m o m e n t c a n be p r e d i c t e d by e l a s t i c t h e o r y .

U l t im a te m o m e n t of p r e s t r e s s e d m e m b e r s of r e c t a n g u l a r and T - s e c t i o n s w i thou t w eb r e i n f o r c e m e n t i s the s a m e a s the c r a c k i n g m o m e n t d e t e r m i n e d a c c o r d i n g to St. V e n a n t 1 s t o r s ion t h e o r y an d the m o d i f i c a t i o n of C o w a n ' s c r i t e r i o n of f a i l u r e .

Z ia found th a t am o n g h i s n o n - p r e s t r e s s e d s p e c i m e n s the o n e s

with web r e i n f o r c i n g h a d th e s a m e s t r e n g t h a s s i m i l a r s p e c i m e n s

w i thou t web s t e e l . He found th a t the p r e s e n c e of web s t e e l i n c r e a s e d

th e to u g h n e s s of the s p e c i m e n but not i t s s t r e n g t h . T h r e e of Z i a ' s

c o n c lu s io n s d e a l t with w eb r e i n f o r c i n g .

A c o n c r e t e m e m b e r w i thou t web r e i n f o r c e m e n t f a i l s a b r u p t l y u n d e r t o r s i o n . T h i s type of sudden f a i l u r e can be a v o id ed b y u s in g w eb s t e e l a s t i e s s p a c e d not m o r e th an 0. 4 of the depth of the m e m b e r . T h i s d e l a y e d f a i l u r e w a s fu l ly

32. Z ia ( I960) , p. 58.

33. Zia (1961), pp. 1357-1358.

34. Z ia (1961), p. 1358.

35. Z ia (1961), p. 1358.

17

d e m o n s t r a t e d by the s p e c i m e n s con ta in ing w eb s t e e l of about1. 5 p e r c e n t of the v o lu m e of the c o r e e n c l o s e d w i th in the t i e s .

The u se of web r e i n f o r c e m e n t h a s no a p p a r e n t e f fec t on the e l a s t i c b e h a v i o r of a m e m b e r .

U l t im a te s t r e n g t h of p r e s t r e s s e d m e m b e r s with web s t e e l is equa l to the su m of the c r a c k i n g m o m e n t of the m e m b e r and the m o m e n t r e s i s t e d by the web r e i n f o r c e m e n t . ^

Z i a ' s l o a d - d e f o r m a t i o n c u r v e s i n d ic a te h i s co n ce p t io n of

t o u g h n e s s . Inc luded h e r e a r e the l o a d - d e f o r m a t i o n c u r v e s fo r r e c

t a n g u l a r m e m b e r s .

w y \ ^ iQEYwefCMS

) o -----

-I---------

A A tq u e . t w i s t /N r v - r i A / c

Z i a ' s T o r q u e - T w is t C u r v e s fo r R e c t a n g u l a r S e r i e s ' ^

F i g u r e 3

35. Zia (1961), p. 1358.

36. Z ia ( I960) , p. 99.

TE ST PROGRAM

I. T e s t B e a m s

F o r th i s in v e s t ig a t i o n r e c t a n g u l a r b e a m s s ix in c h e s by s i x

t e e n in c h e s in c r o s s s e c t io n w e r e p r e s t r e s s e d by the p r e t e n s i o n i n g

m e th o d . C o n c r e t e s t r e n g th , p r e s t r e s s i n g f o r c e , and long i tud ina l

r e i n f o r c i n g w e r e c o n s t a n t s . The only v a r i a b l e w a s the a m o u n t of

w eb r e i n f o r c i n g in the f o r m of c l o s e d s t i r r u p s . T h e s e s t i r r u p s o r

t i e s w e r e a l l of the s a m e b a r s ize . The v a r i a t i o n w as a c h ie v e d by

v a r y in g the s t i r r u p spac ing .

T e s t B e a m s F i g u r e 4

19

The b e a m s w e r e d e s ig n e d with an a r m p r o j e c t i n g f r o m each

s ide . The d i s t a n c e b e tw e e n the a r m s w a s s e v e n fe e t . The a r m s

a l lo w ed t o r s i o n to be a p p l i e d to the b e a m by d i r e c t f o r c e . By a p p l y

ing a v e r t i c a l f o r c e a t the i n t e r s e c t i o n of the a r m with the b e a m and

an o p p o s i t e f o r c e a t the end of th e a r m a m o m e n t w a s i n t r o d u c e d in

a p la n e n o r m a l to th e a x i s of the b e a m . The m a i n body of the b e a m

e x ten d e d beyond th e a r m s to p r o v i d e the n e c e s s a r y t r a n s f e r leng th

fo r the p r e s t r e s s i n g s t r a n d and a l s o to c o u n t e r b a l a n c e the p o s i t i v e

m o m e n t o v e r the m i d d l e o r t e s t p o r t i o n of the m e m b e r . The to ta l

l eng th of th e b e a m w a s tw e lv e fee t . The s t i r r u p s p a c in g w a s v a r i e d

f r o m b e a m to b e a m in the t e s t p o r t i o n only. I m m e d i a t e l y a d j a c e n t

to th e m o m e n t a r m s s t i r r u p s w e r e c l o s e l y s p a c e d to p r e v e n t f a i l u r e

o c c u r r i n g t h e r e .p

The long i tu d in a l r e i n f o r c i n g w a s fo u r #3 b a r s , one in e a c h

c o r n e r of the c l o s e d s t i r r u p o r hoop. The b a r s c o n f o r m e d to ASTM

A 15, I n t e r m e d i a t e G r a d e , and h ad d e f o r m a t i o n s in a c c o r d a n c e w i th

ASTM A 30 5. T h ey h a d an a v e r a g e y ie ld po in t of 55, 900 p s i and an

a v e r a g e u l t i m a t e s t r e n g t h of 7 9 ,0 9 0 p s i . The a c tu a l a r e a of the #3

b a r s w a s 0 . 1 1 2 s q u a r e i n c h e s . Th is w a s 0. 015% of the a r e a of the

b e a m .

The s t i r r u p s w e r e f a b r i c a t e d by C o m s t o c k S tee l C om pany .

The #2 b a r , ASTM A 15, I n t e r m e d i a t e G r a d e , w a s w i thou t d e f o r m a

t io n s . The b a r w a s b en t a r o u n d a o n e - a n d - o n e - h a l f - i n c h pin . The

>------- 3 ^ — TRST AKEA — UNqiTtiONAi-rrr 4 ct-rmvs

20

— 2- — 4 cf

■— * -

f t A M

<5 -2

'z fterTEssiNî 2TJO K.

Trr 6 Drrmv)

S C C T I Q /^ •

B eam D ra w in g s F i g u r e 5

B 2 | * - I 2 1

B 3 -*| |h

B4 rao ■s+i'r-mp . hznc

B 5 I | 4 - M ‘W -m i l l .

B6 i r i,c

»s“- I'-O"

S t i r r u p Spac ings F i g u r e 6

22

leng th of the b a r b e f o r e f a b r i c a t i o n w a s 3 ' - 7 " , p ro v id in g s t a n d a r d

13 5° hooks with t a i l s a s shown in F i g u r e 5. An a t t e m p t w a s m a d e

to ob ta in c o n s i s t e n c y in the wid th of th e s t i r r u p s . In s t a n d a r d shop

p r a c t i c e , h o w e v e r , 1 /4 inch t o l e r a n c e w a s the m i n i m u m th a t cou ld

be e x p ec te d . The m a j o r i t y of the s t i r r u p s w e r e fo u r an d one - e igh th

i n c h e s wide; th e m a x i m u m width w a s f o u r and t h r e e - e i g h t h s i n c h e s .

The depth w a s c o n s i s t e n t l y f o u r t e e n i n c h e s . The a v e r a g e y ie ld poin t

of the #2 b a r w a s 53, 7 50 p s i . U l t im a te s t r e n g t h w a s 81, 420 ps i .

