THE EQUILIBRIUM OF THE CIRCULAR-ARC BOW-GIRDER. A401 
The results are plotted as curves in figs. 5 and 6, and by substitution from these 
in equations (4), (5), (12), and (13), the values of the bending and twisting moments and 
of the deflections at any point of the girder, may be obtained. 
Special Cases. 
Semicircular Bow-Girder with single load W in any position.—Here a+ 6 = 180° ; 
@=0; and the foregoing equations simplify. The values of the various constants for 
such a girder have been calculated for the case where H1=1'24CJ, and are given 
in the following table. 
a 0 15° 30° 45 60 15° 90 
Ry 
W 1:00 | 990 ‘940 870 764 640 500 
R, 
W 0:0 0104 060 ‘131 236 “361 500 
M, 
Wo 0:0 239 428 | ‘642 590 O71 500 
r | 
M, 
Wr 0-0 “0200 0725 165 276 395 500 
Als 
Ww. 0-0 0251 0662 “115 "155 181 182 
Y 
T, 
aaa 0-0 0118 0382 082 128 ‘161 | ollie 
Wr 
In the particular case where a=90°=1°5708 radians (7.e. weight at centre of 
span) from symmetry, 
R, =R, = ‘500W 
M,=M,=‘5Wr 
he = it 
d ah ele 
From (10) the value of = at the weight (« = ’) is given by 
2 _t 1 re T 9 = 2 72 ; z 
oor (2 5) tats | - apy | We(1-5-2) 27. Py lon ae {Wo 5) rata 
From symmetry this equals zero ; 
zs T,=Wr(" z *) = -182Wr. 
aT 
and in this case both M, and T, are independent of the relative values of EI and OJ. 
Experimental Verification.—As a check, a series of measurements of deflection 
EI 
were made on a small semicircular bow-girder, 10°10 ins. in radius. = = 1°24. 
CJ 
