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研究生:黃俊賢
研究生(外文):Jiun-Shian Huang
論文名稱:開口薄壁斷面翹曲常數-理論與數值化分析-
論文名稱(外文):Warping Constants of Open Thin-walled Sections -Theory and Numerical Analysis-
指導教授:呂東苗
指導教授(外文):Dung Miau Lue
學位類別:碩士
校院名稱:國立中興大學
系所名稱:土木工程學系所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:173
中文關鍵詞:開口薄壁斷面翹曲常數
外文關鍵詞:Warping Constants of Open Thin-walled Sections
相關次數:
  • 被引用被引用:4
  • 點閱點閱:317
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
在鋼結構開口薄壁斷面設計中,進行斷面之扭轉分析時,必須考慮純扭曲剪應力(pure torsional shear stress)與翹曲應力(warping stress),而翹曲應力之分析包括翹曲剪應力(warping shear stress)與翹曲正向應力(warping normal stress),其中翹曲應力之分析常面臨之困難為翹曲常數(warping constant Cw)之取得,而其之所以困難在於計算太過繁雜,對於一般從事實務的工程師而言並不方便,故往往忽略與翹曲應力相關的計算,而採取較保守之設計,如此提高了材料費用。有鑑於此,本研究將針對開口薄壁斷面翹曲常數之理論作有系統的整理,並且推導其翹曲常數數值公式,再將繁雜的公式運算交由Microsoft office Excel或Visual Fortran來執行,如此便能準確地分析開口薄壁斷面的扭轉行為,而有效地降低材料成本。
從研究結果得知,本研究根據開口薄壁斷面翹曲常數之理論公式,整理與推導開口薄壁斷面翹曲常數之數值公式,該數值公式適用於任一開口薄壁斷面,即熱軋鋼、冷軋鋼與任何組合開口薄壁斷面,並且提供了所有AISC Manual of Steel Construction (1989,2001)之WC section (Wide Flange with Channel)的翹曲常數值,解決工程師在分析、設計WC section所面臨之困擾。
A cold-formed steel open section subjected to torsional moment will result in pure torsional shear, warping shear, and warping normal stresses. Evaluation of these torsion induced stresses is not a routine job for practicing engineers as one of major difficulties arises from the determination of sectional warping constant (Cw).
Calculation of the warping constant (Cw) for a thin-walled open section is a tedious and difficult task and thus presenting an obstacle to routine design. Although Cw formulas and values for selective cold-formed steel sections are available in the AISI manual, most practicing engineers have no idea of evaluating Cw constants for sections not listed in the AISI manual. This paper provides a detailed step-by-step numerical procedure for evaluating the Cw value of a general thin-walled open section. Comparison between the calculated values and those listed in AISI manual shows virtually zero differences. This implies that the proposed procedure is a very reliable and useful tool for computing the Cw constant for any cold-formed steel open section, which does not require the use of a sophisticated computer software.
中文摘要 i
英文摘要 ii
目次 iii
表目次 vi
圖目次 xiii
符號說明 xvi
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.3 研究動機 2
1.4 研究方法與目標 2
第二章 開口薄壁斷面翹曲常數之理論與數值公式 6
2.1 前言 6
2.2 斷面形心 6
2.3 斷面剪力中心 7
2.4 翹曲變形 17
2.5 翹曲常數Cw之理論推導 22
2.6 翹曲常數Cw之數值公式推導 27
第三章 九種常見開口薄壁斷面翹曲常數之公式推導 32
3.1 前言 32
3.2 C-section with and without lips 35
3.3 Z-section with and without lips 44
3.4 Equal Leg Angles with and without lips 54
3.5 Hat section 61
3.6 W-shape 70
3.7 WC section 76
第四章 九種常見開口薄壁斷面翹曲常數之數值化計算與比較 90
4.1 前言 90
4.2 C-section without lips 90
4.3 C-section with lips 95
4.4 Z-section without lips 101
4.5 Z-section with lips 105
4.6 Equal Leg Angles without lips 111
4.7 Equal Leg Angles with lips 115
4.8 Hat section 120
4.9 W-shape 126
4.10 WC section 132
4.11 比較結果整理 142
第五章 結論 146
參考書目 147
附錄A 公式推導 149
A.1 翹曲慣性積Iwx與Iwy之數值公式 149
A.2 翹曲常數Cw之數值公式 152
附錄B 斷面探討 154
B.1 斷面板元素之積分方向討論 154
B.2 Z形斷面之細節討論 158
附錄C Fortran程式 160
C.1 程式流程 160
C.2 程式使用說明 160
C.3 程式例題說明 161
C.4 程式碼 / Source Code 162
附錄D WC section之翹曲常數值 169
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16. D. S. Ellifritt and D. M. Lue (2003), “ Numerical Evaluation for Warping Constant of Built-up Crane Runway Beam, ”SSRC Annual Meeting Proceedings, April 2~5, Baltimore Maryland, U.S.A, pp 213-232.
17. W. W. Yu (1991), “ Cold-Formed Steel Design, ” Second Edition, Wiley- Interscience Publication, New York, pp. 522-540.
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