Vibration of Suspension Bridges under Moving Loads

The problem relates to the transient vibration of a single-span suspension bridge which is traversed by a constant force moving with constant velocity or a pulsating force moving with constant velocity. Damping is zero and there is no mass associated with the moving forces. Equations of motion are derived and solved. Solutions are obtained for the deflections and stresses of the truss and for the increase in horizontal component of cable tension. The theory is based on the deflection theory equations of suspension bridges. It is linearized by assuming that the increase in cable tension due to live load is small compared to the dead load cable tension. A numerical example illustrates the theory. The results of the example show large magnifications of stress (on the order of 2.70) when the moving pulsating force is driven at the frequency of the first symmetric mode. Also, in general, there is no appreciable dynamic effect associated with moving constant forces on long-span bridges. The dynamic effect of moving constant forces, however, becomes more pronounced on short-span bridges having a low frequency associated with the first asymmetric mode.