Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR SLABS
where z 0 is the simple beam deflection given by (115), and where f6
is given in Appendix B.
27. Concentrated Loads Giving a Slab Deflection Which Is Antisymmetrical
With Respect to the Longitudinal Center Line.-The neglect
of the effect of twisting of the beams and the fact that there is
no deflection of the longitudinal center line permit the corresponding
solutions given in Chapter V, Sections 20 and 21 to be used also when
the slab is continuous over a longitudinal center stringer. These
anti-symmetrical solutions may be combined with the corresponding
symmetrical solutions to obtain the effect of a single concentrated
load at any point on the slab.
28. Load Uniformly Distributed Over the Entire Slab.*-Section 22
gives the solution for the uniformly loaded slab with edge stiffeners
only, namely
4pa 4
wi = ---
1
- (1 - b cosh ay + ca ay sinh ay) sin ax (166)
7T'iV ,-- n
where b 3 and ca are given in Appendix B. To this a second solution,
4pa 4 k,
2 (f cosh ay - sinh ay
7r N .-. n 6 (167)
+ ay cosh ay - f 3 ay sinh ay) sin ax,
similar to (109), may be added to correct for the effect of the center
/ L zoao p A's" Urn'" Aree / b/
FiG. 29
*This problem has been treated previously in an approximate manner. See Hjalmar Granholm,
"'Om Lastf6rdelning Mellan Balkar Med SArskild HAnsyn Till Farbaneplattans Inverkan," Betong,
1936, No. 4, pp. 139-219, Stockholm. Granholm takes account of the interaction between the beams
and slab and also includes the effect of torsional rigidity of the beams in his analyses, but considers
the slab to be replaced by a series of thin strips which act independently of each other.