Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR
SLABS
according to the assumptions of the solution, will transmit no load.
Its effect will then be to twist the stringers.
35. Rectangular Slab, Having Two Opposite Edges Simply Supported
and Two Edges Stiffened, Loaded by Symmetrical Concentrated
Loads Placed on the Center Line Normal to the Stiffened Edges.-The
slab is shown in Fig. 38 where it will be noted that the axes have been
FIG. 38
rotated and shifted from the position given in the corresponding
solution of Section 17. The purpose of the change is to put the
solution into a form which, for small values of b/a, can utilize the
well known solution for an infinitely long slab, having a span 2b = s,
simply supported on the edges x = + b, and supporting the given pair
of concentrated loads. For all values of b/a the solution may, however,
be stated in a form which contains, in part, the solution of
the rectangular slab, simply supported on four edges, and carrying
the given loads.
Consider the portion of the slab between the limits x = ±v.
The deflection, wi, is given by the sum of Equations (94) and (96)
provided that proper correction is made for the position of the pair
of loads and for the changed axes. One finds
Pa 2 1 1
wi - 1 { [b, + (1 + av) e-"'] cosh ax
n 3 -N ) s..c
(192)
where bi and cl are given in Appendix B.
- (c, + e- ") ax sinh ax } cos ay