The b e a m s w e r e m a n u f a c t u r e d a t th e J o h n so n C o n s t r u c t io n

C o m p a n y p r e s t r e s s i n g y a r d in T u c so n , A r i z o n a . A t e m p o r a r y p r e

s t r e s s i n g bench w a s s e t up on an e x i s t in g bed. T h i r t y - f o o t long

10 W7 66 c o lu m n s e c t io n w e r e e m p lo y e d a s th e c o m p r e s s i o n m e m

b e r s . A s b u lk h e a d s , 14 b e a m s w e r e p o s i t i o n e d to t a k e a d v a n ta g e

of t h e i r s t r o n g a x e s . A p lyw ood soff i t w a s c o n s t r u c t e d on the s l ab

to p r o v i d e a l e v e l w o rk in g s u r f a c e .

T he p r e s t r e s s i n g s t r a n d w a s 1 /2 inch d i a m e t e r , 270 K

g r a d e , 7 - w i r e u n c o a te d , s t r e s s - r e l i e v e d s t r a n d m a n u f a c t u r e d by

C o lo r a d o F u e l and I ron . The m o s t r e c e n t l y p u b l i s h e d lo a d - e l o n g -

a t ion c u r v e f o r 1 /2 inch s t r a n d i s a c c o m p a n i e d by th e fo l lowing

da ta .

M i n i m u m U l t im a te S t r e n g th 41, 300 lb s .N o m in a l S tee l A r e a 0. 153 sq . in.E l o n g a t io n in 10 ft.

a t 28, 900 lb s . 0. 812 in.

The P r e s t r e s s i n g B ench F i g u r e 7

F a b r i c a t e d and t e s t e d ina c c o r d a n c e with ASTM A 416 59T a n d 15% s t r o n g e r . ^

When the bed w a s t e n s i o n e d in p r e p a r a t i o n fo r the f i r s t p o u r a fau l t

in th e h y d r a u l i c s y s t e m e n a b le d th e r a m to dev e lo p only 4700 p s i

p r e s s u r e . O r d i n a r i l y 4900 p s i i s u s ed , pu l l ing the s t r a n d to 28. 9i

k ip s , 70% of i t s u l t i m a t e . At 4700 p s i t h e c a l i b r a t i o n c u r v e i n d i c a

t e d a f o r c e of .27. 6 k ip s . The m o d e l F M J 2 4 r a m h a d a 24" s t r o k e

and a 6 " - 1 0 , 000 p s i gauge . The gauge w a s r e c e n t l y c a l i b r a t e d by

E n g i n e e r s T e s t in g L a b o r a t o r i e s . The g au g e and i t s c a l i b r a t i o n

c u r v e h a s b e e n shown by e lo n g a t io n c h e c k s on b e d s of l e n g th s a r o u n d

200 f e e t to be v e r y a c c u r a t e . The 27. 6 kip f i g u r e i s t h e r e f o r e p r e

s u m e d to be r e l i a b l e . A l l s t r a n d w a s t e n s i o n e d to th e s a m e v a lu e .

E lo n g a t io n s m e a s u r e d d u r in g the s ec o n d t e n s io n in g o p e r a t i o n v a r i e d

f r o m two and o n e - q u a r t e r i n c h e s to two and f i v e - e i g h t h s in c h e s . The

e x p e c t e d e lo n g a t io n w a s c a l c u l a t e d to be 2. 51 i n c h e s . On a s h o r t bed

the m e a s u r e m e n t of e longa t ion , a l though v a lu a b l e f o r c o n f i r m a t io n ,

i s l e s s a c c u r a t e t h a n the gauge r e a d in g .

A f t e r th e s t r a n d w a s t e n s i o n e d the s t i r r u p s w e r e p o s i t i o n e d

a r o u n d th e s t r a n d an d the s t e e l c ag e w a s t i ed . The c ag e w a s s u p p o r

t e d on c h a i r s and a l s o s u s p e n d e d by t i e w i r e f r o m the f o r m s p r e a d e r s .

37. C o lo r a d o F u e l and I r o n C o r p o r a t i o n , " T y p ic a l L o a d E l o n g a t io n C u rv e , " r e c h e c k e d 3 - 1 - 6 4 .

25

Diff icu l ty w as e n c o u n t e r e d in a l ign ing the r e i n f o r c i n g . The c l e a r a n c e ,

d e t a i l e d a s one inch, v a r i e d f r o m o n e - h a l f inch to o n e - a n d - o n e - q u a r t e r

i n c h e s .

F L A N •

P r e s t r e s s i n g Bench D e ta i l s F i g u r e 8

F o r m s w e r e c o n s t r u c t e d of p lyw ood and w e r e o i led with Nox-

c r e t e . D ur ing the p lac ing of c o n c r e t e fo r b e a m B 1 a s id e f o r m tha t

h a d no t b e e n c o m p l e t e l y n a i l e d in p l a c e b e c a m e lo o se . The f o r m w as

r e p a i r e d and c o n c r e t i n g w a s con t inued . The b e a m w as not a p p a r e n t l y

i m p a i r e d . B e c a u s e of the p o s s i b i l i t y of u n d e te c t e d i r r e g u l a r i t i e s ,

h o w e v e r , B 1 w as d e s i g n a t e d a p i lo t s p e c i m e n . B4 w a s o r i g i n a l l y

d e s ig n e d with s t i r r u p s a t s ix in c h e s on c e n t e r but w a s c o n s t r u c t e d

without s t i r r u p s in o r d e r to r e p l a c e B1 in the s eq u e n c e .

The c o n c r e t e m i x fo r one cub ic y a r d w as :

c e m e n t , Type III 733 pounds

26

s a n d 1288 pounds

c o a r s e a g g r e g a t e 1770 pounds

w a t e r 40 g a l lo n s

PDA 60 o u n c e s

The c e m e n t f a c t o r w a s 7. 8 s a c k s p e r y a r d . Type III p o r t l a n d c e m e n t

i s u s u a l l y d e s i g n a t e d a s h i g h - e a r l y - s t r e n g t h c e m e n t . T he w a t e r -

c e m e n t r a t i o fo r th e above m i x w a s 5. 1 g a l lo n s p e r s ack . A dd i t io n a l

w a t e r w a s a d d ed in the m i x e r . The s an d and th e c o a r s e a g g r e g a t e

w e r e f r o m the San ta C r u z R iv e r and w e r e p r o c e s s e d by B u i l d e r s R ock

& Sand C om pany . PDA is a w a t e r - r e d u c i n g a d m i x t u r e , a c a l c i u m

l ign in s u l fo n a te in l iq u id s t a t e .

Two b e a m s w e r e c a s t in e a c h of t h r e e s e p a r a t e p o u r s . E ach

p a i r of t e s t b e a m s r e q u i r e d only t h r e e - q u a r t e r s of a cub ic y a r d of

c o n c r e t e , bu t the b a tch s i z e v a r i e d f r o m o n e - a n d - o n e - h a l f to t w o - a n d -

o n e - h a l f cub ic y a r d s . F o u r c o n c r e t e t e s t c y l i n d e r s w e r e t a k e n a t

e a c h p o u r . The c y l i n d e r s w e r e t r a n s p o r t e d to E n g i n e e r s T e s t in g

L a b o r a t o r i e s on th e t h i r d d ay a f t e r the p o u r . R e s u l t s of c y l i n d e r

t e s t s a r e shown in F i g u r e 11.

The c o n c r e t e w a s v i b r a t e d c o n t in u o u s ly du r in g p la c in g in

the f o r m s . The s lu m p v a r i e d f r o m one to t h r e e i n c h e s . The c o n

c r e t e r e c e i v e d a w o o d - f l o a t f in i sh . C u r in g com pound w a s a p p l i e d

to th e top s u r f a c e of th e b e a m s .

i Ji-'

27

T e n s io n in g th e S t r a n dF ig u r e 9

28

R e in fo rc in g and F o r m w o r k F i g u r e 10

co

/vsm

css

.i'y

c

u&

s,.

/ sc

^.

