Solutions for certain rectangular slabs continuous over flexible ...

76 ILLINOIS ENGINEERING EXPERIMENT STATION
33. Rectangular Slab Having Edge and Center Stringers and a Continuous
Diaphragm on the Lateral Center Line; Concentrated Load at
the Center of the Slab.-The slab is shown in Fig. 34 (a). The dia-
(a)-S/ructure With Diaphragm (b)-Equivalent St-rucfure
(c) -D/aphragm
FIG. 34
phragm is assumed to have no contact with the slab, to be simply
supported at the outer stringers, and to be continuous across the
center stringer. Since the connections of an actual diaphragm would
not provide perfect continuity across the center stringer but would
offer some restraint at the edge beams, these assumptions are somewhat
compensating in their effect on load transmission to the outer
beams.
Let Q be the end reaction on the diaphragm as shown in Fig. 34 (c).
The deflection of the center of the diaphragm relative to the ends is
then Qb 3 /(3E 3 I3).
The total deflection of the slab for y > 0 may be obtained by
combining solutions of the types given in Sections 25 and 26. The
net load over the middle beam is P - 2Q and the outer loads are
each equal to Q as shown in Fig. 34 (b). Then, from (155) and (164),
the deflection of Beam 1 at x = a/2 is found to be
- 2(P - 2Q)a 3 k 2 fl Zj = - --
4Qa 3 + --- E
k 2 f -- 2
fa/2 4ElI u.. n 4 ý'IEJl.. 115.. n 4 (187)
2Pa 3 k 2 f 1 4Qa 3 k
- 7r 4 EYI 1 + _ A. 2 (ff2 - fl).
r4E'i n4
n ...
,,.. n 44i Y 2