THE EQUILIBRIUM OF THE CIRCULAR-ARC BOW-GIRDER. 405 
From symmetry is zero at the centre of the span where => -¢, and by 
y 
dé 
substituting this value for ®, in (20), and by also substituting for M, its value 
wr L— = p- Ts) tan and equating to zero, the value of T, may be obtained, 
l wr 
after which the values of M, and T, for any point on the girder may be obtained 
by substitution in (18) or (19). 
Lo 
Bo 
= a 
—— | 
SS wa 
SS Ss a 
Sa a, 
CSG] EES Pan & Na 
} S|} fF \ 4 
"GO SS eas5 
SNe eee eee CES 
2 ES eee Eee 
SSS ae ee A) 
SS es Sa ee eS 
a a Sas SS 
a a 
| ag 5 : < Pes 
22> ae a SP SG 
re) SSS Se a eo, DRESS 
~ EEE SS ee Ee * oy oC 
SS =a SS eee aN 
7s) ees ee eee ag PS AO 
Saas mee Gi SS 
SS SS = —— 
, SSS SS SS SS 
“00 SAGES aR] SE a a a Sen es 
a ae Sasi a3 = 
= = 
8 eS as es 
Y 1 =a 
eg eS = 
Saas rot a ol 
o S 
(Or /0° Oe 30° Ys Way 50° ‘Avon o° 8 
SI 
— Vaives of O MEASURED FROM ONE SUPPORT — 
eee eee ee eee 
Fic. 8.—Bending Moment Diagrams for one-half of uniformly loaded circular are subtending an angle of (180 — 29°). 
The values of M,, T,, M,, T, have been calculated from the foregoing equations 
for one-half of a uniformly loaded girder for a series of values of ¢, and of @ for each 
value of ¢. These values depend slightly on the relative value of EI and of OJ, and 
in fig. 7 values of M, and of T, are plotted for the case in which the ratio of EI : OJ 
is 1°24. In figs. 8 and 9, values of M, and ‘I’, are plotted for the same case, and for 
purposes of practical design these values may he taken as sensibly accurate for any 
other likely values of the ratio. In the case of the semicircular girder, the moments 
are independent of this ratio. The following table shows values of M, and T,, also 
for the case where EI = 2CJ :— 
