正八边形孔蜂窝梁的挠度计算研究
|
摘要
蜂窝梁作为一种新型钢构件,由于其截面形式合理、自重轻、承载能力高、美观经济等优点,因而常被应用于大跨结构中。但是我国并没有制定相关的规范或标准来指导应用设计,这严重制约了蜂窝梁在我国的广泛应用。目前,蜂窝梁的挠度并没有简单而统一的计算公式,所以进一步的研究非常有必要。本文对正八边形孔蜂窝梁的挠度计算研究做了如下工作:
(1)本文参考国内外相关资料,总结了圆孔(椭圆孔)、六边形孔、八边形孔以及对应的楔形蜂窝梁的制作方法。
(2)本文依据经典材料力学的理论,阐述了费氏空腹桁架法的理论推导,并讨论了其表达式中参数的取值。提出了等效刚度法并推导出其计算表达式,采用有限元进行大量计算分析并拟合出等效抗弯刚度和等效抗剪刚度的表达式,且验证了它们的准确性。
(3)本文参考国内外相关资料并结合本文推导的计算式,总结了蜂窝梁挠度不同的计算方法,并讨论了常用的ANSYS法、费氏空腹桁架法和等效刚度法的区别和联系。
(4)本文基于ANSYS分析,对不同参数蜂窝梁在不同的荷载作用下的挠度的理论计算公式进行了精度评价,发现简化理论计算公式精确度很高且略大于真实值,所以将该公式应用于工程中是偏安全的。
(5)本文讨论了蜂窝梁的八种影响因素对蜂窝梁挠度的影响,并计算和修正了蜂窝梁挠度增大系数η在不同扩大比、高跨比和荷载类型条件下的值。本文讨论了常用的几种标准孔型蜂窝梁在不同荷载和参数下挠度的变化,为工程实践中选用不同类型蜂窝梁提供参考建议。最后,本文提出了一套适用于工程的蜂窝梁挠度的简化计算公式。
As a new steel menber, castelled beam is often used in long-span structures because it has many advantages, such as the rational section form, light-weight, high load-carrying capacity, and so on. But at present, there is no technical standard or specification on it to guide applications and design in our country. This severely restricts the castelled beam’s widely use in China. At present, there is no conveniend or uniform calculation method to the deflection of castelled beam. Therefore, it is necessary to do more researches on the existent problems. The main research work on the deflection of octagonal hole castelled beam covers the following aspects:
(1) According to the domestic and overseas references, this article summarizes the method of making circular hole(elliptical hole), hexagonal hole, octagonal hole and the corresponding tapered castellated beam.
(2) Based on the classical theory of mechanics of materials, this article describes the theoretical derivation of the Altfillisch, which is assumed the castellated beam as a vierendeed truss, and discusses the values of the parameters of its expression. Equivalent stiffness method is proposed and its calculation expression is derived in this article. Using amounts of the finite element analysis fits out the equivalent bending stiffness and the equivalent shear stiffness’s expressions, and verifies their accuracy.
(3) According to the domestic and overseas references and the expressions which are derived in this article, this article summarized the different methods of caculating the deflection of castellted beam, and discusses the difference and connection of the common methods-the FEA, the Altfillisch and the equivalent stiffness method.
(4) Based on the FEA, this article evaluates the precision of the oretical formula of the deflection of castellted beam on the different parameters and under different load. And found that the accuracy of simplified theoretical formula is very high and the caculation value is slightly larger than the true value, so the formula used in the project is biased safe.
(5) This article discusses the impact of eight factors on the deflection of castellted beam. And also calculate and correct the value of the magnification factorηat different expansion ratio, different high-span ratio and under different load. This article discusses the changes of the deflection of several the commonly used standard castellted beam which is under different load and parameters. And this can provide reference and proposal for selecting different types of castellted beam in engineering practice. Finally, this article presents a simplified formula which can be used in engineering practice for the deflection of castellted beam.
