Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIR F.T'J(4TNEE14TN(5 TYP TMEYSTm RT A
At the center of the beam this moment becomes
2Pa 1
max Mbeam -- -- (1 + av) e-I
2 1,3,, .. n 2 S(42)
Pv lrv 2Pa 1
- loge coth - + - -- e- .
r 2a r 2 1,,.. n 2
8. Numerical Computations of Moments in the Infinitely Long Slab
Having a Rigid Cross Beam and Supporting a Concentrated Load.-
Numerical values* of the corrective bending moments M ' 1 and M 1)
under the load, computed from (30) and (35) for I. = 0.15, are
TABLE 1
CORRECTIVE MOMENTS UNDER THE LOAD DUE TO A RIGID CROSS BEAM
Concentrated load on the infinitely long slab of span a having a rigid cross beam. The load is
at a distance u from one of the edges of the slab and at a distance v from the cross beam. Numerical
values of MW() and M,0) in the table are corrective moments under the load, due to the presence of the
beam, and were computed from Equations (30) and (35). The corrective moments are to be added to
the corresponding moments found under the load on the infinitely long slab without the cross beam.
Poisson's ratio, p = 0.15. Curves of moments are shown in Fig. 5 and Fig. 6.
u
a
v
M,.()
P
M,(1)
P
u
a
v
a
M,(1)
P
M4(1)
P
0.1
or
0.9
0.2
or
0.8
0.3
or
0.7
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
1.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
1.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
1.00
-0.1547
-0.0869
-0.0522
-0.0334
-0.0159
-0.0087
-0.0051
-0.0031
-0.0012
-0.0005
-0.2162
-0.1501
-0.1101
-0.0821
-0.0473
-0.0283
-0.0174
-0.0109
-0.0043
-0.0016
-0.2460
-0.1812
-0.1420
-0.1135
-0.0736
-0.0478
-0.0309
-0.0199
-0.0080
-0.0031
-0.0627
-0.0193
-0.0066
-0.0024
+0.0001
+0.0006
+0.0007
+0.0006
+0.0004
+0.0002
-0.1170
-0.05821
-0.0298
-0.0149
-0.0026
+0.0011
+0.0020
+0.0020
+0.0013
+0.0007
-0.1456
-0.0840
-0.0506
-0.0299
-0.0084
+0.0001
+0.0030
+0.0035
+0.0024
+0.0012
0.4
or
0.6
0.5
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
1.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
1.00
-0.2610
-0.1966
-0.1580
-0.1299
-0.0892
-0.0607
-0.0406
-0.0267
-0.0109
-0.0043
-0.2656
-0.2014
-0.1630
-0.1350
-0.0942
-0.0651
-0.0441
-0.0292
-0.0121
-0.0047
-0.1602
-0.0978
-0.0629
-0.0400
-0.0135
-0.0014
+0.0033
+0.0045
+0.0033
+0.0017
-0.1647
-0.1022
-0.0669
-0.0434
-0.0154
-0.0021
+0.0033
+0.0048
+0.0036
+0.0019
*Numerical values of the hyperbolic functions were obtained from the British Association for the
Advancement of Science, Mathematical Tables, V. 1, London, 1931.