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研究生： 斐牧和
Mohamed, Beidari
論文名稱： 鋼板側向扭轉挫屈之數值研究
Numerical studies of lateral torsional buckling of steel plates
指導教授： 王雲哲
Wang, Yun-Che
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2011
畢業學年度： 99
語文別： 英文
論文頁數： 42
中文關鍵詞： 側向扭轉挫曲 、穩定性 、鋼板 、懸臂樑 、有限元素分析
外文關鍵詞： Lateral-torsional buckling, Stability problem, Steel plates, Cantilever Beams
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    • 本論文應用有限元素軟體ABAQUS，探討細窄斷面懸臂鋼樑，受載重下，由沿強軸彎曲產生側向扭轉挫曲行為(Lateral torsional buckling, LTB)，導致部份變形改為沿弱軸彎曲。彎曲與扭轉間的變形模態轉換為一挫曲行為，其物理機制為材料內所儲存的彎曲變形能高於鄰近的扭轉變形模態，使得此懸臂樑改變變形模態。在凝靜態的假設下，此改變發生於ㄧ瞬間。本文在凝靜態的假設下，分析不同尺寸的懸臂樑，探討幾何對側向扭轉挫曲的影響。分析結果顯示，在不發生側向扭轉挫曲的條件下，欲增加承載能力，懸臂樑的長度要小、寬度及深度要大。此外、有限元分析與解析解一致，解析解中由變分近似(Rayleigh-Ritz)所得的解或由低自由度模型所得的解，亦為可接受的近似解。

    This thesis studies a stability problem in steel structures, that involves lateral-torsional buckling (LTB) of steel cantilever beam under point-load or distributed bending. The physical mechanisms of the transition from pure bending along the major axis to LTB are based on the low energy in the twisted configuration. Theoretical results are provided to compare finite element calculations. Linear and non-linear finite element analyses have been carried out to detect the LTB with ABAQUS. We focused on thin plates with a rectangular cross-section and assume it as a cantilever beam with a small thickness to do our investigation. Various geometrical parameters are used to study the effect of geometry on LTB. It is found that, to increase loading capacity in avoiding LTB, the longer, wider and deeper beams can perform better. The calculated results have been compared to theory, and reasonable agreements are achieved.

    CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Differential Equation for Elastic Lateral-Torsional Buckling . . . . . . 3 1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 Discrete theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Continuum theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Finite element calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1 Finite element backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.1 Solutions techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1.2 Linear eigenvalue buckling analysis . . . . . . . . . . . . . . . . . . . 21 3.1.3 Nonlinear collapse and postbuckling analysis . . . . . . . . . . . . . . 22 3.2 Finite element modeling details . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1 Linear behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.1.1 Theoretical methods compare with FEA method . . . . . . . . . . . . 29 4.1.2 Theoretical methods compare with FEA method . . . . . . . . . . . . 30 4.2 Geometric nonlinear effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2.1 Load-displacement analysis . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Energy-displacement analysis . . . . . . . . . . . . . . . . . . . . . . 31 4.2.3 Load-displacement analysis . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.4 Energy-displacement analysis . . . . . . . . . . . . . . . . . . . . . . 32 5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

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