本文主要是使用離散拉格朗日法(Discrete Lagrangian Method, DLM)針對鋼結構構架進行輕量化設計，最佳化設計的束制條件是根據AISC-LRFD規範之局部挫屈及強度檢核公式來建立，構材斷面則限制由AISC-LRFD設計手冊中的型鋼斷面選取。構架系統可為斜撐構架或空構架，斜撐型式為對角斜撐以及K型斜撐。結構分析時採線性分析，並可考慮P-D效應。平面鋼構架的設計結果顯示：含K型斜撐的鋼構架雖可大幅度降低其結構重量，但因柱構材的勁度相對較低，易於過早形成塑鉸，故透過非線性側推分析的結果顯示構架的極限側向變位反而降低。另外，在本研究的算例中，P-D效應的影響並不明顯，以單跨十層樓平面構架的算例為例，設計時考慮P-D效應只會使得結構重量較重約2%，差異並不大。會造成此P-D效應影響較小的原因，主要是設計時考慮樓層相對位移的束制條件，使得P-D效應的影響因而降低。 In this report, the minimum weight design of 2-D and 3D steel frameworks using the discrete Lagrangian method (DLM) is presented. The strength and serviceability requirements specified in the AISC-LRFD specifications are used to construct the constraint functions for the design problems. All the members are selected from the standard hot-rolled steel sections available in the AISC-LRFD design manual. The structural systems can be braced and unbraced steel frameworks. Linear-elastic analysis, with or without P-D effect, are implemented in the DLM design procedure. Several benchmark problems are designed using the proposed DLM searching procedure. Comparison of DLM design results with those presented in the literature are discussed. The optimum weight and ultimate lateral load capacities of diagonal-braced, K-braced and unbraced steel frameworks are also discussed in this report. It is shown that the final weight of the designed frameworks with K-bracings is the lowest; while its ultimate lateral displacement is also the lowest one. Because story drift constraint has been considered in the design, the optimum weights of the designed structures are not significantly influenced by the P-D effect.