(r<v

5 5 \ 65> » 1 s t (%u

5 4 C5<i » Zf^rcyar-

5 1 ^ B'Z. o 2 ^ itur.

14-7 Z 8C o n c r e t e C y l in d e r T e s t s A ^ £

F i g u r e 11/ M o a v s ru

sO

, 30

When c a s t i n g took p l a c e the a i r t e m p e r a t u r e w a s in the h igh

s e v e n t i e s an d low e i g h t i e s . R e la t iv e h u m i d i t y r a n g e d f r o m t e n to

tw e n ty - tw o p e r cen t . The w e a t h e r w a s su n n y and windy.

On th e m o r n i n g of th e t h i r d day a f t e r c a s t in g , th e f o r m s

w e r e s t r i p p e d . The p r e s t r e s s i n g f o r c e w a s t r a n s f e r r e d to th e b e a m s

by cu t t ing the s t r a n d wi th a t o r c h . To m i n i m i z e e c c e n t r i c i t y a t the

b u lk h e ad th e s t r a n d w a s cu t a t a po in t b e tw e e n the b e a m s . B e c a u s e

of s h r i n k a g e of th e c o n c r e t e , t h e f o r c e a t the b u lk h e a d a t t h a t t i m e

w a s a s s u m e d to be g r e a t e r th a n th e in i t i a l f o r c e . The s t r a n d w e r e

cu t in t h i s o r d e r : top , b o t to m , u p p e r m i d d l e , an d l o w e r m id d le .

The b e a m s w e r e t r a n s p o r t e d by t r u c k to the C iv i l E n g i n e e r

ing Bui ld ing . The b e a m s m o s t r e c e n t l y c a s t w e r e f ive d a y s o ld a t

t h a t t i m e .

31

i

P la c in g C o n c re teF ig u r e 12

C utting S t r a n d

T r a n s p o r t in g th e B e a m sF ig u r e 13

33

II. T e s t A r r a n g e m e n t

A s t r u c t u r a l t e s t f l o o r i s i n c o r p o r a t e d in th e f a c i l i t i e s of

th e G r a d u a t e S t r u c t u r e s L a b o r a t o r y in th e C iv i l E n g i n e e r i n g Build ing

a t the U n i v e r s i t y of A r i z o n a . The t e s t f l o o r i s a c o n c r e t e s l a b t h r e e

f e e t t h i c k wi th a c c e s s s p a c e be low . T h e r e a r e tw o - i n c h d i a m e t e r

h o l e s t h r o u g h th e s l a b a t t h r e e f e e t on c e n t e r in each d i r e c t io n .

The m a i n c o m p o n e n t s of the t e s t s t a n d w e r e two s t e e l b e a m s ,

12 B 22 by t e n fee t , an d fo u r one - an d - one - qua r t e r inch r o d s by e l e v e n

f e e t s ix i n c h e s . The b e a m s th a t w e r e a v a i l a b l e h a d b e e n f a b r i c a t e d

f o r u s e with th e t e s t f lo o r . The b e a m s h a d s l e e v e s s ix i n c h e s f r o m

e ac h end to r e c e i v e the r o d s . E a c h s t e e l b e a m w a s u s e d to p r o v id e

a d o w n w a r d f o r c e on a m o m e n t a r m . S tee l a n g le s w e r e w e ld e d to

th e b o t t o m s of th e s t e e l b e a m s to p r o v i d e k n i f e - e d g e r e a c t i o n s . The

t h r e a d e d r o d s w e r e th e t e n s i o n m e m b e r s b e tw e e n th e s t e e l b e a m s

an d the t e s t f lo o r . The v e r t i c a l u p w a r d r e a c t i o n on th e t e s t s p e c i

m e n s w a s a p p l i e d by a j a c k u n d e r e a c h i n t e r s e c t i o n of an a r m with

th e t e s t b e a m .

The j a c k s w e r e S I M P L E X R E - M O - T R O L RAM, M odel No.

R306, t h i r t y - to n c a p a c i ty , s ix - inch t r a v e l , m a n u f a c t u r e d by T e m p l e

ton Ken ly and C om pany , B ro a d v ie w , I l l in o i s . The r a m s h a d a p i s to n

wi th an e f fec t iv e a r e a of 6. 53 s q u a r e i n c h e s . The c o n s o le f o r the

h y d r a u l i c s y s t e m h a d a tw e n t y - i n c h gauge .

34

r e ^ r r- A-V) LOCATION JAC-K

T l a m<c2A4-tL 11 e I - <?*

TEST ZSEA/A -_

T rL C O K . S L A B

T e s t Stand F i g u r e 14

35

T e s t S tand w ith B5F ig u r e 15

36

eosrT^lperD ^ > .ues.

AK/A

M e a s u r in g A p p a ra tu sP ' ig u re 16

E a c h t e s t b e a m w e ig h ed a p p r o x i m a t e l y 1450 pounds . A fo rk

l if t w a s u s e d to p l a c e the b e a m on a dolly . The b e a m cou ld th en be

m a n e u v e r e d into p l a c e by two p eop le . The s t e e l b e a m s r e m a i n e d

fixed , the j a c k s be ing u s e d to r a i s e eac h t e s t s p e c i m e n in to pos i t ion .

To m e a s u r e t w i s t in the b e a m a v e r t i c a l i n d i c a t o r w as

c l a m p e d to the s ide of the b e a m at the i n t e r s e c t i o n of e ac h a r m . E a c h

i n d i c a t o r p r o j e c t e d one m e t e r above the top of the b e a m . A s c a l e

r e a d in g in c e n t i m e t e r s w as s u s p e n d e d f r o m an in d e p en d e n t r ig i d f r a m e

w o rk . The s c a l e w as p o s i t i o n e d h o r i z o n t a l l y i m m e d i a t e l y beh ind the

p o in t e r .

The fo llowing p r o c e d u r e w a s e m p lo y e d fo r e ac h of the five

t e s t s . An o p e r a t o r c o n t r o l l e d the load ing co n so le . The h y d r a u l i c

s y s t e m w a s h e ld s t e a d y fo r abou t t h r e e to five m i n u t e s wi th only

enough p r e s s u r e to h o ld the t e s t b e a m snug ly in p l a c e a g a i n s t the

knife ed g es on the s t e e l b e a m s . Load ing w a s then begun . O b s e r v e r s

s t a t i o n e d at e ac h end of the b e a m took r e a d i n g s a s the o p e r a t o r r e

p o r t e d the a t t a i n m e n t of p r e a r r a n g e d load i n t e r v a l s . The r a t e of

load ing w a s k ep t c o n s t a n t and a s slow a s the e q u ip m e n t p e r m i t t e d .

The e n t i r e load ing c y c le took a p p r o x i m a t e l y t e n m i n u t e s .

TE ST R E S U L T S

I. N u m e r i c a l D a ta

The f i r s t b e a m t e s t e d w as B l . It w as u s e d a s a p i lo t t e s t .

One of the j a c k s l e a k e d o il a s the p r e s s u r e w a s i n c r e a s e d in the

h y d r a u l i c s y s t e m . C o n se q u e n t ly no r e l i a b l e r e a d i n g s c o u ld be o b

t a in e d f o r c a l c u l a t i n g t o r q u e . No r e a d i n g s w e r e t a k e n f o r c a l c u l a t

ing th e a m o u n t of tw i s t . The b e a m f a i l e d su d d en ly a n d w i thou t w a r n

ing. T h e r e w a s no p r e l i m i n a r y n o i s e ; th e n o i s e th a t o c c u r r e d when

th e b e a m f r a c t u r e d w a s no t g r e a t . An a p p a r e n t t e n s i o n f a i l u r e on

th e n e a r f a c e w a s a c c o m p a n i e d by a c o m p r e s s i o n f a i l u r e on the o t h e r

s ide of the b e a m .

