圆孔蜂窝拱形曲梁弹性弯扭屈曲分析
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摘要
圆孔蜂窝拱形曲梁有着自重轻、承载力高、经济美观等特点,近年来在实际工程中应用越来越广泛,然而作为一种新型构件,其受力性能较一般构件的受力性能更为复杂。其稳定问题包括平面内的弯曲屈曲和平面外的弯扭屈曲问题,但弯扭屈曲的临界荷载往往低于弯曲屈曲的临界荷载,若不能提供足够的侧向支撑,往往会先发生弯扭屈曲。因此本文的研究重点为圆孔蜂窝拱形曲梁的弹性弯扭屈曲。
本文主要依靠的分析手段是运用大型有限元分析软件ANSYS进行有限元分析。由于截面特性以及开孔率对梁的弯扭屈曲影响已经研究比较透彻,本文主要考虑参数为曲率,以弧长一定,不同圆心角来实现曲率的变化。
本文先对已有的在均布径向荷载下两端铰接实腹拱形曲梁的弯扭屈曲临界轴力计算公式和在两端大小相等方向相反的弯矩作用下简支实腹拱形曲梁的弯扭屈曲临界弯矩计算公式分别和圆孔蜂窝直梁腹板等效刚度公式进行组合,但由于腹板等效刚度未考虑曲率的影响,因此通过有限元分析,分析了曲率对弯扭屈曲的影响,将有限元结果与组合公式计算值进行比较,并将两者的比值进行回归分析,拟合出修正系数的计算公式,对组合公式加以修正,从而得出以上两种特殊荷载下的圆孔蜂窝拱形曲梁弯扭屈曲临界内力的计算公式。
圆孔蜂窝拱形曲梁的内力情况与压弯构件的受力情况相似,本文对其发生弯扭屈曲时的最大轴力和最大弯矩分别与已经给出两种特殊荷载下得出的弯扭屈曲临界轴力和临界弯矩的比值进行压弯相关分析。由于一般荷载下曲梁的平衡微分方程没有解析解,本文根据压弯相关分析的结果进行回归分析,得出圆孔蜂窝拱形曲梁在一般荷载下弯扭屈曲的内力判定公式。
The circular hole castellated vaulted curved beams have the advantages of light weight, high bearing capacity, economy, beauty and so on, so they are have been used in more and more practical engineering in resent years. However, as a kind of new-type members, the mechanical behavior of the circular hole castellated vaulted curved beams is more complicated than the common members. The stability problem includes flexural buckling and flexural-torsional buckling, but the critical load about the flexural-torsional buckling is usually lower than that about flexural buckling, so if there is not enough lateral bracing, the flexural-torsional buckling will occur first. Therefore, the research emphases of this paper is elastic flexural-torsional buckling of the circular hole castellated vaulted curved beams.
The main analysis method in this paper is the finite element analysis by ANSYS. For the effects of the sectional characteristic and the open porosity to the flexural-torsional buckling have been researched deeply, the main considered parameter in this paper is curvature, and it is realized by fixing the arc length and changing the central angle.
Firstly, this paper combines the formula of the critical axial force about the flexural-torsional buckling occurred in the solid-web vaulted curved beams under the action of the uniform radial load and the formula of the critical moment about the same beams under the action of the same end bending moment with the web equivalent stiffness formula in circular hole castellated straight beams separately. For the web equivalent stiffness formula didn't considered the effect of the curvature, this paper analyzed the effect of the curvature to the flexural-torsional buckling by finite element analysis, compared the finite element results with the result of the combinatorial formula, made regression analyze on the ratio and fitted the formula of the correction factor to the combined formula. Finally, the formula of the critical internal force under the action of the two special loads of the circular hole castellated vaulted curved beams.
The internal force of the circular hole castellated vaulted curved beams is similar to that of the compression-bending member, and therefore, this paper made compression-bending correlation analyze on the ratio of the maximum axial force with the critical axial force under the action of the uniform radial load and the maximum moment with the critical moment under the action of the same end bending moment. Because there isn't analytical solution about flexural-torsional buckling of the curved beams under the action of the common load, this paper summarized the internal force judgement formula about the flexural-torsional buckling based on the result of the compression-bending regression analyze.
