30 Hoskins—Maximum Stresses in Bridge Members. 
F' G' be the other chord member cut. Then C and D are the 
projections of G' and F' upon the horizontal reference line 
A B. Evidently ^coincides with D , so that n 2 —0, n x —n. With 
these substitutions, equations (2), (3) and (4) give the values of 
the compressions in H K due to loads on A C, CD and D B , and 
the total compression is given by equation (5); hence the result 
of the foregoing discussion applies to the present case. 
If HL were the member considered we should have n x —0, n 2 —n. 
Web Member. 
1st.-—Case in which l x andn x are negative. —Let If K (Fig. 1) be 
the member under discussion, and let K L be the member of the 
loaded chord cut by the section M N. Let F\ the intersection of 
the two chord members cut, fall so that F is at the left of A. 
Then loads on A C, D B and C D respectively will produce stresses 
in H K whose values are readily seen to be given by equations 
(2), (3) and (4); the stress being in each case computed as if it 
were a tension, and regard being had to the signs of n x and l x . 
Also, by examination of the general value of T due to all loads 
(equation (5) ), it is seen that the limits of integration as there 
given are correct for the present case, remembering that l x and 
n x represent negative quantities. 
If the stress is computed as a compression, the sign of every 
term in the value of T must be changed. 
2nd,—Case in which l x is positive and n x negative. —This case 
occurs if the point F is between A and G , and is shown in 
Fig. 3. If the deduction of equations (2), (3) and (4) be fol¬ 
lowed through for this case, it is seen that the only changes 
necessary in the reasoning will be introduced by having regard 
for the negative sign of n x . The limits of the integrals in 
equation (5) are also correct for this case if regard be had for 
the sign of n x . 
3rd. — Case in tvhich l x = 0.—This is a limiting case between 
the two preceding cases, and needs no special discussion. The 
form assumed by equation (7) in this case will be considered 
later. 
4th .— Web member in deck truss. — This case needs only a 
passing mention, since evidently the [foregoing discussion be- 
