Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
than 0.4. The moment M. is affected over a wider range of values
of v/a; however, for every position of the load across the span, the
reduction in M. at v/a = 0.5 is less than 0.05 P.
As an example of the influence of the beam in reducing the bending
moments under the load, consider the specific case of a central load P,
uniformly distributed over a small circle of diameter c = a/10, on a
slab having a ratio of span to thickness, a/h, equal to 12 and assuming
that Poisson's ratio u = 0.15. Without the cross beam the moments
per unit of length in the slab under the load are*
MA0) = 0.3154P
yv
MA (°) = (0.3154 - 0.0676) P = 0.2478 P.
y-v
Adding to these moments the corrections given in Table 1 and Figs.
5 and 6 for u/a = 0.5 gives the final moments shown in Fig. 7.
FIG. 7
*H. M. Westergaard, Computation of Stresses in Bridge Slabs Due to Wheel Loads, Public Roads,
V. 11, No. 1, March, 1930, p. 9, Table 1.