According to experiments which have been made with wires 1,000 feet long, their expansion, caused by an increase of temperature of one degree, is l/146000 and for 100 degrees 1/1460. The average length of cables between the
chains is 1,227 feet. Therefore, their
expansion from 100° is 1227/1460, which is equal to 0 8404
feet. Now suppose the deflection of cables at a temperature of
0° to be 57 feet, we find half the length of catenary, by
using the formula in Appendix C.
| Now substitute for X . . . . . . . | 57 feet. |
| for Y, or half the chord . . . . . | 410.666 " |
| or Z = . . . . . . . . . . | 415.9009 feet. |
| Now add elongation of half the length of cables, due to 100 degrees . . . . | 0 .4202 feet. |
| and we get half the elongated cable = . . | 4163211 feet. |
To find deflection due to this elongation,
apply the formula for X in Appendix C.
| Substitute for Z . . . . . . . | 416.3211 |
| and for Y . . . . . . . . . | 410.6666 |
| or X = | 59.25 feet. |
| deduct deflection at 0° | 57.00 |
| difference arising from 100° | 2.25 feet. |
Therefore a change of temperature of 100° causes a difference in the level of the floor of 2 feet 3 inches, which calculation very nearly agrees with my observations.
The lower floor or river stays have
enough of slack or deflection to adjust themselves under these
changes. The only difference will be, that they are tighter in
winter than in summer, consequently that the equilibrium of the
bridge will be less affected by passing trains in cold weather
than in warm.