钢箱梁在弯矩和扭矩联合作用下受力性能研究
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摘要
箱形截面梁由于较其它形式截面具有较好的两个主轴方向抗弯刚度和抗扭刚度,随着钢结构的不断发展,箱形构件制作工艺的完善和日趋成熟,箱形截面构件的应用越来越广,尤其是在多高层建筑中。
本文主要采用有限元分析方法,研究了双轴对称箱形截面钢梁在弯矩和扭矩联合作用下的弹塑性荷载位移特性、强度极限承载力和刚度。本文的分析中考虑了由材料屈服所引起的材料非线性以及由大变形所引起的几何非线性的影响,对箱形截面钢梁在无侧向支撑时在弯矩和扭矩联合作用下的弹塑性荷载位移特性进行了分析,并和有跨中侧向支撑时梁的荷载位移特性进行了对比分析,说明了箱形截面钢梁具有较好的整体稳定性。研究还发现,在弯矩和扭矩联合作用下,由于弯曲和扭转变形所产生的几何非线性使梁跨中转角增大,并会降低扭转刚度。本文在考虑这种增大影响的基础上,提出了梁由于受到弯矩和扭矩联合作用而得到放大的跨中点截面处的二阶转角公式。
本文对箱形截面钢梁在弯矩和扭矩联合作用下的弯扭相关性进行了探讨,并考虑了构件跨度、截面高宽比、高厚比及宽厚比等各因素的影响,在经过大量模型分析计算后,提出了一套基于ANSYS分析平台的对箱形截面钢梁在弯矩和扭矩联合作用下的弹塑性承载力进行分析的流程和方法,得出了箱形截面钢梁在弯矩和扭矩作用下的强度极限承载力计算公式。并指出圆曲线交互方程对本文所研究的箱形截面钢梁而言,有其局限性。
最后,本文对兼承扭矩的箱形截面钢梁的刚度进行了探讨和研究,得出了在刚度控制条件下弯曲和扭转联合作用时梁的承载力计算公式。该公式是对弹性状态下梁受跨中集中荷载时的挠度计算公式进行修订,考虑了受弯构件同时受扭的影响,把扭矩转化成相应的弯矩来计算跨中的挠度值。
本文对箱形截面钢梁在弯矩和扭矩联合作用下的受力性能进行了研究,所得计算公式供规范修订和工程设计参考。
With the continuous development of steel structure and the producing process of component member improving and becoming more mature, steel box girder, due to its good bending stiffness of the two axis directions and torsional stiffness, compared with other forms, is more widely used in application now, especially in the high-rise building.
In this paper, the elastic-plastic load-deformation relationships, ultimate strength and stiffness of steel box girder are investigated by using the finite element method (FEM) under combined bending and torsion. Taking into account the effects of large deformation, material inelasticity and geometric imperfections, the characteristics of load-deformation relationships are analyzed of steel box girder with no lateral supporting, and then compared with that of box girder with mid-point supporting, illustrating that steel box girder has a better overall stability. The study also found that the first-order rotation due to pure torque may be amplified by flexural-torsional buckling effects, which reduce the effective torsional stiffness. Then the amplified elastic twist rotation formula is suggested, taking into the effects.
The study also found that the combined effects of bending moment and torque, due to bending and torsional deformation of the geometric nonlinearity arising in the corner across the beam increased, this increase in considering the impact of this proposed based on the beam as by the combined effects of the bending moment and torque are enlarged cross-section mid-point of the corner office of the second order formula.
The interactions between in-plane bending and torsion are studied, considering the member span, section properties, the thickness of the flange and the web and other factors. A practical user-defined inelastic analysis procedure based on ANSYS program is proposed after analyzing a large number of models, and the ultimate strength formula for the design of steel box girder under combined bending and torsion is proposed. It is found that a commonly quoted circular interaction equation for combined bending and torsion dose not always provide a true lower bound for steel box girder.
Finally, some research and discussion are conducted on the bending stiffness of steel box girder under combined bending and torsion and the carrying capacity formula of steel box girder under the control of stiffness conditions is obtained, which is a revised formula. The purpose of the formula is to calculate the mid-span deflection under concentrated load in elastic state, taking into account the effect of torsion at the same time and making some modification of the torque into appropriate bending moment, then to sum up to the two parts of moment to calculate the deflection of steel box girder.
In this paper, some research on the carrying properties of steel box girder under combined bending and torsion is conducted, and the formulas proposed can be applied in Practical Engineering Design.
