166 
In investigations respecting braced girders, it is desirable, as in other 
researches, to proceed from the simpler to the more complex case. I 
shall, therefore, first consider the strains produced by a single weight, 
in a girder containing but one system of triangles (Fig. 1). And I would 
here observe, that this paper contains merely a modification and exten- 
sion of the principles of bracing already ably investigated by W. B. 
Blood, Esq., and R. H. Bow, Esq., who were the first to apply accurate 
methods of calculation to diagonally braced girders. 
Wy i Wein. Wen Wa Weds We uuWae We 
Suppose that the weight W, divides the girder into segments con- 
taining respectively m and x bays. On the principle of the lever, the 
; W, that on the left = <W; lrepre- 
senting the number of bays in the whole span (= m+7). 
Now each of these components of the weight is transferred to 
the abutments through the diagonals, for vertical forces cannot pass 
pressure on the right abutment = 
along the horizontal flanges. Consequently, +W is transmitted through 
each diagonal on the right of W; and this quantity is the vertical com- 
ponent of the strain in each of these diagonals. The actual strain is to 
its vertical component as the length of the diagonal is to the depth of the 
girder, or, calling the angle of inclination of a diagonal to a vertical line 
6, we have the strain in each diagonal in the right segment— 
Strain =") W see 8. (L) 
In the left segment— 
Strain => W sec 0. (II.) 
The strains in the diagonals of each segment are alternately compressive 
‘and tensile. — = 
If the load be uniformly distributed, so that the same weight rests 
upon each apex, or if it be symmetrically disposed on either side of the 
centre, the strains in the diagonals gradually increase from the centre 
towards the ends. Any two diagonals equally distant from the centre 
sustain all the intermediate load. If they are tension diagonals, the 
weight is suspended, as it were, between them; if they are compression 
diagonals, it is supported by them as oblique props. Each diagonal 
conveys therefore to the abutment the pressure of the weights between 
it and the centre, and the sum of these weights constitutes its vertical 
