169 
Class B. 
Girders in which the first loaded apex is distant one half-bay from the 
abutment. The strain produced by the weight at— 
The 1st apex = = sec 0. 
W 
2nd apex = a sec 0. 
8rd apex =5 = sec 0. 
n* apex = (2n—- iy sec 0. 
Summing up these, we have— 
Max. strain= {1+34+5+... (2n-1)}-% see 0 
si 
Max. strain =5 T see 0. CYS) 
Example:—The maximum tension in diagonal 11, Fig. 1, occurs 
when weights 1, 2, 3, 4, and 5 rest upon the girder, in which case » = 5, 
and we have— 
Max. strain = = x 7% 1:154=18 tons. 
This should equal the maximum tension in diagonal 6, already tabu- 
lated, which it does. 
Lattice Girders. 
To proceed, next, to the lattice girder.—And first, I may remark, 
that latticed bracing has no theoretic advantage over a single system 
of triangulation; its advantages are entirely of a practical nature, 
consisting in the frequent support which the tension diagonals give to 
those in compression and which both give to the flanges. 
Long pillars are serious practical difficulties, and the lattice tension 
bars subdivide what would otherwise be long pillars into a series of 
shorter ones, and hold them in the direction of the line of thrust. That 
this does not injuriously affect the tension diagonals will be evident 
when we reflect that the longitudinal strain produced in them by the 
deflection of a strut bears the same ratio to the strain transmitted 
through the strut as the deflection or versine of the curve bears to the 
half strut—an amount quite inappreciable in practice. If, for instance, 
a strut be ten feet long, and its central deflection equal one-inch (an 
amount much greater than ever occurs in practice), the longitudinal 
strain produced by this deflection in the tension bar, which intersects 
the centre of the strut, and restrains it from further deflection, equals 
goth of the thrust passing through the strut; so that in most cases a 
stout wire in tension would be sufficiently strong to hold the struts in 
