171 
p =the integer number of times that its own system occurs between 
the b top ofthe given diagonal and the further abutment, 
ottom 
t ; 
when the load traverses the {ott flange, = the integral 
part of 
Let there be » bays between the diagonal 4 and the right abutment; 
then, on the principle of the lever, the portion of W; which is transmitted 
to the left abutment through d equals +W; of W, equals E =. 
The maximum compressive strain in diagonal 4 is equal to the sum 
of these quantities multiplied by sec 9, and equals— 
{n+ (n-2a))¥ sec 8, 
In general, the maximum strain in any given diagonal equals— 
{n+(n-2d)+(n-4d)+(n-6d)+. _+(n=2pd)}™ see 6. 
Max. strain = (n~—pd) .(p+1) = sec 8. (VI.) 
In diagonal a, for example, we have— 
uo 
a2°2 
p= 2 
P1x 
Hence 
Max. strain = (9-22). (241) see 0= 15 see. 
This diagonal is never subject to tension from a passing load on the 
top flange, since there is no upper apex belonging to its system in the 
left segment. 
When the load is uniform, the strains in the bracing may be calcu- 
lated by equation ITI., observing that the coefficient » will, in a lattice 
girder, represent the number of those weights which occur between any 
given diagonal and the centre of the girder, and which rest only on the 
apices belonging to its system of triangulation. When a lattice girder 
contains three or more systems of triangles, a slight ambiguity occurs 
respecting the strains, if the load be disposed on both sides of the centre. 
Take, for example, W; and W., which belong to different systems, but 
rest on apices equally distant from the centre. The whole of W; may 
be conveyed to the left abutment through diagonals a and e, and the 
whole of W, to the right abutment, through diagonals ¢ and d, without 
producing strains in the other diagonal of either system, which, indeed, 
might be suppressed as far as these weights are concerned. But, again, 
Paths of W, may be transmitted to the right abutment, and ~2. ths to the 
