Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
where
(2ab - av) sinh av - av sinh (2ab - av)
c4 = (208)
(sinh 2ab - 2ab) (cosh 2ab - 1)
Equation (207) is valid over the entire loaded panel. It also represents
the total deflection in the unloaded panel provided that x is
taken positive to the left.
One has, therefore, the deflection of the slab, for x > 0,
W = Wo + Wcor
where w 0 is the deflection of a rectangular slab, b by a, simply supported
on all edges and loaded as in the right-hand panel of Fig. 40,
and w,or is given by Equation (207). When the ratio b/a is small,
that is when (b/a) < 0.4, one may take wo as approximately equal
to the deflection of the infinitely long slab of span b. Then
Pb 2 1 nry \ "ry nrV mrX
Wo = - + - ) e sin - sin - .(209)
2r-N ... n 3 b b b
The bending moment M. in the slab over the interior beam is
M = -N-- = -N--]
x=0 ax X0=0 aX2
(210)
P ( -- 1) sinh av -sinh (2ab-av)
Pv _v
= - cos ay.
a 75.. sinh 2ab - 2ab
38. The Infinitely Long Slab Simply Supported at the Edges,
Continuous Over a Central Line Support, and Carrying a Concentrated
Load.-In the preceding solution, by allowing the supports at
y = ± a/2 to recede sufficiently far from the load, one may determine
approximately the deflection of an infinitely long slab having a