Abstract—This article uses dynamic Bernoulli-Euler beam theory to establish a footbridge analysis model with several elastic supports and uses equivalent spring representation of pier to state the elastic impact. By adopting the Semi-analytic method, calculates multi-span footbridge natural vibration frequency and vibration mode. The orthogonality of mode shapes of the analytical model was verified. Then, the modal superposition method is used to solve the lateral vibration response of footbridges under the action of pedes-trian load. Finally, the calculation results are compared with the finite element simulation results. It shows that the theo-retical method is consistent with the finite element simula-tion results. This method can be used to study the dynamic response of multi-span footbridges under pedestrian load and provide a theoretical basis for the rational design of pedestrian bridges.
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