薄壁箱梁约束扭转的有限元分析及弯扭力矩新算法
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摘要
利用初参数法和传递矩阵,建立了薄壁箱梁约束扭转分析的有限元列式,导出了均布扭矩和均布双力矩的非结点荷载的等效公式.基于约束扭转的有限元位移解,进一步建立了弯扭力矩新算法,导出相应的刚度矩阵、均布扭矩和均布双力矩作用下的固端力公式,方便正应力和剪应力的计算.算例表明,本文的计算结果与理论值完全符合,所建立的薄壁箱梁约束扭转有限元列式、均布扭矩和均布双力矩的非结点荷载等效公式、弯扭力矩新算法公式正确.
Using initial parameter solutions and transfer matrix method,the finite element formulation for restrained torsion of a thin-walled box girder was presented. The equivalent nodal forces of distributing torque and bi-moment acted on an element were also derived. Based on the displacement solutions of the finite element method for restrained torsion, a new algorithm for calculating the flexural-torsional moment was developed. The relevant stiff-ness matrix and fixed-end forces for distributing torque and bimoment acted on the element were established. It fa-cilitated the calculation of normal stress and shear stress. The examples show that the calculation results of the pro-posed method agree well with the theoretical solutions, which proves that the stiffnesses for restrained torsion, equiv-alent nodal forces for distributing torque and bimoment acted on element as well as new algorithm for flexural-tor-sional moment are exact.
Using initial parameter solutions and transfer matrix method,the finite element formulation for restrained torsion of a thin-walled box girder was presented. The equivalent nodal forces of distributing torque and bi-moment acted on an element were also derived. Based on the displacement solutions of the finite element method for restrained torsion, a new algorithm for calculating the flexural-torsional moment was developed. The relevant stiff-ness matrix and fixed-end forces for distributing torque and bimoment acted on the element were established. It fa-cilitated the calculation of normal stress and shear stress. The examples show that the calculation results of the pro-posed method agree well with the theoretical solutions, which proves that the stiffnesses for restrained torsion, equiv-alent nodal forces for distributing torque and bimoment acted on element as well as new algorithm for flexural-tor-sional moment are exact.
引文
[1]GENDY A S.Generalized thin-walled beam models for flexural torsional analysis[J].Computers&Structures,1992,12(4):531-550.
[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,2008:9-10,78-84.GUO J Q,FANG Z Z,ZHENG Z.Design theory of box girder[M].2nd ed.Beijing:China Communications Press,2008:9-10,78-84.(In Chinese)
[3]包世华,周坚.薄壁杆件结构力学[M].北京:中国建筑工业出版社,2006:38-161.BAO S H,ZHOU J.Structural mechanics of thin-walled bar[M].Beijing:China Architecture and Building Press,2006:38-161.(In Chinese)
[4]徐勋.大跨度混凝土箱梁结构空间效应研究[D].成都:西南交通大学土木工程学院,2009:15-37.XU X.Research of spacial effects of concrete box girder structure with long span[D].Chengdu:School of Civil Engineering,Southwest Jiaotong University,2009:15-37.(In Chinese)
[5]聂国隽,钱若军.考虑约束扭转的薄壁梁单元刚度矩阵[J].计算力学学报,2002,19(3):344-348.NIE G J,QIAN R J.Element stiffness matrix of thin-walled beam considering restrained torsion[J].Chinese Journal of Computational Mechanics,2002,19(3):344-348.(In Chinese)
[6]杨绿峰,任晓军,陈建芳.有限元法研究闭口薄壁杆件约束扭转[J].广西大学学报(自然科学版),2008,33(1):1-4.YANG L F,REN X J,CHEN J F.Torsional analysis and application of thin walled bar with closed profile[J].Journal of Guangxi University(Natural Science Edition),2008,33(1):1-4.(In Chinese)
[7]苏贤锋.箱梁桥扭转与畸变应力分析及程序设计[D].湘潭:湖南科技大学土木工程学院,2011:47-49.SU X F.Stress analysis and program design for torsion and distortion of box girder bridge[D].Xiangtan:School of Civil Engineering,Hunan University of Science and Technology,2011:47-49.(In Chinese)
[8]谢旭,黄剑源.薄壁箱形梁桥约束扭转下翘曲、畸变和剪滞效应的空间分析[J].土木工程学报,1995,28(4):3-14.XIE X,HUANG J Y.Three dimensional analysis for warping,distortion and shear lag effect of thin walled box girder under restrained torsion[J].China Civil Engineering Journal,1995,28(4):3-14.(In Chinese)
[9]朱德荣,张元海,林丽霞.特殊支承条件下连续箱梁桥的约束扭转分析[J].中南大学学报(自然科学版),2016,47(4):1312-1318.ZHU D R,ZHANG Y H,LIN L X.Restraint torsion analysis of continuous box girder bridge with special supports[J].Journal of Central South University(Science and Technology),2016,47(4):1312-1318.(In Chinese)
