Solutions for certain rectangular slabs continuous over flexible ...

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ILLINOIS ENGINEERING EXPERIMENT STATION Fia. 37 for successive values of HI = H 2 = H of 1.0, 2.0 and 4.0, and for various values of H 3 . The conditions represented in Figs. 34 and 36 are extreme as to position of the load and the effect of the diaphragm. In one case the diaphragm is dished to its greatest extent, and in the other case it is humped its maximum amount. There is an intermediate position of the load on the slab for which the diaphragm will be straight and,
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
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H ILL I N 0 I S UNIVERSITY OF ILLIN
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3000-5-38-14400 pEssF II
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CONTENTS (CONTINUED) V. THE RECTANG
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CONTENTS (CONCLUDED) PAGE 36. Recta
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SOLUTIONS FOR CERTAIN RECTANGULAR S
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