Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR
SLABS
in which
2 (V 0.4c 2 + h 2 - 0.675h) for c < 3.45h
c for c > 3.45h
where
c = diameter of a small circular area assumed to be uniformly
loaded,
h = thickness of slab.
In much of the work that follows, the results are presented in the
form of corrections to be added to the corresponding basic quantities
given in the foregoing.
III. THE INFINITELY LONG SLAB WITH SIMPLY SUPPORTED EDGES
6. Concentrated Load at Any Point on the Infinitely Long Slab
Having a Rigid Cross Beam.-Figure 3 shows the slab and the orienta-
FIG. 3
tion of the axes relative to the cross beam and the load. Without
the cross beam, the deflection of the slab is given by w 0 of Equation
(9). The deflection due to a line load of unknown distribution upon
the line y = 0 is given by the equation
Pa 2 an
i = 2- 1 -3,. (1 + a-y\) e-"0 sin au sin a x
wl 2drN i.e.3.. n 3
where the load distribution factor a. is to be determined by the
boundary condition at y = 0. The total deflection is then
W = W 0 +
Wi.