Geometrically nonlinear analysis of steel structures with nonsymmetric sections under elevated temperatures

Steel members using nonsymmetric sections are envisioned as popular because of the advancement in manufacturing techniques, in which frame analysis method under extreme scenarios, such as fire hazards, has not been thoroughly established. The element formulation for those members has been commonly derived based on either the updated-Lagrangian (UL) or the total-Lagrangian (TL) methods. However, the UL method is difficult to analyze the steel member exposed to fires because the previous equilibrium conditions may be destroyed due to the material stiffness degradation at elevated temperatures. Nevertheless, the TL method can be used for studying steel members under fire, but it is inefficient, time-consuming, and requires starting-over computation at every temperature increment. To this, the co-rotational (CR) method could be a promising solution for tackling the analysis problems of steel members in fire efficiently and accurately. The CR method separately describes the element and its rigid body movements, such that the material stiffness degradation can be considered at the element level without the starting-over computation at new temperature increments, which is numerically efficient. This paper reformulates the beam-column element formulation with the warping degree of freedom for nonsymmetric section members using the CR method, which can conveniently consider the material degradation and the thermal expansion for the analysis of steel members at elevated temperatures. The lateral-torsional and flexural-torsional buckling of nonsymmetric section members can be captured robustly. Detailed derivation for element formulation is given, and several examples are provided for verifying the accuracy and examining the robustness of the proposed method.