Dynamic Response of Reinforced Concrete Bridge Piers to Vehicle Impact: A Duhamel-Based SDOF Analysis and Parametric Study
Abstract
This study develops a transparent analytical framework for evaluating the dynamic response of a circular reinforced concrete (RC) bridge pier subjected to lateral vehicle impact. The pier is represented by an equivalent single-degree-of-freedom (SDOF) system in which the distributed mass is replaced by a first-mode-equivalent lumped mass at the pier head. Three idealized impact pulses—rectangular, half-sine, and symmetric triangular—are compared using the same peak force and load duration. Closed-form displacement solutions are obtained from the Duhamel integral and verified through numerical integration using MATLAB ODE45. For the representative load-duration ratio td/T=0.822, the predicted peak displacements are 9.48, 8.34, and 7.36 mm for the rectangular, half-sine, and triangular pulses, respectively, corresponding to dynamic magnification factors of 2.010, 1.768, and 1.560. The analytical and numerical results agree within 0.74%. A parametric analysis over 0.2≤td/T≤2.0 demonstrates that the predicted response is strongly influenced by both pulse shape and loading duration. The rectangular-to-triangular amplification ratio reaches approximately 1.55 near td/T=0.5, while at the representative design point the rectangular pulse predicts a peak displacement 29% greater than that predicted by the triangular pulse. These differences are explained by the combined effects of pulse impulse and frequency content. The results demonstrate that the selection of a simplified impact pulse can materially affect preliminary displacement estimates and should therefore reflect the expected vehicle–pier force–time history.
Keywords: reinforced concrete bridge pier; vehicle impact; single-degree-of-freedom model; Duhamel integral; dynamic magnification factor; impact pulse shape; shock spectrum.
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