34 Hoskins—Maximum Stresses in Bridge Members. 
be proportional to the lengths of these segments , that is, to l t 
and l 2 . 
8. Discrimination between Maxima and Minima in case of Chord 
Members. —We have now to examine the sign of the value of 
d 2 T 
^- 8 i n equation (8). 
(a) Member of loaded chord.—It has already been mentioned 
that in the case of concentrated loads equation (7) requires that 
a load shall be at some one or more of the points A, B, C and D. 
It is evident also that generally only one of these positions will 
be occupied by a load at any one time. Hence, when equation 
(7) is satisfied, one of the four quantities a', b' , c' and d ; will in 
general be very great and the other three zero. If l v l 2 , n x and 
d 2 T 
n 2 are all positive, as in Fig. 2, equation (8) shows that 
is negative when a load is at C or D but not otherwise; and 
positive when a load is at A or B but not otherwise. Hence 
when the stress in H K is a maximum a load is at C or D, 
and when it is a minimum a load is at A or B. Conversely, 
if equation (7) is satisfied and a load is at C or D the stress 
is a maximum; and if (7) is satisfied while a load is at A or B , 
the stress is a minimum. [The last statement does not hold 
if, when equation (7) is satisfied, a load is at A or B and 
d 2 T 
another at C or D: since this would make the value of , „ 
dz 2 
the algebraic sum of two terms, one positive and the other neg¬ 
ative. This case will arise only by a rare coincidence of di¬ 
mensions.] 
If F falls at C or between A and C, so that n x is zero or neg- 
d 2 T 
ative, the value of can be negative only when a load is at 
C ; if n 2 is zero or negative ( F falling between D and B), a 
d 2 t 
load must be at D to make - z negative. 
( b ) Member of unloaded chord.—In case of a member of the 
chord not carrying moving loads, either n x or n 2 is necessarily 
zero. Hence the discussion just given applies to this case, and 
the conclusion need not be repeated. 
9. Application of General Condition to Web Member—First 
Case. —In considering web members two cases are to be distin- 
