翼板变厚度箱形梁的剪力滞效应分析
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摘要
针对翼板厚度沿截面宽度方向线性变化的混凝土箱形梁,利用势能变分原理对其进行剪力滞效应分析.选取剪力滞效应引起的附加挠度作为描述剪力滞变形状态的广义位移,并考虑轴力平衡条件对剪力滞效应的影响.将简支箱梁在均布荷载和集中荷载作用下的理论计算值与有限元值进行对比,结果表明:采用该文分析方法得到的计算值与有限元值吻合良好,证实了该文分析方法的正确性.与将翼板变厚度箱梁简化为等厚度箱梁的计算方法相比,考虑翼板厚度变化的计算方法可提高计算精度,误差减小量最大达到了5.65%.
For concrete box girders with flanges of linearly variable thicknesses along the cross section widths, shear lag effects were analyzed according to the potential energy variation principle. The additional deflection caused by the shear lag effect was used as the generalized displacement to describe the shear lag deformation state, in view of the influence of the axial force equilibrium condition on the shear lag. The calculation results of several simply supported box girders subjected to uniform loads and concentrated loads were compared. The results show that, the proposed method gives stresses in good agreement with those obtained from the finite element method, which confirms the correctness of this method. Compared with the simplified calculation method for box girders with equivalent uniform-thickness flanges, this method has enhanced accuracy for real box girders with variable-thickness flanges, and the error reduction is up to 5.65%.
For concrete box girders with flanges of linearly variable thicknesses along the cross section widths, shear lag effects were analyzed according to the potential energy variation principle. The additional deflection caused by the shear lag effect was used as the generalized displacement to describe the shear lag deformation state, in view of the influence of the axial force equilibrium condition on the shear lag. The calculation results of several simply supported box girders subjected to uniform loads and concentrated loads were compared. The results show that, the proposed method gives stresses in good agreement with those obtained from the finite element method, which confirms the correctness of this method. Compared with the simplified calculation method for box girders with equivalent uniform-thickness flanges, this method has enhanced accuracy for real box girders with variable-thickness flanges, and the error reduction is up to 5.65%.
引文
[1] 张士铎,邓小华,王文洲.箱形薄壁梁剪力滞效应[M].北京:人民交通出版社,1998:111-132.(ZHANG Shiduo,DENG Xiaohua,WANG Wenzhou.Shear Lag Effect in Thin-Walled Box Girder[M].Beijing:China Communications Press,1998:111-132.(in Chinese))
[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,2008:1-50.(GUO Jinqiong,FANG Zhenzheng,ZHENG Zhen.Design Theory of Box Girder[M].2nd ed.Beijing:China Communications Press,2008:1-50.(in Chinese))
[3] 周旭辉,罗旗帜,张琪.薄壁箱梁剪力滞动力特性的有限段法[J].佛山科学技术学院学报(自然科学版),2017,35(1):70-75.(ZHOU Xuhui,LUO Qizhi,ZHANG Qi.Finite segment method for analyzing the dynamic characteristics of thin-walled box girder considered the shear lag effect[J].Journal of Foshan Institute of Science and Technology(Natural Science Edition),2017,35(1):70-75.(in Chinese))
[4] 黄敦文,舒小娟,沈明燕,等.载荷横向变位对箱梁剪力滞效应的影响[J].力学与实践,2015,37(6):719-724.(HUANG Dunwen,SHU Xiaojuan,SHEN Mingyan,et al.The shear lag effect of box beams with varying lateral loading locations[J].Mechanics in Engineering,2015,37(6):719-724.(in Chinese))
[5] REISSNER E.Analysis of shear lag in box beams by the principle of minimum potential energy[J].Quarterly of Applied Mathematics,1946,5(3):268-278.
[6] MANOJ L,SAGAR S.Influence of box shape on structual behaviour of RC box girder bridgers[J].Indian Concrete Journal,2007,81(6):55-62.
