臺灣博碩士論文加值系統

由於箱型鋼梁是薄壁結構，理論上應使用板殼元素為分析元素較能反映實際的受力及變位。為有效進行設計與分析，已有多種商業軟體，但是在確定分析元素與分析之前置作業也相當繁雜費時，而造成初步設計的困難。因此如何利用平板力學相關學理推導箱型鋼梁受力變位近似公式將可幫助箱型鋼梁設計者減少非必要之工作負擔。
本文的探討方法是將箱型鋼梁上翼鈑變位分為上翼鈑與腹鈑交界處變位及上翼鈑變位這兩種變位之疊加，上翼鈑與腹鈑交界處變位用Euler-Bernoulli梁理論來推導，用兩種獨立載重情況之變位平均值來計算上翼鈑變位。第一種情況為兩端相對簡支、兩端相對自由之平板在承受均佈載重q之作用，用Lévy’s Method分析，求得是上翼鈑最大變位情況。第二種情況為兩端相對固定、兩端相對自由之平板變位在承受均佈載重q之作用，用Ritz Method分析，求得是上翼鈑最小變位情況。
梁長30m，梁寬2m，梁高1.5m直線型式等斷面簡支箱型鋼梁，配合不同的翼鈑厚與腹鈑厚用有限元素法編寫之SAP2000軟體進行準確度之比較，近似公式之誤差百分比為 - 7.91% ~ + 2.94%，尚在初步設計的容許誤差範圍內。

The advantage of using steel box girders to transfer and distribute wheel load over a wide area is attributed to their structural efficiency and the need for reducing the self-weight of superstructure. For the simplicity of design process, it is helpful, in the early stage of a project, to have an understanding about how the bridge deck deforms under loading, in order to select an adequate member so that the preliminary design needs not be substantially modified in the subsequent stages. In engineering practice, analysis and design of bridge girders is primarily carried out through application of commercial software. Even in this situation, considerable efforts are still required to get through the solution procedure, not only in the preparation of input data but also in the interpretation of the outcome. The complexity of the analysis process may give rise to unpredictable errors, thus requiring approximate formulas to check the validity of the analysis results. This thesis is aimed to derive explicit expressions that can be used to give a crude approximation for the behavior of a deck slab under uniformly distributed loading. Results obtained by the proposed formulas are compared to those analyzed by means of the finite element program SAP 2000.

摘 要 I
ABSTRACT II
目　錄 III
圖目錄 V
表目錄 VII

第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧與研究方法 2
1.3 研究範圍 3
第二章 理論分析 5
2.1 板理論分析 6
2.1.1 基本假設 6
2.1.2 兩端相對簡支、兩端相對自由之平板變位 7
2.1.3 兩端相對固定、兩端相對自由之平板變位 10
2.2 箱型鋼梁上翼鈑變位近似公式 18
第三章 工程實例數值分析與比較 20
3.1 分析元素之形狀與種類 22
3.1.1 分析元素形狀之確定 22
3.1.2 分析元素種類之確定 26
3.2 數值分析結果與比較 30
第四章 結論與未來研究方向 34
4.1 結論 34
4.2 未來研究方向 34
參考文獻 34
附錄 A　初步設計流程圖 34
附錄 B　細部設計流程圖 34
附錄 C　SAP2000之輸出檔 34
附錄 D　試算表之說明 34

1.A. Prokić, “New finite element for analysis of shear lag”, Computers and Structures, 80, pp.1011-1024, 2002.
2.Ansel C. Ugural, “Stresses In Plates And Shells”, 2nd Ed., McGraw-Hill, 1999.
3.Kang, L. C., Wu, C. H., and Steele, C. R., “Fourier Series for Polygonal Plate Bending: A Very Large Plate Element” Applied Mathematics and Computation, Vol. 67, pp.197-225, 1995.
4.A. K. Tripathy, H. J. Patel, S. S. Pang, “Bending Analysis of Laminated Composite Box Beams”, Journal of Engineering Materials and Technology, Vol.116, pp.121-129, 1994.
5.S. Timoshenko, S. Woinowsky-Krieger, “Theory of plates and shell”, 2nd Ed., McGraw-Hill, New York, 1987.
6.S. S. Rao, “The Finite Element Method In Engineering”, Pergamon Press, New York, 1982.
7.M. S. Troitsky, “Stiffened Plates Bending, Stability, and Vibration”, New York, Elasevier Scientific Pub Co., 1976.
8.Computers and Structures, Inc. “SAP2000 Analysis Reference Manual”, Version 8.0, 2002.
9.鄧建剛、鄭復平, “Fourier級數展開式的方法於箱式構造應力分析之應用”, 技術學刊, 第十五卷, 第一期, pp.167-177, 2000.
10.Christion Meyer著；蕭仲光、沈孝光 譯, “’鋼筋混凝土結構設計”, 滄海書局, 1998.
11.蘇建中, “正交異向性板之有限元素法靜態分析”, 國立台灣海洋大學造船工程研究所碩士學位論文, 1998.
12.交通部, 交通技術標準規範公路類公路工程部, “公路橋梁設計規範”, 幼獅文化事業公司, 2001.
13.歐文爵, “梁理論的討論”, 國立台灣大學土木工程學系研究所碩士學位論文, 1992.
14.王如鈺、王雲程, “鋼橋概要”, 憬藝企業有限公司, 1996.
15.聯邦工程顧問股份有限公司, “SAP2000入門與工程上之應用”, 科技圖書出版, 2002.
16.洪維恩, “數學運算大師Mathematica 4”, 碁峰資訊, 2001.