The r e m a i n i n g f ive b e a m s w e r e t e s t e d by the p r o c e d u r e

d e s c r i b e d in th e p r e c e d i n g c h a p t e r , T e s t P r o g r a m . The t e s t d a ta

a r e a r r a n g e d in a s c e n d in g o r d e r a c c o r d i n g to th e a m o u n t of w eb r e i n

f o r c in g in the s p e c i m e n t e s t e d . The d a t a a r e p r e s e n t e d in the f o r m

in wh ich th e y w e r e r e c o r d e d . T h e ^ f i r s t c o lu m n r e p r e s e n t s the d i s

p l a c e m e n t , d, in c e n t i m e t e r s , r e a d f r o m the s c a l e a t t h e le f t end of

th e b e a m . The c e n t e r c o lu m n i s the gauge r e a d in g in p s i of th e p r e s

s u r e in the h y d r a u l i c s y s t e m . The t h i r d c o lu m n r e p r e s e n t s th e s c a l e

r e a d i n g of the d i s p l a c e m e n t a t the r ig h t end of th e b e a m . A c c o m p a n y

ing s k e t c h e s i l l u s t r a t e th e i n t e r s e c t i o n of t h e f a i l u r e p lan e w i th the n e a r ,

s ide , top, and f a r s id e of e a c h b e a m .

. 39

T ab le 1 T e s t Data

40

B4d^(cm.) gau g e (p s i ) d9 (cm.)

0 . 0 200 0 . 00.1 400 0 .00 .3 600 0.00 .4 800 0 .00 . 6 1000 0 . 00 . 8 1200 0 .01.0 1400 0.01.1 1600 0 .01.5 1800 0 .3

..................... ■

............ - _______r4------ --------------------------------^ ^

z---- —/

d^(cm.)B2

gauge(ps i ) d2(cm.)

0 .0 200 0 .00.2 400 0.00 .3 600 0 .30 .3 800 0 .40 .3 1000 0.50 .3 1200 0 .80 .3 1400 1.00.1 1600 1.4

1680

(cm.)

0 . 00 . 00 . 00 . 00 . 0

-0 .5-0 .50 .0

B3*gauge(ps i )

300400600800

10001200140016001900

I.;, (cm.)

0 . 00 . 00 . 20 . 61 .01 .62 . 02.4

J l

I I

* Specimen B3 was a c c id e n t ly loaded to f a i l u r e during the process of p o s i t i o n i n g ; d isp lacements were measured in a r e lo a d in g c y c le .

41

Table 1 - Continued

d^(cm.)B5

gauge(ps i ) 82 (err .)

0 .0 400 0 . 00 .2 600 0 .00 .4 800 0 .00 .6 1000 0 .00 . 8 1200 0 . 01.0 1400 0 .01.2 1600 0 .01.2 1700 0 .01.3 1800 0 .01.3 1900 0 .21.4 2000 0 .31.4 2100 0.51.9 2200 3.83.4 2300 5.0

2340

r t \ ________V _ a Aa i N T E z y i u e F A I L U R E "

B6 *(cm.) g auge (ps i ) d2 (cm.)

0 .0 200 0 .00.5 300 0 .00 .6 400 0 .00 .8 600 0 .00 .9 800 0 .01.0 1000 0 .11.1 1200 0 .11.2 1400 0 .21.3 1600 0 .31.5 1800 0 .41.6 2000 0 .61.7 2100 0 . 81 .8 2200 1.12.3 2300 1.32 .6 2400 1.63.1 2500 3.93.7 2600

27004 .8

II

n 'N[ --------- Z.

/M AIN T T N S I L E f=A IL a<B -

f

42

II. L o a d -D e fo rm a t io n R e la t io n s h ip

A. T o rq u e - T w is t C u rv e s

In to r s io n , the load is a to r s io n a l m o m e n t o r to rq u e . The

to rq u e i s the p ro d u c t of a fo r c e and a m o m e n t a r m . In the s ix t e s t s

th e f i f t e e n - in c h m o m e n t a r m w as c o n s ta n t . The m o m e n t a r m is d e

p ic te d in F ig u r e 18. The fo r c e e x e r t e d by a j a c k w as the p ro d u c t of

the p is to n a r e a , 6. 53 sq. in. , and the p r e s s u r e in the h y d ra u l ic s y s

te m . The e f fe c t iv e t o r q u e - p r o d u c in g f o r c e w as the fo r c e a t a j a c k

m in u s the r e a c t io n f r o m the d ead lo ad of the b e am . The f o r m u la

u s e d to c a lc u la te to rq u e w as

w h e re p is in k ip s p e r s q u a r e inch , the b e a m r e a c t io n is in k ip s ,

and the to rq u e is in in c h - k ip s .

In to r s io n , the d e fo rm a t io n i s a tw is t e x p r e s s e d a s an an g le

change p e r un it len g th . The an g le in r a d i a n s w as a s s u m e d to be equal

to th e ta n g e n t of the an g le . The b e a m w a s a s s u m e d to p ivo t on the

T = 1 5 . 0 ( 6 . 53p - 0. 725)

L eng th of M o m en t A rm F ig u r e 18

t

43

to p s of the j a c k s , lo c a t in g the c e n t e r of ro ta t io n a t the bo tto m of the

b e a m . The d i s ta n c e f r o m th is po in t to th e s c a le w as 141 c e n t i m e te r s ,

W h e r e v e r the c e n t e r of r o ta t io n a c tu a l ly o c c u r r e d ,

A s s u m e d lo c a t io n of ! c e n t e r of r o ta t io n K L ir

- i

r

E

A ngle of R o ta t io n F ig u r e 19

i t s lo c a t io n m a y be a s s u m e d to h av e b e en the s am e in each of the

t e s t s . The leng th of b e a m b e tw ee n the in d ic a to r s w as 84 in c h e s .

The tw is t in r a d i a n s p e r inch w as c a lc u la te d by d iv id ing the to ta l

an g le of ro ta t io n by the leng th ;

d l + d2 $ = 6 / L = --------:-----

141 x 84e

T o r q u e - tw i s t c u r v e s fo r the five b e a m s t e s t e d a r e shown

in F ig u r e 20 and F ig u r e 21.

Sd )~

- H

^>IVI

W/

-3

44

too

5T W I S T /H AAl S

T o rq u e - T w is t C u rv e s fo r B4, B2, and B3 F ig u r e 20

45

65 ,

Z lo o

100 i s o ITS

IM O H X l O ' 6,TW I S T ZM fÂDl AM e

T o rq u e - T w is t C u rv e s fo r B5 and B6F ig u r e 21

46

B. T o u g h n e s s

In a c o m p a r i s o n of the t o r q u e - t w i s t c u r v e s fo r th e v a r io u s

s p e c im e n s th e m o s t s t r ik in g p h en o m en o n i s th e g r e a t e r to u g h n e s s e x

h ib i te d by s p e c im e n s B5 and B6. The i n c r e a s e in to u g h n e s s c o m p r i s e s

both an i n c r e a s e in u l t im a te s t r e n g th an d an i n c r e a s e in d u c t i l i ty .

T he i n c r e a s e in d u c t i l i ty i s by f a r the g r e a t e r co m p o n en t .

M o du lus of to u g h n e s s m a y be c o m p u te d f r o m s t r e s s - s t r a i n

c u r v e s . T he r e s u l t in g d im e n s io n s a r e in c h - k ip s p e r cub ic inch , and

th e v a lu e s r e p r e s e n t e n e r g y a b s o r b e d p e r u n it v o lu m e . The r e l a t i v e

a r e a s u n d e r th e l o a d - d e f o r m a t io n c u r v e s a r e a d e q u a te f o r c o m p a r i s o n

of r e l a t i v e to u g h n e s s . T he a r e a s u n d e r the t o r q u e - t w i s t c u r v e s w e re

a p p r o x im a te d w ith th e u s e of an a r b i t r a r y g r id . T he d im e n s io n s of

th e a c tu a l a r e a s a r e k i p - r a d i a n s ; c o m p u ta t io n of th e s e v a lu e s h a s

l i t t l e m e a n in g . M ak ing th e s m a l l e s t a r e a e q u a l to one, th e r e l a t i v e

a r e a s a r e a s fo l lo w s;

T a b le 2R e la t iv e T o u g h n e s s of S p e c im e n s

S p e c im e n R e la t iv e A r e a u n d e r T o r q u e - T w is t C u rv e

B4 1 .2

B2 1 .0

B3 2 .0

B5 18 .0

B6 1 7 .0

S p e c im e n s B5 an d B6 h a d an a v e r a g e to u g h n e s s abou t tw e lv e t im e s a s

g r e a t a s th a t of th e m o r e l ig h t ly r e i n f o r c e d s p e c im e n s .

