Every train that passes over the bridge causes an actual elongation of the cables, and consequently produces a depression. If the train is long, covers nearly the whole length of the bridge, and is uniformly loaded, the reduction of the camber or curvature of the track will be uniform. If the train is short, and covers only a part of the floor, the depression will be less general and more local, and will be the joint result of an elongation of the cables, and of a disturbance of the equilibrium. Depressions will be in direct proportion to the loads, and indirectly as the length of the trains. After the passage of a train the equilibrium of the work is restored, and it rises again to its former level. The elasticity of the cables is fully equal to this task, and will not be impaired by the constant repetition of this process. Nor will the wooden superstructure be affected by it. The worst that can result is a certain degree of looseness, either by further shrinkage or working, which can easily be corrected by tightening the bolts. My observations since the 18th of March have confirmed this opinion.
On this last mentioned day the railroad
floor was opened for business by passing an experimental freight
train, composed of twenty full-loaded cars, pushed by a 26 ton
engine, from the Canada to the New York depot.
| The gross weight was estimated at . . . . . | 326 tons. |
| Tension of cables resulting . . . . . . . | 520 tons |
| Aggregate section of cables . . . . . . . | 240 sq. in. |
| Therefore tension per square inch . . . . . | 4917 lbs. |
| " " of single wire . . . . . . . . . . | 82 lbs. |
| Average length of cables and chains . . . . | 1359 feet. |
| Elongation of wire per square inch caused by 2,240 lbs. | 1/10,000 |
| Elongation of cables by 2,240 lbs . . . . | 0.1359 feet. |
From these data we can now find the
elongation of the cables caused by 326 tons,
The depression of the bridge, caused
by this elongation, is found by the following formula (see Appendix C):
| where Z expresses half length of curve, or | 416 feet. |
| Y represents half length of chord, or . . | 410 .66 " |
| The deflection was . . . . . . . | 57.50 " |
| The elongation of the whole cable . . . | 0.2983 " |
| One half . . . . . . . . . . | 0.1491 " |
| Add value of Z . . . . . . . . | 416.0000 " |
| Gives value of Z to be substituted in formula . . . | 416.1491 " |
| The above quantities substituted, make |
| or X = . . . . . . . . . . . . | 58.34 feet. |
| deduct former deflection . . . . . . . | 57.50 " |
| And we get the depression caused by the load . | 0.84 feet. |
The actual depression ascertained by the instrument was 0 .82 feet.
Calculation, therefore, and fact, agree almost exactly.
On the removal of this train the structure
rose again to its former level. Ordinary freight, or large passenger
trains, cause a depression of 3 to 5 inches, which is as much
the result of elongation as of disturbance of equilibrium. A short
heavy freight train will produce as much, or rather more, depression
than a very long passenger, or empty freight train of greater
weight, for the single reason, that the equilibrium is more disturbed
by the short train than by the long one. To construct a
suspension bridge which shall not sink under heavy loads, or by
an increase of temperature, cannot be done. These motions are
a legitimate result of the nature of a suspension bridge, and
are rendered harmless by its elastic properties.