本文主要依靠的分析手段是运用大型有限元分析软件ANSYS进行有限元分析。由于截面特性以及开孔率对梁的弯扭屈曲影响已经研究比较透彻,本文主要考虑参数为曲率,以弧长一定,不同圆心角来实现曲率的变化。
本文先对已有的在均布径向荷载下两端铰接实腹拱形曲梁的弯扭屈曲临界轴力计算公式和在两端大小相等方向相反的弯矩作用下简支实腹拱形曲梁的弯扭屈曲临界弯矩计算公式分别和圆孔蜂窝直梁腹板等效刚度公式进行组合,但由于腹板等效刚度未考虑曲率的影响,因此通过有限元分析,分析了曲率对弯扭屈曲的影响,将有限元结果与组合公式计算值进行比较,并将两者的比值进行回归分析,拟合出修正系数的计算公式,对组合公式加以修正,从而得出以上两种特殊荷载下的圆孔蜂窝拱形曲梁弯扭屈曲临界内力的计算公式。
圆孔蜂窝拱形曲梁的内力情况与压弯构件的受力情况相似,本文对其发生弯扭屈曲时的最大轴力和最大弯矩分别与已经给出两种特殊荷载下得出的弯扭屈曲临界轴力和临界弯矩的比值进行压弯相关分析。由于一般荷载下曲梁的平衡微分方程没有解析解,本文根据压弯相关分析的结果进行回归分析,得出圆孔蜂窝拱形曲梁在一般荷载下弯扭屈曲的内力判定公式。
The circular hole castellated vaulted curved beams have the advantages of light weight, high bearing capacity, economy, beauty and so on, so they are have been used in more and more practical engineering in resent years. However, as a kind of new-type members, the mechanical behavior of the circular hole castellated vaulted curved beams is more complicated than the common members. The stability problem includes flexural buckling and flexural-torsional buckling, but the critical load about the flexural-torsional buckling is usually lower than that about flexural buckling, so if there is not enough lateral bracing, the flexural-torsional buckling will occur first. Therefore, the research emphases of this paper is elastic flexural-torsional buckling of the circular hole castellated vaulted curved beams.
The main analysis method in this paper is the finite element analysis by ANSYS. For the effects of the sectional characteristic and the open porosity to the flexural-torsional buckling have been researched deeply, the main considered parameter in this paper is curvature, and it is realized by fixing the arc length and changing the central angle.
Firstly, this paper combines the formula of the critical axial force about the flexural-torsional buckling occurred in the solid-web vaulted curved beams under the action of the uniform radial load and the formula of the critical moment about the same beams under the action of the same end bending moment with the web equivalent stiffness formula in circular hole castellated straight beams separately. For the web equivalent stiffness formula didn't considered the effect of the curvature, this paper analyzed the effect of the curvature to the flexural-torsional buckling by finite element analysis, compared the finite element results with the result of the combinatorial formula, made regression analyze on the ratio and fitted the formula of the correction factor to the combined formula. Finally, the formula of the critical internal force under the action of the two special loads of the circular hole castellated vaulted curved beams.
The internal force of the circular hole castellated vaulted curved beams is similar to that of the compression-bending member, and therefore, this paper made compression-bending correlation analyze on the ratio of the maximum axial force with the critical axial force under the action of the uniform radial load and the maximum moment with the critical moment under the action of the same end bending moment. Because there isn't analytical solution about flexural-torsional buckling of the curved beams under the action of the common load, this paper summarized the internal force judgement formula about the flexural-torsional buckling based on the result of the compression-bending regression analyze.