本文主要采用有限元分析方法,研究了双轴对称箱形截面钢梁在弯矩和扭矩联合作用下的弹塑性荷载位移特性、强度极限承载力和刚度。本文的分析中考虑了由材料屈服所引起的材料非线性以及由大变形所引起的几何非线性的影响,对箱形截面钢梁在无侧向支撑时在弯矩和扭矩联合作用下的弹塑性荷载位移特性进行了分析,并和有跨中侧向支撑时梁的荷载位移特性进行了对比分析,说明了箱形截面钢梁具有较好的整体稳定性。研究还发现,在弯矩和扭矩联合作用下,由于弯曲和扭转变形所产生的几何非线性使梁跨中转角增大,并会降低扭转刚度。本文在考虑这种增大影响的基础上,提出了梁由于受到弯矩和扭矩联合作用而得到放大的跨中点截面处的二阶转角公式。
本文对箱形截面钢梁在弯矩和扭矩联合作用下的弯扭相关性进行了探讨,并考虑了构件跨度、截面高宽比、高厚比及宽厚比等各因素的影响,在经过大量模型分析计算后,提出了一套基于ANSYS分析平台的对箱形截面钢梁在弯矩和扭矩联合作用下的弹塑性承载力进行分析的流程和方法,得出了箱形截面钢梁在弯矩和扭矩作用下的强度极限承载力计算公式。并指出圆曲线交互方程对本文所研究的箱形截面钢梁而言,有其局限性。
最后,本文对兼承扭矩的箱形截面钢梁的刚度进行了探讨和研究,得出了在刚度控制条件下弯曲和扭转联合作用时梁的承载力计算公式。该公式是对弹性状态下梁受跨中集中荷载时的挠度计算公式进行修订,考虑了受弯构件同时受扭的影响,把扭矩转化成相应的弯矩来计算跨中的挠度值。
本文对箱形截面钢梁在弯矩和扭矩联合作用下的受力性能进行了研究,所得计算公式供规范修订和工程设计参考。
With the continuous development of steel structure and the producing process of component member improving and becoming more mature, steel box girder, due to its good bending stiffness of the two axis directions and torsional stiffness, compared with other forms, is more widely used in application now, especially in the high-rise building.
In this paper, the elastic-plastic load-deformation relationships, ultimate strength and stiffness of steel box girder are investigated by using the finite element method (FEM) under combined bending and torsion. Taking into account the effects of large deformation, material inelasticity and geometric imperfections, the characteristics of load-deformation relationships are analyzed of steel box girder with no lateral supporting, and then compared with that of box girder with mid-point supporting, illustrating that steel box girder has a better overall stability. The study also found that the first-order rotation due to pure torque may be amplified by flexural-torsional buckling effects, which reduce the effective torsional stiffness. Then the amplified elastic twist rotation formula is suggested, taking into the effects.
The study also found that the combined effects of bending moment and torque, due to bending and torsional deformation of the geometric nonlinearity arising in the corner across the beam increased, this increase in considering the impact of this proposed based on the beam as by the combined effects of the bending moment and torque are enlarged cross-section mid-point of the corner office of the second order formula.
The interactions between in-plane bending and torsion are studied, considering the member span, section properties, the thickness of the flange and the web and other factors. A practical user-defined inelastic analysis procedure based on ANSYS program is proposed after analyzing a large number of models, and the ultimate strength formula for the design of steel box girder under combined bending and torsion is proposed. It is found that a commonly quoted circular interaction equation for combined bending and torsion dose not always provide a true lower bound for steel box girder.
Finally, some research and discussion are conducted on the bending stiffness of steel box girder under combined bending and torsion and the carrying capacity formula of steel box girder under the control of stiffness conditions is obtained, which is a revised formula. The purpose of the formula is to calculate the mid-span deflection under concentrated load in elastic state, taking into account the effect of torsion at the same time and making some modification of the torque into appropriate bending moment, then to sum up to the two parts of moment to calculate the deflection of steel box girder.
In this paper, some research on the carrying properties of steel box girder under combined bending and torsion is conducted, and the formulas proposed can be applied in Practical Engineering Design.