[7] 蔺鹏臻,杨子江,刘凤奎,等.混凝土箱梁考虑翼板厚度变化的剪力滞效应[J].土木建筑与环境工程,2013,35(1):76-79,116.(LIN Pengzhen,YANG Zijiang,LIU Fengkui,et al.Shear lag effect of concrete box girders considered varying flange-depths[J].Journal of Civil Construction and Environmental Engineering,2013,35(1):76-79,116.(in Chinese))
[8] 张玉平,胡火全,李传习,等.薄壁箱梁剪力滞翘曲位移函数的改进与对比分析[J].应用力学学报,2016,33(6):1099-1105,1126.(ZHANG Yuping,HU Huoquan,LI Chuanxi,et al.An improvement and comparative analysis of shear lag warping displacement function in thin-walled box girder[J].Chinese Journal of Applied Mechanics,2016,33(6):1099-1105,1126.(in Chinese))
[9] 肖军,李小珍,刘德军,等.不同位移函数对箱梁剪力滞效应的影响[J].中国公路学报,2016,29(9):90-96.(XIAO Jun,LI Xiaozhen,LIU Dejun,et al.Influence of different displacement functions on shear lag effect of box girders[J].China Journal of Highway and Transport,2016,29(9):90-96.(in Chinese))
[10] 陈常松,邓安.高次位移函数时箱梁剪滞效应变分法解[J].重庆交通大学学报(自然科学版),2009,28(1):5-7,44.(CHEN Changsong,DENG An.Variational solution of shear lag effect of box girder in high order displacement function[J].Journal of Chongqing Jiaotong University(Natural Science),2009,28(1):5-7,44.(in Chinese))
[11] 张慧,张玉元,张元海,等.单箱双室简支箱梁剪切变形及剪力滞双重效应分析[J].应用数学和力学,2016,37(8):791-803.(ZHANG Hui,ZHANG Yuyuan,ZHANG Yuanhai,et al.Analysis on shear deformation and shear-lag effects on twin-cell box girders[J].Applied Mathematics and Mechanics,2016,37(8):791-803.(in Chinese))
[12] 甘亚南,周广春.薄壁箱梁纵向剪滞翘曲函数精度选择的研究[J].工程力学,2008,25(6):100-106.(GAN Yanan,ZHOU Guangchun.An approach for precision selection of longitudinal shear lag warping displacement function of thin-walled box girders[J].Engineering Mechanics,2008,25(6):100-106.(in Chinese))
[13] 谢旭,黄剑源.薄壁箱型梁剪力滞效应分析的刚度法[J].工程力学,1995,12(2):95-102.(XIE Xu,HUANG Jianyuan.Stiffness method for analysis of shear lag effect on thin-walled box girder[J].Engineering Mechanics,1995,12(2):95-102.(in Chinese))
[14] 张元海,白昕,林丽霞.箱形梁剪力滞效应的改进分析方法研究[J].土木工程学报,2012,45(11):153-158.(ZHANG Yuanhai,BAI Xin,LIN Lixia.An improve approach for analysis shear lag effect of box gieders[J].China Civil Engineering Journal,2012,45(11):153-158.(in Chinese))
[15] 倪元增,钱寅泉.弹性薄壁梁桥分析[M].北京:人民交通出版社,2000:77-98.(NI Yuanzeng,QIAN Yinquan.Elastic Analysis if Thin-Walled Beam Bridges[M].Beijing:China Communications Press,2000:77-98.(in Chinese))
[16] 张元海,李琳,林丽霞,等.以附加挠度作为广义位移时薄壁箱梁剪力滞效应的梁段有限元分析[J].土木工程学报,2013,46(10):100-107.(ZHANG Yuanhai,LI Lin,LIN Lixia,et al.Beam-segment finite element analysis on shear lag effect of thin-walled boc girder adopting additional deflection as generalized displacement[J].China Civil Engineering Journal,2013,46(10):100-107.(in Chinese))
[17] 张元海,李乔.箱形梁剪滞效应分析中的广义力矩研究[J].铁道学报,2007,29(1):77-81.(ZHANG Yuanhai,LI Qiao.Study on the generalized moment in shear lag effect analysis of the box girder[J].Journal of the China Railway Society,2007,29(1):77-81.(in Chinese))
[18] 蔺鹏臻,刘凤奎,冀伟,等.变分原理分析混凝土箱梁的剪力滞效应[J].铁道学报,2013,35(2):93-98.(LIN Pengzhen,LIU Fengkui,JI Wei,et al.Analysis on shear lag effect of concrete box beam by variational principle[J].Journal of the China Railway Society,2013,35(2):93-98.(in Chinese))
[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,2008:1-50.(GUO Jinqiong,FANG Zhenzheng,ZHENG Zhen.Design Theory of Box Girder[M].2nd ed.Beijing:China Communications Press,2008:1-50.(in Chinese))
[3] 周旭辉,罗旗帜,张琪.薄壁箱梁剪力滞动力特性的有限段法[J].佛山科学技术学院学报(自然科学版),2017,35(1):70-75.(ZHOU Xuhui,LUO Qizhi,ZHANG Qi.Finite segment method for analyzing the dynamic characteristics of thin-walled box girder considered the shear lag effect[J].Journal of Foshan Institute of Science and Technology(Natural Science Edition),2017,35(1):70-75.(in Chinese))
[4] 黄敦文,舒小娟,沈明燕,等.载荷横向变位对箱梁剪力滞效应的影响[J].力学与实践,2015,37(6):719-724.(HUANG Dunwen,SHU Xiaojuan,SHEN Mingyan,et al.The shear lag effect of box beams with varying lateral loading locations[J].Mechanics in Engineering,2015,37(6):719-724.(in Chinese))
[5] REISSNER E.Analysis of shear lag in box beams by the principle of minimum potential energy[J].Quarterly of Applied Mathematics,1946,5(3):268-278.