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)：3-4
[2]陈绍蕃.钢结构设计原理.第三版.北京：科学出版社,2005,25-223
[3]杨葬康,李家宝.结构力学.第四版.北京：高等教育出版社,1998,63
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[5]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
[6]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
[7]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
[8]黄李骥.腹板开洞工形截面拱的稳定性能及设计方法研究：[清华大学博士论文].北京：清华大学,2005,10-12
[9]刘振华,楼听,孙绍霞.基于ANSYS的圆孔蜂窝拱形曲梁静力有限元分析.见：第十三届全国工程建设计算机应用学术会议论文集.广东佛山：中国土木工程学会,2006,177-181
[10]许钧陶,童根树.任意开口薄壁截面圆弧曲梁弯扭精确分析.建筑结构学报,1997,18(3)：22-28
[11]S.P.铁摩辛柯,J.M.盖莱.弹性稳定理论.张福范.第二版.北京：科学出版社,1965,297-338
[12]T. Usami, S.Y. Koh., Large displacement theory of thin-walled curved members and its application to lateral-torsional buckling analysis of circular arches, International Journal of Solids and Structures,1980,16(1):71-95
[13]Yoo.C.H, Flexural-Torsional Stability of Curved Beams. J.E.M., ASCE,1982, 108(6):1351-1369
[14]S. Rajasekaran, E. Ramm, Discussion of'Flexural-Torsional Stability of Curved Beams'by Chai Hong Yoo, Journal of Structural Engineering, ASCE,1984, 110(1):144-148
[15]Yeong-Bin Yang, Shyh-Rong Kuo. Static Stability of Curved Thin-Walled Beams. Journal of Structural Engineering, ASCE,1986,112(8):821-841
[16]Yeong-Bin Yang, Shyh-Rong Kuo. Effect of Curvature on Stability of Curved Beams. Journal of Structural Engineering, ASCE,1987,113(6):1185-1202
[17]Nicholas S. Trahair, John P. Papangelis. Flexural-Torsional Buckling of Monosymmetric Arches. Journal of Structural Engineering, ASCE,1987, 113(10):2271-2288
[18]John P. Papangelis, Nicholas S. Trahair. Flexural-Torsional Buckling Tests on Arches. Journal of Structural Engineering, ASCE,1987,113(7):1433-1443
[19]Kang,Y.J., Yoo,C.H., Thin walled curved beams:I:Formulation of Nonlinear Equations. Journal of Structural Engineering, ASCE,1994,120(10):2072-2101
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[21]Yoo,C.H., Kang,Y.J., Davidson J.S., Buckling Analysis of Curved Beams by Finite-Element Discretization. Journal of Engineering Mechanics, ASCE, 1996,122(8):762-770
[22]李国豪.大曲率薄壁箱梁的扭转和弯曲.土木工程学报,1987,20(1)：65-75
[23]段炼.曲梁弯扭屈曲分析.工程力学,1989,6(3)：41-54
[24]夏淦.变曲率曲梁挠曲扭转分析.土木工程学报,1991,24(2)：68-74
[25]王金明,顾海涛.Ⅰ型截面薄壁圆弧曲梁的稳定性分析.哈尔滨工程大学学报,2000,21(6)：57-63
[26]李琰,辛克贵.薄壁曲梁的横向弯曲稳定分析.工程力学,2005,22(1)：69-74
[27]杨永华.弹性开口薄壁截面圆弧钢拱的稳定承载力研究：[同济大学博士论文].上海：同济大学,2006：5-96
[28]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
[29]Umesh C. Pattanayak, Eugene Jr. Chesson. Lateral Instability of Castellated Beams. Engineering Journal, AISC,1974,11(3):73-79
[30]Sri.S.L. Srimani, P.K.Das. Finite element analysis of castellated beams. Computers & Structures,1978,9(2):169-174
[31]Richard Redwood, Sevak Demirdjian. Castellated Beam Web Buckling in Shear. Journal of Structural Engineering,1998,124(10):1202-1207
[32]Amin Mohebkhah. The Moment-gradient Factor in Iateral-torsional Buckling on Inelastic Castellated Beams. Journal of Constructional Steel Research,2004, 60(10):1481-1494
[33]Amin Mohebkhah, Hossein Showkati. Bracing requirements for Inelastic Castellated Beams. Journal of Constructional Steel Research,2005,61(10): 1373-1386
[34]Tadeh Zirakian, Hossein Showkati. Distortional buckling of castellated beams. Journal of Constructional Steel Research,2006,62(9):863-871
[35]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
[36]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
[37]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
[38]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
[39]张益凡.蜂窝梁的整体和局部稳定分析：[中南大学硕士论文].湖南：中南大学,2008,7
[40]罗鹏.孔角修圆蜂窝梁的弹性分析与设计：[中南大学硕士论文].湖南：中南大学,2008,1
[41]杨永华,陈以一.双轴对称截面薄壁圆弧曲梁的弹性稳定平衡方程.力学季刊,2006,27(3)：387-396
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[43]王新敏ANSYS工程结构数值分析.北京：人民交通出版社,2007,410-411
[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]李黎明ANSYS有限元分析使用教程.北京：清华大学出版社,2005,1