(1)本文参考国内外相关资料,总结了圆孔(椭圆孔)、六边形孔、八边形孔以及对应的楔形蜂窝梁的制作方法。
(2)本文依据经典材料力学的理论,阐述了费氏空腹桁架法的理论推导,并讨论了其表达式中参数的取值。提出了等效刚度法并推导出其计算表达式,采用有限元进行大量计算分析并拟合出等效抗弯刚度和等效抗剪刚度的表达式,且验证了它们的准确性。
(3)本文参考国内外相关资料并结合本文推导的计算式,总结了蜂窝梁挠度不同的计算方法,并讨论了常用的ANSYS法、费氏空腹桁架法和等效刚度法的区别和联系。
(4)本文基于ANSYS分析,对不同参数蜂窝梁在不同的荷载作用下的挠度的理论计算公式进行了精度评价,发现简化理论计算公式精确度很高且略大于真实值,所以将该公式应用于工程中是偏安全的。
(5)本文讨论了蜂窝梁的八种影响因素对蜂窝梁挠度的影响,并计算和修正了蜂窝梁挠度增大系数η在不同扩大比、高跨比和荷载类型条件下的值。本文讨论了常用的几种标准孔型蜂窝梁在不同荷载和参数下挠度的变化,为工程实践中选用不同类型蜂窝梁提供参考建议。最后,本文提出了一套适用于工程的蜂窝梁挠度的简化计算公式。
As a new steel menber, castelled beam is often used in long-span structures because it has many advantages, such as the rational section form, light-weight, high load-carrying capacity, and so on. But at present, there is no technical standard or specification on it to guide applications and design in our country. This severely restricts the castelled beam’s widely use in China. At present, there is no conveniend or uniform calculation method to the deflection of castelled beam. Therefore, it is necessary to do more researches on the existent problems. The main research work on the deflection of octagonal hole castelled beam covers the following aspects:
(1) According to the domestic and overseas references, this article summarizes the method of making circular hole(elliptical hole), hexagonal hole, octagonal hole and the corresponding tapered castellated beam.
(2) Based on the classical theory of mechanics of materials, this article describes the theoretical derivation of the Altfillisch, which is assumed the castellated beam as a vierendeed truss, and discusses the values of the parameters of its expression. Equivalent stiffness method is proposed and its calculation expression is derived in this article. Using amounts of the finite element analysis fits out the equivalent bending stiffness and the equivalent shear stiffness’s expressions, and verifies their accuracy.
(3) According to the domestic and overseas references and the expressions which are derived in this article, this article summarized the different methods of caculating the deflection of castellted beam, and discusses the difference and connection of the common methods-the FEA, the Altfillisch and the equivalent stiffness method.
(4) Based on the FEA, this article evaluates the precision of the oretical formula of the deflection of castellted beam on the different parameters and under different load. And found that the accuracy of simplified theoretical formula is very high and the caculation value is slightly larger than the true value, so the formula used in the project is biased safe.
