剪切变形对箱形梁畸变效应的影响
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摘要
为揭示剪切变形对箱形梁畸变效应的影响规律,在合理假设畸变翘曲位移函数和切向位移函数的基础上,应用最小势能原理建立了考虑剪切变形的箱形梁畸变控制微分方程和相应边界条件,并通过数值算例分析了剪切变形及几何参数变化对箱形梁畸变效应的影响。结果表明:考虑剪切变形时的畸变翘曲应力与ANSYS壳单元的计算结果更为接近;与忽略剪切变形时的结果相比,畸变翘曲正应力的降低幅度不超过5%,畸变翘曲剪应力的降低幅度不超过10%;剪切变形对畸变位移的影响很小;随着跨高比的增加,畸变翘曲正应力沿梁跨度的分布曲线由单峰向双峰转变,畸变翘曲剪应力发生正负号改变的截面位置向梁端移动;随着箱壁厚度的减小,畸变翘曲应力显著增大。
In order to reveal the influence of shear deformation on the distortional effect of box girders,based on the assumptions for distortional warping and tangential displacement functions,the distortional governing differential equations and corresponding boundary conditions of box girders with shear deformation were derived by applying the minimum potential energy principle.A numerical example was used to analyze the influences of shear deformation and geometric parameters on distortional effect of box girders.The research results show that the values of distortional warping stresses with shear deformation are closer to those obtained by using the shell element in ANSYS.Compared with the results without shear deformation,the distortional warping normal stresses with shear deformation decreas by no more than 5%,and the distortional warping shear stresses decrease by no more than 10%.Shear deformation imposes little influence on distortional displacement.With the increase of span to height ratio,the distribution curves of distortional warping normal stresses along the girder span vary from single-peak to twin-peak form and the cross section where the sign of distortional warping shear stresses changes moves towards the ends of the box girder.The distortional warping stresses increase significantly with the decrease of the wall thickness of the box girder.
In order to reveal the influence of shear deformation on the distortional effect of box girders,based on the assumptions for distortional warping and tangential displacement functions,the distortional governing differential equations and corresponding boundary conditions of box girders with shear deformation were derived by applying the minimum potential energy principle.A numerical example was used to analyze the influences of shear deformation and geometric parameters on distortional effect of box girders.The research results show that the values of distortional warping stresses with shear deformation are closer to those obtained by using the shell element in ANSYS.Compared with the results without shear deformation,the distortional warping normal stresses with shear deformation decreas by no more than 5%,and the distortional warping shear stresses decrease by no more than 10%.Shear deformation imposes little influence on distortional displacement.With the increase of span to height ratio,the distribution curves of distortional warping normal stresses along the girder span vary from single-peak to twin-peak form and the cross section where the sign of distortional warping shear stresses changes moves towards the ends of the box girder.The distortional warping stresses increase significantly with the decrease of the wall thickness of the box girder.
引文
[1]SENNAH K M,KENNEDY J B.Literature Review in Analysis of Box-girder Bridge[J].Journal of Bridge Engineering,2002,7(2):134-143.
[2]郭金琼,房贞政,郑振.箱形梁设计理论[M].2版.北京:人民交通出版社,2008.
[3]项海帆.高等桥梁结构理论[M].2版.北京:人民交通出版社,2013.
[4]CHIDOLUE C A,AMADOU A,EZEAGU C A.Torsional-distortional Performance of Multi-cell Trapezoidal Box Girder with All Inclined Web Members[J].Journal of Engineering Research and Applications,2015,5(2):45-51.
[5]YOO C H,KANG J,KIM K.Stresses Due to Distortion on Horizontally Curved Tub-girders[J].Engineering Structures,2015,87:70-85.
[6]WRIGHT R N,ABDEL-SAMAD S R,ROBINSON A R.BEF Analogy for Analysis of Box Girder Bridges[J].Journal of Structural Division,1968,94(7):1719-1743.
[7]张元海,王晨光,林丽霞.箱形梁布置双层悬臂板时的畸变效应分析[J].中国公路学报,2016,29(6):214-220.ZHANG Yuanhai,WANG Chenguang,LIN Lixia.Distortion Effect Analysis of Box Girders with Double-Level Cantilever Slab[J].China Journal of Highway and Transport,2016,29(6):214-220.
[8]马磊,万水,蒋正文.单箱双室波形钢腹板箱梁扭转与畸变性能研究[J].中国公路学报,2016,29(10):77-85.MA Lei,WAN Shui,JIANG Zhengwen.Research on Torsion and Distortion Performance of Single Box Double-cell Girder with Corrugated Steel Webs[J].China Journal of Highway and Transport,2016,29(10):77-85.
[9]徐勋,叶华文,强士中.考虑剪切变形的薄壁箱梁畸变分析[J].计算力学学报,2013,30(6):860-866.XU Xun,YE Huawen,QIANG Shizhong.Distortion of Thin-walled Box Girder Taking Account of Shear Deformation[J].Chinese Journal of Computational Mechanics,2013,30(6):860-866.
