Solutions for certain rectangular slabs continuous over flexible ...
Solutions for certain rectangular slabs continuous over flexible ...
Solutions for certain rectangular slabs continuous over flexible ...
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SOLUTIONS FOR CERTAIN RECTANGULAR SLABS<br />
When the loads are within the central region of the slab, that is<br />
within the middle quarter of the span in either the x or y direction,<br />
Equations (105), evaluated <strong>for</strong> x = u = a/2, may be used <strong>for</strong> an<br />
approximate computation of the corrective moments under the loads.<br />
The approximation is possible because the correction is a symmetrical<br />
edge effect which varies but little <strong>over</strong> the central area of the slab.<br />
18. Concentrated Load on the Longitudinal Center Line.-When the<br />
/a________________ a/<br />
FIG. 20<br />
load is on the longitudinal center line, as shown in Fig. 20, the deflection<br />
of the slab <strong>for</strong> b > y > 0 is<br />
where<br />
and<br />
w = wo + w' (106)<br />
Pa 2 1<br />
wo - - (1 + ay) e - 5 sin au sin ax (107)<br />
2r N w n'<br />
Pa 2 1<br />
w' = --- [(fR- 1) cosh ay - (f - 1) aysinhay] sin ausin ax. (108)<br />
2r 3 N ,... n 3<br />
The complete deflection of the slab <strong>for</strong> b > y > 0 is<br />
Pa 2 1<br />
w<br />
=<br />
- E (fi c osh ay -sinh ay<br />
27rN , ns c2,<br />
+ ay cosh ay -f3 ay sinh ay) sin au sin ax.<br />
(109)
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