Effective length coefficient of pier of multi-span continuous rigid-frame bridge based on transfer matrix method with branch

The effective length coefficient of the pier (ECP) is important for both the stability and the strength of the piers. The ECP of multi-span continuous rigid-frame bridge is calculated by a new model and the corresponding semi-analytical solution method in order to solve the stability of the bridge pier. Firstly, a general mechanical model of the n-span rigid-frame bridge is established, and its characteristic equation for the in-plane stability under consideration of self-weight load is derived using the transfer matrix method (TMM). The elastic buckling load and the ECP are obtained, and are compared with the results acquired by the finite element method to verify the correctness of the proposed theory and method. At the same time, the ECP is investigated when the pier is reinforced by carbon fiber reinforced polymer (CFRP) and ultra-high performance concrete (UHPC), respectively. Additionally, the effects of the ratio of side span to mid span, deck girder stiffness and pier stiffness on the ECP are also explored. The results show that enhancing the stiffness of the overall structure is more effective than enhancing that of the local structure to improve stability, and the ECP is affected significantly by the variation of side span or mid span. Interestingly, a unique bimodal effect is also observed in the ECP curves with the change in the CFRP reinforcement height.