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<br />
SLABS<br />
Pa 2 1<br />
wi = E - {[a' + k1 + (1 + av) e-""] sinh ax<br />
27rN ns..'<br />
- (c' - k f• + e-) ax sinh ax (205)<br />
+ (d' - k' - e - ") ax cosh ax } cos ay<br />
which is valid when 0 < x < v. In this equation the quantities<br />
having primes are each equal to the corresponding unprimed quantities<br />
evaluated at Ei1 = E21 2 =<br />
o . The unprimed quantities are<br />
stated in Appendix B.<br />
If the slab is cut on the line x = 0, thus dividing it into two<br />
<strong>rectangular</strong> <strong>slabs</strong> simply supported on all edges, the deflection <strong>for</strong><br />
0 < x < v may be found from Section 20 to be<br />
Pa 2 1<br />
w[ = -- - {[a I + (1 + av) e-" ] sinh ax<br />
7 3-N ..... n 1<br />
(<br />
(206)<br />
+ (d' - e -" ") ax cosh ax} cos ay. (206)<br />
The difference between (205) and (206) is, there<strong>for</strong>e, a corrective<br />
deflection function which provides <strong>for</strong> the continuity across the center<br />
beam.<br />
One has<br />
Wcor = W - W<br />
Pa 2 1<br />
-- Er -- {[a' - k' + (1 + av) e - "v] sinh ax<br />
2r"N ,,7.. n<br />
+ (c' - k'-f' + e- ') ax sinh ax<br />
+ (d' + k' - e-"v) ax cosh ax } cos ay.<br />
After substituting the values of a', c', d', k' and f, into this equation,<br />
and reducing the resulting expression, one finds<br />
Pal c4<br />
Wcor =- [(2ab - ax) sinh ax<br />
2r'N n. nh.... ](207)<br />
- ax sinh (2ab - ax)] cos ay
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