Nonlinear Analysis Of Reinforced Concrete Frame Based On The QR Method

Because of the good integrality, cheap cost, reinforced concrete structure has be widely used in industrial and civil buildings. The concrete with characteristics of multiphase, non-homogeneity,shrinkage,creep, bar-slip and the crack produce and development in nomal service state, result in the big error of linear analysis when suffering stong earthquake or rare earthquake, so the nonlinear analysis of reinforced concrete frame structure based on the rod model is very meaningful.This paper based on the QR method,comprehesively considered the material nonlinearity of concrete and steel,and the second order effect, established a new computing scheme of the static and dynamic nonlinear analysis with reinfored concrete frame,compiled the corresponding C language program, checked calculation by a typical example. The main research content is as follows:(1) considering the development of plastic along the sectional height, using the layer fiber beam model to calculate the sectional instantaneous tensile stiffness EA and flexural rigidity El of the reinforced concrete beam-conclumn,anlysising the correlation of section stiffness and the axial force and moment.(2)considering the plasticity-spreading along the element length, the element stiffness of Roufaiel three-stage variable stiffness layer fiber beam model deduced,based on the assumption of moment linear distribution. (3) considering the plasticity-spreading along the sectional height and the element length,using the secant stiffness of complete quantity to perform unbalance iteraion, established the computing scheme of the nonlinear static analysis with reinfored concrete frame struction based on QR method, compiled the corresponding program using C langurage, checking the validity of model and alforithm with the experimental results for comparison. (4) using Roufaiel three-stage variable stiffness layer fiber beam model, further considering the second-order effect,using lumped mass and Rayleigh damping model,established the computing scheme of the first-order nonlinear and second-order nonlinear dynamic anlysis with reinforced concrete frame structure based on QR method, using the Newmark-P and Lyapunov method to solve dynamic differential equation, the secant stiffness method is adopted for unbalance iteration,using C langurage to compile the corresponding program,and using a typical example of framework for seismic response analysis to anlysis the seismic behavior of framework and verify the feasibility of the algorithm.The results show that:Roufaiel three-stage variable stiffness layer fiber beam model comprehensively considered the correlation of axial force and moment for sectional instantaneous stiffness, not only considered the meaterial plasticity-spreading development along the section height and the element length, but also considered the second order effect, improved calculation accuracy without the increse of the element basic unknown. Using QR method to solve the nonlinear problem of reinforced concrete frame strcture is effective, with the simple format and less unkown and meeting the accuracy requriements. The secant stiffness method for unbalanced iteration guarantees the convergence and stablity of the nonliner solution; The Lyapunov method for the solution of nonlinear dynamic differential equation with reinforced concrete framework structure can improve the accuracy of structural dynamic response; the consideration of second order effec can improve the lateral displacement and internal force response of the structure,and the degree of plasticity is also be incresed.