28 
Hoskins—Maximum Stresses in Bridge Members. 
Thus, if T now means the total tension in H K, we have 
z + L—n. x + l 
l r l C 
T = ^ J w[x—z)dx+ Yt j w (. z + l— x )dx 
Z X + I-l+Uz 
z + l x + n 2 
+ ?2 fw( z + h + n z-x)dx 
z l 1 —n 1 
Z+li+Tlz 
-f w ( x ~ z ~ii +n dd x .( 5 ) 
z + l 1 —n 1 
Since w is in general a function of x , the integrations cannot 
be performed unless the form of this function is known. We can, 
however, apply the condition for maximum or minimum values 
of T. namely, 
dT 
dz 
= 0 . 
Let the values of w at A , B , C and D, respectively, be ab r , 
c' and^'. Then by differentiation, 
r z + l x —n i 
dT U r .ii-| 
dz It 
e' (ii-»i)-/' 
wdx 
d (I 2 n%) 
z + I 
+ f'tvdx 
Z + Z^ + 71 2 “ 
h di n j) 
71 l t 
i Ah— n %) 
71 11 
Z + l x + 7l 2 
— c'n + J wdx 
Z + I 1 —7l 1 
X + lx+tl 9 
d'n — J"w dx 
Z + lx—Tlj 
In this expression all terms except those involving definite 
integrals balance each other. Also, if the total loads on A C, 
B D and C B respectively are denoted by P x , P 2 and Q , we have 
X+lx—Tlx 
ftvdx =P 1 , 
z + l 
j*tv d x =P 2 , 
Z + lx+712 
Z + li+712 
Jwdx =Q, 
Z+l 1 —7l 1 