(5) This article discusses the impact of eight factors on the deflection of castellted beam. And also calculate and correct the value of the magnification factorηat different expansion ratio, different high-span ratio and under different load. This article discusses the changes of the deflection of several the commonly used standard castellted beam which is under different load and parameters. And this can provide reference and proposal for selecting different types of castellted beam in engineering practice. Finally, this article presents a simplified formula which can be used in engineering practice for the deflection of castellted beam.
引文
[1]王洪范,王立新.蜂窝梁的应用与计算方法.工业建筑, 1994, 8(8): 3-4
[2]罗晓霖.蜂窝梁的整体稳定性能分析: [同济大学硕士学位论文].上海:同济大学, 2005, 1-15
[3]刘文如,朱聘儒,张培卿.蜂窝梁檩条的试验研究.哈尔滨建筑工程学院学报, 1993, 26(1): 101-105
[4] Estrada H, Jimenez J J, Aguiniga F. Cost Analysis in the Design of Open-Web Castellated Beams, AEI, 2006, 15(10): 1-10
[5] Knowles P R. Castellated beams. London: Proceedings of the Institution of Civil Engineers, 1991, 521-536
[6]倪富生,胡泰祥,胡嗣元等.蜂窝梁的应力分布及设计计算探讨.工业建筑, 1984, 8(8): 27-35
[7]郑坤龙.变高度工字截面圆孔蜂窝梁的挠度计算: [中南大学硕士学位论文].湖南:中南大学, 2007, 1-34
[8]刘鑫.考虑孔况影响的蜂窝梁设计计算研究: [中南大学硕士学位论文].湖南:中南大学, 2006, 1-25
[9]李霞.卧式似椭圆孔蜂窝梁的制作与设计计算方法: [中南大学硕士学位论文].湖南:中南大学, 2007, 1-24
[10]周丽.圆孔蜂窝拱形曲梁弹性弯扭屈曲分析: [湖南大学硕士学位论文].湖南:湖南大学, 2010, 3-8
[11]张兴杰.蜂窝梁的抗弯刚度分析和挠度计算: [同济大学硕士学位论文].上海:同济大学, 2006, 1-61
[12]苏益生.圆形孔蜂窝梁简化计算与试验的对比分析.红水河, 2002, 22(2): 46-57
[13]杨坛.基于ANSYS的圆孔蜂窝钢梁承载力研究: [广西大学硕士学位论文].广西:广西大学, 2007, 7-71
[14]苏益生.圆孔蜂窝梁验算截面的确定及梁桥高度取值分析.红水河, 1994, 13(2): 39-43
[15]包头钢铁设计研究总院,中国钢结构协会房屋建筑钢结构协会.钢结构设计与计算.第2版.北京:机械工业出版社, 2006, 214-221
[16] Srimani S L. Development of Design load Table for Castellated Beams. Indian Journal of Technology, 1980, 18(12): 494-497
[17]渡边邦夫,大泽茂树,内藤龙夫等著.钢结构设计与施工.周耀坤.北京:中国建筑工业出版社, 2000, 1-100
[18]汤庆轩,侯兆欣,吴明超.简支蜂窝梁整体稳定的研究承载力有限元分析.钢结构, 2005, 20(4): 32-35
[19]罗烈,罗晓霖.蜂窝梁设计规范的比较研究.建筑钢结构进展, 2005, 7(2): 43-47
[20]罗鹏.孔角修圆蜂窝梁的弹性分析与设计: [中南大学硕士学位论文].湖南:中南大学, 2008, 27-43
[21] Altfillisch M D, Cooke B R, Toprac A A. An Investigation of Welded Open-web Expanded Beams. Welding Research Supplement. 1957, 22(22): 77-88
[22] Kolosowski J. Stresses and deflections in castellated beams. The Structural Engineer. 1964, 42(42): 19-24
[23]陈录如.蜂窝梁的简化计算与试验研究.工业建筑, 1985, 5(5): 31-38
[24] Faltus F. Berechnung von Wabentragern Acier, 1966, 5(5): 245-248
[25] Mandle J A, Brenman P J. Stress Distribution of Castellated Beams. ASCE Struct Div.97, 1971, 97(7) : 47-67
