臺灣博碩士論文加值系統

傳統的鋼筋混凝土構件之設計程序，不外乎根據構件
承受載重之狀況，假設構件斷面尺寸大小及鋼筋量，並依
據相關規範規定逐一迭代試誤而求得理想的設計結果。一
般設計結果皆能滿足規範的要求及安全上的考量，卻無法
確保工程造價的經濟性。
本文的目的係利用離散式拉格朗日法，來進行鋼筋混
凝土樑最佳化設計，並配合程式語言的撰寫，進而研發出
一套能直接尋求最佳化之鋼筋混凝土結樑斷面尺寸、鋼筋
量及同時滿足經濟與安全考量的自動化設計程式。
本文係以鋼筋混凝土樑之斷面尺寸及鋼筋量為設計變
數，鋼筋混凝土樑之成本函數為目標函數；鋼筋混凝土樑
之設計規範及斷面尺寸範圍為約束條件。有關本論文離散
式拉格朗日法的應用與效率，可透過鋼筋混凝土樑設計案
例來說明、探討，以供工程設計之參考。

The required reinforcement analysis of reinforced concrete structure is based on the initial designed cross - section subjected to the maximum .
According to the specifications for making the ideal designed result.
The common designed result can content the Specifications and scruple , but not ensure the minimum cost design . The purpose of this study is to apply the Discrete Lagrangian Methods for finding the minimum cost design of reinforced concrete beams . A pilot computer program is developed for the optimal preliminary design of reinforced concrete beams .
The width ,depth ,and longitudinal reinforcement of the beam cross-section are take as the design variables . The objective function is a cost function and the constrains are the specifications,cross-section . Several numerical examples for minimum cost design of the reinforced concrete beams
are used to illustrate the efficiency of Discrete Lagrangian Method .

第一章 緒論 ……………………………………………………………. 1
1.1 研究動機 …………………………………………………… 1
1.2 文獻回顧 …………………………………………………… 2
1.3 本文內容 …………………………………………………… 4
第二章 DLM理論 ………………………………………………………..6
2.1 連續性函數之最佳化問題 ………………………………… 6
2.2 不連續性函數之最佳化問題 ……………………………… 9
2.2.1 DLM之定義 …………………………………………. 9
2.2.2 DLM解等約束最佳化問題 ………………………… 12
2.2.3 DLM解不等約束最佳化問題 ……………………… 13
2.3 Lagrange 乘子的更新 …………………………………… 14
第三章 目標函數 ……………………………………………………… 16
3.1 前言 ……………………………………………………… 16
3.2 目標函數的建立 ………………………………………… 16
3.2.1 單筋矩形樑斷面…………………………………. 16
3.2.2 雙筋矩形樑斷面 ………………………………… 17
3.2.3 單筋T形樑斷面 …………………………………. 18
第四章 鋼筋混凝土樑設計理論 ……………………………………. 19
4.1 基本假設 ………………………………………………… 19
4.2 相關規範規定 …………………………………………… 20
4.3 單筋混凝土矩形樑斷面 ………………………………… 20
4.4 雙筋混凝土矩形樑斷面 ………………………………… 21
4.5 單筋混凝土T形樑斷面 ………………………………… 22
4.6 鋼筋混凝土樑斷面之剪力強度 ………………………… 23
第五章 約束條件 ……………………………………………………. 24
5.1 前言 …………………………………………………….. 24
5.2 約束條件的建立 ………………………………………… 24
5.2.1 鋼筋之保護層 …………………………………… 24
5.2.2 抗彎強度約束條件 ……………………………… 25
5.2.3 抗剪強度約束條件 ………………………………. 25
5.2.4 斷面尺寸約束條件 ………………………………. 27
5.2.4 延展性約束條件 …………………………………. 29
5.2.6 T形樑結構約束條件 …………………………… 30
第六章 範例與結果 …………………………………………………. 31
6.1 單筋混凝土矩形樑斷面 ………………………………… 31
6.2 雙筋混凝土矩形樑斷面 ………………………………… 32
6.3單筋混凝土T形樑斷面 ………………………………… 33
第七章 討論與建議 …………………………………………………. 34
參考文獻 ………………………………………………………………. 39

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