Solutions for certain rectangular slabs continuous over flexible ...
Solutions for certain rectangular slabs continuous over flexible ...
Solutions for certain rectangular slabs continuous over flexible ...
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SOLUTIONS FOR CERTAIN RECTANGULAR SLABS<br />
TABLE 2<br />
BENDING MOMENT My IN THE SLAB OVER THE CROSS BEAM<br />
The slab is infinitely long and has a rigid cross beam as shown in Fig. 3. Numerical values were<br />
computed from Equation (32). The corresponding curves are shown in Fig. 8. These moments are<br />
independent of Poisson's ratio.<br />
v<br />
a<br />
My-<br />
P<br />
when<br />
u/a =<br />
0.1<br />
Mr<br />
P<br />
when<br />
u/a =<br />
0.2<br />
_M_<br />
P<br />
when<br />
u/a =<br />
0.3<br />
Mr<br />
P<br />
when<br />
u/a =<br />
0.4<br />
0.05<br />
0.0637<br />
0.1498<br />
0.0734<br />
0.0275<br />
0.0069<br />
0.0027<br />
0.0013<br />
0.0007<br />
0.0004<br />
0.0002<br />
0.0001<br />
0.0275<br />
0.0764<br />
0.1567<br />
0.0776<br />
0.0302<br />
0.0082<br />
0.0034<br />
0.0017<br />
0.0009<br />
0.0005<br />
0.0002<br />
0.0069<br />
0.0302<br />
0.0782<br />
0.1580<br />
0.0786<br />
0.0309<br />
0.0086<br />
0.0036<br />
0.0018<br />
0.0009<br />
0.0004<br />
0.0027<br />
0.0082<br />
0.0309<br />
0.0788<br />
0.1584<br />
0.0789<br />
0.0312<br />
0.0087<br />
0.0036<br />
0.0017<br />
0.0007<br />
0.10<br />
0.0783<br />
0.1273<br />
0.1053<br />
0.0636<br />
0.0224<br />
0.0097<br />
0.0049<br />
0.0027<br />
0.0016<br />
0.0009<br />
0.0004<br />
0.0636<br />
0.1152<br />
0.1497<br />
0.1197<br />
0.0733<br />
0.0273<br />
0.0124<br />
0.0065<br />
0.0036<br />
0.0020<br />
0.0009<br />
0.0224<br />
0.0733<br />
0.1220<br />
0.1546<br />
0.1233<br />
0.0760<br />
0.0289<br />
0.0133<br />
0.0069<br />
0.0036<br />
0.0016<br />
0.0097<br />
0.0273<br />
0.0760<br />
0.1241<br />
0.1562<br />
0.1245<br />
0.0769<br />
0.0293<br />
0.0133<br />
0.0065<br />
0.0027<br />
0.20<br />
0.0479<br />
0.0795<br />
0.0875<br />
0.0781<br />
0.0474<br />
0.0266<br />
0.0153<br />
0.0091<br />
0.0055<br />
0.0032<br />
0.0014<br />
0.0781<br />
0.1103<br />
0.1269<br />
0.1230<br />
0.1047<br />
0.0627<br />
0.0357<br />
W•0208<br />
0.0123<br />
0.0069<br />
0.0032<br />
0.0474<br />
0.1047<br />
0.1304<br />
0.1422<br />
0.1348<br />
0.1138<br />
0.0682<br />
0.0388<br />
0.0222<br />
0.0123<br />
0.0055<br />
0.0266<br />
0.0627<br />
0.1138<br />
0.1375<br />
0.1477<br />
0.1390<br />
0.1170<br />
0.0697<br />
0.0388<br />
0.0208<br />
0.0091<br />
0.40<br />
0.0315<br />
0.0417<br />
0.0472<br />
0.0484<br />
0.0466<br />
0.0381<br />
0.0284<br />
0.0201<br />
0.0135<br />
0.0083<br />
0.0039<br />
0.0472<br />
0.0780<br />
0.0845<br />
0.0853<br />
0.0816<br />
0.0750<br />
0.0582<br />
0.0419<br />
0.0284<br />
0.0174<br />
0.0083<br />
0.0466<br />
0.0853<br />
0.1065<br />
0.1085<br />
0.1054<br />
0.0982<br />
0.0885<br />
0.0665<br />
0.0458<br />
0.0284<br />
0.0135<br />
0.0381<br />
0.0750<br />
0.1054<br />
0.1152<br />
0.1200<br />
0.1193<br />
0.1137<br />
0.0924<br />
0.0665<br />
0.0419<br />
0.0201<br />
As the distance u from the beam to the load increases, the moments<br />
are seen to rise in magnitude until they approach the values <strong>for</strong> the<br />
infinitely long slab without a cross beam.<br />
Numerical values of the bending moments M, in the slab <strong>over</strong><br />
the beam, computed from (32), are given in Table 2, and are shown<br />
in Fig. 8 <strong>for</strong> various positions of the load on lines at distances of 0.1,<br />
0.2, 0.3 and 0.4 of the span from one edge. Similar moments, computed<br />
from (36), are given in Table 3 and are shown in Fig. 9 <strong>for</strong> the
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