BEAM OF EECTANGULAR CROSS-SECTION UNDER ANY SYSTEM OF LOAD. 87 
v = ^s 
sinh 27i7r&/(X 
+ 
fjM 7 sinh4?i7r6/«' + AzmThja 
yW ” cosh ( 2 » + 1 ) irhla 
ybci 0 (4» + 2) irhla — (4?i + 2) -irlja 
/ 
( 
COS ^mrxja cosh ^mryja 
cos (2n + 1) 7r.T?/a sinh (2w. + 1) 77«//a 
/I 1 \ . . . ,, 1 2?z7r& 
\ A 7 -,-f- - ) sinh 2mrhla ^- 
W “ a \y + /jL fjbj ' fM a 
cosh 2n7rhja- 
a 1 2mr 
a 
sinh ^tmrhja + ■inirhla 
^ -h cosh 2n + iTrhja 
\ + fj. /jb/ 
1 2ra+ lirh . . X , 
H-sinh 2%+ l7r?>/a 
a ' 
COS 2mrxja sinh ^mryja 
a 7 (2% +1) TT sinh (4?i + 2) irhja. — (4% +2) TThja 
1 
W,7 
r3\ V 
_ Wy , -O 
7 {2n + 1)3 Ec 
cos (2?t-l-l) TTxja cosh (2^^+l) Try/a 
.(67), 
where B is a constant depending on the origin from which the displacement is to be 
measured. 
p _ _ 
y 
- (271 + 1)3 
” 2W sinh 2mThja — {2mrhla) cosh 2nTrbla 
1 « 
sinh Anirhla + 4%7r6/a 
cos 2mTxla cosh ^mryja 
” 2W (2mry I a) sinh 2nrrhla 
1 a sinh 4?i7r/)/« + 4r)7r/>/« 
COS 2inrxla sinh ^mryla 
* 2'W cosh 277-+1 rrhia — {2n+lirhja) sinh 2n+l'nhla ''—^ ^ 
: 7^ smh(4» + 2)^S/«-(4»+2)^!,/«-3«+ Ux/a smh 2«+ !,.<//« 
* 2W (271+iTry/a) cosh 2ft+iVS/tt 
7 a sinh (471 + 2) irhja — (477 + 2) irhja 
cos 271+1 TTic/a cosh 277-1-l7r7//a . . . (68). 
^ W ^ 2W sinh 2nirhla + {2nirhja) cosh 2nirhja 
^ - t +-^ ''OS 2niTxla cosh 2niryla 
+ 
2a. 1 a sinh 4:nirhja + 4:nirhja 
2W (2niryja) sinh 2nirhja 
a sinh Anirhja + -imrhji 
COS 2mrxla sinh ^mryja 
_ "S' 
0 a 
2W cosh 277 + i7r&/a. + {2n+lirhja) sinh 277+l7r5/7i 
sinh \n-\-2irhja — \n-\-2irhja 
COS 272+ liTxIa sinh 2n+ l7r7//a 
+ S 
0 ct 
2'W (277+ liryja) cosh 277+ lirhj^ 
a 
sinh 477 + 2irhja — \n-{-2irhja 
COS 277+ iTTxja cosh 277+ liryja 
(G9). 
