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are taken i n t o account. S i m i l a r l y , the influence of unequal span lengths are considered. I n the discussion t o the paper on frame analysis, (15) i t was suggested that an approximate method be used f o r computing deflections. This prodedure uses a one f t wide s t r i p along one of the diagonals of a panel. Deflection at midspan of the s t r i p i s calculated assuming f i x e d ends. Load applied t o the beam i s one-half the design load. Moment of i n e r t i a of the beam i s based on the uncracked section. Deflections were computed using t h i s approximate method and taking i n t o account the difference i n moment of i n e r t i a between the s o l i d portion and the waffle portion of the slab. Deflections computed by t h i s shortcut method underestimated deflections measured i n the loaded panels of the t e s t struotxjre. Calc\ilated deflections were about one-half t o one-quarter of the measured deflections. Even considering the slab cracked, deflections are s t i l l somewhat less than computed. I t appears that f o r t h i s structtire the approximate method does not adequately predict behavior. STRENGTH UNDER OVERLOAD Strength under overload was governed by sudden shear pvmching i n a l l three t e s t s ; f l e x u r a l capacity was not reached. Only i n Test I I I was substantial y i e l d i n g noted before shear f a i l u r e occurred. Test I . The structure behaved " e l a s t i c a l l y " u n t i l f a i l u r e occurred. Above service loads, load-deflection and load-strain relationships remained very nearly l i n e a r . Even at an applied load of 843 psf (dead load plus 2.7 l i v e loads), deflections a t the center of loaded psmels were less than 0.70 i n . This d e f l e c t i o n corresponds to a r a t i o of about L/500. S i m i l a r l y , r e i n - forcement stresses were low. The reinforcement stress increased by 20,000 p s i under an applied load of 843 psf at only one location. At most other locations, reinforcement stresses were 10,000 psi or less. 1- 50
Test t o calculated r a t i o s i n Table XI show tha t f o r mechanisms A, B, and C maximum load during t e s t was only about one-half of the computed load. This corresponds to t e s t observations since no f i i l l y developed y i e l d pattern was noted. I n each of the three t e s t s , shear f a i l t i r e of the slab prevented development of a f l e x u r a l mechanism. In Test I I I , however, a y i e l d l i n e pattern was p a r t i a l l y developed. As described e a r l i e r , reinforcement y i e l d occurred i n the positive moment region of the slab. I n Mechanisms A, B, and C, i t was assiamed th a t y i e l d l i n e s were w i t h i n the te s t areas. Cracks that formed i n the slab during the tests indicated y i e l d l i n e s could develop outside the loaded panels. Flexural capacities f o r Test I a f t e r f i r s t f a i l u r e and Tests I I and I I I before f i r s t f a i l u r e were evaluated assuming y i e l d l i n e s outside the loaded areas. In Test I , loading was continued sifter punching occurred a t Column Ck. A sketch of cracking on top of the roof i s shown i n Fig. 3Ì . These cracks circumscribe the test area and are located i n the v i c i n i t y of cu t - o f f of negative moment reinforcement. Only temperature steel reinforced the cracked sections f o r negative moment at these locations. The crack pattern indicated t h a t negative moment y i e l d l i n e s had formed at the locations of the cracks. Mechanism D shown i n Fig. 58 represents the collapse mechan- ism. Computations were based on the assumption that Column CU carried no load. This pemitted the four panel t e s t area to act as one large panel. The four t r i a n g u l a r areas th a t include the load must rotate about axes through column Lines B, 5* and 3- This requires the slab t o deflect downward within the loaded area and t o raise upward beyond the axes of ro t a t i o n . Slab elements outside the negative y i e l d l i n e s rotate about the positive moment y i e l d l i n e s . This mechanism agrees w e l l with the de- formation of the structure observed near the end of Test I . Using the p r i n c i p l e of v i r t u a l work, t o t a l load t o form Mechanism D was computed to be 690 psf. This quantity compares w e l l with the maximvmi load of 799 psf that could be applied a f t e r Column Ch punched through the slab. The t e s t t o calculated r a t i o i s I.16 f o r t h i s mechanism. This r a t i o i s not unduly high since s t r a i n hardening and a x i a l forces i n the slab were ignored. 1-51
