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Numerical Evaluations of Warping Constants For Unsymmetrical Built-up Sections
|關鍵字:||翹曲常數;warping constants;組合型鋼斷面;非對稱組合型鋼斷面;剪力中心;built-up sections;unsymmetrical built-up sections;shear center||出版社:||土木工程學系所||引用:||American Institute of Steel Construction (1989), Manual of Steel Construction, Allowable Stress Design, Ninth Edition, AISC, Chicago, Illinois. American Institute of Steel Construction (1994), Torsional Analysis of Structural Steel Members, Second Edition, AISC, Chicago, Illinois. American Iron and Steel Institute (1991), Load and Resistance Factor Design For Cold-Formed Steel Structure Members, 1991 Edition, AISI, Washington, DC. Anderson, J. M. and Trahair, N. S. (1972), "Stability of Monosymmetric Beams and Cantilever," Journal of the Structural Division, ASCE, Vol. 98, No. ST1, pp. 269-286. Boresi, A. P. and Sidebottom, O. M. (1985) "Advanced Mechanics of Materials," Fourth Edition, John Wiley and Sons, Inc.,. pp.326-328 Bleich, Friedrich (1952), "Buckling Strength of Metal Structures," McGraw-Hill Book Company, New York, pp. 104-123. Clark, J. W. and Hill, H. N. (1960), "Lateral Buckling of Beams," Journal of the Structural Division, ASCE, Vol. 86, No. ST7, pp.175-196. Ellifritt, D. S., Wine, G., Sputo, T. and Samuel, S. (1992), "Flexural Strength of WT Sections," Engineering Journal, AISC, Second Quarter, pp.67-74. Ellifritt, D. S. and Lue, Dung M. (1998), "Design of Crane Runway Beam with Channel Cap," Engineering Journal, AISC, Second Quarter, pp.41-49. Gere, J. M. and Timoshenko, S. P. (1972), "Mechanics of Materials", Wadsworth, Inc., Belmont, California, pp. 257-287. Galambos, T. V. (1968), "Structural Members and Frames," Prentice-Hall, Englewood Cliffs, New Jersey, pp. 80-158. Heins, C. P. (1975), "Bending and Torsional Design in Structural Members," Lexington Book Co., Lexington, MA. Hancock, G. J. (1978), "Local Distortion and Lateral Buckling of I-Beams," Journal of the Structural Division, ASCE, Vol. 104, No. ST11, pp.1787-1800. Hechtman, R. A. and Hattrup, J. M. (1955), "Lateral Buckling of Rolled Steel Beams," Journal of the Engineering Mechanics Division, ASCE, Vol. 81, No. 797, pp.797-830. Kollbrunner, C. F. and Basler, K. (1969), "Torsion in Structures," Springer-Verlag, New York, pp. 96-130. Kubo, M. and Fukumoto, Y. (1988), "Lateral Torsional Buckling of Thin-Walled I-Beams," Journal of the Structural Division, ASCE, Vol. 114, No. ST 4, pp. 841-855. Kitipornchai, S. and Trahair, N. S. (1980), "Buckling Properties of Mono-symmetric I-Beam," Journal of the Structural Division, ASCE, Vol. 106, No. ST5, pp. 941-957. Kitipornchai, S., Wang, Chien Ming and Trahair, N. S. (1986),"Buckling of Monosymmetric I-Beam Under Moment Gradient," Journal of Structural Engineering, ASCE, Vol. 112, No. 4, pp.781-799. Kitipornchai, S. and Chung, A. D. (1987)," Inelsatic Buckling of Welded Monosymmetric I-Beam, " Journal of Structural Engineering, Vol.113, No. 4, pp.740-756. Lue, Tony and Ellifritt, D. S. (1993), "The Warping Constant for the W-Section with a Channel Cap," Engineering Journal, AISC, First Quarter, pp.31-33. Nethercot, D. A. (1983), "Elastic Lateral Buckling of Beam," Beams and Beam Columns-Stability in Strength (ed. R. Narayanan), Barking, Essex, England: Applied Science Publishers. Pi, Y. L. and Trahair, N. S. (1992) " Prebuckling deflections and lateral buckling theorem " Journal of the Structural