不同孔况下蜂窝梁的整体稳定分析
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摘要
蜂窝梁是工字钢或热轧H型钢腹板上按一定的线形进行经切割、组装、焊接而成的空腹梁。蜂窝梁具有自重轻、承载力高、经济、美观、方便等优点,它的截面高度为同原型钢的1.3～1.6倍,因而较大地提高了型钢梁的抗弯强度和刚度。它比实腹梁可节约钢材25%～50%,节省油漆和安装运输费用15%～34.6%。蜂窝梁腹板的孔洞既美观又便于安设管道和电线,因此蜂窝梁在工程实际应用中具有很大的实用价值,正得到越来越广泛的应用。
钢梁的稳定性是决定其承载力的一个重要因素。钢梁的稳定性包括平面内的弯曲失稳和平面外的弯扭失稳。若不能提供足够的侧向支撑,往往会先发生平面外的弯扭屈曲。蜂窝梁由于腹板开孔,相对等高度实腹梁其侧向刚度被削弱,在荷载作用下更容易发生整体失稳或局部失稳的情况。
本文以能量法为基础,理论分析为补充,将相同孔高的六边形孔和圆孔蜂窝梁的整体稳定进行分析研究对比。研究蜂窝梁在两端等弯矩、横向集中荷载和横向均布荷载三种特殊荷载作用下的弹性弯扭屈曲。同时通过体积和惯性矩相等原则,推导出蜂窝梁弯扭屈曲分析的相关等效刚度。
本文通过有限元分析软件ANSYS进行实例计算后与公式的计算结果进行对比分析,以验证理论计算的准确性,并分析出误差产生的原因。本文还拟合了圆孔蜂窝梁转化为六边形蜂窝梁临界弯矩的转化等效系数的回归公式。为我国钢结构设计规范制定蜂窝梁的整体稳定公式提供了参考,同时对实际工程也有一定的价值。
Castellated beams are steel I-beams or Hot-rolled H-beams with a certain line on the web by cutting, assembling and welding,which have holes on the web. Castellated beams have the advantages of light weight,high bearing capacity, economy, beauty and so on, because they are with the original height of cross section of 1.3 to 1.6 times the beam, greatly improved the steel beams bending strength and stiffness. They can save more than steel solid web beam of 25% to 50%, save the paint and installation of transpotation costs 15% to 34.6%. Holes in the castellated beam web is beautiful and easy to install pipes and wires,therefore,practical applications in engineering castellated beam has great practical value, castellated beams are being more widely used.
The stability of steel beams to determine their carrying capacity is an important factor. The stability of steel beams including the In-plane bending buckling and Outside the plane bending buckling, if it can not provide enough lateral support, often occurs the plane bending buckling. With the web openings, castellated beam is weakened by such a high degree of relative lateral stiffness of solid web beam. Under the loading, castellated beams more likely occur the case of overall instability or local instability.
In this paper, based on energy method, and theoretical analysis will be complemented, comparative the castellated beams with the same opening hole high by hexagon and circle. Analysis the castellated beams with various moments of critical load about flexural-torsional buckling. And by the principle of equal size and moment of inertia castellated beams are derived contortion equivalent stiffness of the relevant. In this paper, the finite element analysis software ANSYS will be used to check the precision of the formula,and analyze the reason of error. Based on the regressive computation of the results of the finite element analysis, the paper offers the design formula about the equivalent conversion coefficient of the circle hole castellated beam changing into the hexagon hole castellated beam. The study of this paper can serve as some reference for the setup of the formula in codes for design of steel structures to accurately calculate the overall stability of castellated beams and for the engineering practice.
