26 Hoskins—Maximum Stresses in Bridge Members. 
Case of Member of Loaded Chord. 
The case in which F falls between C and D may occur when 
the member whose stress is under consideration belongs to 
that chord along which the moving loads are applied to the 
truss. This case is represented in Fig. 2 , H K being the mem¬ 
ber in question. 
Let 0 be a point on A B which is fixed relatively to the loads, 
but moves with them. Instead of considering the loads to move, 
we shall, for convenience, assume the truss to move while the 
loads remain stationary. The point 0 thus remains fixed, while 
A, B , (7, D and F move. Let 0 A—z; then the position of the 
truss relatively to the loads is given by assigning values to the 
variable z. If the loads move to the left, we assume the truss 
to move toward the right, &o that z increases; and vice versa. 
Let the load have any fixed distribution along the horizontal, 
w being the load per unit length at a point whose abscissa 
reckoned from 0 is x. We shall assume at first that w is 
either zero or finite at every point, reserving for later discussion 
the case of concentrated loads, in which w becomes infinite at. 
certain points. We shall now determine the value of the tension 
in H K produced by a load P in any position on the truss. 
Three different expressions are needed, according as the load is 
on A (7, DB, or CD. 
1st. Tension due to a load on A C. — Let T be the tension in 
H K due to a load P on A C. Let x — distance from 0 to point 
of application of P, and let z = 0 A as before. Then the reac¬ 
tion at B due to P is 
P(x-z) 
l 
Now cutting the truss by a section M FT as shown (Fig. 2), it 
is seen that the reaction at B is in equilibrium with the in¬ 
ternal forces in the the members cut; hence, taking moments 
about F ', and letting t represent the perpendicular distance 
from F’ to H K , we have (remembering that F B — If) 
or 