[26] Srimani S L, Das P K. Finite element analysis of castellated beams. Computers & Structures, 1978, 9(2): 169-174
[27] Zaarour W, Redwood R. Web Buckling in Thin Webbed Castellated Beams. Journal of Structural Engineering, 1996, 122(8): 860-866
[28] Redwood R, Demirdjian S. Castellated Beam Web Buckling in Shear. Journal of Structural Engineering, 1998, 124(10): 1202-1207
[29] Mohebkhah A. The Moment-gradient Factor in Iateral-torsional Buckling on Inelastic Castellated Beams. Journal of Constructional Steel Research, 2004, 60(10): 1481-1494
[30] Mohebkhah A, Showkati H. Bracing requirements for Inelastic Castellated Beams. Journal of Constructional Steel Research, 2005, 61(10): 1373-1386
[31] Zirakian T, Showkati H. Distortional buckling of castellated beams. Journal of Constructional Steel Research, 2006, 62(9): 863–871
[32]陈月明,谢贝琳.蜂窝梁的非线性分析.哈尔滨建筑大学学报, 1997, 30(4): 30-34
[33]何一民,李鹏鸿,于力.蜂窝梁挠度的实用计算方法.工业建筑, 1994, 8(8): 9-15
[34]白凤军,马克俭.蜂窝梁的静力分析.贵州工业大学学报, 2002, 31(6): 32-35
[35]吴迪,武岳.圆孔蜂窝梁的力学性能.建筑科学与工程学报, 2007, 24(1):47-51
[36]武岳,吴迪.六边形孔蜂窝梁力学性能与计算方法.哈尔滨工业大学学报, 2009, 41(2): 5-8
[37]邹锦华,魏德敏,苏益生.蜂窝梁的简化计算及其试验对比.华南理工大学学报, 2005, 33(1): 47-51
[38]苏益生,王良才.圆孔蜂窝梁及其强度计算.广西大学学报(自然科学报), 1993, 18(3): 63-69
[39]胡飞鹏,姚维盛,苏益生.圆孔蜂窝钢梁补强分析.广西大学学报, 2007, 32(z2): 285-287
[40]苏益生,圆形孔与多边形孔蜂窝钢梁的试验分析.广西大学学报, 2003, 28(1): 5-9
[41]郎婷,赵滇生.蜂窝钢梁的强度和刚度研究.浙江工业大学学报, 2005, 33(5): 538-543
[42]张益凡.蜂窝梁的整体和局部稳定分析: [中南大学硕士学位论文].湖南:中南大学, 2008, 1-3
[43]周朝阳,罗鹏.修圆矩形孔蜂窝梁的成孔方法及刚度计算.铁道建筑技术, 2008, 3(3): 72-77
[44]周朝阳,周云峰.蜂窝梁等效抗弯刚度的确定方法.建筑科学与工程学报, 2008, 25(1): 102-115
[45]周朝阳,刘纯洁.蜂窝梁弯曲变形的实用算法.铁道科学与工程学报, 2007, 4(1): 72-76
[46]周朝阳,郑坤龙,李明.成排侧开圆孔受弯构件的应力简化和刚度等效.中南大学学报, 2005, 36(6): 1089-1093
[47]周朝阳,刘澍,欧阳珠子.平行圆管空心板双向抗弯刚度的确定.计算力学学报, 2008, 25(4): 517-520
[48]王森军,郑懿,杨俊杰,邹传仁.蜂窝梁的挠度影响因素分析.钢结构, 2007, 22(8): 24-26
[49]杨茀康,李家宝.结构力学.第四版.北京:高等教育出版社, 1998: 120
[50]邹锦华.圆孔蜂窝梁受力性能试验研究: [广西大学硕士学位论文].广西:广西大学, 2007, 36-40
[51]王新敏. ANSYS工程结构数值分析.北京:人民交通出版社, 2007: 410-411
[52]李黎明. ANSYS有限元分析使用教程.北京:清华大学出版社, 2005:1
[53]邢静忠,李军. ANSYS的建模方法和网格划分.中国水运(学术版), 2006, 06(09): 116-118
[54]杨坛,孙元习,廖良平.基于ANSYS的圆孔蜂窝钢梁有限元分析.广西大学学报, 2006, 31(4): 336-339
[55]贾连光,徐晓霞,康小柱.蜂窝梁抗弯承载力的有限元分析.沈阳建筑大学学报(自然科学版), 2005, 21(3): 196-199
[56] Netherco D A, Chesson E. Lateral Instability of Castellated Beams, Engineering Journal, AISC, 1974, 3(3): 73-79
[57]曹伟良,刘维亚.简支圆孔蜂窝梁挠度分析.钢结构, 2006, 21(6): 25-32
[58]王笑峰,顾敏.异形截面连续开孔构件刚度等效分析.建筑钢结构进展, 2008, 10(2): 31-35
[59]杨建军,金灵芝,何露衡.简支圆孔蜂窝梁受力性能分析.甘肃科技, 2008, 24(7): 116-119
[60] EI-Sawy K M, Sweedan A M, Martini M I. Major-axis elastic buckling of axially loaded castellated steel columns. Thin-Walled Structures, 2009, 47(47): 1295-1304
