| Author: | Li, Guanhua |
| Title: | Second-order direct analysis for fire resistance design of steel structures |
| Advisors: | Liu, Si-wei (CEE) |
| Degree: | Ph.D. |
| Year: | 2026 |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xx, 219 pages : color illustrations |
| Language: | English |
| Abstract: | Steel structures are sensitive to fire, as elevated temperatures can significantly reduce their strength and stiffness. When exposed to fires, the mechanical properties of steel deteriorate rapidly, potentially leading to buckling or loss of load-bearing capacity. Therefore, evaluating the performance of steel structures under fire conditions and ensuring accurate fire resistance design are of critical importance for building safety. At present, two primary fire resistance design approaches are employed: the prescriptive method and the performance-based method. The prescriptive method, grounded in predefined codes and guidelines, is typically derived from physical fire tests and large-scale simulations. Although straightforward and convenient to implement, it is conservative and focused on member level, thereby limiting the economy and flexibility of design. In contrast, the performance-based method relies on advanced computer simulations to assess fire resistance, offering greater flexibility in optimizing fire protection measures. This approach accounts for non-uniform heating at both the member and structural levels under natural fire conditions, thereby providing a more accurate and reliable basis for fire resistance design. Despite its advantages, the performance-based method faces three main challenges: (1) the need for sophisticated modeling and high computational demand; (2) the difficulty in capturing geometric and material nonlinearities under non-uniform fire exposure; and (3) the combination of thermal effects in nature fire scenarios. To address these issues, this thesis extends and refines the Second-Order Direct Analysis (SODA) method for fire resistance design of steel structures, using advanced line finite element methods (LFEMs) that directly account for geometric and material nonlinearities under natural fires. This thesis first develops a refined heat transfer analysis technique for steel members protected with intumescent fire coatings (IFCs), which incorporates various thermal boundary conditions and different thermal conductivity models. The generalized CrankâNicolson method is employed to improve the stability and convergence of the transient heat transfer analysis. Based on the computed temperature field, a novel cross-section analysis method is developed using the proposed thermal deterioration triangle (TDT) elements. The TDT element effectively captures material degradation and thermal expansion within its domain, enabling accurate cross-sectional analysis with fewer elements and improved computational efficiency. This cross-section analysis method provides essential parameters for the SODA method. Subsequently, a stability analysis framework is proposed for steel members with arbitrary cross-sections under fire conditions. A comprehensive parametric study involving a total of 3,168 analyses is conducted to investigate global buckling capacity and to provide practical guidelines for stability design. To enable a more accurate and realistic large deflection analysis, a novel LFEM is proposed for the geometrically nonlinear analysis of steel structures subjected to non-uniform fire exposure. The derived line element formulation incorporates additional torque resulting from the non-coincidence of the shear center and the centroid of the cross-section, thereby enabling accurate analysis of large deflections with twisting effects. Moreover, the proposed LFEM accurately captures the response of steel structures under localized-fire conditions and elucidates twisting effects in steel structures subjected to non-uniform fire. To consider the strength degradation of cross-sections under fire, a rigorous cross-section analysis method using a fiber-based numerical model capable of capturing yield surfaces and moment-curvature relationships is proposed. This approach enables a reliable evaluation of the plastic bearing capacity for arbitrary cross-sections subjected to various fire conditions. A parametric study consisting of 162,000 analysis cases is performed, from which a simplified form of Bresler's yield surface equation is developed and validated. This approach enables evaluation of the ultimate capacity of cross-sections under various load combinations and fire scenarios, thereby laying the foundation for the next chapter. Finally, a more efficient LFEM is proposed for analyzing steel structures exposed to non-uniform heating along both the cross-sectional and longitudinal directions. Based on the moment-curvature relationships under fire mentioned above, a strength reduction formulation is incorporated into the line element featuring zero-length plastic hinge models. This method allows frame structures to be constructed with fewer line elements, thereby achieving significantly higher computational efficiency compared with conventional methods. By simultaneously considering geometric and material nonlinearities as well as thermal effects, the proposed LFEM forms the basis for the SODA method that is applicable to fire resistance design for steel structures. This thesis aims to provide an efficient and accurate second-order analysis framework for fire resistance design of steel structures. By simultaneously accounting for the coupled effects of material degradation, thermal strains and geometric nonlinearity, the proposed approach enhances the efficiency and reliability of structural performance assessments under fire, thereby facilitating the adoption of the SODA method in fire resistance design. |
| Rights: | All rights reserved |
| Access: | open access |
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