A402 PROFESSOR A. H. GIBSON ON 
The following are the deflections corresponding to a load of 1 lb., as obtained by 
measurement and by calculation from formule (12) or (14), with values of T,, M,, ete., 
taken from the table on p. 401. 
Deflection at Weight (ins.). | Deflection at Centre of Span. 
a a —— 
Calculated. Measured. Calculated. Measured. 
30° ‘0430 0432 oi a 
45° 115 lls 148 “150 
60° ‘204 "202 Sn nde 
90° 3075 ‘3075 "3075 "3075 
Circular-Are Girder, subtending an angle less than 180°, and carrying a 
single weight at the centre of the span.—Let 2a=7—2¢ be the angle subtended 
(fig. 4). The moment of the weight about AB=Wr(1~sin®), and as, from 
symmetry, M,=M,; T,=T1,; equation (8) becomes :— 
M, cos ¢-T, sin¢@= Be — sin ¢) 
or 
Wr 3 
= PEs — sin ¢) -- T, tan 4, 
also 
R, = R, = i 
On substituting these values of M, and R,, equation (10) becomes 
Wr /1—sing— T, cect 
val Cs eae - Wien $){a cos a+ sin a} — G ~yi)a cos ¢ | 
dy\  _ 
le Wrl/T, 1 1 singe Ts ‘ sii 
+ acy | (Fem 5) 008 b+ 1 sin o — ( DoE ~ gy, tan #){sina—acos.a} | 
From symmetry this equals zero, and, on substituting for a and # and equating 
to zero, the value of T, is obtained. Except in a semicircular girder (= 0), this value 
depends on the ratio of El: CJ. The following table has been calculated for the cases 
in which this ratio equals 1:24 and 2°0:— 
p 0 15° 30° 45 60° 
M, J EI=1:24CJ 00 “410 “314 223 140 
we EI = 2CJ ‘50 ‘411 “Oli "225 141 
T, {| EI=1:24CJ 182 099 045 0157 0032 
Wr EI =2-0CJ 182 ‘103 ‘050 0185 0041 
