考虑二阶弯矩效应的自由扭转圆曲梁静力分析
|
摘要
针对拱形温室结构在轴向风荷载作用下的受力变形及屋面荷载作用下平面外稳定问题,根据考虑曲梁的大位移特征及二阶弯矩效应,建立圆曲梁的弯矩平衡方程,结合其他平衡方程、几何方程、物理方程,获得非线性圆曲梁挠度和扭转角的控制方程,得到含系数的圆曲梁几何非线性位移、变形和内力模型,给出圆曲梁几何非线性位移及内力的计算方案。鉴于圆曲梁的受力变形与圆拱平面外失稳特征变形的相似性,在此研究的基础上,分析圆拱平面外失稳问题,给出圆拱平面外分岔失稳临界荷载的计算方法。分析结果表明:本研究得到的圆曲梁几何非线性静力分析模型,可用于拱形温室屋面结构的非线性受力分析及平面外分岔及极值点失稳计算。
Aiming at the problem of the behavior of arch greenhouse structure under longitudinal wind load and out-plane stability under roof load,a moment equilibrium equation of circular curved beam was established by taking large displacement and second-order moment effect into account.Combined with other equilibrium equation,geometric equation and physical equation,the deflection and torsion angle control equations of circular curved beam were obtained,respectively.Then the geometric nonlinear displacement,deformation and internal force models including coefficients of circular curved beam were received,and the calculation scheme for geometric nonlinear displacement and internal force of circular curved beam were also gained.Because the deformation of circular curved beam was similar to that of circular arch with out-plane buckling.On the above basis,the out-plane buckling of circular arch was analyzed and the calculation method for critical load of circular arch with out-plane bifurcation buckling was built.The analysis results showed that the geometric nonlinear static analysis model of circular curved beam by the study could be used to calculate the nonlinear behavior of arch greenhouse structure and the out-plane bifurcation buckling.
Aiming at the problem of the behavior of arch greenhouse structure under longitudinal wind load and out-plane stability under roof load,a moment equilibrium equation of circular curved beam was established by taking large displacement and second-order moment effect into account.Combined with other equilibrium equation,geometric equation and physical equation,the deflection and torsion angle control equations of circular curved beam were obtained,respectively.Then the geometric nonlinear displacement,deformation and internal force models including coefficients of circular curved beam were received,and the calculation scheme for geometric nonlinear displacement and internal force of circular curved beam were also gained.Because the deformation of circular curved beam was similar to that of circular arch with out-plane buckling.On the above basis,the out-plane buckling of circular arch was analyzed and the calculation method for critical load of circular arch with out-plane bifurcation buckling was built.The analysis results showed that the geometric nonlinear static analysis model of circular curved beam by the study could be used to calculate the nonlinear behavior of arch greenhouse structure and the out-plane bifurcation buckling.
引文
[1]周长吉,王应宽.中国现代温室的主要型式及其性能[J].农业工程学报,2001,17(1):16-21Zhou C J,Wang Y K.Modern greenhouses and their performances in China[J].Transactions of the Chinese Society of Agricultural Engineering,2001,17(1):16-21(in Chinese)
[2]姚玲森.曲线梁[M].北京:人民交通出版社,1989Yao L S.Curved Beam[M].Beijing:China Communications Press,1989(in Chinese)
[3]郭韦佟,丁敏,邓婷,蒋秀根,王斌泰,黄泽敏.圆拱结构静力分析的直接刚度法[J].广西大学学报:自然科学版,2017,42(4):1351-1360Guo W T,Ding M,Deng T,Jiang X G,Wang B T,Huang Z M.Direct stiffness model for static analysis of circular arch structure[J].Journal of Guangxi University:Natural Science Edition,2017,42(4):1351-1360(in Chinese)
[4]郭韦佟,朱丹,宓林,蒋秀根.拱形屋面温室纵向抗风分析中的曲梁刚度矩阵模型[J].中国农业大学学报,2017,22(10):113-119Guo W T,Zhu D,Mi L,Jiang X G.Curved beam stiffness matrix model for longitudinal wind resistance analysis of arch roof greenhouse[J].Journal of China Agricultural University,2017,22(10):113-119(in Chinese)
