基于修正翘曲位移函数的薄壁箱梁剪力滞效应分析
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摘要
为完善薄壁箱梁剪力滞效应研究,构造余弦函数作为剪力滞效应下纵向翘曲位移分布形态的描述,考虑弯曲剪力流分布对薄壁箱梁弯曲曲率和顶底板纵向翘曲位移的影响,引入顶板悬臂板纵向翘曲位移差函数修正系数及内力平衡因子,基于能量变分法,推导了薄壁箱梁剪力滞效应作用下应力与挠度计算微分方程.针对单箱单室简支箱梁和连续箱梁算例,将理论分析方法得到的应力和挠度计算值与有限元结果和实测值进行对比分析.结果表明,按理论分析方法得到的薄壁箱梁纵向应力值不仅与有限元结果、实测值吻合良好,而且能真实地反映顶板悬臂板应力分布形态.集中荷载和均布荷载作用下,考虑剪力滞效应影响的方法使得薄壁简支箱梁跨中挠度分别增加了25. 34%和19. 22%,与有限元结果的误差分别为1. 31%和1. 83%,精度较高.该理论分析方法可以准确预测薄壁箱梁在任意荷载作用下的截面应力与挠度分布.
To improve the analysis on the shear lag effect in thin-walled box girders,a cosine-function was contrasted to describe the distribution pattern of the longitudinal warping displacement under the shear lag effect. The effect of the shear flowdistribution on the bending curvature of the thinwalled box girder and the difference function of the longitudinal warping displacement in top and bottom flanges were investigated,and the correction factor on the difference function of the longitudinal warping displacement in the top cantilever flanges were introduced. The internal force equilibrium was considered and the internal force balance factor was given. Based on the energy variation method,the differential equations for the normal stress and the vertical displacement were deduced. The examples of simply supported and continuous single-cell thin-walled box girder were chosen. The normal stress and the deflection calculated by the theoretical analysis method were compared with those of the finite element method( FEM) and the experimental study. The results showthat normal stress values of the flanges obtained from the theoretical analysis method is in good agreement with the FEMand experimental results,and can reflect the normal stress distribution pattern of top cantilever flanges. Under the concentrated load and the uniformly distributed load,the deflection at the mid-span calculated by the theoretical analysis method considering the shear lag effect increase by25. 34% and 19. 22%,respectively,and the errors between the results of the theoretical analysis method and those of the FEMare 1. 31% and 1. 83%,respectively,exhibiting the high precision of the theoretical analysis method. This theoretical analysis method can accurately predict the distribution of the normal stress over the cross-section and the displacement under arbitrary load.
To improve the analysis on the shear lag effect in thin-walled box girders,a cosine-function was contrasted to describe the distribution pattern of the longitudinal warping displacement under the shear lag effect. The effect of the shear flowdistribution on the bending curvature of the thinwalled box girder and the difference function of the longitudinal warping displacement in top and bottom flanges were investigated,and the correction factor on the difference function of the longitudinal warping displacement in the top cantilever flanges were introduced. The internal force equilibrium was considered and the internal force balance factor was given. Based on the energy variation method,the differential equations for the normal stress and the vertical displacement were deduced. The examples of simply supported and continuous single-cell thin-walled box girder were chosen. The normal stress and the deflection calculated by the theoretical analysis method were compared with those of the finite element method( FEM) and the experimental study. The results showthat normal stress values of the flanges obtained from the theoretical analysis method is in good agreement with the FEMand experimental results,and can reflect the normal stress distribution pattern of top cantilever flanges. Under the concentrated load and the uniformly distributed load,the deflection at the mid-span calculated by the theoretical analysis method considering the shear lag effect increase by25. 34% and 19. 22%,respectively,and the errors between the results of the theoretical analysis method and those of the FEMare 1. 31% and 1. 83%,respectively,exhibiting the high precision of the theoretical analysis method. This theoretical analysis method can accurately predict the distribution of the normal stress over the cross-section and the displacement under arbitrary load.
引文
[1]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,2008:6-7.
