Second-order direct analysis for design of modern steel structures with nonsymmetric cross-sections

Abstract

Steel members with nonsymmetric cross-sections are widely used in modern steel structures because of their fast construction and structural efficiency. The disadvantage in fabricating nonsymmetric cross-sections is no longer as significant because most steel members can be formed and/or robotically welded, thereby enabling arbitrary shapes to be made easily and economically. Innovative structural forms and section shapes are gradually proposed and employed in modern steel structures. The direct adoption of traditional design methods may be inappropriate because their design formulae are basically derived for regular sections with symmetrical shapes. Therefore, lacking a suitable design method could cause certain obstacles when developing an innovative structural system using nonsymmetric cross-sections with higher structural efficiency in modern steel structures. In view of such a need, this research develops an innovative structural design method, namely the second-order direct analysis, to tackle the problem of designing steel frames using nonsymmetric cross-sections. This thesis proposed a new numerical analysis framework for modern steel frames with nonsymmetric cross-sections using the Line Finite-Element Method (LEM), which is the most practical and widely used method in practice. A refined line element and an improved Gaussian line element for members with nonsymmetric thin-walled sections are introduced. The element formulations are derived based on the nonsymmetrical section assumption, where the Wagner effects and the noncoincidence of the shear center and centroid of the nonsymmetric sections are directly considered, and therefore, the lateral-torsional and flexural-torsional of nonsymmetric section members can be captured robustly. Further, a novel line element for members with nonsymmetric thick-walled sections is proposed, where the non-negligible shear deformation in thick-walled members is considered by incorporating the shear deformation in the element stiffness matrices. More parameters inherent to nonsymmetric sections are required for the analysis, where the Warping and Wagener effects are more critical and need to be reflected through additional coefficients. Therefore, five additional section properties are required, including the coordinates of the shear center and the Wagner coefficients. Two cross-section analysis methods, namely the Coordinate Method and the 2D Finite-Element method, are introduced for the calculation of the section properties of nonsymmetric thin- and thick-walled sections. The successful structural design of steel structures requires a realistic assessment of a structural system's ultimate strength capacity under extreme loading conditions, such as super-typhoon and seismic attacks, to ensure structural safety without collapse. As such, this research proposes a second-order inelastic analysis method for the nonsymmetric members. The concentrated plasticity (CP) model is integrated into the LFEM, and the modified tangent modulus (MTM) approach originally proposed by Ziemian and McGuire (2002) is adopted to represent partial material yielding. Moreover, this research proposes a numerical analysis method for the nonsymmetric members under fire conditions. A novel line element formulation based on the co-rotational (CR) method is developed. The proposed CR line element formulation can conveniently consider the material degradation and the thermal expansion. A refined Newton-Raphson-typed numerical procedure for the analysis at elevated temperatures is proposed and elaborated. A series of verification examples are given to verify the accuracy of the proposed cross-section analysis methods, the line element formulations, and the inelastic analysis method. Results from literatures, experiments, and sophisticated Finite Element Analysis have been used as the benchmark answers. The distinct feature of this research is the development of a second-order direct analysis framework for the steel frames with nonsymmetric cross-sections, integrating the techniques such as robust cross-section analysis methods, LFEM with several line element formulations included, and inelastic analysis method. The research work in the thesis is expected to lead to a significant improvement in the design of more economical and safer structures, enhancement of construction efficiency, and reduction of manpower demands.