In-Plane Stability Analysis Of Continuous Rigid Bridge Piers Based On Transfer Matrix Method

With the rapid development of China’s transportation industry,especially the gradual implementation of the national western development strategy.China has built a number of industry-leading large span continuous rigid frame bridges in the western region.With the increase of span,pier height,thin-walled box girders and wide application of high-strength materials,rigid bridges are facing more challenges in terms of overall stability and local stiffness,so the stability issue becomes more critical and the stability of piers becomes more and more prominent.In order to be able to calculate the in-plane stability of bridge piers more conveniently,the transfer matrix method is used to solve the problem.The main research contents and conclusions of this paper are as follows:(1)The characteristic equations of in-plane stability of n-span rigid frame bridge piers are derived.Firstly,a simplified multi-beam mechanical model of rigid frame bridge is established,and the characteristic equations of in-plane stability of n-span single pier rigid frame bridge considering self-weight load are derived by using transfer matrix method.Then the characteristic equations are extended to the solution of the in-plane stability problem of the rigid frame bridge with double-limb piers.The rigid frame bridge with double-limb piers with tied beams can be regarded as a rigid frame bridge with double-limb piers without tied beams,and the characteristic equations of in-plane stability of nspan single-pier rigid frame bridge piers are derived.Then,the equivalent buckling critical load is obtained by multiplying the stability enhancement coefficient ε of the pier generated by the tie beam with the obtained buckling critical load.(2)The in-plane stability of each pier of a five-span single-pier rigid frame bridge and a three-span inclined-legged rigid frame bridge is analyzed.The established in-plane stable characteristic equations are used,and the specific boundary conditions are substituted into them.The in-plane stability problem of each pier of the five-span single-pier rigid frame bridge and the three-span inclined-leg rigid frame bridge in the completion stage and the along-bridge wind load stage is solved.The finite element model with the same parameters is established and compared with the finite element results.The results are in good agreement with the finite element,which verifies the correctness of the method in this paper.(3)The influence of some parameters on the effective length coefficient of single pier rigid frame bridge pier is explored from the perspective of structure and material analysis.It is found that compared with the change of pier stiffness,the stability of pier is more sensitive to the change of bridge deck stiffness.The looseness of the structure can also affect the stability of the pier.(4)The in-plane stability of a five-span double-pier rigid frame bridge with tie beam is analyzed.Firstly,it is regarded as a rigid frame bridge with double pier without tie beam.Using the established in-plane stability characteristic equations,and then substituting the specific boundary conditions into it,the critical buckling load is obtained.Then the stability enhancement factor ε is taken into account to obtain the equivalent buckling critical load.The in-plane stability problems of the bridge stage and the along-bridge wind load stage are considered respectively,and the effective length coefficient of the pier is used to represent the stable state of the pier.The finite element model with the same parameters is established and compared with the finite element results.The results are in good agreement with the finite element,which verifies the correctness of the method.(5)From the perspective of structure and material analysis,the influence of some parameters on the effective length coefficient of rigid frame bridge piers with double limb piers is explored.It is found that with the increase of CFRP reinforcement height,the effective length coefficient of the pier has a bimodal effect.