Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
5. Solution for the Infinitely Long Slab Supporting a Concentrated
Load.-The slab and loading are shown in Fig. 2 where the edges
FIG. 2
x = 0 and x = a are assumed to be simply supported and where
the slab is assumed to extend sufficiently far in the directions of
positive and negative y that the deflection of the slab practically
vanishes before additional supports or edges are reached. The deflection
of the slab is then given by the equation*
where
Pa 2 1
wo = - (1 + aly - vI) e "EY'V sin au sin ax
2r'N w77-- n 3
a
Nfidait defined a function 0o by means of the equation
P 1
00 = NV 2 wo = --- - e - 'Y -i sin au sin ax
7r 1,2,3,.. n
(10)
and derivedt an expression for 0o in finite form, namely,
P
P0 = --
47r
Bo
loge--
Ao
*See, for example, A. Nadai, Die clastischen Platten, 1925, p. 85; or H. M. Westergaard, Computation
of Stresses in Bridge Slabs Due to Wheel Loads, Public Roads, V. 11, No. 1, March, 1930, p. 6.
Equation (9) has been adjusted for the origin of co6rdinates shown in Fig. 2 and the absolute value of
(y - v) has been introduced to extend the region of applicability of the equation to the entire slab.
See Appendix A for notes on the differentiation with respect to y of functions involving ]y - v\.
tA. NAdai, Die elastischen Platten, 1925, p. 87. (See previous footnote.)
IA. Naidai, Die elastischen Platten, 1925, p. 89.