[6] MANOJ L,SAGAR S.Influence of box shape on structual behaviour of RC box girder bridgers[J].Indian Concrete Journal,2007,81(6):55-62.
[7] 蔺鹏臻,杨子江,刘凤奎,等.混凝土箱梁考虑翼板厚度变化的剪力滞效应[J].土木建筑与环境工程,2013,35(1):76-79,116.(LIN Pengzhen,YANG Zijiang,LIU Fengkui,et al.Shear lag effect of concrete box girders considered varying flange-depths[J].Journal of Civil Construction and Environmental Engineering,2013,35(1):76-79,116.(in Chinese))
[8] 张玉平,胡火全,李传习,等.薄壁箱梁剪力滞翘曲位移函数的改进与对比分析[J].应用力学学报,2016,33(6):1099-1105,1126.(ZHANG Yuping,HU Huoquan,LI Chuanxi,et al.An improvement and comparative analysis of shear lag warping displacement function in thin-walled box girder[J].Chinese Journal of Applied Mechanics,2016,33(6):1099-1105,1126.(in Chinese))
[9] 肖军,李小珍,刘德军,等.不同位移函数对箱梁剪力滞效应的影响[J].中国公路学报,2016,29(9):90-96.(XIAO Jun,LI Xiaozhen,LIU Dejun,et al.Influence of different displacement functions on shear lag effect of box girders[J].China Journal of Highway and Transport,2016,29(9):90-96.(in Chinese))
[10] 陈常松,邓安.高次位移函数时箱梁剪滞效应变分法解[J].重庆交通大学学报(自然科学版),2009,28(1):5-7,44.(CHEN Changsong,DENG An.Variational solution of shear lag effect of box girder in high order displacement function[J].Journal of Chongqing Jiaotong University(Natural Science),2009,28(1):5-7,44.(in Chinese))
[11] 张慧,张玉元,张元海,等.单箱双室简支箱梁剪切变形及剪力滞双重效应分析[J].应用数学和力学,2016,37(8):791-803.(ZHANG Hui,ZHANG Yuyuan,ZHANG Yuanhai,et al.Analysis on shear deformation and shear-lag effects on twin-cell box girders[J].Applied Mathematics and Mechanics,2016,37(8):791-803.(in Chinese))
[12] 甘亚南,周广春.薄壁箱梁纵向剪滞翘曲函数精度选择的研究[J].工程力学,2008,25(6):100-106.(GAN Yanan,ZHOU Guangchun.An approach for precision selection of longitudinal shear lag warping displacement function of thin-walled box girders[J].Engineering Mechanics,2008,25(6):100-106.(in Chinese))
[13] 谢旭,黄剑源.薄壁箱型梁剪力滞效应分析的刚度法[J].工程力学,1995,12(2):95-102.(XIE Xu,HUANG Jianyuan.Stiffness method for analysis of shear lag effect on thin-walled box girder[J].Engineering Mechanics,1995,12(2):95-102.(in Chinese))
[14] 张元海,白昕,林丽霞.箱形梁剪力滞效应的改进分析方法研究[J].土木工程学报,2012,45(11):153-158.(ZHANG Yuanhai,BAI Xin,LIN Lixia.An improve approach for analysis shear lag effect of box gieders[J].China Civil Engineering Journal,2012,45(11):153-158.(in Chinese))
[15] 倪元增,钱寅泉.弹性薄壁梁桥分析[M].北京:人民交通出版社,2000:77-98.(NI Yuanzeng,QIAN Yinquan.Elastic Analysis if Thin-Walled Beam Bridges[M].Beijing:China Communications Press,2000:77-98.(in Chinese))
[16] 张元海,李琳,林丽霞,等.以附加挠度作为广义位移时薄壁箱梁剪力滞效应的梁段有限元分析[J].土木工程学报,2013,46(10):100-107.(ZHANG Yuanhai,LI Lin,LIN Lixia,et al.Beam-segment finite element analysis on shear lag effect of thin-walled boc girder adopting additional deflection as generalized displacement[J].China Civil Engineering Journal,2013,46(10):100-107.(in Chinese))
[17] 张元海,李乔.箱形梁剪滞效应分析中的广义力矩研究[J].铁道学报,2007,29(1):77-81.(ZHANG Yuanhai,LI Qiao.Study on the generalized moment in shear lag effect analysis of the box girder[J].Journal of the China Railway Society,2007,29(1):77-81.(in Chinese))
[18] 蔺鹏臻,刘凤奎,冀伟,等.变分原理分析混凝土箱梁的剪力滞效应[J].铁道学报,2013,35(2):93-98.(LIN Pengzhen,LIU Fengkui,JI Wei,et al.Analysis on shear lag effect of concrete box beam by variational principle[J].Journal of the China Railway Society,2013,35(2):93-98.(in Chinese))
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