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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42 ILLINOIS ENGINEERING EXPERIMENT STATION<br />
The deflection of the center beam is<br />
z<br />
1 2Pa 3 1 ]<br />
= w]i • - . anbn sin au sin ax<br />
7-O 7 rEiEi ,, n 4 (58)<br />
2Pa 3 1 4<br />
= zo - E- an sin alu sin ax<br />
r 4 'ElIi ..- n nrH<br />
in which zo is the deflection of the center beam when it supports the<br />
concentrated load but is detached from the slab; that is<br />
2Pa 3 1<br />
Zo = -- sin au sin ax<br />
ir4Eil 1 ..... n 4<br />
P (a - u) x<br />
= (2au - x 2 - u2) <strong>for</strong> x < u (59)<br />
6EiIia<br />
P (a - x) u<br />
= (2ax - u 2 - x 2 ) <strong>for</strong> x > u.<br />
6E 1 Iia<br />
The deflection of the beam at y = b or at y = -b is<br />
1 8Pa 1 1<br />
= w •z - and, sin au sin ax (60)<br />
y=h - 7r4EjlI , .. n<br />
where an is given by (57) and where<br />
(1 + ab) e-" b<br />
dn = . (61)<br />
nrH 2 [1 + (1 + 2ab) e-2ab] + 4<br />
The bending moment in the center beam is<br />
d 2 zo 2Pa 1 4<br />
Mbeaml = -Eli - - - n- n a. sin au sin ax,<br />
dx 2 2 1,2,3,- 2 n" rH 1<br />
and the bending moment in each of the other beams is<br />
8Pa 1<br />
Mbeam 2 = -- - a,,d, sin au sin ax.<br />
2<br />
,2,3." n 4
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