Assuming the horizontal distances between the centres of the vertical suspenders as five feet, their lengths, then, will be found by formula
X = Y2
b2 × a;
and placing for Y2 the distances 5, 10, 15, 20, etc., we have, commencing at the centre,
| Centre. | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | d |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 52 5002 × 90 | 102 5002 × 90 | 152 5002 × 90 | 202 5002 × 90 | 252 5002 × 90 | 302 5002 × 90 | 352 5002 × 90 | 402 5002 × 90 | 452 5002 × 90 | 502 5002 × 90 | d2 b2 × a |
| 0 | .009 | .036 | .081 | .144 | .225 | .360 | .490 | .576 | .729 | .900 | h |
and so on, until we arrive at the tower. Whatever distance above or below the vertex of the curve the road-way is placed, is of course constant, to be added to or taken from the above lengths.
The manner of putting in any camber is simple both in theory and practice. The strain upon the suspenders is merely the direct weight of the road-way and load. If this is 3,500 lbs. per foot, the five feet supported by two rods (one each side) will weigh 17,500 lbs.; each rod or wire rope must hold 8,750 lbs.; this can be done by a section of one half inch area. For extra strains, however, on so large a span as 1,000 feet, one inch of area is not too large.
OF THE STIFFENING TRUSSES, GIRDERS, AND STAYS.
The object of the girders supporting the rails is to diffuse the applied weight; these girders may be made of a Howe truss four or five feet deep, by trussed girders, only simply deep and stiffly framed track strings. They should be able to distribute the load applied at one point at least fifteen or twenty feet. The side trusses transfer to a still greater extent any applied load. Mr. Roebling estimates the combined effect of trusses and girders in the Niagara bridge as transferring the weight of a locomotive over a length of two hundred feet. This transferring counteracts the local depression. The Niagara truss is formed by a system of vertical posts, five feet apart, and diagonal rods passing from the top of the first post to the foot of the fifth; the inclination being 45°, spreads the weight placed upon any one pair of posts over twice the height of the truss, or about forty feet. As to the actual dimensions of the girders supporting the rails, if we intend them to spread an applied weight over forty feet, they must be as stiff as a bridge of forty feet span. And as regards the truss, if we would effectually distribute the applied weight and check vibration, the trussing should be as strong as the counterbracing in a large span upon the ordinary plans. The principle of trussing a suspension bridge may be thus explained. See fig. 106. Suppose that in place of supporting the three trusses D s w, s m m′, and m′ m d, upon piers at w and m′, we suspend these points from the cable A c B. The cable is flexible, and when we apply a load at m, the truss will assume the position D s c n d, but between D and s, s and n, n and d, the truss will be quite stiff. What we require, then, is to make the figure o p m m′, incapable of changing its form, which is done by diagonal bracing.
Fig. 106.