Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 3
BENDING MOMENT My IN THE SLAB OVER THE CROSS BEAM
Concentrated load in the center of the infinitely long slab having a rigid
cross beam. Numerical values were computed from Equation (36). Curves
have been plotted in Fig. 9 where the coordinate axes are also shown. These
moments are independent of Poisson's ratio.
a
x
P
a
iM
0.05
0.10
0.20
0.30
0.40
0.45
0.50
0.0013
0.0034
0.0086
0.0312
0.0789
0.1585
0.40
0.0284
0.0582
0.0885
0.1137
0.1212
0.1239
0.10
0.10
0.20
0.30
0.40
0.45
0.50
0.0049
0.0124
0.0289
0.0769
0.1247
0.1566
0.50
0.0287
0.0568
0.0825
0.1015
0.1068
0.1086
0.15
0.10
0.20
0.30
0.40
0.45
0.50
0.0099
0.0241
0.0508
0.1043
0.1375
0.1534
0.60
0.0265
0.0516
0.0730
0.0879
0.0919
0.0933
0.20
0.10
0.20
0.30
0.40
0.45
0.50
0.0153
0.0357
0.0682
0.1170
0.1397
0.1491
0.80
0.0197
0.0377
0.0523
0.0619
0.0644
0.0652
0.30
0.10
0.20
0.30
0.40
0.45
0.50
0.0241
0.0522
0.0863
0.1213
0.1334
0.1378
1.00
0.0133
0.0253
0.0349
0.0411
0.0428
0.0433
load on the center of the span and for values of v/a varying from
0.05 to 1.0.
It is significant that the limiting value of My in the slab over the
beam is -P/(2Tr) regardless of the distance u between the load and
the edge of the slab. This limiting value is approached as the load
tends to cross the beam.
When the load is near the cross beam it is permissible to interpret
the slab as a bridge floor which is continuous over stringers and floor
beams. In this case the cross beam corresponds to a floor beam, and
the distance a corresponds to the span of the slab between stringers.
The validity of such an interpretation arises from the condition that
the continuity of the slab across the floor beam is the principal factor