The Theoretical Impact Factor Spectrum for Highway Beam Bridges

Abstract

The impact effect of vehicle loads is an important and challenging problem in bridge engineering. In the last few decades, experimental and numerical researches on this problem have been extensively carried out, but a satisfactory formula that can take various factors into account has not been obtained. The vehicle–bridge interaction (VBI) under the excitation of road roughness is essentially a nonstationary random vibration problem. In this paper, the random load of a bridge is expanded into an expression in both the time and frequency domains using Fourier series; the dynamic response of the bridge under the moving random load is solved by the modal superposition method; an analytical solution of the second-order statistical characteristics of the vibration response of the bridge in the form of series is obtained; and on these bases, a theoretical formula of the impact factor (IM) spectrum is obtained. This approach is more scientific and reasonable in theory than the traditional deterministic approach because the theoretical IM spectrum is based on the second-order statistical characteristics of bridge dynamic responses. Moreover, the theoretical IM spectrum can more comprehensively reflect the various influencing factors of vehicle impact effects on the bridge.