In recent years, the increased use of slender components in buildings and bridges has made it necessary to pay more attention to stability. The problem is addressed in this study by the development of a second-order nonlinear analysis program using a flexural stiffness model and a second-order stiffness formulation.
Material nonlinearities are included in a flexural stiffness model by using an elasto-plastic model for the steel and a Shah & Wang's stress and strain curve for concrete. The effects of nonlinear geometry are included in a second-order stiffness formulation by using modified member stiffness based on finite deflection theory. The loading is assumed to be static and monotonic. The desired load for structure is applied in increments. For each increment of load, the secant stiffness is calculated using the flexural stiffness model and for a certain load, a second-order stiffness is calculated using previous forces and displacements. Then incremental displacements corresponding to an applied load can be found through an iterative solution in each step.
Using this second-order nonlinear program, reinforced concrete structures are analyzed by load incremental method until ultimate strength state. On the whole, this analytical program accurately predicted the stability behaviors of reinforced concrete frames.