引文
[1]范重.国家体育场大跨度结构设计中的新技术.工程力学,2006,23(sup.Ⅱ)：78-84
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[5]Praween Chusilp, Tsutomu Usami. Strength and Ductility of Steel Box Girders under Cyclic Shear. Journal of Structural Engineering, ASCE,2002,128(9): 1130-1138
[6]范重,彭翼,王喆,等.国家体育场主结构扭曲箱形构件设计研究.建筑结构学报,2007,28(2)：97-103,111
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[9]邓娟红,宋一凡,陈至辰.钢箱梁开口加劲肋设计探讨.钢结构,2005,5(20)：29-31
[10]郭金琼,房贞政,郑振.箱形梁设计理论.北京：人民交通出版社,2008,1-10
[11]吕烈武,沈世钊,沈祖炎,等.钢结构构件稳定理论.北京：中国建筑工业出版社,1983,12-20
[12]包世华,周坚.薄壁杆件结构力学.北京：中国建筑工业出版社,2006,91-160
[13]朱俞江.箱形截面梁和梁柱的弹塑性稳定极限承载力分析：[浙江大学硕士学位论文].杭州：浙江大学,2003,1-20
[14]W. Y. Li, L. G. Tham, Y. K. Cheung. Curved box girder bridges. Journal of Structural Engineering, ASCE,1988,114(6):1324-1338
[15]Martti J. M., Paavola J.. Finite element analysis of box girder. Journal of Structural Engineering, ASCE,1980,106(10):1343-1357
[16]潘有昌.单轴对称箱形简支梁的整体稳定性.钢结构研究论文报告选集(第二册),1983：40-57
[17]P. Waldron. Sectorial Properties of Straight Thin-walled Beams. Computers and Structures,1986,24(1):147-156
[18]Lando Mentrasti. Torsional Stress Concentration in Thin-Walled Beams. Journal of Engineering Mechanics, ASCE,1989,115(9):1882-1903
[19]顾强,陈绍番.厚板焊接箱形截面柱残余应力的实验研究.西安冶金建筑学院学报,1992,24(4)：365-369
[20]Yoshitaka Suetake, Masaharu Hirashima. Extended Trigonometric Series Analysis of Box Girders with Diaphragms. Journal of Engineering Mechanics, ASCE,1997,123(4):293-301
[21]鲍永方,黄文彬.矩形箱梁约束扭转理论的分析与比较.工程力学,1997,14(3)： 132-137
[22]Tsutomu Usami, Yi Zheng, Hanbin Ge. Seismic Design Method for Thin-Walled Steel Frame Structure. Journal of Structural Engineering, ASCE,2001, 127(2):137-144
[23]Tore Tryland, Odd S. Hopperstad, et al. Finite-Element Modeling of Beams under Concentrated Loading. Journal of Structural Engineering, ASCE,2001, 127(2):176-185
[24]何保康,周天华.矩形钢管截面b/t、h/t的限值确定.钢结构,2001,16(2)：29-31,38
[25]Fidelis Rutendo Mashiri, Xiao-Ling Zhao, et al. Fatigue Tests and Design of Welded T Connections in Thin Cold-Formed Square Hollow Sections under In-Plane Bending. Journal of Structural Engineering, ASCE,2002, 128(11):1413-1422
[26]Magdi Mohareb M., Istemi F. Ozkan. Plastic Interaction Relationships for Square Hollow Structural Sections:Lower Bound Solution. Journal of Structural Engineering, ASCE,2004,130 (9):1381-1391
[27]范重,范学伟,刘先明.焊接薄壁箱形构件设计方法研究.建筑结构进展,2006,8(3)：34-40
[28]陈华春,舒赣平.具有初始扭转的箱形截面梁的极限抗弯承载力研究.工业建筑(增刊),2009,1685-1693
[29]Yong Lin Pi, N. S. Trahair. Inelastic Bending and Torsion of Steel I-beams. Journal of Structural Engineering, ASCE,1994,120 (12):3397-3417
[30]Yong Lin Pi, N. S. Trahair. Plastic Collapse Analysis of Torsion. Journal of Structural Engineering, ASCE,1995,121 (10):1389-1395
[31]N. S. Trahair, Yong Lin Pi. Torsion, Bending and Buckling of Steel Beams. Engineering Structures,1997,19 (5):372-377
[32]Yong Lin Pi, N. S. Trahair. Inelastic Torsion of Steel I-beams. Journal of Structural Engineering, ASCE,1995,121 (4):609-620
[33]Yong Lin Pi, Mark A., N. S. Trahair. Inelastic Analysis and Behavior of Steel I-Beams Curved in Plan. Journal of Structural Engineering, ASCE,2000,126(7): 772-779
[34]Yong Lin Pi, Mark A. Strength Design of Steel I-Section Beams Curved in Plan. Journal of Structural Engineering, ASCE,2000,126(7):772-779
[35]白永生,蒋永生,梁书亭.单轴对称的开口薄壁梁弯、剪、扭相关性.东南大学(自然科学版),2000,32(6)：955-959
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[2]范重,范学伟,刘岩.焊接薄壁箱形构件在国家体育场中的应用研究.工程建设与设计,2005,1：21-24
