Refined line-element-based formulation for second-order analysis of steel structures under localized fires

Second-order analysis of steel structures achieves a balance between safety and cost-effectiveness in design by enabling accurate prediction of structural responses. However, in real fire scenarios, only parts of the members or frames are affected by elevated temperatures, while other parts remain at nearly room temperature, resulting in significant thermal gradients within the structure. These gradients induce non-uniform material degradation and thermal expansion, complicating the development of second-order analysis methods of steel structures and requiring substantial computational resources. This study proposes a finite element method employing a novel line element that can accurately capture the behaviors of steel structures under localized fires. The proposed line element accounts for variations of stiffness and strength degradation through derived cross-section varying factors, aiming to minimize the number of elements used. A rigorous cross-section analysis technique is applied to determine the cross-sectional properties and moment-curvature relationships for the line element. Eccentricity matrices are derived using the principle of complementary virtual work and equilibrium equations. Second-order analysis is conducted using the co-rotational method within the updated Lagrangian framework, enabling efficient and accurate simulation of thermally induced effects. Finally, the proposed method is validated through extensive examples and compared with other numerical methods to demonstrate accuracy and efficiency.