C. M odulus of R ig id i ty

In the e l a s t i c r a n g e .the r a t io of s h e a r in g s t r e s s to s h e a r in g

s t r a in , r / & , i s c o n s id e r e d a c o n s ta n t f o r m a t e r i a l s c o n fo rm in g to

H o o k e 's Law . T h is c o n s ta n t is d en o ted by the l e t t e r G and is c a l l e d

the s h e a r in g m o d u lu s of e l a s t i c i t y o r the m o d u lu s of r ig id i ty .

On the c o m p o s i te r e p r e s e n t a t i o n of t o r q u e - t w i s t c u r v e s a

s t r a ig h t l ine w as ex ten d e d f r o m th e o r ig in th ro u g h the v i s u a l ly e s t i

m a te d a v e r a g e of th e p o in ts in the e l a s t i c r a n g e . The s lo p e of th is

l in e w as 200 in c h - k ip s d iv id ed by 20 x 1 0 '^ r a d ia n s p e r inch .

£3

loo -•

P o r t io n of C u rv e s in E l a s t i c Range F ig u r e 22

If- - I O ^

I AOIAN5/7KO\

T W I S T , ^ , IN KAZAKS/ inch ^ (c &

48

F r o m the t h e o r y of e l a s t i c i ty , th e m o d u lu s of r ig id i ty f o r a r e c t a n g u

l a r s e c t io n isT

G = ------ . -----1

$ k j(2 b ) (2 a )

w h e re the c o n s ta n t k j d ep en d s upon th e s h ap e of the r e c ta n g le ,

v a lu e s of k^ a r e show n in F ig u r e 23.

38 The

<[PC- t<ATtc> k / a .

C o n s ta n t R e la t in g T o rq u e and T w is t F ig u r e 23

S u b s ti tu t in g ,200 1

G = = 1140 k s i .20 x 10~5 0. 253 x 16 x 6 3

Z ia , in h is s e r i e s of r e c t a n g u l a r b e a m s w ith w eb r e i n f o r c

ing, o b ta in e d v a lu e s f o r th e m o d u lu s of r ig id i ty f r o m 1400 to 1870

k s i . 39

38. T im o sh e n k o and G o o d ie r , p. 278.

39. Z ia (I9 6 0 ) , p. 103.

t

K em p u s e d v a lu e s f o r th e sh e a r in g m o d u lu s v a r y in g f r o m 1300 to 1900

40k s i . C o m p a r e d to t h e s e f ig u r e s th e v a lu e o b ta in e d f o r the m o d u lu s

of r ig id i ty in th e p r e s e n t r e s e a r c h i s r a t h e r s m a l l . The c o n c r e te a v e r

a g e d o v e r 5000 p s i in c o m p r e s s i v e s t r e n g th . One w ou ld e x p e c t a m o d

u lu s of r ig id i ty of a p p r o x im a te ly 1500 p s i .

III. U l t im a te S tre n g th

Two t h e o r i e s a r e a d v o c a te d fo r th e p r e d ic t io n of th e u l t im a te

s t r e n g th of p r e s t r e s s e d m e m b e r s w ithou t w eb r e in f o r c in g . N y la n d e r

p o s tu la te d th a t a t f a i l u r e th e e n t i r e s e c t io n a c te d p l a s t i c a l ly . He co n -

41e lu d e d th a t th e p l a s t i c th e o r y sh o u ld be u s e d f o r d e s ig n . C ow an,

H u m p h re y , a n d Z ia f a v o r th e e l a s t i c th e o r y . D e sp i te th e . d i s s i m i l a r -

i ty of th e o ry , th e r e s u l t i n g v a lu e s fo r p r e d i c t e d u l t im a te s t r e n g th a r e

n e a r l y eq u a l , e s p e c i a l l y f o r r e c t a n g u l a r s e c t io n s .

Only one r e s e a r c h e r h a s in v e s t ig a te d the e f fe c t o f w eb r e i n -

42f o r c in g on u l t im a te s t r e n g th . T e s t in g b e a m s w ith w eb r e in f o r c in g ,

Z ia found th a t th e u l t im a te t o r s io n a l s t r e n g th i s th e su m of th e y ie ld -

s t r e s s to r q u e of th e s t e e l and th e c r a c k in g to rq u e of th e p r e s t r e s s e d

c o n c r e te s e c t io n w ith o u t w eb r e in f o r c in g . The u l t im a te s t r e n g th of

a p r e s t r e s s e d m e m b e r w ith w eb r e in f o r c in g m a y th u s be e x p r e s s e d

40. K em p, p. 100.

41. N y la n d e r , p. 132.

42. Z ia (I960 ).

50

a s

^ t p ^ ^ t s *

T he p r e d ic t e d t o r s i o n a l r e s i s t a n c e o f f e re d by th e w eb r e i n -

f0 rC i" g i e ° - 8 X1 Y! A sv £syMt s = -------------------------------

s

w h e re A sv i s th e a r e a of tw o le g s of a s t i r r u p . In th e t e s t b e a m

w ith s t i r r u p s a t tw e lv e in c h e s on c e n t e r , f o r e x a m p le ,

0 .8 x 4 x 1 3 .7 5 x 0. 10 x 5 3 .7 5M. = --------- :---------------------------------------- = 19. 8 in c h - k ip s.

tS 12

A c e r t a i n a m o u n t of lo n g i tu d in a l r e in f o r c in g i s n e c e s s a r y

to e n a b le th e s t i r r u p s to a c t e f fe c t iv e ly . Z ia r e c o m m e n d e d th a t the

a r e a of lo n g i tu d in a l r e in f o r c in g be su ch th a t th e v o lu m e of lo n g i tu

d in a l r e in f o r c in g i s eq u a l to th e v o lu m e of th e s t i r r u p s . H is f o r m u la

a s a d o p ted by th e A u s t r a l i a n Code is

X1 + y l 43A s = A s v s

F o r th e t e s t b e a m w ith s t i r r u p s a t tw e lv e in c h e s on c e n te r th e lo n g i

tu d in a l s t e e l r e q u i r e d by th e f o r m u la w ould be 0. 444 s q u a r e in c h e s .

T he fo u r #3 b a r s u s e d in e a c h of th e s p e c im e n s p r o v id e d a lo n g i tu d

in a l s t e e l a r e a of 0. 44 s q u a r e in c h e s . A c c o rd in g to th e f o r m u la ,

th en , on ly the s p e c im e n w ith s t i r r u p s a t two in c h e s on c e n t e r h a d

in a d e q u a te lo n g i tu d in a l r e in f o r c in g .

43. Cf. Z ia (I9 6 0 ) , p. 125 a n d Cow an (1965), p. 38.

51

F r o m th e f o r m u la p r e s c r i b e d by th e co d e , the p r e d i c t e d

t o r s io n a l m o m e n t r e s i s t e d by th e s t i r r u p s i s a s fo llow s .

T ab le 3P r e d i c t e d T o rq u e R e s i s t e d by S t i r r u p s

B e a m D e s ig n a t io n S t i r r u p Spacing M ts (in c h ~

B4 no s t i r r u p s 0. 0

B2 12" o. c. 19. 8

B3 8" o . c . 29. 7

B5 4 " o. c. 59. 4

B6 2" o . c . 118. 8

The in i t i a l p r e s t r e s s i n g f o r c e on e a c h b e a m w a s 4 x 27. 6 =

1 1 0 .4 k ip s . P r e s t r e s s l o s s e s in c lu d e th e e f fe c ts of e l a s t i c s h o r te n in g

of c o n c r e te , c r e e p of c o n c r e te , s h r in k a g e of c o n c r e te , r e l a x a t io n of

s t e e l s t r e s s , and s e a t in g of a n c h o r a g e s . In p r a c t i c e th e to ta l lo s s in

p r e s t r e s s fo r b e a m s s i m i l a r to th e t e s t b e a m s i s a s s u m e d to be 15%.

