Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR
SLABS
When the load is in the center of Beam 1 the bending moment in
that beam, under the load, is
max Mbeam 1 =
Pa 8 1 4
4 r 2 1 •.. n 2 n-rH
Formulas which express the moments in the slab are readily
obtained by differentiation of (56).
IV. THE SEMI-INFINITE SLAB CARRYING A CONCENTRATED LOAD
AND HAVING THE LONG EDGES SIMPLY SUPPORTED
12. The Finite Edge Simply Supported.-The effect of a pair of
loads on the infinitely long slab, one upward and one downward at
the same distance u from the y axis, has been discussed by Nadai*
and by Westergaardt who point out that the slab deforms as if it
were cut and simply supported on a line midway between the loads.
By a simple expedient, therefore, one obtains the deflection of the
semi-infinite slab having simply supported edges and carrying a
concentrated load.
FIG. 14
The slab to be considered is shown in Fig. 14.
may be composed of two parts,
w = Wo - w'o,
The deflection
(63)
in which wo, given by Equation (9), is the deflection of an infinitely
long slab due to a concentrated load at the point x = u, y = v, and
*A. Nadai, Die elastischen Platten, 1925, p. 158.
tH. M. Westergaard, Computation of Stresses in Bridge Slabs Due to Wheel Loads, Public Roads,
V. 11, No. 1, March, 1930, p. 17.