[10]李育楷,王全凤.考虑剪切变形的矩形截面薄壁杆件畸变分析[J].计算力学学报,2004,21(2):247-252.LI Yukai,WANG Quanfeng.Distortion of Thin-walled Bar with Rectangular Section Taking Account of Shear Deformation[J].Chinese Journal of Computational Mechanics,2004,21(2):247-252.
[11]徐勋,叶华文,强士中.带悬臂板薄壁箱梁的扭转和畸变分析[J].铁道学报,2015,37(10):83-91.XU Xun,YE Huawen,QIANG Shizhong.Torsion and Distortion Analysis of Thin-walled Box Girder with Cantilever Flanges[J].Journal of the China Railway Society,2015,37(10):83-91.
[12]汪洋生,张元海.斜腹板薄壁箱梁横向内力分析及其参数影响研究[J].铁道学报,2017,39(3):104-111.WANG Yangsheng,ZHANG Yuanhai.Research on Transverse Internal Force and Parameter Influence of Thin-walled Box Girder with Inclined Webs[J].Journal of the China Railway Society,2017,39(3):104-111.
[13]JANG G W,KIM M J,KIM Y Y.Analysis of Thinwalled Straight Beams with Generally Shaped Closed Sections Using Numerically Determined Sectional Deformation Functions[J].Journal of Structural Engineering,2012,138(12):1427-1435.
[14]LI Haifeng,LUO Yongfeng.Application of Stiffness Matrix of a Beam Element Considering Section Distortion Effect[J].Journal of Southeast University,2010,26(3):431-435.
[15]RAZAQPUR A G,LI H G.Thin-walled Multicell Boxgirder Finite Element[J].Journal of Structural Engineering,ASCE,1991,117(10):2953-2971.
[16]PARK N H,CHOI S,KANG Y J.Exact Distortional Behavior and Practical Distortional Analysis of Multicell Box Girders Using an Expanded Method[J].Computers and Structures,2005,83(19/20):1607-1626.
[17]谢旭,黄剑源.薄壁箱形梁桥约束扭转下翘曲、畸变和剪力滞效应的空间分析[J].土木工程学报,1995,28(4):3-14.XIE Xu,HUANG Jianyuan.Three Dimensional Analysis for Warping,Distortion and Shear Lag Effect of Thinwalled Box Girder Bridge under Restrained Torsion[J].China Civil Engineering Journal,1995,28(4):3-14.
[18]蔺鹏臻,孙理想,冀伟,等.时速250km/h铁路双线箱梁的畸变效应研究[J].铁道科学与工程学报,2016,13(4):595-599.LIN Pengzhen,SUN Lixiang,JI Wei,et al.Distortion Effect of Double Track Railway Box Girders with Speed of250km/h[J].Journal of Railway Science and Engineering,2016,13(4):595-599.
[19]张莉.横隔板及几何特征对钢箱梁畸变效应的影响[J].铁道工程学报,2013(8):68-73.ZHANG Li.Influences of Diaphragm Plate and Geometric Characteristics on Distortion Effect of Steel Box Girder[J].Journal of Railway Engineering Society,2013(8):68-73.
[20]张文献,庞姝,黄金芬,等.大翼缘箱梁畸变效应的试验研究[J].东北大学学报(自然科学版),2009,30(7):1047-1050.ZHANG Wenxian,PANG Shu,HUANG Jinfen,et al.Experimental Investigation on Distortion Effect of Widelyflanged Box Girders[J].Journal of Northeastern University(Natural Science Edition),2009,30(7):1047-1050.
[21]刘保东,冯文章,任红伟,等.波纹钢腹板连续刚构桥扭转与畸变的试验研究[J].中国铁道科学,2015,35(4):40-46.LIU Baodong,FENG Wenzhang,REN Hongwei,et al.Experimental Study on Torsion and Distortion of Continuous Rigid Frame Bridge with Corrugated Steel Webs[J].China Railway Science,2015,35(4):40-46.
[2]郭金琼,房贞政,郑振.箱形梁设计理论[M].2版.北京:人民交通出版社,2008.
[3]项海帆.高等桥梁结构理论[M].2版.北京:人民交通出版社,2013.
[4]CHIDOLUE C A,AMADOU A,EZEAGU C A.Torsional-distortional Performance of Multi-cell Trapezoidal Box Girder with All Inclined Web Members[J].Journal of Engineering Research and Applications,2015,5(2):45-51.
[5]YOO C H,KANG J,KIM K.Stresses Due to Distortion on Horizontally Curved Tub-girders[J].Engineering Structures,2015,87:70-85.
[6]WRIGHT R N,ABDEL-SAMAD S R,ROBINSON A R.BEF Analogy for Analysis of Box Girder Bridges[J].Journal of Structural Division,1968,94(7):1719-1743.
