170 
the line of thrust; and this reasoning applies to deflections both in the 
plane of the girder and at right angles to it. 
This consideration shows that the apprehension of long compressive 
bars yielding by flexure—an apprehension expressed by the most eminent 
advocates of the plate or continuous web—need not deter us from apply- 
ing diagonal bracing to girders exceeding in length any girder-bridge 
hitherto constructed. 
It also serves to explain the otherwise anomalous strength and rigi- 
dity of lattice girders whose struts as well as ties are formed of thin bars. 
Such a mode of construction is, however, more or less defective. The 
struts should be formed of angle-iron, or the material should be thrown 
into some other form than that of a thin bar, which is quite unsuitable 
for resisting flexure at right angles to the plane of the web. 
Tn order to calculate the strains of a lattice girder, we must consider 
each system of triangulation separately. 
Suppose, for instance, a load distributed over the upper flange of 
the girder represented in Fig. 2— 
YY; \N 
7 \\ 
The strains in any diagonal, b for example, are produced. by the 
weights resting upon the apices of its own system of triangulation, Wi, 
W;, and W,, and the weights on the other apices do not affect it at all. 
The maximum compressive strain in diagonal 6 occurs when apices 5 
and 9 of its system alone are loaded, and 1 is free from load, and in 
general, the maximum strain in any diagonal occurs when ‘the moving 
load covers the greater segment of the girder, but is due merely to 
those weights which rest on the apices of its own system. The end 
pillars act as girders as well as pillars, for they transmit to the flanges 
the horizontal resultant of the strains in the diagonals which intersect 
them. This resultant is in general of small value, for it is the difference 
between the horizontal components of the strains in the intersecting 
diagonals. The strains in the bracing of lattice girders may be obtained 
by tabulating the strains produced by each weight separately, as already 
explained. This is, however, a tedious process, and they may be more 
conveniently obtained by the use of an equation obtained as follows :— 
Let W =the weight liable to rest on each apex. 
1=the number of bays in the span. 
d= the number of bays in the depth. 
n =the number of bays between the Tey of the given diago- 
nal and the further abutment, when the load traverses 
the Fuerte flange. 
