Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR SLABS
Fic. 24
in Fig. 24, the deflection w may be taken as the sum of the deflection
of a uniformly loaded beam,
w 4pa 4 _1 p
= N-
E
sin ax = (x 4 -
N .... n
24N
2 a x 3
+ a 3 x), (131)
and a correction
4pa 4 1
w" - • -E (b3 cosh ay-C3 ay sinh ay) sin ax. (132)
75N 17.,. nI
Thus, for any value of y within the slab,
4pa 4 1
w = - (1-b 3 cosh ay+c 3 ay sinh ay) sin ax. (133)
75N i,3,•,..n 5
The boundary conditions at y = b, similar to (97) and (98),
when applied to w, give the results:
Ab3 = 2n7rH 2 (2 cosh ab + ab sinh ab)
+ 2A [(1 - A) ab cosh ab - (1 + u) sinh ab], (134)
Ac 3 = 2nrH 2 cosh ab + 2 ju (1 - p) sinh ab, J
where A is given in Appendix B. In the special case when H 2 = 0
this solution reduces to that given by Holl.* In the other limiting
case, when H 2 = oo, the solution reduces to that given by NAdait for
the uniformly loaded rectangular slab simply supported on four sides.
*D. L. Holl, "Analysis of Thin Rectangular Plates Supported on Opposite Edges," Bulletin 129,
Iowa Engineering Experiment Station, Iowa State College, 1936, pp. 15, 87, and 88.
tA. Nadai, Die elastischen Platten, 1925, p. 123.