[7]张元海,王晨光,林丽霞.箱形梁布置双层悬臂板时的畸变效应分析[J].中国公路学报,2016,29(6):214-220.ZHANG Yuanhai,WANG Chenguang,LIN Lixia.Distortion Effect Analysis of Box Girders with Double-Level Cantilever Slab[J].China Journal of Highway and Transport,2016,29(6):214-220.
[8]马磊,万水,蒋正文.单箱双室波形钢腹板箱梁扭转与畸变性能研究[J].中国公路学报,2016,29(10):77-85.MA Lei,WAN Shui,JIANG Zhengwen.Research on Torsion and Distortion Performance of Single Box Double-cell Girder with Corrugated Steel Webs[J].China Journal of Highway and Transport,2016,29(10):77-85.
[9]徐勋,叶华文,强士中.考虑剪切变形的薄壁箱梁畸变分析[J].计算力学学报,2013,30(6):860-866.XU Xun,YE Huawen,QIANG Shizhong.Distortion of Thin-walled Box Girder Taking Account of Shear Deformation[J].Chinese Journal of Computational Mechanics,2013,30(6):860-866.
[10]李育楷,王全凤.考虑剪切变形的矩形截面薄壁杆件畸变分析[J].计算力学学报,2004,21(2):247-252.LI Yukai,WANG Quanfeng.Distortion of Thin-walled Bar with Rectangular Section Taking Account of Shear Deformation[J].Chinese Journal of Computational Mechanics,2004,21(2):247-252.
[11]徐勋,叶华文,强士中.带悬臂板薄壁箱梁的扭转和畸变分析[J].铁道学报,2015,37(10):83-91.XU Xun,YE Huawen,QIANG Shizhong.Torsion and Distortion Analysis of Thin-walled Box Girder with Cantilever Flanges[J].Journal of the China Railway Society,2015,37(10):83-91.
[12]汪洋生,张元海.斜腹板薄壁箱梁横向内力分析及其参数影响研究[J].铁道学报,2017,39(3):104-111.WANG Yangsheng,ZHANG Yuanhai.Research on Transverse Internal Force and Parameter Influence of Thin-walled Box Girder with Inclined Webs[J].Journal of the China Railway Society,2017,39(3):104-111.
[13]JANG G W,KIM M J,KIM Y Y.Analysis of Thinwalled Straight Beams with Generally Shaped Closed Sections Using Numerically Determined Sectional Deformation Functions[J].Journal of Structural Engineering,2012,138(12):1427-1435.
[14]LI Haifeng,LUO Yongfeng.Application of Stiffness Matrix of a Beam Element Considering Section Distortion Effect[J].Journal of Southeast University,2010,26(3):431-435.
[15]RAZAQPUR A G,LI H G.Thin-walled Multicell Boxgirder Finite Element[J].Journal of Structural Engineering,ASCE,1991,117(10):2953-2971.
[16]PARK N H,CHOI S,KANG Y J.Exact Distortional Behavior and Practical Distortional Analysis of Multicell Box Girders Using an Expanded Method[J].Computers and Structures,2005,83(19/20):1607-1626.
[17]谢旭,黄剑源.薄壁箱形梁桥约束扭转下翘曲、畸变和剪力滞效应的空间分析[J].土木工程学报,1995,28(4):3-14.XIE Xu,HUANG Jianyuan.Three Dimensional Analysis for Warping,Distortion and Shear Lag Effect of Thinwalled Box Girder Bridge under Restrained Torsion[J].China Civil Engineering Journal,1995,28(4):3-14.
[18]蔺鹏臻,孙理想,冀伟,等.时速250km/h铁路双线箱梁的畸变效应研究[J].铁道科学与工程学报,2016,13(4):595-599.LIN Pengzhen,SUN Lixiang,JI Wei,et al.Distortion Effect of Double Track Railway Box Girders with Speed of250km/h[J].Journal of Railway Science and Engineering,2016,13(4):595-599.
[19]张莉.横隔板及几何特征对钢箱梁畸变效应的影响[J].铁道工程学报,2013(8):68-73.ZHANG Li.Influences of Diaphragm Plate and Geometric Characteristics on Distortion Effect of Steel Box Girder[J].Journal of Railway Engineering Society,2013(8):68-73.
[20]张文献,庞姝,黄金芬,等.大翼缘箱梁畸变效应的试验研究[J].东北大学学报(自然科学版),2009,30(7):1047-1050.ZHANG Wenxian,PANG Shu,HUANG Jinfen,et al.Experimental Investigation on Distortion Effect of Widelyflanged Box Girders[J].Journal of Northeastern University(Natural Science Edition),2009,30(7):1047-1050.
[21]刘保东,冯文章,任红伟,等.波纹钢腹板连续刚构桥扭转与畸变的试验研究[J].中国铁道科学,2015,35(4):40-46.LIU Baodong,FENG Wenzhang,REN Hongwei,et al.Experimental Study on Torsion and Distortion of Continuous Rigid Frame Bridge with Corrugated Steel Webs[J].China Railway Science,2015,35(4):40-46.
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