167 
component. Hence, if there be x weights between any given diagonal 
and the centre, we have for a uniform load 
strain = 2W sec @, (IIT.) 
W being the weight resting on each apex. 
When the load is a moving load, such as a railway train, the maxi- 
mum strain in any diagonal occurs when the front or end of the train 
is passing it. If, for instance, a train of carriages cover the right seg- 
ment of the girder, diagonal 11 sustains the maximum compression 
which the train can produce in it; for if a weight rest upon any apex 
in the other segment, some portion of this weight will tend to pass to 
the right abutment through diagonal 11, producing in it a tensile strain, 
that is, a strain of an opposite kind to that produced by the train, and 
so will diminish the amount of the compression which existed before 
the additional weight was added. 
On the other hand, the maximum tension in diagonal 11 occurs 
when the train covers the left segment, and any weight resting upon 
the right segment will tend to diminish this. Hence, the maximum 
strains in any diagonal occur when the passing load covers one or other 
segment into which it divides the girder; and these strains may be ob- 
tained by tabulating those produced by each weight separately, and 
then selecting that combination which produces maximum strains. 
2 The annexed Table represents this method applied to the girder, 
ap 
The length of the girder = 80 feet, and the load =1 ton per running 
foot, which is equivalent to 10 tons resting upon each apex. Let the 
angle 0 = 30°,—whence sec @= 1-154; and let / = the number of bays 
in the span, = 8. 
Wi | We!} Ws| Wa | Ws | We | Wz | We 
Maximum 
Compression. 
Maximum 
Tension, 
Uniform 
Load 
1 | +108 |4+ 9:4] +7:9| +65 |+5:1|+3°6]+2-2]-+0-7|| 4+ 46-2 0-0 | + 46:2 
2 | +4 o7 |—9:4]—7:9| —@5 | —5-1|—3:6|—2:2|—0-7 || + 0-7 | — 35-4 | — 34-7 
3 | — o7 }+9:4]4+7-9| +65 |+51|+3°6/+2-2|+0-7)| +354 | — 0-7 | +347 
4 |4+ 0-7 |+2:2|—7-9|—6-5|—5-1|—3°6|—2:2}—0-7 |] + 2:9 | —26-0 | — 23-1 
5 |— o7 |—2:2/4+7:9/465!/4+5:1'+3-6/+22/+0-7)] +260] — 2:9] +931 
6 | + o-7 |+2:2}+3-6|—65|—5:1|—36|}—2-2|—0-7|] + 65 | —181 | —11-6 
7 |— o7 |—2-2|—3-6|+65|+5:1]+3-6]+22|+0-7]| +181 | — 65 | +11°6 
8 {+ o7 |42-2)+4+3-6|+5-1|—5-1|—3-6|—2-2|-0 -7|/ +11-6 | —11°6 0-0 
The letters in the upper row represent the weights at each apex, 
and the numbers in the first column, the diagonals in order of position. 
