变截面薄壁箱梁剪力滞计算的板元梁段法
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摘要
为了计算分析变截面薄壁箱梁剪力滞效应及其参数的敏感性,提出一种考虑剪力滞效应的三节点板元梁段法。基于箱梁截面内应变-位移-基本变形之间的关系,以形函数作为单元内高度变化的插值函数,利用最小势能原理推导出梁段法对应的等参有限元行列式。使用编写的有限元程序对算例进行计算,梁段单元法计算结果与模型的实测值及有限元数值结果均吻合良好,验证了理论方法与公式推导的正确性和可靠性;在集中和均布荷载2种工况下,分别考察变截面薄壁箱梁剪力滞效应分析中常见影响参数的敏感性,研究结果表明:翼宽比、宽跨比和腹板倾角是影响变截面箱梁剪力滞效应的主要因素。文中方法计算精度好、效率高,对分析变截面箱梁的剪力滞效应具有一定的参考价值。
In order to calculate shear lag effect of Thin-walled box girder with variable section and analyse parametric sensitivity,this paper presents a three nodes board beam segment method considering shear lag effect.Based on the relation among strain,displacement and deformation in box girder section,and regarding shape functions as interpolation functions of variable height within element,the determinant of isoparametric finite element corresponding to beam segment method had been established by using the minimum potential energy principle.Computing a model by using the complied finite element program,whose theoretical results agree well with experimental value and the finite element results,it verified the correctness and reliability of the theoretical method and deduced formulas;Finally,the parametric sensitivity analysis about some common influence factors was also launched under concentrated and uniform load,when analyzing shear lag of thin-walled box girder with variable cross section.The results show that the flange width ratio,width span ratio and inclination of webs are the main factors that influence the shear lag of box girder with variable section.The accuracy and efficiency of the method given in the paper can provide certain reference value for the shear lag effect of box girder with variable section.
In order to calculate shear lag effect of Thin-walled box girder with variable section and analyse parametric sensitivity,this paper presents a three nodes board beam segment method considering shear lag effect.Based on the relation among strain,displacement and deformation in box girder section,and regarding shape functions as interpolation functions of variable height within element,the determinant of isoparametric finite element corresponding to beam segment method had been established by using the minimum potential energy principle.Computing a model by using the complied finite element program,whose theoretical results agree well with experimental value and the finite element results,it verified the correctness and reliability of the theoretical method and deduced formulas;Finally,the parametric sensitivity analysis about some common influence factors was also launched under concentrated and uniform load,when analyzing shear lag of thin-walled box girder with variable cross section.The results show that the flange width ratio,width span ratio and inclination of webs are the main factors that influence the shear lag of box girder with variable section.The accuracy and efficiency of the method given in the paper can provide certain reference value for the shear lag effect of box girder with variable section.
引文
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[8]吴幼明,罗旗帜,岳珠峰.薄壁箱梁剪力滞计算的梁段有限元法[J].中国铁道科学,2003,24(4):64-68.WU Youming,LUO Qizhi,YUE Zhufeng.Finite element method for calculating the shear lag in box girders[J].China Railway Science,2003,24(4):64-68.
[9]ZHANG Y H,LIN L X.Shear lag analysis of thin-walled box girders based on a new generalized displacement[J].Engineering Structures,2014,61(1):73-83.
[10]何志刚,蔺鹏臻.考虑截面配筋的变截面悬臂梁剪力滞效应研究[J].铁道科学与工程学报,2017,14(10):2154-2161.HE Zhigang,LIN Pengzhen.Study on shear lag effect of varying section cantilever beam in consideration of section reinforcement[J].Journal of Railway Science and Engineering,2017,14(10):2154-2161.
[11]韦成龙,李斌,曾庆元.变截面连续箱梁桥剪力滞及剪切变形双重效应分析的传递矩阵法[J].工程力学,2008,25(9):111-117.WEI Chenglong,LI Bin,ZENG Qingyuan.Transfer matrix method considering both shear lag and shear deformation effects in non-uniform continuous box girder[J].Engineering Mechanics,2008,25(9):111-117.
[12]丁南宏,林丽霞,钱永久.变截面箱梁剪力滞及剪切变形效应近似计算方法[J].铁道科学与工程学报,2011,8(1):14-18.DING Nanhong,LIN Lixia,QIAN Yongjiu.An approximate method to analyze the effect of shear lag and shear deformation of box beam with varing depth[J].Journal of Railway Science and Engineering,2011,8(1):14-18.
[13]魏丽娜,方放,余天庆,等.变截面箱形梁桥剪滞效应的近似计算方法[J].土木工程学报,1997,2(1):64-72.WEI Lina,FANG Fang,YU Tianqing,et al.An approximate method for calculating shear lag in variable cross-section box girders[J].China Civil Engineering Journal,1997,2(1):64-72.
[14]王银辉,陈山林.考虑初曲率影响的变曲率箱梁空间有限元分析[J].中国公路学报,2007,20(6):18-21.WANG Yinhui,CHEN Shanlin.Spatial finite element analysis for variable-curvature box girder with initial curvature[J].China Journal of Highway and Transport,2007,20(6):18-21.
[15]H?gsberg J,Krenk S.Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements[J].Computers&Structures,2014,134(4):88-101.
[16]孙林林,蒋丽忠,周旺保.钢-混凝土组合箱梁剪力滞系数实用计算方法[J].铁道科学与工程学报,2017,14(6):1289-1295.SUN Linlin,JIANG lizhong,ZHOU Wangbao.Practical calculation method of shear lag coefficient of steel-concrete composite box beam[J].Journal of Railway Science and Engineering,2017,14(6):1289-1295.
