Influence Lines & Moving Loads

An influence line plots one response — a reaction, a shear, the moment at one point — as a unit load moves across the structure. Multiply an ordinate by a concentrated load, or the area under it by a uniform load, to get the response.

Worked: a two-axle load on a 40 ft span

For the moment at 10 ft from A: the peak ordinate is 10 × 30/40 = 7.5 ft, and at 24 ft the line has fallen to 10 × 16/40 = 4.0 ft. With the 32 kip axle at the peak: M = 32 × 7.5 + 8 × 4.0 = 272 ft-kips. Turned round, with the 8 kip axle at the peak and the 32 behind it: 8 × 7.5 + 32 × 4.0 = 188 ft-kips. A 0.64 kip/ft lane load over the whole span adds 0.64 × ½ × 40 × 7.5 = 96 ft-kips.