406 PROFESSOR A. H. GIBSON ON 
d 0° 15° 30° 45° 60° 
M, { EI=1-240J 1:00 686 424 230 0974 
wre \ EL = 2CIJ 1:00 688 427 239 0983 
Ey ee CJ 298 135 0490 0156 00199 
wre \ EI =2CI 298 140 0542 ‘0178 00251 
= Stare of Jy, sep = 
— Values of O measured from one Support — 
Fic. 9.—Twisting Moment Diagrams for one-half of uniformly loaded circular are subtending an angle of (180 —2¢) . 
Special Case. 
Semicircular Girder with uniform load. —Here ¢=0, and we have :— 
Ni eh : “wr : 
We | ’ : 
—_| (T, — Rar) 0, sin 0, + 2wr? sin 6, | 
) ~ Zils ; ; : (? ) 
7 + sal (T,, — R,7)6, sin 6, + 2R,7(1 — cos 8,) — 2awr?(@, -— sin 6.) | 
sa — R,")(sin 6, — 6, cos 0,) — 2rr?(cos 6, — 1)| 
Yo, = 
+ sql (Te - R,7/)(sin 6, — @, cos 6,) + 2R,7(8, — sin 6,) — 2aore( Ex + cos 6, — 1) | 
Substituting for M, and R, in (20’), and equating to zero, gives 
Ns Kae “i 9 
T= wr? x —(— —2)='298wr?, 
4 
T 
