Geometrical Nonlinearity Analysis Of Cable-Stayed Bridges Based On CR Formulation

Geometric nonlinearity analysis of cable-stayed bridges mainly considered the equivalent modulus to cable sag effect,stability function or the geometric stiffness matrix to beam-column effect,the Lagrangian Incremental formulation(TL or UL formulation)to large displacement.Because of wide-span cable-stayed bridge,how long-span structures should consider the effects of geometric non-linearity is not clearly defined。When calculation the cable-stayed bridge for span between 400～600m,most of researchers only using the equivalent modulus method to consider effect of cable sag and simplify consideration of geometric nonlinearity.This paper,used the improved CR-UL formation and catenary cable element to simulat the cable-stayed,accurate analysis the geometrically nonlinear problem of the 400～600m span cable-stayed bridge.The main research contents are as follows:1.Summarizing the characteristics of TL,UL and CR formulation,Indicating their respective advantages and disadvantages from Formula Derivation.Authenticating accuracy of CR-UL formulation on geometric nonlinear analysis,and validating that there ie a Larger error on UL formulation for Calculation of geometric non-linear.Providing the theoretical basis for Nonlinear Finite Element analysis of cable-stayed bridge.2.Comparing P-Delta analysis principle with non-linear analysis principle then proved that,when the structure have small displacement,the results from the P-Delta analysis is similar to the results from non-linear analysis.3.Reviewing the basic equation of catenary cable element and derivation process of tangent stiffness matrix.Verified it is accuracy that use the cable element to simulate stay cable when analysis the cable sag effect.It provides a theoretical basis for use the cable element to simulate stay cable.4.Taking Two similar cable-stayed bridges of steel box as an example,based on CR-UL formulation,the catenary cable element was used to simulate stay cable,through the Simulation of full-bridge,Calculating the effects of geometric non-linear on cable-stayed bridge in the construction phase and use phase.And compareing with other four methods, obtaining the main conclusions:①The influence of geometric non-linear of cable-stayed bridge is small,so use linear second order P-Delta analysis or geometric nonlinear analysis based on the CR formation to consider the nonlinear beam-column will be able to meet the engineering requirements;②400-meter cable-stayed bridge using the equivalent modulus method to consider effect of sag,calculation of linear second-order effect and the large displacement beam-column will be able to meet the engineering requirements;However,as the span increased the impact of geometric nonlinearity is also increased,600-meter cable-stayed bridge suggest to using catenary cable element to simulation the cable-stayed,and using uonlinear geometric stiffness matrix to calculat the beam-column effect and the large displacement.