Amplification factor analysis of a simply supported beam under moving loads

An analytical solution for vertical vibrations of a simply supported bridge under the action of moving loads is derived and validated. The effect of bridge frequency, span length and vehicle length on the amplification factor of mid-span displacement is discussed using theoretical formulas and numerical results. The study finds and validates that the maximum bridge amplification factor is function of the length ratio of the bridge-to-vehicle. When the speed of the vehicle is high enough to cause bridge resonance, the maximum amplification factor of the bridge is a certain value, which has no relation to bridge's frequency. The frequency only affects the speed the maximum amplification factor appears. The changes in the amplification factor are analyzed with the bridge-to-vehicle length ratio, which provides a basis for the selection of bridge span length. A simplified, practical formula for calculating the amplification factor is given. The presented results will be particularly useful for railway bridge preliminary design for high-speed trains and assessment of the expected maximum vibration levels.