[46]郭运瑞,谭德俊.概率论与数理统计.北京：人民出版社,2006,226-240
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[2]陈绍蕃.钢结构设计原理.第三版.北京：科学出版社,2005,25-223
[3]杨葬康,李家宝.结构力学.第四版.北京：高等教育出版社,1998,63
[4]童根树,许强.薄壁曲梁线性和非线性分析理论.北京：科学出版社,2004,2-4
[5]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
[6]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
[7]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
[8]黄李骥.腹板开洞工形截面拱的稳定性能及设计方法研究：[清华大学博士论文].北京：清华大学,2005,10-12
[9]刘振华,楼听,孙绍霞.基于ANSYS的圆孔蜂窝拱形曲梁静力有限元分析.见：第十三届全国工程建设计算机应用学术会议论文集.广东佛山：中国土木工程学会,2006,177-181
[10]许钧陶,童根树.任意开口薄壁截面圆弧曲梁弯扭精确分析.建筑结构学报,1997,18(3)：22-28
[11]S.P.铁摩辛柯,J.M.盖莱.弹性稳定理论.张福范.第二版.北京：科学出版社,1965,297-338
[12]T. Usami, S.Y. Koh., Large displacement theory of thin-walled curved members and its application to lateral-torsional buckling analysis of circular arches, International Journal of Solids and Structures,1980,16(1):71-95
[13]Yoo.C.H, Flexural-Torsional Stability of Curved Beams. J.E.M., ASCE,1982, 108(6):1351-1369
[14]S. Rajasekaran, E. Ramm, Discussion of'Flexural-Torsional Stability of Curved Beams'by Chai Hong Yoo, Journal of Structural Engineering, ASCE,1984, 110(1):144-148
[15]Yeong-Bin Yang, Shyh-Rong Kuo. Static Stability of Curved Thin-Walled Beams. Journal of Structural Engineering, ASCE,1986,112(8):821-841
[16]Yeong-Bin Yang, Shyh-Rong Kuo. Effect of Curvature on Stability of Curved Beams. Journal of Structural Engineering, ASCE,1987,113(6):1185-1202
[17]Nicholas S. Trahair, John P. Papangelis. Flexural-Torsional Buckling of Monosymmetric Arches. Journal of Structural Engineering, ASCE,1987, 113(10):2271-2288
[18]John P. Papangelis, Nicholas S. Trahair. Flexural-Torsional Buckling Tests on Arches. Journal of Structural Engineering, ASCE,1987,113(7):1433-1443
[19]Kang,Y.J., Yoo,C.H., Thin walled curved beams:I:Formulation of Nonlinear Equations. Journal of Structural Engineering, ASCE,1994,120(10):2072-2101
[20]Kang,Y.J., Yoo,C.H., Thin walled curved beams:II:Analytical solution for buckling of arches. Journal of Structural Engineering, ASCE,1994,120(10): 2102-2125
[21]Yoo,C.H., Kang,Y.J., Davidson J.S., Buckling Analysis of Curved Beams by Finite-Element Discretization. Journal of Engineering Mechanics, ASCE, 1996,122(8):762-770
[22]李国豪.大曲率薄壁箱梁的扭转和弯曲.土木工程学报,1987,20(1)：65-75
[23]段炼.曲梁弯扭屈曲分析.工程力学,1989,6(3)：41-54
[24]夏淦.变曲率曲梁挠曲扭转分析.土木工程学报,1991,24(2)：68-74
[25]王金明,顾海涛.Ⅰ型截面薄壁圆弧曲梁的稳定性分析.哈尔滨工程大学学报,2000,21(6)：57-63
[26]李琰,辛克贵.薄壁曲梁的横向弯曲稳定分析.工程力学,2005,22(1)：69-74
[27]杨永华.弹性开口薄壁截面圆弧钢拱的稳定承载力研究：[同济大学博士论文].上海：同济大学,2006：5-96
[28]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
[29]Umesh C. Pattanayak, Eugene Jr. Chesson. Lateral Instability of Castellated Beams. Engineering Journal, AISC,1974,11(3):73-79
[30]Sri.S.L. Srimani, P.K.Das. Finite element analysis of castellated beams. Computers & Structures,1978,9(2):169-174
[31]Richard Redwood, Sevak Demirdjian. Castellated Beam Web Buckling in Shear. Journal of Structural Engineering,1998,124(10):1202-1207
[32]Amin Mohebkhah. The Moment-gradient Factor in Iateral-torsional Buckling on Inelastic Castellated Beams. Journal of Constructional Steel Research,2004, 60(10):1481-1494
[33]Amin Mohebkhah, Hossein Showkati. Bracing requirements for Inelastic Castellated Beams. Journal of Constructional Steel Research,2005,61(10): 1373-1386
[34]Tadeh Zirakian, Hossein Showkati. Distortional buckling of castellated beams. Journal of Constructional Steel Research,2006,62(9):863-871
[35]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
[36]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
[37]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
[38]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
[39]张益凡.蜂窝梁的整体和局部稳定分析：[中南大学硕士论文].湖南：中南大学,2008,7
[40]罗鹏.孔角修圆蜂窝梁的弹性分析与设计：[中南大学硕士论文].湖南：中南大学,2008,1
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