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[4] Kzmanovic B O,Graham H J. Shear lag in box girders[J]. Journal of the Structural Division,1981,107(9):1701-1712.
[5] Dezi L,Mentrasti L. Nonuniform bending-stress distribution(shear lag)[J]. Journal of Structural Engineering,1985, 111(12):2675-2690. DOI:10. 1061/(asce)0733-9445(1985)111:12(2675).
[6]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. DOI:10. 15951/j. tmgcxb. 2012. 11. 005.Zhang Yuanhai,Bai Xin,Lin Lixia. An improved approach for analyzing shear lag effect of box girders[J].China Civil Engineering Journal,2012,45(11):153-158. DOI:10. 15951/j. tmgcxb. 2012. 11. 005.(in Chinese)
[7] Zhang Y H,Lin L X. Shear lag analysis of thin-walled box girders based on a newgeneralized displacement[J]. Engineering Structures,2014,61:73-83. DOI:10. 1016/j. engstruct. 2013. 12. 031.
[8]钱寅泉,倪元增.单室箱桥的剪力滞分析[J].中国公路学报,1989,2(2):28-38.Qian Yinquan, Ni Yuanzeng. Analysis of shear lag effect in single cell box girder bridges[J]. China Journal of Highway and Transport,1989,2(2):28-38.(in Chinese)
[9]钱寅泉,倪元增.箱梁剪力滞计算的翘曲函数法[J].铁道学报,1990,12(2):57-70.Qian Yinquan, Ni Yuanzeng. Warping displacement function method for calculation of shear lag effect in box girder[J]. Journal of the China Railway Society,1990,12(2):57-70.(in Chinese)
[10]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)
[11]蔺鹏臻,周世军.基于剪切变形规律的箱梁剪力滞效应研究[J].铁道学报,2011,33(4):100-104.DOI:10. 3969/j. issn. 1001-8360. 2011. 04. 015.Lin Pengzhen, Zhou Shijun. Analysis on shear-lag effect of box girders based on flange-slab shear deformation law[J]. Journal of the China Railway Society,2011,33(4):100-104. DOI:10. 3969/j. issn. 1001-8360. 2011. 04. 015.(in Chinese)
[12] Luo Q Z,Wu Y M,Li Q S,et al. A finite segment model for shear lag analysis[J]. Engineering Structures,2004,26(14):2113-2124. DOI:10. 1016/j.engstruct. 2004. 07. 010.
[13]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.(in Chinese)
[14]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. DOI:10. 15951/j. tmgcxb.2015. 06. 006.Zhang Yuanhai, Hu Yuru, Lin Lixia. Analysis on shear lag effect of thin-walled box girders based on a modified warping displacement mode[J]. China Civil Engineering Journal,2015,48(6):44-50. DOI:10.15951/j. tmgcxb. 2015. 06. 006.(in Chinese)
[15] Luo Q Z,Li Q S,Tang J. Shear lag in box girder bridges[J]. Journal of Bridge Engineering,2002,7(5):308-313. DOI:10. 1061/(asce)1084-0702(2002)7:5(308).
[16]张元海,林丽霞.薄壁箱梁剪力滞效应分析的初参数法[J].工程力学,2013,30(8):205-211.Zhang Yuanhai,Lin Lixia. Initial parameter method for analyzing shear lag effect of thin-walled box girders[J]. Engineering Mechanics,2013,30(8):205-211.(in Chinese)
[17]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,1991:3-6.
[18]姚浩,程进.基于变分原理的波形钢腹板箱梁挠度计算解析法[J].工程力学,2016,33(8):177-184.Yao Hao,Cheng Jin. Analytical method for calculating defection of corrugated box girders based on variational principle[J]. Engineering Mechanics,2016,33(8):177-184.(in Chinese)
[2]罗旗帜,俞建立.钢筋混凝土连续箱梁桥翼板横向裂缝问题[J].桥梁建设,1997,27(1):41-45.Luo Qizhi,Yu Jianli. Problems of transverse cracking in flange slabs of reinforced concrete continuous box girder bridge[J]. Bridge Construction,1997,27(1):41-45.(in Chinese)
[3] Reissner E. Analysis of shear lag in box beams by the principle of minimum potential energy[J]. Quarterly of Applied Mathematics,1946,4(3):268-278. DOI:10.1090/qam/17176.
