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A Simplified Linear Approach for Elastic Collision Analysis between the Fixed Middle Pier and the 2-Span Continuous Girder

Based on a collision analysis between the fixed middle girder and the 2-span continuous girder in longitudinal direction, motion equations of the girder and the pier are established by mode decomposition method. Displacements’ relationship at the collision interface is used to establish the equation about the collision force, and Duhamel integrals in the equation are eliminated so as to get a 6 order homogeneous ordinary differential equation about the collision force. Then an approach to solve the equation is put forward. The analysis results show that the time history curve of collision force is a half sine waveform, and the initial velocity of girder towards pier top is proportional to the peak collision force but has nothing to do with the duration of collision.