Division, ASCE, Vol. 118, No. 11, pp. 2946-2966. Salmon, G. Charles and Johnson, E. John (1994), "Steel Structures: Design and Behavior," Emphasizing Load and Resistance Factor Design, Fourth Edition, pp.484-542. Trahair, N. S. (1977), "The Behavior and Design of Steel Structures," First Edition, A Division of John Wiley and Sons, New York, pp.283-316. Trahair, N. S. (1993), "Flexural-Torsional and Buckling of Structures," First Edition, CRC Press, pp.304-356. Ugural, A.C. (1987) "Advanced Strength and Applied Elasticity," Second Edition, Elsevier, New York, pp.445-457. Wang, Chien-Ming and Kitipornchai, S. (1986), "Buckling of Monosymmetric I-Beam Under Moment Gradient," Journal of Structural Engineering, ASCE, Vol. 112, No. 4, pp.781-799. Yu, Wei-Wen (1991), "Cold-Formed Steel Design," Second Edition, A Wiley-Interscience Publication, New York, pp.522-540 邱培智 (2002), "AISI開口斷面翹曲常數之數值化分析",國立中興大學土木工程學系碩士論文. 黃宗勇 (2001), "開口薄壁斷面翹曲常數之電腦化分析",國立中興大學土木工程學系碩士論文. 黃俊賢 (2006), "開口薄壁斷面翹曲常數-理論與數值化分析",國立中興大學土木工程學系碩士論文. 賴亮宇 (1999), "組合單對稱樑之斷面挫曲常數",國立中興大學土木工程學系 碩士論文.||摘要:||
在結構工程上常見之開口薄壁斷面(open thin-walled section)組合構件，在工業廠房中已被廣泛使用；當構件受到扭力作用時其斷面之分析包括純扭曲應力(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)，其中翹曲剪應力之分析常面臨之困難為翹曲常數(warping constant, Cw)之計算。雖然許多常見開口斷面之翹曲常數，在AISC規範中已有現成表列值可用，但是僅侷限於單一或雙對稱斷面。開口斷面其翹曲常數之取得，往往包括斷面剪力中心位置之確定與翹曲常數本身之計算，其過程牽涉複雜之積分運算，這對一般從事例行實務設計之工程師而言是非常困難的，更何況是非對稱開口薄壁組合型鋼斷面。
本研究群透過最近幾年之研究，試以一階分析(first-order analysis)為基礎整理、推導以積分式表示之理論公式，採用Heins理論考慮斷面係由薄壁板元素(thin-walled plate element)組成之特性，將理論積分式改成數值公式並使用Excel軟體，由電腦執行非對稱開口薄壁組合型鋼斷面翹曲常數之複雜運算。
In the practice of structural engineering, members with open thin-walled section have been widely used. When the member is subjected to torsion, the stress analysis of section includes both the pure torsion stress and the warping stress. The warping stresses which are composed of warping shear and warping normal stresses. The analysis of warping shear stress is not an easy task for general practicing engineers. The difficulty comes from the evaluation of warping constant (Cw) of open thin-walled section. Although many of the open thin-walled sections of warping constants, already existing in the AISC Specifications tabulated values are available, but only limited to a single or double symmetrical section. The calculation of warping constant, which includes the locating of shear center, is not a routine process and is a tough task for general engineers.
This study intends to obtain the exact formulas derived based on first-order analysis. The formulas are obtained and expressed in terms of mathematical integration. Considering the property that the section is made of thin-walled plate elements, the theoretical formulas can be written in terms of numerical expressions. The numerical expressions are calculated by Excel. The evaluation of Cw is finally carried out by the computer.
In the AISC-ASD design manual (1989), three kinds of unsymmetrical built-up open thin-walled sections, warping constants are not listed. This implies that the evaluation of Cw has its difficulties. A theoretical way to obtain the Cw values of the three unsymmetrical built-up thin-walled sections has been through a series of calculation and verification of shear center by Heins. It is belived that the works have great help for structural engineering, and provides a valuable reference value for the AISC design manual.
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