钢筋混凝土槽形薄壁梁弯剪扭复合作用非线性分析
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摘要
混凝土槽形薄壁梁近年来在城市轨道交通桥梁中得到了广泛应用,但其在弯剪扭复合作用下的力学性能研究相对滞后,已制约了其应用和发展。基于Vlasov开口薄壁构件弹性理论及本课题组所建立的钢筋混凝土槽形薄壁纯扭构件非线性分析模型,引入弯矩的影响,建立了钢筋混凝土槽形薄壁梁弯剪扭复合作用的非线性模型。该模型考虑了裂缝出现前后自由扭转刚度的变化;借助条带法、面积等效代换和修正坐标系等方法,得到翘曲扭转刚度与扭转角二阶导数的关系;最后采用四阶龙格-库塔法求解扭转平衡微分方程,得到扭矩-扭转角全过程曲线。根据求解过程编制了非线性分析程序,分析结果与本课题组已完成的两根梁的试验结果吻合良好,表明所建立的力学模型及分析程序可应用于弯剪扭复合作用下开口薄壁梁的受力分析和承载力预测。
Thin-walled RC channel beams have been widely applied in construction projects of urban rail viaduct recently.However,research related to the performance of thin-walled RC channel beams under combined bending shear and torsion is extremely rare,which has constrained its application and development.Based on the Vlasov′s elastic theory for open thin-walled beams and the nonlinear analysis model of thin-walled RC channel beams under pure torsion,which is derived by our research group,a nonlinear analysis model of thin-walled RC channel beams under combined bending shear and torsion is established.The change of circulatory torsion stiffness is considered in this model.By using strip method,the equivalent area method and transforming the coordinate system,the relationship between warping torsion stiffness and the second derivative of angle of torsion is derived.At last,the torque equilibrium differential equation is solved by Runge-Kutta method and the torque-rotation curve is printed.A corresponding analysis program is designed by using the analysis mode.The nonlinear analysis results of the program agree well with the data of the two experiments conducted by our research group,and it proves that the model and the program can be used in predicting response of thin-walled open RC members under combined bending shear and torsion.
Thin-walled RC channel beams have been widely applied in construction projects of urban rail viaduct recently.However,research related to the performance of thin-walled RC channel beams under combined bending shear and torsion is extremely rare,which has constrained its application and development.Based on the Vlasov′s elastic theory for open thin-walled beams and the nonlinear analysis model of thin-walled RC channel beams under pure torsion,which is derived by our research group,a nonlinear analysis model of thin-walled RC channel beams under combined bending shear and torsion is established.The change of circulatory torsion stiffness is considered in this model.By using strip method,the equivalent area method and transforming the coordinate system,the relationship between warping torsion stiffness and the second derivative of angle of torsion is derived.At last,the torque equilibrium differential equation is solved by Runge-Kutta method and the torque-rotation curve is printed.A corresponding analysis program is designed by using the analysis mode.The nonlinear analysis results of the program agree well with the data of the two experiments conducted by our research group,and it proves that the model and the program can be used in predicting response of thin-walled open RC members under combined bending shear and torsion.
引文
[1]VLASOV V Z.Thin-walled elastic beams[M].New York:National Technical Information Service,1984:111-167.
[2]KRPAN P,COLLINS M P.Testing thin-walled open RC structure in torsion[J].Journal of the Structural Division,1981,107(6):1129-1140.
[3]KRPAN P,COLLINS M P.Predicting torsional response of thin-walled open RC members[J].Journal of the Structural Division,1981,107(6):1107-1127.
[4]HWANG C S,HSU T T.Mixed torsion analysis of reinforced concrete channel beams-a fourier series approach[J].ACI Journal,1983,80(5):377-386.
[5]CHEN S,DIAO B,GUO Q,et al.Experiments and calculation of ushaped thin-walled RC members under pure torsion[J].Engineering Structures,2016(106):1-14.
[6]宋冠中,叶英华,陈圣刚,等.钢筋混凝土U型薄壁纯扭构件截面翘曲效应非线性分析[C]//全国结构工程学术会议,2015.
[7]宋冠中,叶英华,陈圣刚,等.U型薄壁RC受扭构件非线性分析模型及应用[J].哈尔滨工业大学学报,2017,49(6):40-47.
[8]CHEN S,YE Y,GUO Q,et al.Nonlinear model to predict the torsional response of u-shaped thin-walled RC members[J].Structural Engineering and Machanics,2016,60(6).
[9]郝际平,钟炜辉.薄壁杆件的弯曲与扭转[M].北京:高等教育出版社,2006.
[10]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.
[11]江见鲸,陆新征.混凝土结构有限元分析(第二版)[M].北京:清华大学出版社,2013.
[2]KRPAN P,COLLINS M P.Testing thin-walled open RC structure in torsion[J].Journal of the Structural Division,1981,107(6):1129-1140.
[3]KRPAN P,COLLINS M P.Predicting torsional response of thin-walled open RC members[J].Journal of the Structural Division,1981,107(6):1107-1127.
[4]HWANG C S,HSU T T.Mixed torsion analysis of reinforced concrete channel beams-a fourier series approach[J].ACI Journal,1983,80(5):377-386.
[5]CHEN S,DIAO B,GUO Q,et al.Experiments and calculation of ushaped thin-walled RC members under pure torsion[J].Engineering Structures,2016(106):1-14.
[6]宋冠中,叶英华,陈圣刚,等.钢筋混凝土U型薄壁纯扭构件截面翘曲效应非线性分析[C]//全国结构工程学术会议,2015.
[7]宋冠中,叶英华,陈圣刚,等.U型薄壁RC受扭构件非线性分析模型及应用[J].哈尔滨工业大学学报,2017,49(6):40-47.
[8]CHEN S,YE Y,GUO Q,et al.Nonlinear model to predict the torsional response of u-shaped thin-walled RC members[J].Structural Engineering and Machanics,2016,60(6).
[9]郝际平,钟炜辉.薄壁杆件的弯曲与扭转[M].北京:高等教育出版社,2006.
[10]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.
[11]江见鲸,陆新征.混凝土结构有限元分析(第二版)[M].北京:清华大学出版社,2013.