Solutions for certain rectangular slabs continuous over flexible ...

ILLINOIS ENGINEERING EXPERIMENT STATION
The derivatives of ¢, needed in Equations (23) are
7r (X + ±u)ry U)
i (v ± yl)
sin
Q(> P c
A + - sinh +
ax 4a AL2
a
a
sin
r (x - u)
a
-B2 B( +
1I
7rv
- sinh
r ( + \yl))
a a /
-(28)*
a4 1 P sgn y / 1 1 r r(v+ y) rv -r(v+Iy)
S--- sinh -- cosh--
ay 4a A 1 B/L a a a
+ -
a
+ -) sinh 2
B, )
S(v + y) D
a
I
The corrective moments due to wi are
1 -+ A 1 - Al 01
M- •1 = --
+ - y --
2 2 ay
1 + p 1 - p 0€1
Mi ' = - ---- y
2 2 9y
(29)
1 - A (r1
xy - y ,
2 ax
in which 01 and its derivatives are given by (24) and (28).
*See Appendix A for a discussion of the change of sign represented by the function "sgn y," namely,
sgn y = algebraic sign of y = { for >0
1 for y