Dynamic Response of RC Bridge Piers under Vehicle Impact: Duhamel-Based SDOF Analysis with Parametric Evaluation
Abstract
This study presents an analytical investigation of the dynamic response of a circular reinforced concrete (RC) bridge pier subjected to lateral vehicle impact loading. The pier is idealized as an equivalent single-degree-of-freedom (SDOF) system, in which the distributed mass is represented by a lumped mass at the pier head based on first-mode participation. Three commonly used simplified impact load models—rectangular, half-sine, and triangular pulses—are considered, each defined by the same peak force and duration. Closed-form solutions are derived using the Duhamel integral to evaluate the displacement response under transient loading, and the analytical results are validated against numerical integration performed using MATLAB ODE45. For the representative case with a load-duration ratio of td/T=0.822t_d/T = 0.822td/T=0.822, the peak displacements are 9.48 mm, 8.34 mm, 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. A parametric study over 0.2≤td/T≤2.00.2 \leq t_d/T \leq 2.00.2≤td/T≤2.0 shows that the rectangular pulse consistently produces the highest response, with the rectangular-to-triangular amplification ratio reaching approximately 1.55 in the intermediate dynamic regime. The results are interpreted in terms of the impulse and frequency-domain characteristics of the load functions. The findings highlight the significant influence of load shape on the predicted structural response and demonstrate that the selection of a simplified pulse model can alter displacement estimates by up to 29%, providing important implications for impact-resistant bridge pier design.
Keywords: bridge pier dynamics; vehicle impact loading; SDOF idealization; Duhamel integral; dynamic magnification factor; shock spectrum; rectangular pulse; half-sine pulse; triangular pulse; parametric study.
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