[61] Smoke R P, Dinehart D W, Gross S P. Seismic Performance of Connections for Cellular Beams in Steel Moment Frames. Structures Congress, 2010, 967-978
[62]杨永华,陈以一.连续开孔梁的抗弯刚度和挠度的等效计算.结构工程师, 2006, 22(3): 33-35
[63]陈绍蕃.钢结构设计原理.第三版.北京:科学出版社, 2005: 25-223
[64]王新敏. ANSYS工程结构数值分析.北京:人民交通出版社, 2007: 410-411
[2]罗晓霖.蜂窝梁的整体稳定性能分析: [同济大学硕士学位论文].上海:同济大学, 2005, 1-15
[3]刘文如,朱聘儒,张培卿.蜂窝梁檩条的试验研究.哈尔滨建筑工程学院学报, 1993, 26(1): 101-105
[4] Estrada H, Jimenez J J, Aguiniga F. Cost Analysis in the Design of Open-Web Castellated Beams, AEI, 2006, 15(10): 1-10
[5] Knowles P R. Castellated beams. London: Proceedings of the Institution of Civil Engineers, 1991, 521-536
[6]倪富生,胡泰祥,胡嗣元等.蜂窝梁的应力分布及设计计算探讨.工业建筑, 1984, 8(8): 27-35
[7]郑坤龙.变高度工字截面圆孔蜂窝梁的挠度计算: [中南大学硕士学位论文].湖南:中南大学, 2007, 1-34
[8]刘鑫.考虑孔况影响的蜂窝梁设计计算研究: [中南大学硕士学位论文].湖南:中南大学, 2006, 1-25
[9]李霞.卧式似椭圆孔蜂窝梁的制作与设计计算方法: [中南大学硕士学位论文].湖南:中南大学, 2007, 1-24
[10]周丽.圆孔蜂窝拱形曲梁弹性弯扭屈曲分析: [湖南大学硕士学位论文].湖南:湖南大学, 2010, 3-8
[11]张兴杰.蜂窝梁的抗弯刚度分析和挠度计算: [同济大学硕士学位论文].上海:同济大学, 2006, 1-61
[12]苏益生.圆形孔蜂窝梁简化计算与试验的对比分析.红水河, 2002, 22(2): 46-57
[13]杨坛.基于ANSYS的圆孔蜂窝钢梁承载力研究: [广西大学硕士学位论文].广西:广西大学, 2007, 7-71
[14]苏益生.圆孔蜂窝梁验算截面的确定及梁桥高度取值分析.红水河, 1994, 13(2): 39-43
[15]包头钢铁设计研究总院,中国钢结构协会房屋建筑钢结构协会.钢结构设计与计算.第2版.北京:机械工业出版社, 2006, 214-221
[16] Srimani S L. Development of Design load Table for Castellated Beams. Indian Journal of Technology, 1980, 18(12): 494-497
[17]渡边邦夫,大泽茂树,内藤龙夫等著.钢结构设计与施工.周耀坤.北京:中国建筑工业出版社, 2000, 1-100
[18]汤庆轩,侯兆欣,吴明超.简支蜂窝梁整体稳定的研究承载力有限元分析.钢结构, 2005, 20(4): 32-35
[19]罗烈,罗晓霖.蜂窝梁设计规范的比较研究.建筑钢结构进展, 2005, 7(2): 43-47
[20]罗鹏.孔角修圆蜂窝梁的弹性分析与设计: [中南大学硕士学位论文].湖南:中南大学, 2008, 27-43
[21] Altfillisch M D, Cooke B R, Toprac A A. An Investigation of Welded Open-web Expanded Beams. Welding Research Supplement. 1957, 22(22): 77-88
[22] Kolosowski J. Stresses and deflections in castellated beams. The Structural Engineer. 1964, 42(42): 19-24
[23]陈录如.蜂窝梁的简化计算与试验研究.工业建筑, 1985, 5(5): 31-38
[24] Faltus F. Berechnung von Wabentragern Acier, 1966, 5(5): 245-248
[25] Mandle J A, Brenman P J. Stress Distribution of Castellated Beams. ASCE Struct Div.97, 1971, 97(7) : 47-67
[26] Srimani S L, Das P K. Finite element analysis of castellated beams. Computers & Structures, 1978, 9(2): 169-174
[27] Zaarour W, Redwood R. Web Buckling in Thin Webbed Castellated Beams. Journal of Structural Engineering, 1996, 122(8): 860-866
[28] Redwood R, Demirdjian S. Castellated Beam Web Buckling in Shear. Journal of Structural Engineering, 1998, 124(10): 1202-1207
