Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR
SLABS
The deflection of the slab is given by the sum of (9) and (84) with
c. and d. given by (85). When ElI approaches o the solution
reduces to that given in Section 12 under the assumption of a simply
supported edge at y = 0; when Eli1 approaches zero the solution
reduces to that given in Section 14 under the assumption that the
finite edge is free.
16. Three Edges Simply Supported; Rigid Cross Beam.-The slab,
FIG. 18
having the dimensions shown in Fig. 18, has a deflection
W = Wo - W' + W4
where wo and w' are deflections of the infinitely long slab due to
loads P at points (u, v) and (u, -v), respectively, and where
Pa 2 k
=
27 [1 + a (y + b)] e-a(y+b
2rN ... " n (88)
- (1 + a|y-bl) e- al
- b i I sin ausin ax
gives the effect of the beam reaction on the slab.
The quantity k is to be determined from the boundary condition
w = 0.
J y=b