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 />
the modulus of elasticity and moment of inertia of the<br />
are not zero.<br />
edge beams,<br />
The deflection of each of the edge beams becomes<br />
where<br />
SPa<br />
2<br />
1<br />
z = w - f7 sin au sin ax<br />
J y-b rW 3 N 1,2,3, n 3<br />
2Pa 3 1<br />
= o - , - fs sin au sin ax<br />
r 4 E I 2 1,2,3, n 4<br />
2Pa 3 1<br />
z o- = - sin au sin ax<br />
r E2I2 1.3.. n 4<br />
(114)<br />
P (a - u) x<br />
(a= u) (2au - X 2 - u2)<br />
6E212a<br />
<strong>for</strong><br />
x < u<br />
(115)<br />
P (a - x) u<br />
= x- (2ax - u 2 - x 2 )<br />
6E212a<br />
<strong>for</strong> x > u.<br />
Here zo is the simple beam deflection <strong>for</strong> the edge beam supporting<br />
the concentrated load, but without the effect of the slab. The<br />
quantities f7 and fs are given in Appendix B.<br />
The bending moment in either edge beam is<br />
d 2 zo 2Pa 1<br />
Mbeam = - Ed 2<br />
S<br />
2 fs sin au sin ax.<br />
da;" T 1- .-. n<br />
When the loads are at the center of the edge beams, the moment under<br />
each load becomes<br />
Pa/ f<br />
max. Mbeam -- 11- 8 )<br />
4 \ 72 n1,,.. 2 /<br />
At the edge of the slab the bending moment My is zero and<br />
M u = Mbeam.<br />
y- aH2<br />
(116)
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