[17]HU S,YU J,WEI C,et al.Shear lag behavior and parametric sensitivity analysis of steel-concrete composite structure with double-box[J].Archive of Applied Mechanics,2017,87(10):1-15.
[2]孙璐,王文雷,吴国琦,等.客运专线箱梁端部裂纹成因分析及施工控制[J].铁道工程学报,2007,24(10):44-49.SUN Lu,WANG Wenlei,WU Guoqi,et al.Analyses of the causes for crack on the end side of box girder for railway passenger dedicated line and its construction control[J].Journal of Railway Engineering Society,2007,24(10):44-49.
[3]张元海,胡玉茹,林丽霞.基于修正翘曲位移模式的薄壁箱梁剪力滞效应分析[J].土木工程学报,2015,48(6):44-50.ZHANG Yuanhai,HU Yuru,LIN Lixia.Analysis on shear lag effect of thin-walled box girders based on a modified warping displacement mode[J].Journal of Civil Engineering,2015,48(6):44-50.
[4]CHANG S T,YUN D.Shear lag effect in box girder with varying depth[J].Journal of Structural Engineering,1988,114(10):2280-2292.
[5]周勇超,郝宪武,李子青.变截面波形钢腹板组合梁剪力滞效应[J].长安大学学报(自然科学版),2014,34(4):62-69.ZHOU Yongchao,HAO Xianwu,LI Ziqing.Shear lag effect of non-uniform composite beam with corrugated steel web[J].Journal of Changan University(Nature Science),2014,34(4):62-69.
[6]刘世忠,欧阳永金,吴亚平.变截面薄壁箱梁剪力滞剪切变形效应分析[J].中国公路学报,2002,15(3):61-67.LIU Shizhong,OUYANG Yongjin,WU Yaping,et al.Non-uniform thin wall box analysis of considering both shear lag and shear deformation[J].China Journal of Highway&Transport,2002,15(3):61-67.
[7]罗旗帜.变截面多跨箱梁桥剪滞效应分析[J].中国公路学报,1998,11(1):63-70.LUO Qizhi.Analysis of the shear lag effect on continuous box girder bridges with variable depth[J].China Journal of Highway and Transport,1998,11(1):63-70.
[8]吴幼明,罗旗帜,岳珠峰.薄壁箱梁剪力滞计算的梁段有限元法[J].中国铁道科学,2003,24(4):64-68.WU Youming,LUO Qizhi,YUE Zhufeng.Finite element method for calculating the shear lag in box girders[J].China Railway Science,2003,24(4):64-68.
[9]ZHANG Y H,LIN L X.Shear lag analysis of thin-walled box girders based on a new generalized displacement[J].Engineering Structures,2014,61(1):73-83.
[10]何志刚,蔺鹏臻.考虑截面配筋的变截面悬臂梁剪力滞效应研究[J].铁道科学与工程学报,2017,14(10):2154-2161.HE Zhigang,LIN Pengzhen.Study on shear lag effect of varying section cantilever beam in consideration of section reinforcement[J].Journal of Railway Science and Engineering,2017,14(10):2154-2161.
[11]韦成龙,李斌,曾庆元.变截面连续箱梁桥剪力滞及剪切变形双重效应分析的传递矩阵法[J].工程力学,2008,25(9):111-117.WEI Chenglong,LI Bin,ZENG Qingyuan.Transfer matrix method considering both shear lag and shear deformation effects in non-uniform continuous box girder[J].Engineering Mechanics,2008,25(9):111-117.
[12]丁南宏,林丽霞,钱永久.变截面箱梁剪力滞及剪切变形效应近似计算方法[J].铁道科学与工程学报,2011,8(1):14-18.DING Nanhong,LIN Lixia,QIAN Yongjiu.An approximate method to analyze the effect of shear lag and shear deformation of box beam with varing depth[J].Journal of Railway Science and Engineering,2011,8(1):14-18.
[13]魏丽娜,方放,余天庆,等.变截面箱形梁桥剪滞效应的近似计算方法[J].土木工程学报,1997,2(1):64-72.WEI Lina,FANG Fang,YU Tianqing,et al.An approximate method for calculating shear lag in variable cross-section box girders[J].China Civil Engineering Journal,1997,2(1):64-72.
[14]王银辉,陈山林.考虑初曲率影响的变曲率箱梁空间有限元分析[J].中国公路学报,2007,20(6):18-21.WANG Yinhui,CHEN Shanlin.Spatial finite element analysis for variable-curvature box girder with initial curvature[J].China Journal of Highway and Transport,2007,20(6):18-21.
[15]H?gsberg J,Krenk S.Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements[J].Computers&Structures,2014,134(4):88-101.
[16]孙林林,蒋丽忠,周旺保.钢-混凝土组合箱梁剪力滞系数实用计算方法[J].铁道科学与工程学报,2017,14(6):1289-1295.SUN Linlin,JIANG lizhong,ZHOU Wangbao.Practical calculation method of shear lag coefficient of steel-concrete composite box beam[J].Journal of Railway Science and Engineering,2017,14(6):1289-1295.
[17]HU S,YU J,WEI C,et al.Shear lag behavior and parametric sensitivity analysis of steel-concrete composite structure with double-box[J].Archive of Applied Mechanics,2017,87(10):1-15.