钢梁的稳定性是决定其承载力的一个重要因素。钢梁的稳定性包括平面内的弯曲失稳和平面外的弯扭失稳。若不能提供足够的侧向支撑,往往会先发生平面外的弯扭屈曲。蜂窝梁由于腹板开孔,相对等高度实腹梁其侧向刚度被削弱,在荷载作用下更容易发生整体失稳或局部失稳的情况。
本文以能量法为基础,理论分析为补充,将相同孔高的六边形孔和圆孔蜂窝梁的整体稳定进行分析研究对比。研究蜂窝梁在两端等弯矩、横向集中荷载和横向均布荷载三种特殊荷载作用下的弹性弯扭屈曲。同时通过体积和惯性矩相等原则,推导出蜂窝梁弯扭屈曲分析的相关等效刚度。
本文通过有限元分析软件ANSYS进行实例计算后与公式的计算结果进行对比分析,以验证理论计算的准确性,并分析出误差产生的原因。本文还拟合了圆孔蜂窝梁转化为六边形蜂窝梁临界弯矩的转化等效系数的回归公式。为我国钢结构设计规范制定蜂窝梁的整体稳定公式提供了参考,同时对实际工程也有一定的价值。
Castellated beams are steel I-beams or Hot-rolled H-beams with a certain line on the web by cutting, assembling and welding,which have holes on the web. Castellated beams have the advantages of light weight,high bearing capacity, economy, beauty and so on, because they are with the original height of cross section of 1.3 to 1.6 times the beam, greatly improved the steel beams bending strength and stiffness. They can save more than steel solid web beam of 25% to 50%, save the paint and installation of transpotation costs 15% to 34.6%. Holes in the castellated beam web is beautiful and easy to install pipes and wires,therefore,practical applications in engineering castellated beam has great practical value, castellated beams are being more widely used.
The stability of steel beams to determine their carrying capacity is an important factor. The stability of steel beams including the In-plane bending buckling and Outside the plane bending buckling, if it can not provide enough lateral support, often occurs the plane bending buckling. With the web openings, castellated beam is weakened by such a high degree of relative lateral stiffness of solid web beam. Under the loading, castellated beams more likely occur the case of overall instability or local instability.
In this paper, based on energy method, and theoretical analysis will be complemented, comparative the castellated beams with the same opening hole high by hexagon and circle. Analysis the castellated beams with various moments of critical load about flexural-torsional buckling. And by the principle of equal size and moment of inertia castellated beams are derived contortion equivalent stiffness of the relevant. In this paper, the finite element analysis software ANSYS will be used to check the precision of the formula,and analyze the reason of error. Based on the regressive computation of the results of the finite element analysis, the paper offers the design formula about the equivalent conversion coefficient of the circle hole castellated beam changing into the hexagon hole castellated beam. The study of this paper can serve as some reference for the setup of the formula in codes for design of steel structures to accurately calculate the overall stability of castellated beams and for the engineering practice.
引文
[1]陈骥.钢结构稳定理论与设计.第二版.北京:科学出版社, 2001, 314-363
[2]夏志斌,姚谏.钢结构—原理与设计.北京:中国建筑工业出版社, 2004, 238-260
[3]周绪红,郑宏.钢结构稳定.北京:中国建筑工业出版社, 2004, 2-4
[4]杨坛.基于ANSYS的圆孔蜂窝钢梁承载力研究: [广西大学硕士论文].广西:广西大学, 2007: 1
[5]苏益身,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
[6]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].长沙:中南大学, 2008, 1-2
[7]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, 4-27
[8]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): 72-77
[9]谢赐身,胡柏上.钢结构蜂窝梁的制造工艺.安装, 2003, (6), 13-14
