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By the ACI method, moment e f f e c t s were ignored, and i t was assumed that shear s t r e s s was uniformly distributed around the c r i t i c a l section. I t should be expected that shear s t r e s s e s from dead load can be approximated c l o s e l y assigning a uniform d i s t r i b u t i o n . However, a t a comer column i n the single panel t e s t , the s t r e s s d i s t r i b u t i o n would not be escpected to be uniform for applied load. To get into the coliann, load wooild come p r i n c i p a l l y through the two sides facing the loaded area. Shear strength using the ACI s t r e s s l i m i t a t i o n was recomputed for the slab at Column C5. I t was assumed that dead load supported by the column was uniformly distributed at d / 2 from the column. Live load was then assiuned to be distributed uniformly on a section at d / 2 from the two sides of the column jo i n i n g the loaded area. The difference between the l i m i t i n g s t r e s s , h^i, and the nominal dead load s t r e s s , "Vjyjjlod, was assumed to be available to carry l i v e load. The shear capacity computed using these assumptions was 7 0 0 kips. This value i s i n good agreement with the mea- sured ultimate shear. While seemingly conservative, the assumptions made in t h i s a n a l y s i s c l o s e l y predict the r e s u l t s of t h i s t e s t . FLEKURAL STRENGTH In Test I I I , y ielding of reinforcement i n the positive moment region i n d i - cated that f l e x u r a l capacity was approached. Shear f a i l \ i r e prevented de- velopment of negative moment yi e l d i n g i n the slab during t h i s t e s t . After shear f a i l u r e i n Test I , load required to deform the structure became l e s s as deflections increased. This behavior plus observed cracking indicated formation of a f l e x u r a l mechanism. Since the t e s t slab was underreinforced at a l l sections, f l e x u r a l strength was governed by yielding of the reinforcement. F l e x u r a l strength of a slab i s reached under a load that produces f l e x u r a l y i e l d i n g along an adequate nvmiber of l i n e s to produce a collapse mechanism. An ana l y s i s based on y i e l d l i n e mechanisms was developed by I n g e r s l e v ( 2 2 ) and modified by Johansen. ( 2 3 ) In t h i s a n a l y s i s , i t i s assumed that the y i e l d - l i n e sections possess adequate rota t i o n a l capacity for the mechanism to form completely. 1- k3
The y i e l d - l i n e mechanism that corresponds to the f l e x u r a l strength of a slab i s the one produced by the lowest load. SeveraJ. t r i a l s may be necessary to se l e c t the governing mechanism. I n most cases, load determined by t e s t w i l l be greater than that computed from y i e l d l i n e a n a l y s i s . This r e s u l t s from ignoring i n the analysis both s t r a i n hardening of the reinforcement and a x i a l forces induced i n the slab. Y i e l d l i n e analyses were made for each of the three t e s t s . I n computing mo- ment along hinging l i n e s , y i e l d s t r e s s for a l l reinforcement was assimied to be 42 k s i . V/here possible, e f f e c t i v e depth was based on measured section thickness. Average concrete strength of 5 2 4 0 p s i was used for a l l c a l c \ i l a - t i o n s . Ultimate moment calculations were made according to provisions i n the 1 9 6 3 ACI Code. The strength reduction factor, cp, was taken as 1 . 0 . For a l l sections, temperature reinforcement was included i n cal c u l a t i o n of moment. Patterns of y i e l d l i n e s are shown in F i g . 5 6 , 5 8 , 59> and 6 0 . Calculated f l e x u r a l strengths and maximum loads i n the t e s t s are l i s t e d i n Table XI. These loads are applied loads plus the actual dead weight of the slab and loading equipment. Y i e l d - l i n e mechanisms A, B, and C are patterns commonly assumed for the three t e s t conditions. Negative moment y i e l d l i n e s are located at the periphery of the loaded panels. Positive moment y i e l d l i n e s i n t e r s e c t within the loaded panels. TABLE XI FLEXURAL STRENGTH Test Calculated Y i e l d Strength Maximum Total Load during Maximum Test Load No. Mechanism* Load, psf Test, psf Calc. Y i e l d Load I A D 2l40 6 9 0 1 1 1 5 7 9 9 0 . 5 2 1 . 1 6 I I B E 1 5 5 0 l4lO 842 8 4 2 0 . 5 4 0 . 6 0 I I I C F 3 9 8 0 2 4 8 0 2 2 0 2 2 2 0 2 0 . 5 5 0 . 8 9 1 - 4 4
There i s r e l a t i v e l y l i t t l e difference i n load between Mechanisms E and B for Test I I before shear f a i l i i r e occurred. Positive moment y i e l d l i n e s for both mechanisms are assumed to be located within the loaded area. Neg- ative moment y i e l d l i n e s f or E are located i n panels adjacent to the t e s t area at the bar cut-off l i n e . Positive moment y i e l d l i n e s are located adjacent to the wall along Lines 1 and E and at the face of columns along Lines C and 6 . For Mechanism E, a f a i l u r e load of iklO psf i s calculated. This i s somewhat l e s s than the 1 5 5 0 psf computed for Mechanism B. Both the loads axe about twice the load i n t e n s i t y at shear f a i l u r e i n the t e s t . Various mechanisms were investigated for Test I I I . In these patterns, the negative y i e l d l i n e s were extended beyond the four sides of the loaded panel. The lowest applied load was found for Mechanism F shown i n F i g . 60, the negative moment y i e l d l i n e s being p a r a l l e l to the panel diagonals. The computed load of 2^*80 psf i s only s l i g h t l y greater than the maximum t e s t load. Test to calculated r a t i o f o r t h i s mechanism i s O . 8 9 . During the t e s t , y i e l d s t r a i n s were measured in much of the positive moment reinforce- ment. I t i s apparent that the y i e l d l i n e mechanism had almost completely formed when Column C5 punched through the slab. Cracking observed on top of the slab a f t e r Test I I I , i s shown i n Fig. 5 1 . At the time Test I I I was started, shear f a i l u r e had occurred at Colimns Ck, Bk, Ek, and E 3 . Consequently there was l i t t l e or no support of the slab at these coliamns. Crack 1 was observed before f a i l u r e occurred at Column C5. After C5 punched through the slab. Cracks 2 , h, and 5 were noted. F i n a l l y , Crack 3 formed a f t e r both Columns C5 and D5 had punched through. Except for Crack 2 adjacent to Coliarins C6 and D6, cracks formed at the cut-off of negative s t e e l . Considerable positive moment cracking was noted on the underside of the slab a f t e r Test I I I was completed. The column s t r i p along Line C between Lines k and 5 was severely cracked. Along t h i s section no positive mo- ment reinforcement was provided. Consequently, moment capacity of t h i s section was only that of the p l a i n concrete section before the crack formed and was zero a f t e r the crack formed. 1 - 4 5
After Colvmms C5 and D5 had punched through, a load of about 650 psf could be applied to the panel. I n t e n s i t y of applied load did not drop off with continvied deformation of the slab. I t appears that a y i e l d mechanism was forming. However, the damaged condition of the structure prevented deter- mination of the location of a well defined mechanism. The structure, even though severely damaged, did possess the capacity to r e s i s t moderate loads. Shear f a i l u r e s prevented development of f u l l y i e l d - l i n e mechanisms i n each of the three t e s t s . Consequently, no information was obtained on possible strengthening e f f e c t s from a x i a l force in the slab. l-k6
