BEAM OF EECTANGULAR CEOSS-SECTION UNDEE ANY SYSTEM OF LOAD. 73 
expressions (31), we obtain eight typical equations for the constants which, when 
combined in pairs, may be written in the simpler form: 
(A' - C') cosh mb - 2mh A' sinh mb = ] 
(32) 
(A' + C') sinh mb + 2mb AJ cosh ml> = ' 
2 
(B — 1^0 sinh ml) — 2ml) cosh mh 
(B' -j- D') cosh mh -f- 2mb B' sinh mb 
(E' — G') cosh mb — 2mb E' slidi mb = 
(E' + G') sinh ml) + 2mb E' cosh mb 
_ /3«. 
— 2 
_ K^n + V„ 
~ ^ 2 
_ 7« + 
2 
_ G - e,, 
(F' — H') sinh mb — 2mb F' cosh mb = 
G + S)i 
(F' + fl') cosh mb + 2mb F' sinh mb = — 
2 
These equations solve in j^airs. We find easily 
+ /3h sinh mh . k„ — p,, cosh mh 
A' = 
2 sinh 2)jih + 2mh 
+ 
sinh 2vih + 2mh 
Q' — _ +_/5« sin h mh + 2mh c osh mh ^ /c„ - v„ cos h mh - 2mh sinli mh 
2 sinh 2mh + 2ml 2 sinh 2nih + 2inh 
cosh vih 
sinh 2mh — 2)nh 
+ 
+ Vn 
sinli mh 
2 sinh 2mh — 2mh 
p)' — ■_^ cosh mh + 2mh sinh m h + p,, sinh mh — 2mh cosli mh 
2 &mh2mh-2mh 2 ~ ~ sinhAwF-2mG~' 
E'= - 
7« + G 
sinh mb 
sinh 2mh + 2mh 
+ 
G - Oa 
cosh mh 
sinh 2mh + 2mh 
Q/ _ 7« + G sinh mh + 2mh cosli mh G_TL^ ~ sinh mh 
2 sinh 2mh + 2mh 2 sinh 2mh + 2mh 
F' = 
H'= - 
7n — 
cosh mh 
G + On _ sinh mh 
2 sinli 2mh — 2ml> 
2 sinli 2inh — 2mh 
~ G cosh mh + 2mh sinh mh G + sinh mh — 2mh cosh m.h 
sinh 2mh — 2mh 
sinh 2mh — 2mh 
where in the above n corresponds to a positive integer. 
The ca.se viiere it = 0 has to be investigated separately 
VOL. GCI,—A. I 
( 33 )> 
( 34 ), 
(35), 
(.36), 
(37) , 
(38) , 
( 3 !>), 
(40) , 
(41) , 
(42) , 
(43) , 
