Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
-7 _ ea- Z Ez 7
o/-. ----- • /-• 7_r 7
Beam 2 62 2
FIGa. 27
in which the load is over the center stringer as shown in Fig. 27.
total deflection of the slab for y > 0 is found to be
2Pa 3 ks
w = -- Z (fi cosh ay - sinh ay
7'Eili ,.... n 4
where
where
+ ay cosh ay - f-ay sinh ay) sin au sin ax
n-Hi +f nrH 1
The
(153)
(154)
and where fi and f3 are functions given in Appendix B.
The deflection of the center beam is
2Pa 3 k 2 fl
Zi = - - sin au sin ax
,=O r4Eij 1,2,3,.. n4
2Pa 3 1 4
= zo - k 2 sin au sin ax
7 EJi ..... .n 4 nTrHi
(155)
where z 0 is the deflection of the center beam supporting the concentrated
load, but without the restraining effect of the slab; that is
2Pa 3 1
Zo -= - sin au sin ax
7r4Eil i,-. n 4
S6E- (2au - x - u 2 )
6ElIia
P (a - x) u
= (2ax - u 2 -- a 2 )
6Edlia
for x < u (156)
for x > u.