Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
where
as = 2 + (1 -
i) ab coth ab,
AAlk = a 5 sinh av - (1 - p) av cosh av,
(202)
and Ai is given in Appendix B.
When b/a < 0.4 one may take w 0 as approximately equal to the
deflection of an infinitely long slab, of span 2b = s, supporting the
given loads. Then, for y > 0,
Ps 2 1
wo = --- .-- 1 +
TrN 2,4,6 n 3 - e ' sin
s /
n-v
--- sin
nx. (203)
--. (203)
8
The same reciprocal relationship mentioned in Section 35 may be
seen to apply also to the slab loaded by the anti-symmetrical loads
considered here.
The beam deflection at x = b is
P a 2 1
z = w =- Fcos ay.
J] P= rN, n-'
(204)
37. Rectangular Slab, Simply Supported on Four Edges, Having a
Rigid Support Along the Longitudinal Center Line and Carrying a
Concentrated Load on the Lateral Center Line.-The axes may be
FiG. 40
oriented as shown in Fig. 40. A combination of the solutions given
in Sections 20 and 24, when u = a/2 and EJI1 = E212 = °, then
gives a deflection function