A c c o rd in g to th i s e s t i m a te , th e p r e s t r e s s i n g f o r c e a t t im e of te s t in g

w as a p p r o x im a te ly 93. 8 k ip s . The c o m p r e s s i v e s t r e s s due to p r e

s t r e s s i n g w a s f = P /A = 978 p s i .

T he fo llow ing ta b le show s p r e d i c t e d to r q u e r e s i s t e d by con - '

c r e t e . T he to r s i o n a l s t r e n g th of the c o n c r e te w a s a p p r o x im a te d a s

t Q = 0. 68 ( f ' c ) ^ 4 - M o m e n ts a r e in in c h -k ip s.

T ab le 4P r e d i c t e d T o rq u e R e s i s t e d by C o n c r e te

S p e c im e n f ' c (psi) T 0 (psi) Mt p (H u m p h r e y s )a M. (M o d if ied b ‘-P Cowan)

B4 6300 483 118 122

B2 5300 422 109 112

B3 6800 510 122 129'

B5 6800 510 122 129

B6 6300 483 118 122

a. See R ev iew of E x p e r im e n ta l R e s e a r c h , p. 11.

b. The u l t im a te to r q u e p r e d ic t e d by the M o d if ied Cow an T h e o ry w as c o m p u te d w ith th e a id of Z i a ' s " I n te r a c t io n C u rv e s fo r M o d if ied C o w a n 's C r i t e r i o n of F a i l u r e , " Z ia (I960 ) , p. 65.

To o b ta in M^ p r e d ic te d , th e p r e d ic t e d to r q u e r e s i s t e d by

th e s t i r r u p s (T ab le 3) w as ad d ed to th e p r e d i c t e d to rq u e r e s i s t e d

by th e p r e s t r e s s e d c o n c r e te (T ab le 4). A c o m p a r i s o n of p r e d ic t e d

u l t im a te to rq u e w ith t e s t v a lu e s i s show n in T ab le 5. A ll t o r s io n a l

m o m e n ts a r e in i n c h - k i p s .

53

T ab le 5T e s t V a lu e s and P r e d i c t e d U l t im a te T o rq u e

S p e c im e n M j. p r e d i c t e d t e s t t e s t / p r e d i c t e d

B4 122 166 1 .3 6

B2 132 154 1. 17

B3 159 175 1. 10

B5 188 219 1. 16

B6 241 254 1. 05

The u l t im a te s t r e n g th o b ta in e d b y te s t in g w a s 5% to 36%

g r e a t e r th a n p r e d ic te d . If s p e c im e n B6, h a v in g in a d e q u a te lo n g i tu d

in a l s te e l , w e r e o m i t te d f r o m th e c a lc u la t io n , th e a v e r a g e of the t e s t

v a lu e s i s 20% h ig h e r th a n the p r e d i c t e d u l t im a te to r q u e s .

R e p r e s e n t in g p r e s t r e s s l o s s e s a s f i f te e n p e r c e n t m a y h av e

c o n t r ib u te d to the d i f f e r e n c e b e tw e e n p r e d i c t e d to r q u e a n d t e s t v a lu e s .

F o r d e s ig n p u r p o s e s p r e s t r e s s l o s s e s a r e e s t i m a te d c o n s e r v a t iv e ly .

A lso , th e s p e c im e n s w e r e f r o m tw e n ty - f iv e to t h i r t y - o n e d a y s o ld a t

th e t im e of te s t in g . Only a s m a l l am o u n t o f th e to ta l e x p e c te d c r e e p

w ou ld h av e ta k e n p la c e in th e c o n c r e te d u r in g th is t im e in te r v a l .

It sh o u ld a l s o be n o te d th a t Z ia , in com pu ting p r e d i c t e d u l t i -

44m a te to rq u e , u s e d 33 k s i fo r th e y ie ld s t r e s s in th e s t i r r u p s .

T h i r t y - t h r e e k s i m a y w e l l h a v e b e en th e g u a r a n te e d m in im u m y ie ld .

A c tu a l y ie ld s t r e s s of th e s t i r r u p s te e l , 53. 75 k s i , w a s u s e d in th e

44. Z ia (I960 ) , p. 126.

IV. N o n - n u m e r ic B e h a v io r

A s soon a s the f i r s t c r a c k b egan , the c r a c k fo llow ed a s t r a ig h t

line and c o m p r e s s io n b e c a m e c r i t i c a l on the o p p o s i te s id e . The s lo p e

^T tA Ô N A L T E M Sk-M r A I U j< £ M S l I ^

— HA! Llir-E. s t p e

Te n s i l e . fA im fC E . a l l a ^ t u n dnec^: zrr<rMALK

F a i lu r e S u r fa c e s F ig u r e 24

of the te n s i l e f r a c t u r e in a p la in c o n c r e t e s p e c im e n te n d s to be 45°.

B e c a u se of th e p r e s t r e s s i n g fo r c e the t e n s i l e f r a c t u r e in each of

th e s p e c im e n s t e s t e d m a d e an an g le of 30° w ith th e h o r iz o n ta l .

F ig u r e 25 show s the s id e s of B1 and B3 th a t f a i le d in d ia g o n a l te n s io n .

In s p e c im e n s B l , B2, B3, and B4 the d i f f e r e n c e s b e tw ee n the s id e th a t

D iagonal T e n s io n C r a c k sF ig u r e 25

56

fa i le d in d iag o n a l te n s io n and th e s id e th a t f a i le d in c o m p r e s s io n w e re

im m e d ia te ly a p p a r e n t . F ig u r e 27 show s th e s id e s of B2 and B3 th a t

f a i le d in c o m p r e s s io n . In e ac h of the f i r s t fo u r s p e c im e n s t h e r e w as

c l e a r l y on ly one f r a c t u r e s u r f a c e .

S p e c im e n s B5 and B6 e x h ib i te d d i s t in c t ly d i f f e r e n t b e h a v io r

f r o m th e o th e r b e a m s t e s t e d . T h ey e m i t t e d c r a c k in g n o i s e s th r o u g h

out m u c h of th e lo ad ing c y c le . T hey d ev e lo p e d m u l t ip le h a i r l i n e

c r a c k s and s e v e r a l c o m p le te f a i lu r e s u r f a c e s . J a g g e d i r r e g u l a r

c r a c k s took th e p la c e of th e long S - s h a p e d c o m p r e s s io n f a i lu r e th a t

w a s c h a r a c t e r i s t i c in th e s p e c im e n s w ith l e s s r e in fo r c in g . The a r e a

of th e f a i lu r e s u r f a c e s w a s h e a v i ly d e b r i s e d .

A s e x p ec te d , th e c ra c k in g lo a d and th e u l t im a te s t r e n g th

i n c r e a s e d a s the a m o u n t of w eb r e in f o r c in g in c r e a s e d . The a b i l i ty

to d e fo rm th ro u g h a l a r g e an g le w as m a r k e d l y g r e a t e r in th e two

b e a m s w ith th e m o s t w eb r e in f o r c in g . The s p e c im e n s w ith l e s s r e i n

fo rc in g fa i le d on one s u r f a c e w hile th e s p e c im e n s w ith m o r e s t i r r u p s

d e v e lo p e d a s m a n y a s fo u r o r five h a i r l i n e c r a c k s in d iag o n a l te n s io n

b e fo re f a i lu r e b e c a m e c o m p le te . A s u r p r i s i n g o b s e r v a t io n w as th a t

the g r e a t e r the n u m b e r of s t i r r u p s in a b e a m , the s m a l l e r lo ad r e

q u i r e d to in i t i a te c r a c k in g n o i s e s .

