Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR
SLABS
The deflection of the continuous edge beam is
1 4pa 4 1 Qa 2 1
z=w ] = 4 -- d 3 sin ax- --
Jy=b 5 N .s,,.- n T- ,N,.- n 3 f 7 sin avsin ax. (179)
One finds, for zero deflection at the interior supports, that the
concentrated reactions are given by the equation
1
4a --
d3 sin av
Q 1= f4s-n (180)
7r 2 1f7 sin2 av
3
1 n2,3,
The functions b 3 , cs, d 3 , f2, f4 and f7 are given in Appendix B.
31. Rectangular Slab Having Two Opposite Edges Simply Supported
and Two Edges Supported on Beams Which Are Continuous
Over Interior Supports at the Third-Points; Concentrated Load on the
Longitudinal Center Line.-The slab is shown in Fig. 32 where each
/ Con'/nuoous F/exib/e Beam E42
- -
X--
£2
FIG. 32
of the interior reactions at x = a/3 is represented as having a magnitude
of (Q1 + Q 2 )/2 and the remaining interior reactions are each
represented as having a magnitude of (Q1 - Q2)/2. From (109)
and (113) one obtains a deflection function for b > y > 0: