Second order nonlinear inelastic of composite steel-concrete members. II: Applications

In the companion paper, a total Lagrangian finite element (FE) model was formulated for the second order nonlinear inelastic analysis of steelââ"šÂ¬Ã¢â‚¬Å“concrete composite members. This paper describes the implementation of the incrementalââ"šÂ¬Ã¢â‚¬Å“iterative procedure for the FE model. It has been found that using the standard tangent modulus matrix in an incrementalââ"šÂ¬Ã¢â‚¬Å“iterative solution procedure may cause error accumulations. These errors in turn lead to an unsafe drift from the yield surfaces, and the yield criteria may be violated. Consequently, the quadratic asymptotic rate of convergence of the Newtonââ"šÂ¬Ã¢â‚¬Å“Raphson method is lost. To solve this problem, a consistent tangent modulus matrix is needed in the incrementalââ"šÂ¬Ã¢â‚¬Å“iteration solution process, and this is described. This paper presents the implementation of the FE model and shows how to use the constitutive models in the companion paper in association with the uniaxial stressââ"šÂ¬Ã¢â‚¬Å“strain relations including that for confined concrete. Some of the applications of the FE model to various problems are also shown in this paper. The comparisons between numerical and experimental results demonstrate that the FE model provides excellent numerical performance for the nonlinear inelastic analysis of steelââ"šÂ¬Ã¢â‚¬Å“concrete composite members.