Solutions for certain rectangular slabs continuous over flexible ...

SOLUTIONS FOR CERTAIN RECTANGULAR
SLABS
Equations (29) are of particular interest under the load, where
they become
v-v
7-
(1+/,)P A' Pv 1 1 inh 2rv
---- logeB----4 --- )sinh-a
87T B' 4a B' A' a
sinh 2 -
±rv(1 -p)
a
S2a A' '
S(1+,)P A' Pv 1 1 F 27rv
M) = -(
;
)loge-; - ( -- p sinh-
SJ o87 e B' 4a B' A' a
V=v
-(30)
rv(1 -- )
2a
sinh 2 -
a
A'
Mwhe
27ru
sin --
(1 -, )Pv a
U8a
A
Trv
a
27 v
sinh ---
a
A'
where
2rv 27ru
A' = cosh --- cos -,
a a
2irv
B' = cosh --- 1. (31)
a
Equations (30) give corrective moments under the load which are
to be added to the corresponding moments in the infinitely long slab
without a cross beam, as given by Equations (18), in order to obtain
the resultant moments under the load. Numerical values of corrective
bending moments computed from (30) are given and discussed
in Section 8.