36 
Hoskins—Maximum Stresses in Bridge Members , 
If this equation cannot be satisfied by any position for which 
P 2 = 0, we may write (9) in the form 
Q = n:() W - P °) .< n > 
and seek to satisfy it by a position making P 2 as small as pos¬ 
sible. 
If H K is treated as a tension member, the load is brought on 
from the right to such a position that D B is fully loaded and 
A C free from loads, if this can be done consistently with equa¬ 
tion (7) or (9). Putting P 1 — 0, (9) may be written 
« < 7 ' ir .< l -> 
Or, if it is found that P x cannot be taken zero, the equation 
may be written 
q=iXt w - p o . (i3) 
Case of Parallel Chords. —If the chords are parallel, the point 
F is at an infinite distance, and l Vj l 2 , n x and n 2 become infinite. 
But since in this limiting case 
ii=i, !t=i, ”=o, *= 0 , 
n x n 2 n i n 2 
equations (11) and (13) both reduce to 
Q^W 
or 
.(15) 
10. Discrimination between Maxima and Minima in Case of 
d 2 T 
Web Members. —We have now to examine the sign of —- 
6 dz 2 
as given by equation (8), with reference to the case of a web 
member. As already stated, all but one of the four quantities 
a\ b', c' and d f will in general be zero when equation (7) is sat¬ 
isfied ; each having a positive value whenever a load is at the 
corresponding point of the truss. 
The value of T from which equation (8) was derived applies 
to the case shown in Fig. 1 (which is the case now under dis¬ 
cussion) only on the supposition that UK is in compression. If 