[4] Kzmanovic B O,Graham H J. Shear lag in box girders[J]. Journal of the Structural Division,1981,107(9):1701-1712.
[5] Dezi L,Mentrasti L. Nonuniform bending-stress distribution(shear lag)[J]. Journal of Structural Engineering,1985, 111(12):2675-2690. DOI:10. 1061/(asce)0733-9445(1985)111:12(2675).
[6]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. DOI:10. 15951/j. tmgcxb. 2012. 11. 005.Zhang Yuanhai,Bai Xin,Lin Lixia. An improved approach for analyzing shear lag effect of box girders[J].China Civil Engineering Journal,2012,45(11):153-158. DOI:10. 15951/j. tmgcxb. 2012. 11. 005.(in Chinese)
[7] Zhang Y H,Lin L X. Shear lag analysis of thin-walled box girders based on a newgeneralized displacement[J]. Engineering Structures,2014,61:73-83. DOI:10. 1016/j. engstruct. 2013. 12. 031.
[8]钱寅泉,倪元增.单室箱桥的剪力滞分析[J].中国公路学报,1989,2(2):28-38.Qian Yinquan, Ni Yuanzeng. Analysis of shear lag effect in single cell box girder bridges[J]. China Journal of Highway and Transport,1989,2(2):28-38.(in Chinese)
[9]钱寅泉,倪元增.箱梁剪力滞计算的翘曲函数法[J].铁道学报,1990,12(2):57-70.Qian Yinquan, Ni Yuanzeng. Warping displacement function method for calculation of shear lag effect in box girder[J]. Journal of the China Railway Society,1990,12(2):57-70.(in Chinese)
[10]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)
[11]蔺鹏臻,周世军.基于剪切变形规律的箱梁剪力滞效应研究[J].铁道学报,2011,33(4):100-104.DOI:10. 3969/j. issn. 1001-8360. 2011. 04. 015.Lin Pengzhen, Zhou Shijun. Analysis on shear-lag effect of box girders based on flange-slab shear deformation law[J]. Journal of the China Railway Society,2011,33(4):100-104. DOI:10. 3969/j. issn. 1001-8360. 2011. 04. 015.(in Chinese)
[12] Luo Q Z,Wu Y M,Li Q S,et al. A finite segment model for shear lag analysis[J]. Engineering Structures,2004,26(14):2113-2124. DOI:10. 1016/j.engstruct. 2004. 07. 010.
[13]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.(in Chinese)
[14]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. DOI:10. 15951/j. tmgcxb.2015. 06. 006.Zhang Yuanhai, Hu Yuru, Lin Lixia. Analysis on shear lag effect of thin-walled box girders based on a modified warping displacement mode[J]. China Civil Engineering Journal,2015,48(6):44-50. DOI:10.15951/j. tmgcxb. 2015. 06. 006.(in Chinese)
[15] Luo Q Z,Li Q S,Tang J. Shear lag in box girder bridges[J]. Journal of Bridge Engineering,2002,7(5):308-313. DOI:10. 1061/(asce)1084-0702(2002)7:5(308).
[16]张元海,林丽霞.薄壁箱梁剪力滞效应分析的初参数法[J].工程力学,2013,30(8):205-211.Zhang Yuanhai,Lin Lixia. Initial parameter method for analyzing shear lag effect of thin-walled box girders[J]. Engineering Mechanics,2013,30(8):205-211.(in Chinese)
[17]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,1991:3-6.
[18]姚浩,程进.基于变分原理的波形钢腹板箱梁挠度计算解析法[J].工程力学,2016,33(8):177-184.Yao Hao,Cheng Jin. Analytical method for calculating defection of corrugated box girders based on variational principle[J]. Engineering Mechanics,2016,33(8):177-184.(in Chinese)