None of the f a i l u r e s cou ld be t e r m e d v io le n t . T he f a i l u r e s in

th e f i r s t fo u r s p e c im e n s w e r e su d d en an d w ithou t w a rn in g . The m o r e

h e a v i ly r e in f o r c e d s p e c im e n s g ave c o n s id e r a b le w a rn in g and f a i lu r e

B5 C o m p r e s s io n Side

B5 T e n s io n Side F ig u r e 26

58

S -S h ap ed C o m p r e s s io n F a i l u r e s F ig u r e 27

T e s t S p e c im e n s B l , B3, B2, B4, and B6F ig u r e 28

59

w as g ra d u a l . A t no t im e d id the r e l e a s e of th e p r e s t r e s s i n g fo r c e

c a u s e fly ing d e b r i s . ^

V. R ev iew of R e in fo rc in g

A u th o rs and a g e n c ie s e m p lo y v a r io u s m e th o d s of e x p r e s s in g

a m o u n t of web r e in f o r c in g . The B PR p r e s c r i b e s , a s m in im a l , s t i r

ru p s hav in g an a r e a equa l to a g iv en c r o s s - s e c t io n a l a r e a of the b e am

and s p a c e d a t a g iv en m a x im u m sp ac in g . The AC1-ASCE Jo in t C o m m i t

te e r e q u i r e s th a t the a r e a of two le g s of a s t i r r u p be a g iv en p e r c e n ta g e

46of a h o r i z o n ta l s e c t io n th ro u g h the web. Z ia e x p r e s s e s web r e in f o r c -

47ing a s a p e r c e n t of the v o lu m e of the c o r e e n c lo s e d w ith in the t i e s .

F ig u r e 29 i l l u s t r a t e s th e l a t t e r two m e th o d s of e x p r e s s in g am o u n t of

w eb r e in fo r c in g .

r ! b'

!♦ -S- *i

r A S Y

b ' s

I

i

M eth o d s of E x p r e s s in g A m ount of Web R e in fo rc in gF ig u r e 29

45. Cf. L in , p. 547.46. See above , " In t ro d u c t io n , " p. 6.47. Ibid. , p. 13.

In th e fo llow ing ta b le the w eb r e in f o r c in g in th e s p e c im e n s

t e s t e d i s e x p r e s s e d a c c o rd in g to th e two m e th o d s i l l u s t r a t e d on th e

p r e v io u s p ag e . The s t i r r u p sp ac in g i s a l s o e x p r e s s e d in r a t i o s w ith

th e d ep th an d w ith th e w id th of the b e a m .

T a b le 6 A m o u n t of Web R e in fo rc in g

S p e c im e n #2 S t i r r u p s % of b ' s % of v o lu m e of c o r e s / d s / b

B4 none 0. 0 0. 0 - -

B2 1 2 11 o. c. 0. 14 0. 27 0. 75 2. 00

B3 8 " o. c. 0. 21 0. 40 0. 50 1. 33

B5 4 " o. c. 0. 42 • 0. 80 0. 25 0. 67

B6 2 " o. c . 0. 83 1. 61 0. 12 0. 33

The d u c t i le b e h a v io r of th e f i r s t t h r e e s p e c im e n s l i s t e d w as

e s s e n t i a l l y th e s a m e . Only B5 and B6 sh o w ed an a p p r e c ia b le a m o u n t

of d u c t i l i ty . In th e m o r e d u c t i le m e m b e r s , th e l e a s t am o u n t of web

r e in f o r c in g w a s 0. 8% of th e v o lu m e of th e c o r e . T he w eb re in fo r c in g

of Z i a ' s d u c t i le s p e c im e n s w a s 1. 5% of th e v o lu m e of th e c o r e . ^ The

l a r g e s t s t i r r u p sp ac in g in th e d u c t i le m e m b e r s t e s t e d w a s 0. 25 t im e s

th e dep th . Z ia r e c o m m e n d e d f o u r - t e n th s th e dep th a s m a x im u m s t i r

ru p sp a c in g to o b ta in d u c t i l i ty . A sp a c in g e x p r e s s e d a s a r a t i o w ith

th e dep th of th e m e m b e r m a y not be a s m e a n in g fu l a s a n e x p r e s s io n

co n ta in in g th e l e a s t d im e n s io n of th e m e m b e r . T he s p e c im e n s w ith

~ 4& Z ia (I9 6 0 ) , p. .140.

m a r k e d d u c t i l i ty h a d s t i r r u p sp ac in g of not m o r e th a n tw o - th i rd s the

l e a s t d im e n s io n of th e m e m b e r .

CONCLUSIONS

I. D e s ig n A p p l ic a t io n s

T he t e s t r e s u l t s d e m o n s t r a t e th a t t o r s io n a l to u g h n e s s can be

o b ta in e d in p r e s t r e s s e d c o n c r e te m e m b e r s by the u s e of a su f f ic ie n t

a m o u n t of web r e in f o r c in g . T he t e s t s p e c im e n s w h ich e x h ib i te d c o n

s id e r a b ly i n c r e a s e d to u g h n e s s h ad s t i r r u p s s p a c e d a t a m a x im u m of

t w o - th i r d s th e l e a s t d im e n s io n of th e m e m b e r . The v o lu m e of th e

s t i r r u p s w as 0. 08% of th e v o lu m e of th e e n c lo s e d c o re .

The p r e s e n t r e s e a r c h is no t in te n d e d to e s t a b l i s h s t a n d a r d s

of p r a c t i c e . In s te a d , i t h a s a t t e m p te d to d e m o n s t r a t e a m e a n s of

a c h ie v in g d u c t i l i ty . The d e g r e e of t o r s i o n a l to u g h n e s s sough t m u s t

d ep en d on th e d e s i g n e r ' s a s s e s s m e n t of th e b e h a v io r d e s i r e d of a

p a r t i c u l a r m e m b e r .

T he t e s t s p e c im e n s w ith su f f ic ie n t w eb r e in f o r c in g to i n

c r e a s e d u c t i l i ty a l s o h a d an a v e r a g e of 43% g r e a t e r u l t im a te s t r e n g th .

T he c o n s e r v a t iv e n e s s of the f o r m u la s p r e s e n t e d in th e A u s t r a l i a n

code is s u p p o r te d b y th e t e s t r e s u l t s . It i s doubtfu l, h o w e v e r , th a t

p ro v id in g a d d i t io n a l s t i r r u p s is an e c o n o m ic a l m e th o d of a t ta in in g

g r e a t e r t o r s i o n a l c a p a c i ty .

62

63

II. I m p r o v e m e n t of T e s t D esign

A w e a k n e s s in th e p r e s e n t t e s t d e s ig n w as th e in a d e q u a c y of

c o n t ro l in the a p p l ic a t io n of lo a d s . It w a s d if f ic u l t to h o ld p r e s s u r e

c o n s ta n t in th e h y d r a u l ic s y s te m d u r in g th e p r o c e s s of p o s i t io n in g th e

b e a m . In s u b s e q u e n t t e s t s , i n s t r u m e n ta t i o n sh o u ld be p ro v id e d to

m e a s u r e the a n g le of r o ta t io n w ith g r e a t e r p r e c i s io n . If g r e a t e r a c c u r

a c y of c o n t ro l an d in s t r u m e n ta t io n w e r e a c h ie v e d , m o r e r e l i a b l e in d ic e s

to a c tu a l b e h a v io r cou ld be e s ta b l i s h e d . It i s fe l t th a t the p r e s e n t r e

s e a r c h w a s a v a l id d e m o n s t r a t io n of th e r e l a t i v e e f fe c t s o f v a ry in g

a m o u n ts of w eb r e in f o r c in g .

It i s u n fo r tu n a te th a t th e t e s t s p e c im e n d e s ig n e d to h av e

49s t i r r u p s a t s ix in c h e s on c e n t e r w as not c o n s t r u c t e d a s p lan n ed .

