Calculation of second-order bearing capacity of members subjected to axial load and biaxial bending

Abstract

The second-order effects of biaxial bending members involve dual non-linear problems, namely material nonlinearity and geometric nonlinearity. These problems typically require iterative calculations and cannot be solved manually. To address this issue, this paper founded upon the strain-based resolution of stress and internal forces, deduces the formula for calculating the load-bearing capacity of the cross-section. The elastoplastic second-order deformation is then calculated at the member level, and the final result is presented in the form of a dimensionless nomogram for calculating the second-order biaxial bending members. In this paper, the limit range of section strain is determined based on the constitutive relationship of concrete and reinforcement. This range is divided into three limited strain areas, which enable the calculation of section bearing capacity and limit curvature, and subsequently the second-order bearing capacity of the member. The results are in good agreement with experimental data. The dimensionless nomogram in this paper considers the complete parabolic and rectangular of concrete stress-strain relationship and the ideal elastoplastic constitutive relationship of reinforcement and the second-order effect. It does not require iteration. It can quickly calculate the reinforcement or check the section bearing capacity by hand. It can be used to check the calculation results of engineering software and provides ideas for the design method of member subjected to axial load and biaxial bending based on seismic restoring force.