Modal-superposition-based response spectrum method for calculating pier responses under vehicle collisions

Although studies have examined vehicle impact on bridge piers and the resulting pier responses, no mature simplified method yet exists for calculating the dynamic response of piers under vehicle impact. This paper establishes an analytical model for pier responses under a half-sine impact load simulating the dominant component of vehicle-impact loading, investigates key parameters including the frequency ratio and offset ratio, and examines the critical section for impact-resistant design, pier modal response characteristics, and the applicability of the equivalent SDOF model. Results show that the impulsive nature of vehicle impact and the asymmetric loading location along the pier height make higher-order modes significantly influence responses, so simplifying the pier as an equivalent SDOF model may cause large errors. Therefore, a modal-superposition-based response spectrum method is proposed to combine higher-order modal responses for rapid and accurate prediction of pier responses, providing a theoretical method for bridge impact-resistant design and safety assessment.