[3]裘伯永,盛兴旺,乔建东,等.桥梁工程.北京：中国铁道出版社,2001,1-10
[4]Byung H. Choi, Chai H. Yoo. Strength of Stiffened Flanges in Horizontally Curved Box Girders. Journal of Engineering Mechanics,ASCE,2005,131 (2): 167-176
[5]Praween Chusilp, Tsutomu Usami. Strength and Ductility of Steel Box Girders under Cyclic Shear. Journal of Structural Engineering, ASCE,2002,128(9): 1130-1138
[6]范重,彭翼,王喆,等.国家体育场主结构扭曲箱形构件设计研究.建筑结构学报,2007,28(2)：97-103,111
[7]赵作周,彭明英,钱稼茹,等.国家体育场扭曲箱形构件拉伸试验.建筑结构学报,2007,28(2)：104-111
[8]王立福.横隔板设置对钢板箱形梁畸变的影响研究：[重庆大学硕士学位论文].重庆：重庆大学,2004,1-15
[9]邓娟红,宋一凡,陈至辰.钢箱梁开口加劲肋设计探讨.钢结构,2005,5(20)：29-31
[10]郭金琼,房贞政,郑振.箱形梁设计理论.北京：人民交通出版社,2008,1-10
[11]吕烈武,沈世钊,沈祖炎,等.钢结构构件稳定理论.北京：中国建筑工业出版社,1983,12-20
[12]包世华,周坚.薄壁杆件结构力学.北京：中国建筑工业出版社,2006,91-160
[13]朱俞江.箱形截面梁和梁柱的弹塑性稳定极限承载力分析：[浙江大学硕士学位论文].杭州：浙江大学,2003,1-20
[14]W. Y. Li, L. G. Tham, Y. K. Cheung. Curved box girder bridges. Journal of Structural Engineering, ASCE,1988,114(6):1324-1338
[15]Martti J. M., Paavola J.. Finite element analysis of box girder. Journal of Structural Engineering, ASCE,1980,106(10):1343-1357
[16]潘有昌.单轴对称箱形简支梁的整体稳定性.钢结构研究论文报告选集(第二册),1983：40-57
[17]P. Waldron. Sectorial Properties of Straight Thin-walled Beams. Computers and Structures,1986,24(1):147-156
[18]Lando Mentrasti. Torsional Stress Concentration in Thin-Walled Beams. Journal of Engineering Mechanics, ASCE,1989,115(9):1882-1903
[19]顾强,陈绍番.厚板焊接箱形截面柱残余应力的实验研究.西安冶金建筑学院学报,1992,24(4)：365-369
[20]Yoshitaka Suetake, Masaharu Hirashima. Extended Trigonometric Series Analysis of Box Girders with Diaphragms. Journal of Engineering Mechanics, ASCE,1997,123(4):293-301
[21]鲍永方,黄文彬.矩形箱梁约束扭转理论的分析与比较.工程力学,1997,14(3)： 132-137
[22]Tsutomu Usami, Yi Zheng, Hanbin Ge. Seismic Design Method for Thin-Walled Steel Frame Structure. Journal of Structural Engineering, ASCE,2001, 127(2):137-144
[23]Tore Tryland, Odd S. Hopperstad, et al. Finite-Element Modeling of Beams under Concentrated Loading. Journal of Structural Engineering, ASCE,2001, 127(2):176-185
[24]何保康,周天华.矩形钢管截面b/t、h/t的限值确定.钢结构,2001,16(2)：29-31,38
[25]Fidelis Rutendo Mashiri, Xiao-Ling Zhao, et al. Fatigue Tests and Design of Welded T Connections in Thin Cold-Formed Square Hollow Sections under In-Plane Bending. Journal of Structural Engineering, ASCE,2002, 128(11):1413-1422
[26]Magdi Mohareb M., Istemi F. Ozkan. Plastic Interaction Relationships for Square Hollow Structural Sections:Lower Bound Solution. Journal of Structural Engineering, ASCE,2004,130 (9):1381-1391
[27]范重,范学伟,刘先明.焊接薄壁箱形构件设计方法研究.建筑结构进展,2006,8(3)：34-40
[28]陈华春,舒赣平.具有初始扭转的箱形截面梁的极限抗弯承载力研究.工业建筑(增刊),2009,1685-1693
[29]Yong Lin Pi, N. S. Trahair. Inelastic Bending and Torsion of Steel I-beams. Journal of Structural Engineering, ASCE,1994,120 (12):3397-3417
[30]Yong Lin Pi, N. S. Trahair. Plastic Collapse Analysis of Torsion. Journal of Structural Engineering, ASCE,1995,121 (10):1389-1395
[31]N. S. Trahair, Yong Lin Pi. Torsion, Bending and Buckling of Steel Beams. Engineering Structures,1997,19 (5):372-377
[32]Yong Lin Pi, N. S. Trahair. Inelastic Torsion of Steel I-beams. Journal of Structural Engineering, ASCE,1995,121 (4):609-620
[33]Yong Lin Pi, Mark A., N. S. Trahair. Inelastic Analysis and Behavior of Steel I-Beams Curved in Plan. Journal of Structural Engineering, ASCE,2000,126(7): 772-779
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