# 臺灣博碩士論文加值系統

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 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
 1. C. G. Salmon and J. E. Johnson (1996), “ Steel Structures Design and Behavior, ” Emphasizing Load and Resistance Factor Design, Fourth Edition, Chap. 8.2. 陳伯真與胡毓仁 (1998) “ 薄壁結構力學 ”，上海交通大學出版社出版。3. T. V. Galambos (1968), “ Structural Members and Frames, ” Prentice-Hall, New Jersey, pp. 80-158.4. C. P. Heins (1975), “ Bending and Torsional Design in Structural Members, ” Lexington Books , Lexington, Massachusetts, pp. 35-80.5. F. Bleich (1952), “ Buckling Strength of Metal Structures, ” McGraw-Hill Book Company, New York, pp. 104-123.6. N. S. Trahair (1977), “ The Behavior and Design of Steel Structures, ” First Edition, A Division of John Wiley and Sons, New York, pp. 283-316.7. N. S. Trahair (1993), “ Flexural-Torsional and Buckling of Structures, ” First Edition, CRC Press, pp. 304-356.8. S. Kitipornchai, C. M. Wang and N. S. Trahair (1986), ” Buckling of Monosymmetric I-Beam Under Moment Gradient, ” Journal of Structural Engineering, ASCE, Vol. 112, No. 4, pp.781-799.9. M. Kubo and Y. Fukumoto (1988), “ Lateral Torsional Buckling of Thin-Walled I-Beams, ” Journal of the Structural Division, ASCE, Vol. 114, No. ST 4,pp. 841-855.10. J. M. Anderson and N. S. Trahair (1972), “ Stability of Monosymmetric Beams and Cantilever, ” Journal of the Structural Division, ASCE, Vol. 98, No. ST1,pp. 269-286.11. J. W. Clark and H. N. Hill (1960), “ Lateral Buckling of Beams, ” Journal of the Structural Division, ASCE, Vol. 86, No. ST7, pp. 175-196.12. G. J. Hancock (1978), “ Local Distortion and Lateral Buckling of I-Beams, ” Journal of the Structural Division, ASCE, Vol. 104, No. ST11, pp.1787-1800.13. A. C. Ugural (1987), “ Advanced Strength and Applied Elasticity, ” Second Edition, Elsevier, New York, pp. 445-457.14. C. F. Kollbrunner and K. Basler (1969), “ Torsion in Structures, ” Springer-Verlag,New York, pp. 96-130.15. D. S. Ellifritt and D. M. Lue (1998), “ The Warping Constant for the W-Section with a Channel Cap, ” The Engineering Journal, AISC, Second Quarter.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. 522-540.18. American Iron and Steel Institute (2003), Manual Cold-Formed Steel Design, 2002 Edition, AISI, Washington, DC.19. American Institute of Steel Construction (2001), Manual of Steel Construction, Load and Resistance Factor Design, Third Edition, AISC, Chicago, Illinois.20. American Institute of Steel Construction (1989), Manual of Steel Construction, Allowable Stress Design, Ninth Edition, AISC, Chicago, Illinois.
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 1 非對稱組合型鋼斷面翹曲常數之分析 2 單對稱I型懸臂梁側向扭轉挫屈強度分析 3 單對稱Ｉ型與T型梁之標稱彎矩強度研究 4 型鋼斷面受扭力、彎矩和翹曲作用之分析

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