[10]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
[11] Pattanayak U C, Chesson E. Lateral instability of castellated beams. Engineering Journal, AISC, 1974, 11(3): 73-79
[12] Sri S, Srimani P K. Finite element analysis of castellated beams. Computers & Structures, 1978, 9(2): 169-174
[13] Walid Z, Richard R. Buckling in Thin Webbed Castellated Beams. Journal of Structural Engineering, 1996, 122: 860-866
[14] Richard R, Sevak D. Castellated Beam Web Buckling in Shear, Journal of Constructional Steel Research, 1998, 124: 1202-1207
[15] Amin M. The Moment-gradient Factor in Iateral-torsional Buckling on Inelastic Castellated Beams. Journal of Constructional Steel Research, 2004, 60(10): 1481-1494
[16] Amin M, Hossein S. Bracing requirements for Inelastic Castellated Beams. Journal of Constructional Steel Research, 2005, 61(10): 1373-1386
[17] Tadeh Z, Hossein S. Distortional buckling of castellated beams. Journal ofConstructional Steel Research, 2006, 62(9): 863–871
[18]苏益声.蜂窝钢梁受力性能分析.红水河, 1994, 13(1), 31-34
[19]徐德新,史英锐,刘华强.支座降低蜂窝形钢梁整体稳定分析和试验.工业建筑, 1994, (11): 32-36
[20]何一民,郝建丽.蜂窝梁及蜂窝压弯杆件的强度计算.工业建筑, 1994, (8): 5-8
[21]汤庆轩,侯兆欣,吴明超.简支蜂窝梁整体稳定承载力有限元分析.钢结构, 2005, 20(4): 32-35
[22]贾连光,张丽,李娜.纯弯曲蜂窝梁弯扭屈曲的有限元分析.沈阳建筑大学学报(自然科学版), 2006, 22(1): 49-52
[23]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
[24]黄文,陈前钢.蜂窝梁弹塑性受力性能分析.重庆大学学报(自然科学版), 2006, 29(4): 87-91
[25]周丽.圆孔蜂窝拱形曲梁弹性弯扭屈曲分析: [湖南大学硕士论文].湖南:湖南大学, 2010: 10
[26] Marian L, Marcin W. Studies of Castellated Stell I-Beams under Loading by Concentrated Forces. Computers & Structures, 1984, 31: 277-315
[27]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].长沙:中南大学, 2006, 48-68
[28]陈绍藩.钢结构稳定设计指南.第二版.北京:中国建筑工业出版社, 2004, 95-98
[29]张磊.考虑横向正应力影响的薄壁构件稳定理论及其应用: [浙江大学硕士学位论文].杭州:浙江大学, 2005, 30-31
[30]王洪范,王立新.蜂窝梁的应用和计算方法.工业建筑, 1994, 8: 3-4
[31]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
[32]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
[33] Amr M I. Elastic lateral stability of I-shaped cellular stell beams. Journal of Constructional Steel Research, 2011, 67, 151-163
[34]崔勇,马飞.纯弯曲蜂窝梁弯扭屈曲的有限元分析.辽宁建材, 2006(5): 49-51
[35]郭耀杰,方山峰.钢结构构件弯扭屈曲问题的计算和分析.建筑结构学报, 1990, 11(3), 38-36
[36]周朝阳,张益凡.纯弯圆孔蜂窝梁的弯扭屈曲分析.见:第五届全国土木工程研究生学术论坛.长沙:中国土木工程学会教育工作委员会出版, 2007: 174-177
[37]周云峰.基于ANSYS的蜂窝梁优化设计的二次开发: [中南大学硕士学位论文].长沙:中南大学, 2008, 28-30
[38]屈飞林.工字型圆孔蜂窝梁整体稳定性分析方法研究.科技创新导报, 2008, 1: 52-53
[39]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
[40]李鹏飞,姚谦峰,郭猛.蜂窝梁弯扭屈曲分析及整体稳定性的计算方法.北京交通大学学报, 2010, 34(4): 60-64
[41] Nethercot D A, Kerdal D. Lateral-torsional buckling of castellated beams. Structural Engineering Joural, 1982, 60B(3): 53-61
[42]王新敏. ANSYS工程结构数值分析.北京:人民交通出版社, 2007, 7-465
[43]周长城,胡仁喜,熊文波. ANSYS11.0基础与典型范例.北京:电子工业出版社, 2007, 4-58
[44]石少卿,汪敏,刘颖芳等.建筑结构有限元分析及ANSYS范例详解.北京:中国建筑工业出版社, 2008 , 12-182
[45]曾金平.数值计算方法.长沙:湖南大学出版社, 2004, 114-218
[46]宇传华. SPSS与统计分析.北京:电子工业出版社, 2007, 204-241
[47]阮桂海. SPSS实用教程.北京:电子工业出版社, 2000, 131-278
[48]苏益身.圆形孔与多边形孔蜂窝钢梁的试验分析.广西大学学报(自然科学报), 2003, 28(1): 5-9
[49]郭耀杰.钢结构稳定设计.武汉:武汉大学出版社, 2003, 70-71
[2]夏志斌,姚谏.钢结构—原理与设计.北京:中国建筑工业出版社, 2004, 238-260
[3]周绪红,郑宏.钢结构稳定.北京:中国建筑工业出版社, 2004, 2-4
[4]杨坛.基于ANSYS的圆孔蜂窝钢梁承载力研究: [广西大学硕士论文].广西:广西大学, 2007: 1
[5]苏益身,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
