Solutions for certain rectangular slabs continuous over flexible ...

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ILLINOIS ENGINEERING EXPERIMENT STATION One finds (1 -+ a[b-v) e- b- - [1+ a (b + v)]e-(b+v) 1 - (1 + 2ab) e- 2 ab which holds for any position of the load. When the load is in the end panel, as shown in Fig. 18, v for 0
SOLUTIONS FOR CERTAIN RECTANGULAR SLABS and w2 = w"' + w' for b > y > v (93) where wo and wo' represent the deflections, in their respective regions, of the infinitely long slab of span a due to the pair of concentrated loads shown in the figure, and where w' represents the deflection due to corrective moments and shears which are applied to the slab along the edges y = +b in order to produce the proper edge conditions. From the solutions given previously, one finds, where v>y> -v, Pa 2 1 w'= N [(1 +av) cosh ay - ay sinh ay] e - v sin au sin ax (94) VN ,s,.. n 3 and, where b > y > v, Pa 2 1 w'P =-- [(l+ay) cosh av-av sinh av] e-" sin au sin ax. (95) irWN 7- n' The deflection due to the symmetrical edge corrections may be written in the form Pa 2 1 w' = - . - (b, cosh ay - cl ay sinh ay) sin au sin ax (96) where bi and ci are parameters to be determined by the boundary conditions. The boundary conditions are _- + _ -w = 0, (97) yx a 2 yb_ d9z w 2 0 w 2 2 8 q = E2 2 - = N -- + ( 2 -M) , (98) dx 4 3 y=b x 2 y -b where q is the downward load on the beam and z is the downward deflection. Substitution of the derivatives obtained from (95) and (96) into (97) and (98) results in two equations in bi and Ci whose simultaneous solution gives
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Solutions for certain rectangular slabs continuous over flexible ...

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