[29] Mohebkhah A. The Moment-gradient Factor in Iateral-torsional Buckling on Inelastic Castellated Beams. Journal of Constructional Steel Research, 2004, 60(10): 1481-1494
[30] Mohebkhah A, Showkati H. Bracing requirements for Inelastic Castellated Beams. Journal of Constructional Steel Research, 2005, 61(10): 1373-1386
[31] Zirakian T, Showkati H. Distortional buckling of castellated beams. Journal of Constructional Steel Research, 2006, 62(9): 863–871
[32]陈月明,谢贝琳.蜂窝梁的非线性分析.哈尔滨建筑大学学报, 1997, 30(4): 30-34
[33]何一民,李鹏鸿,于力.蜂窝梁挠度的实用计算方法.工业建筑, 1994, 8(8): 9-15
[34]白凤军,马克俭.蜂窝梁的静力分析.贵州工业大学学报, 2002, 31(6): 32-35
[35]吴迪,武岳.圆孔蜂窝梁的力学性能.建筑科学与工程学报, 2007, 24(1):47-51
[36]武岳,吴迪.六边形孔蜂窝梁力学性能与计算方法.哈尔滨工业大学学报, 2009, 41(2): 5-8
[37]邹锦华,魏德敏,苏益生.蜂窝梁的简化计算及其试验对比.华南理工大学学报, 2005, 33(1): 47-51
[38]苏益生,王良才.圆孔蜂窝梁及其强度计算.广西大学学报(自然科学报), 1993, 18(3): 63-69
[39]胡飞鹏,姚维盛,苏益生.圆孔蜂窝钢梁补强分析.广西大学学报, 2007, 32(z2): 285-287
[40]苏益生,圆形孔与多边形孔蜂窝钢梁的试验分析.广西大学学报, 2003, 28(1): 5-9
[41]郎婷,赵滇生.蜂窝钢梁的强度和刚度研究.浙江工业大学学报, 2005, 33(5): 538-543
[42]张益凡.蜂窝梁的整体和局部稳定分析: [中南大学硕士学位论文].湖南:中南大学, 2008, 1-3
[43]周朝阳,罗鹏.修圆矩形孔蜂窝梁的成孔方法及刚度计算.铁道建筑技术, 2008, 3(3): 72-77
[44]周朝阳,周云峰.蜂窝梁等效抗弯刚度的确定方法.建筑科学与工程学报, 2008, 25(1): 102-115
[45]周朝阳,刘纯洁.蜂窝梁弯曲变形的实用算法.铁道科学与工程学报, 2007, 4(1): 72-76
[46]周朝阳,郑坤龙,李明.成排侧开圆孔受弯构件的应力简化和刚度等效.中南大学学报, 2005, 36(6): 1089-1093
[47]周朝阳,刘澍,欧阳珠子.平行圆管空心板双向抗弯刚度的确定.计算力学学报, 2008, 25(4): 517-520
[48]王森军,郑懿,杨俊杰,邹传仁.蜂窝梁的挠度影响因素分析.钢结构, 2007, 22(8): 24-26
[49]杨茀康,李家宝.结构力学.第四版.北京:高等教育出版社, 1998: 120
[50]邹锦华.圆孔蜂窝梁受力性能试验研究: [广西大学硕士学位论文].广西:广西大学, 2007, 36-40
[51]王新敏. ANSYS工程结构数值分析.北京:人民交通出版社, 2007: 410-411
[52]李黎明. ANSYS有限元分析使用教程.北京:清华大学出版社, 2005:1
[53]邢静忠,李军. ANSYS的建模方法和网格划分.中国水运(学术版), 2006, 06(09): 116-118
[54]杨坛,孙元习,廖良平.基于ANSYS的圆孔蜂窝钢梁有限元分析.广西大学学报, 2006, 31(4): 336-339
[55]贾连光,徐晓霞,康小柱.蜂窝梁抗弯承载力的有限元分析.沈阳建筑大学学报(自然科学版), 2005, 21(3): 196-199
[56] Netherco D A, Chesson E. Lateral Instability of Castellated Beams, Engineering Journal, AISC, 1974, 3(3): 73-79
[57]曹伟良,刘维亚.简支圆孔蜂窝梁挠度分析.钢结构, 2006, 21(6): 25-32
[58]王笑峰,顾敏.异形截面连续开孔构件刚度等效分析.建筑钢结构进展, 2008, 10(2): 31-35
[59]杨建军,金灵芝,何露衡.简支圆孔蜂窝梁受力性能分析.甘肃科技, 2008, 24(7): 116-119
[60] EI-Sawy K M, Sweedan A M, Martini M I. Major-axis elastic buckling of axially loaded castellated steel columns. Thin-Walled Structures, 2009, 47(47): 1295-1304
[61] Smoke R P, Dinehart D W, Gross S P. Seismic Performance of Connections for Cellular Beams in Steel Moment Frames. Structures Congress, 2010, 967-978
[62]杨永华,陈以一.连续开孔梁的抗弯刚度和挠度的等效计算.结构工程师, 2006, 22(3): 33-35
[63]陈绍蕃.钢结构设计原理.第三版.北京:科学出版社, 2005: 25-223
[64]王新敏. ANSYS工程结构数值分析.北京:人民交通出版社, 2007: 410-411