T he c r i t i c a l p o in t in to u g h n e s s o c c u r r e d b e tw ee n the b e a m w ith f o u r -

inch s t i r r u p sp ac in g a n d th a t w ith e ig h t - in c h s t i r r u p sp ac in g . The

e x t r e m e d i f f e r e n c e in b e h a v io r b e tw e e n the l a t t e r tw o s p e c im e n s

m a k e s the te s t in g of an i n t e r m e d ia t e s p e c im e n p a r t i c u l a r l y d e s i r a b l e .

P h o to g r a p h ic d o c u m e n ta t io n is an im p o r ta n t p a r t of th e r e

c o r d e d d a ta . It w ould be a d v a n ta g e o u s to be ab le to p h o to g ra p h e ac h

s id e of th e b e a m f r o m a p o s i t io n n o r m a l to th e f a c e of th e b e am . The

b e a m sh o u ld id e a l ly be p h o to g ra p h e d b e fo re i t h a s b e e n r e m o v e d f r o m

th e t e s t s tan d .

49> See ab o v e , p. 25.

III. R e c o m m e n d a t io n s f o r F u r t h e r R e s e a r c h

A s i m i l a r s tu d y cou ld p ro f i t a b ly be m a d e u s in g g r e a t e r p r e

s t r e s s i n g f o r c e s . By in c r e a s in g the b r i t t l e n e s s of th e s p e c im e n s w ith

l e a s t w eb r e in f o r c in g w h ile in c r e a s in g th e u l t im a te s t r e n g th , such

a s tu d y m ig h t show m o r e d r a m a t i c a l l y th e p o s s ib le e f fe c ts of w eb

r e in f o r c in g on d u c t i l i ty .

R e s e a r c h v a r y in g th e lo n g i tu d in a l r e in f o r c in g r e l a t i v e to

c o n s ta n t a m o u n ts of w eb r e in f o r c in g i s n e e d e d to d e te r m in e th e a m o u n t

of lo n g i tu d in a l r e in f o r c in g r e q u i r e d to e n ab le th e s t i r r u p s to a c t e f f e c

t iv e ly .

Study i s a l s o n e e d e d of th e a p p l ic a t io n of l o n g - t e r m load ing ,

im p a c t lo a d s , an d r e p e a t e d lo a d s . In p e r f o r m a n c e , m a n y to r s io n

lo a d s a r e l iv e lo a d s an d and t h e i r e f fe c ts do no t c o r r e s p o n d to th o s e

of s ta t i c load ing .

F u r t h e r e x p e r im e n t s sh o u ld be p e r f o r m e d to in v e s t ig a te the

b e h a v io r o f b e a m s w ith o th e r d e p th -w id th r a t i o s . Such r e s e a r c h m a y

s e r v e to e s t a b l i s h th e v a l id i ty of b a s in g s t i r r u p s p a c in g s on th e l e a s t

d im e n s io n of th e b e a m . t

S E L E C T E D READING

A CI C o m m it te e 318, B u ild ing Code R e q u i r e m e n t s fo r R e in fo rc e d C o n c r e te , A CI 318 -63 (D e tro i t , A m e r i c a n C o n c r e te In s t i tu te , 1963).

A C I - A S C E Jo in t C o m m it te e 323, " T e n ta t iv e R e c o m m e n d a t io n s f o r P r e s t r e s s e d C o n c r e te , " J o u r n a l of the A m e r i c a n C o n c r e te I n s t i tu te XXIX, 7 ( J a n u a r y 1958), 545 -578 .

Chi, M. a n d F . A. B ib e r s t e in , T h e o ry of P r e s t r e s s e d C o n c r e te (E ng lew ood C lif fs , P r e n t i c e - H a l l , 1963).

Cowan, H e n ry J . , "D es ig n of B e a m s S u b jec t to T o r s io n R e la te d to the A u s t r a l i a n C ode, " J o u rn a l of th e A m e r ic a n C o n c r e te In s t i - tu te XXXI, 7 ( J a n u a r y I960), 591 -618 .

Cowan, H e n ry J . , R e in f o r c e d an d P r e s t r e s s e d C o n c r e te in T o r s io n (L ondon, E . A rn o ld , 1965).

F e ld , J a c o b , L e s s o n s f r o m F a i l u r e s of C o n c re te S t r u c t u r e s (D e tro i t , A m e r i c a n C o n c r e te In s t i tu te , an d A m e s , Iowa S ta te U n iv e r s i ty P r e s s , 1964).

F i s h e r , G o rdon P . and P a u l Z ia , "R ev iew of C ode R e q u i r e m e n t s fo r T o r s io n D esig n , " J o u r n a l of th e A m e r i c a n C o n c r e te In s t i tu te , P r o c e e d in g s LXI, 1 ( J a n u a r y 1964), 1 -44 .

Guyon, Y ves, P r e s t r e s s e d C o n c r e te , ed . W. M. Jo h n s , t r a n s . A. J . H a r r i s , J . D. H a r r i s , an d T. O. L a z a r i d e s (L o n d o n ,C o n t r a c to r s R e c o r d L td , , 1953).

H o g n e s ta d , E . , " E f fe c ts of R e s e a r c h on M o d e rn A m e r ic a n S t r u c t u r a l C o n c r e te D esig n , " J o u r n a l of the S t r u c tu r a l D iv is io n , P r o - c e e d in g s of th e A m e r ic a n S o c ie ty o f C iv il E n g in e e r s , P r o c e e d - in g s P a p e r 2034, LXXXV, ST 5 (M ay 1959).

H u m p h re y s , R. , " T o r s io n a l P r o p e r t i e s o f P r e s t r e s s e d C o n c r e te , "The S t r u c t u r a l E n g in e e r , London, XXXV, 6 (June 1957), 2 1 3 -224 .

65

66

K em p, E . L. J r . , "An A n a ly t ic a l and E x p e r im e n ta l Study of T o r s io n in R e in fo rc e d C o n c r e te B e a m s , " P h .D . d i s s e r t a t i o n (U n iv e r s i ty of I l l in o is , 1962).

L ibby, J a m e s R. , P r e s t r e s s e d C o n c r e te (New Y ork , R o n a ld P r e s s , 1961).

L in , T. Y. , D es ig n of P r e s t r e s s e d C o n c r e te S t r u c t u r e s , 2nd ed.(New Y ork , Jo h n W iley, 1955).

M u rp h y , G lenn , P r o p e r t i e s of E n g in e e r in g M a te r i a l s (S c ran to n , I n te r n a t io n a l T ex tb o o k C om pany , 1957).

N adai, A. , T h e o ry of F lo w and F r a c t u r e of S o lid s , 2d ed. (New Y ork, M c G ra w -H i l l , 1950).

N y la n d e r , H. , V r id n in g och v r id n in g s in s p a n n in g v id b e to n g k o n s t ru k - t io n e r ( T o r s io n and T o r s io n a l R e s t r a i n t by C o n c r e te S t r u c t u r e s ) , B u l le t in No. 3 (S tockho lm , S ta te n s K o m m it te b y g g n a d s fo rsk n in g , 1945).

T im o sh e n k o , S. and J . N. G o o d ie r , T h e o r y of E l a s t i c i ty , 2d ed.(New Y ork , M c G ra w -H i l l , 1951).

W in te r , G. , L. C. U rq u h a r t , C. E . O 'R o u rk e , and A. H. N ilso n , D es ig n o f C o n c r e te S t r u c tu r e s , 7 th ed. (New Y ork , M c G ra w - H ill , 1964).

Z ia , P a u l , " T o r s io n a l S tren g th of P r e s t r e s s e d C o n c r e te M e m b e r s , " Ph. D. d i s s e r t a t i o n (U n iv e r s i ty o f F lo r id a , I960).

Z ia , P a u l , " T o r s io n a l S tren g th of P r e s t r e s s e d C o n c r e te M e m b e r s , " J o u r n a l of th e A m e r i c a n C o n c r e te In s t i tu te XXXII, 10 (A p ri l 1961), 1337-1359 .

Documents

Effects of web reinforcing on torsional behavior of prestressed … · 2020. 4. 2. · prestressed by the pretensioning method. The cross section of the member, concrete strength,