[10]华旭刚,杨坤,陈政清.悬索桥钢桁梁断面质量惯性矩简化计算方法[J].湖南大学学报(自然科学版),2017,44(3):1-7.HUA X G,YANG K,CHEN Z Q.A simplified method for calculating mass moment of inertia of stiffening truss in suspendion bridges[J].Journal of Hunan University(Natural Sciences),2017,44(3):1-7.(In Chinese)
[11]吴长青,张志田.悬索桥的静风扭转发散有限元精细化分析[J].湖南大学学报(自然科学版),2016,43(9):88-97.WU C Q,ZHANG Z T.Refined analysis of finite element for torsional divergence of suspension bridges[J].Journal of Hunan University(Natural Sciences),2016,43(9):88-97.(In Chinese)
[12]项海帆.高等桥梁结构理论[M].2版.北京:人民交通出版社,2013:24-35.XIANG H F.Advanced theory of bridge structures[M].2nd ed.Beijing:China Communications Press,2013:24-35.(In Chinese)
[13]黄剑源.薄壁结构的扭转分析(上)[M].北京:中国铁道出版社,1983:148-200.HUANG J Y.Torsional analysis of thin-walled structures[M].Beijing:China Railway Press,1983:148-200.(In Chinese)
[14]夏桂云,李传习.考虑剪切变形影响的杆系理论与应用[M].北京:人民交通出版社,2008:101-106.XIA G Y,LI C X.Frame structure theory and its applications includimg shear deformation effects[M].Beijing:China Communications Press,2008:101-106.(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,2008:9-10,78-84.GUO J Q,FANG Z Z,ZHENG Z.Design theory of box girder[M].2nd ed.Beijing:China Communications Press,2008:9-10,78-84.(In Chinese)
[3]包世华,周坚.薄壁杆件结构力学[M].北京:中国建筑工业出版社,2006:38-161.BAO S H,ZHOU J.Structural mechanics of thin-walled bar[M].Beijing:China Architecture and Building Press,2006:38-161.(In Chinese)
[4]徐勋.大跨度混凝土箱梁结构空间效应研究[D].成都:西南交通大学土木工程学院,2009:15-37.XU X.Research of spacial effects of concrete box girder structure with long span[D].Chengdu:School of Civil Engineering,Southwest Jiaotong University,2009:15-37.(In Chinese)
[5]聂国隽,钱若军.考虑约束扭转的薄壁梁单元刚度矩阵[J].计算力学学报,2002,19(3):344-348.NIE G J,QIAN R J.Element stiffness matrix of thin-walled beam considering restrained torsion[J].Chinese Journal of Computational Mechanics,2002,19(3):344-348.(In Chinese)
[6]杨绿峰,任晓军,陈建芳.有限元法研究闭口薄壁杆件约束扭转[J].广西大学学报(自然科学版),2008,33(1):1-4.YANG L F,REN X J,CHEN J F.Torsional analysis and application of thin walled bar with closed profile[J].Journal of Guangxi University(Natural Science Edition),2008,33(1):1-4.(In Chinese)
[7]苏贤锋.箱梁桥扭转与畸变应力分析及程序设计[D].湘潭:湖南科技大学土木工程学院,2011:47-49.SU X F.Stress analysis and program design for torsion and distortion of box girder bridge[D].Xiangtan:School of Civil Engineering,Hunan University of Science and Technology,2011:47-49.(In Chinese)
[8]谢旭,黄剑源.薄壁箱形梁桥约束扭转下翘曲、畸变和剪滞效应的空间分析[J].土木工程学报,1995,28(4):3-14.XIE X,HUANG J Y.Three dimensional analysis for warping,distortion and shear lag effect of thin walled box girder under restrained torsion[J].China Civil Engineering Journal,1995,28(4):3-14.(In Chinese)
[9]朱德荣,张元海,林丽霞.特殊支承条件下连续箱梁桥的约束扭转分析[J].中南大学学报(自然科学版),2016,47(4):1312-1318.ZHU D R,ZHANG Y H,LIN L X.Restraint torsion analysis of continuous box girder bridge with special supports[J].Journal of Central South University(Science and Technology),2016,47(4):1312-1318.(In Chinese)
[10]华旭刚,杨坤,陈政清.悬索桥钢桁梁断面质量惯性矩简化计算方法[J].湖南大学学报(自然科学版),2017,44(3):1-7.HUA X G,YANG K,CHEN Z Q.A simplified method for calculating mass moment of inertia of stiffening truss in suspendion bridges[J].Journal of Hunan University(Natural Sciences),2017,44(3):1-7.(In Chinese)
[11]吴长青,张志田.悬索桥的静风扭转发散有限元精细化分析[J].湖南大学学报(自然科学版),2016,43(9):88-97.WU C Q,ZHANG Z T.Refined analysis of finite element for torsional divergence of suspension bridges[J].Journal of Hunan University(Natural Sciences),2016,43(9):88-97.(In Chinese)
[12]项海帆.高等桥梁结构理论[M].2版.北京:人民交通出版社,2013:24-35.XIANG H F.Advanced theory of bridge structures[M].2nd ed.Beijing:China Communications Press,2013:24-35.(In Chinese)
[13]黄剑源.薄壁结构的扭转分析(上)[M].北京:中国铁道出版社,1983:148-200.HUANG J Y.Torsional analysis of thin-walled structures[M].Beijing:China Railway Press,1983:148-200.(In Chinese)
[14]夏桂云,李传习.考虑剪切变形影响的杆系理论与应用[M].北京:人民交通出版社,2008:101-106.XIA G Y,LI C X.Frame structure theory and its applications includimg shear deformation effects[M].Beijing:China Communications Press,2008:101-106.(In Chinese)
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