Sectional Optimization Of Steel Framework Based On Second-Order Analysis

The structural design method with linear elastic analysis and member stability check considers only the stability of members, without the interaction of members and the whole structure in strength and stability. Because the analysis method cannot exactly describe the performance of the structure, the assumption of the effective length and the stability check of every member is necessary which is very tedious and may contain potential errors. With the elevated performance of personal computer, nonlinear analysis and advanced analysis based design method will surely be the normal analysis and design method. The traditional structural design procedure need analysis and adjust previous design repeatedly to satisfy the provision of the design code and the resulted design is commonly conservative and material wasted. Structural optimization can effectively decrease building cost and rapidly obtain the optimum design. In this thesis the recent advance in nonlinear analysis and design of steel structure and structural optimization is integrated, the sectional optimization of steel frame based on the second-order analysis and design method is investigated.Sensitivity information is usually used to look for the advanced direction and set the step size in optimization algorithm. Most of the existing sensitivity analysis methods are based on linear analysis. For nonlinear analysis being used in structural optimization, the sensitivity analysis method of displacement and stress of space frames allowing for large deflection is proposed in this thesis, which lays a firm background foundation for nonlinear analysis based optimization research of space frames. The corresponding numerical examples confirm this proposed procedure is accurate and efficient for incremental-iterative type of structural analysis.According to the discrete characteristic of steel sections, the geometrical properties of the member cross-section can be expressed in terms of the axial area by regression analysis and the discrete design variables optimization is transformed into the continuous design variables optimization. To getting better discrete section solution from continuous optimum point, three stage grouping round-off method is proposed. The whole section candidates of members are classified into different groups in which the section types have almost the same height and linear regression analysis can be performed in the group. When the continuous optimum point is rounded off to the discrete commercial sections, the related group of every design variable is first established, then the specific commercial section.Based on the proposed sensitivity analysis method and grouping round-off method, the optimization of steel frames by second-order P-Δ-δanalysis and design method is investigated in this thesis. With members imposed equivalent initial curvature, the effect of residual stress to member strength and stability can be considered the same time of analysis. The member stability check is not necessary in design stage, which simplifies the considered constraints needed in optimization. The numerical examples shows that the proposed optimum design method can greatly improved the economy and safety of steel frames.