[6]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].长沙:中南大学, 2008, 1-2
[7]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, 4-27
[8]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): 72-77
[9]谢赐身,胡柏上.钢结构蜂窝梁的制造工艺.安装, 2003, (6), 13-14
[10]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
[11] Pattanayak U C, Chesson E. Lateral instability of castellated beams. Engineering Journal, AISC, 1974, 11(3): 73-79
[12] Sri S, Srimani P K. Finite element analysis of castellated beams. Computers & Structures, 1978, 9(2): 169-174
[13] Walid Z, Richard R. Buckling in Thin Webbed Castellated Beams. Journal of Structural Engineering, 1996, 122: 860-866
[14] Richard R, Sevak D. Castellated Beam Web Buckling in Shear, Journal of Constructional Steel Research, 1998, 124: 1202-1207
[15] Amin M. The Moment-gradient Factor in Iateral-torsional Buckling on Inelastic Castellated Beams. Journal of Constructional Steel Research, 2004, 60(10): 1481-1494
[16] Amin M, Hossein S. Bracing requirements for Inelastic Castellated Beams. Journal of Constructional Steel Research, 2005, 61(10): 1373-1386
[17] Tadeh Z, Hossein S. Distortional buckling of castellated beams. Journal ofConstructional Steel Research, 2006, 62(9): 863–871
[18]苏益声.蜂窝钢梁受力性能分析.红水河, 1994, 13(1), 31-34
[19]徐德新,史英锐,刘华强.支座降低蜂窝形钢梁整体稳定分析和试验.工业建筑, 1994, (11): 32-36
[20]何一民,郝建丽.蜂窝梁及蜂窝压弯杆件的强度计算.工业建筑, 1994, (8): 5-8
[21]汤庆轩,侯兆欣,吴明超.简支蜂窝梁整体稳定承载力有限元分析.钢结构, 2005, 20(4): 32-35
[22]贾连光,张丽,李娜.纯弯曲蜂窝梁弯扭屈曲的有限元分析.沈阳建筑大学学报(自然科学版), 2006, 22(1): 49-52
[23]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
[24]黄文,陈前钢.蜂窝梁弹塑性受力性能分析.重庆大学学报(自然科学版), 2006, 29(4): 87-91
[25]周丽.圆孔蜂窝拱形曲梁弹性弯扭屈曲分析: [湖南大学硕士论文].湖南:湖南大学, 2010: 10
[26] Marian L, Marcin W. Studies of Castellated Stell I-Beams under Loading by Concentrated Forces. Computers & Structures, 1984, 31: 277-315
[27]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].长沙:中南大学, 2006, 48-68
[28]陈绍藩.钢结构稳定设计指南.第二版.北京:中国建筑工业出版社, 2004, 95-98
[29]张磊.考虑横向正应力影响的薄壁构件稳定理论及其应用: [浙江大学硕士学位论文].杭州:浙江大学, 2005, 30-31
[30]王洪范,王立新.蜂窝梁的应用和计算方法.工业建筑, 1994, 8: 3-4
[31]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
[32]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
[33] Amr M I. Elastic lateral stability of I-shaped cellular stell beams. Journal of Constructional Steel Research, 2011, 67, 151-163
[34]崔勇,马飞.纯弯曲蜂窝梁弯扭屈曲的有限元分析.辽宁建材, 2006(5): 49-51
[35]郭耀杰,方山峰.钢结构构件弯扭屈曲问题的计算和分析.建筑结构学报, 1990, 11(3), 38-36
[36]周朝阳,张益凡.纯弯圆孔蜂窝梁的弯扭屈曲分析.见:第五届全国土木工程研究生学术论坛.长沙:中国土木工程学会教育工作委员会出版, 2007: 174-177
[37]周云峰.基于ANSYS的蜂窝梁优化设计的二次开发: [中南大学硕士学位论文].长沙:中南大学, 2008, 28-30
[38]屈飞林.工字型圆孔蜂窝梁整体稳定性分析方法研究.科技创新导报, 2008, 1: 52-53
[39]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
[40]李鹏飞,姚谦峰,郭猛.蜂窝梁弯扭屈曲分析及整体稳定性的计算方法.北京交通大学学报, 2010, 34(4): 60-64
[41] Nethercot D A, Kerdal D. Lateral-torsional buckling of castellated beams. Structural Engineering Joural, 1982, 60B(3): 53-61
[42]王新敏. ANSYS工程结构数值分析.北京:人民交通出版社, 2007, 7-465
[43]周长城,胡仁喜,熊文波. ANSYS11.0基础与典型范例.北京:电子工业出版社, 2007, 4-58
[44]石少卿,汪敏,刘颖芳等.建筑结构有限元分析及ANSYS范例详解.北京:中国建筑工业出版社, 2008 , 12-182
[45]曾金平.数值计算方法.长沙:湖南大学出版社, 2004, 114-218
[46]宇传华. SPSS与统计分析.北京:电子工业出版社, 2007, 204-241
[47]阮桂海. SPSS实用教程.北京:电子工业出版社, 2000, 131-278
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