[5]郭彦林,窦超.现代拱形钢结构设计原理与应用[M].北京:科学出版社,2013Guo Y L,Dou C.Design Fundamentals and Application of Contemporary Steel Arch Structures[M].Beijing:Science Press,2013(in Chinese)
[6]铁摩辛柯S P,盖莱J M.弹性稳定理论[M].2版.北京:科学出版社,1965Timoshenko S P,Gere J M.Theory of Elastic Stability[M].The second edition.Beijing:Science Press,1965(in Chinese)
[7]项海帆,刘光栋.拱结构的稳定与振动[M].北京:人民交通出版社,1991Xiang H F,Liu G D.Stability and Vibration of Arch Structures[M].Beijing:China Communications Press,1991(in Chinese)
[8]Yoo C H.Flexural-torsional stability of curved beams[J].Journal of the Engineering Mechanics Division,1982,108(6):1351-1369
[9]Yoo C H,Pfeiffer P A.Elastic stability of curved members[J].Journal of Structural Engineering,1983,109(12):2922-2940
[10]Yoo C H,Pfeiffer P A.Buckling of curved beams with in-plane deformation[J].Journal of Structural Engineering,1984,110(2):291-300
[11]Rajasekaran S,Ramm E.Discussion of“Flexural-torsional stability of curved beams”by Chai Hong Yoo[J].Journal of Engineering Mechanics,1984,110(1):144-148
[12]Yoo C H.Closure to‘Flexural-torsional stability of curved beams’[J].Journal of Engineering Mechanics,1984,110(1):148-149
[13]Yang Y,Kuo S,Yau J.Use of straight beam approach to study buckling of curved beams[J].Journal of Structural Engineering,1991,117(7):1963-1978
[14]刘磊,许克宾.曲杆结构非线性分析中的直梁单元和曲梁单元[J].铁道学报,2001,23(6):72-76Liu L,Xu K B.Curved-beam element and straight-beam element used in the nonlinear analysis of curved frame structures[J].Journal of the China Railway Society,2001,23(6):72-76(in Chinese)
[15]Yang Y,Kuo S,Cheng Y D.Curved beam elements for nonlinear analysis[J].Journal of Engineering Mechanics,1989,115(4):840-855
[16]Wen R K.Nonlinear curved-beam element for arch structures[J].Journal of Structural Engineering,1991,117(11):3496-3515
[17]许强.薄壁曲梁线弹性理论和弹塑性稳定极限承载力分析[D].杭州:浙江大学,2002Xu Q.Linearelastic theory and ultimate load carrying capacity analysis of thin-walled curved beams[D].Hangzhou:Zhejiang University,2002(in Chinese)
[18]童根树,许强.工字形截面圆弧曲梁的非线性理论[J].土木工程学报,2004,37(4):1-7Tong G S,Xu Q.Nonlinear theory for round curving beams with I-sections[J].China Civil Engineering Journal,2004,37(4):1-7(in Chinese)
[2]姚玲森.曲线梁[M].北京:人民交通出版社,1989Yao L S.Curved Beam[M].Beijing:China Communications Press,1989(in Chinese)
[3]郭韦佟,丁敏,邓婷,蒋秀根,王斌泰,黄泽敏.圆拱结构静力分析的直接刚度法[J].广西大学学报:自然科学版,2017,42(4):1351-1360Guo W T,Ding M,Deng T,Jiang X G,Wang B T,Huang Z M.Direct stiffness model for static analysis of circular arch structure[J].Journal of Guangxi University:Natural Science Edition,2017,42(4):1351-1360(in Chinese)
[4]郭韦佟,朱丹,宓林,蒋秀根.拱形屋面温室纵向抗风分析中的曲梁刚度矩阵模型[J].中国农业大学学报,2017,22(10):113-119Guo W T,Zhu D,Mi L,Jiang X G.Curved beam stiffness matrix model for longitudinal wind resistance analysis of arch roof greenhouse[J].Journal of China Agricultural University,2017,22(10):113-119(in Chinese)
[5]郭彦林,窦超.现代拱形钢结构设计原理与应用[M].北京:科学出版社,2013Guo Y L,Dou C.Design Fundamentals and Application of Contemporary Steel Arch Structures[M].Beijing:Science Press,2013(in Chinese)
[6]铁摩辛柯S P,盖莱J M.弹性稳定理论[M].2版.北京:科学出版社,1965Timoshenko S P,Gere J M.Theory of Elastic Stability[M].The second edition.Beijing:Science Press,1965(in Chinese)
[7]项海帆,刘光栋.拱结构的稳定与振动[M].北京:人民交通出版社,1991Xiang H F,Liu G D.Stability and Vibration of Arch Structures[M].Beijing:China Communications Press,1991(in Chinese)
[8]Yoo C H.Flexural-torsional stability of curved beams[J].Journal of the Engineering Mechanics Division,1982,108(6):1351-1369
[9]Yoo C H,Pfeiffer P A.Elastic stability of curved members[J].Journal of Structural Engineering,1983,109(12):2922-2940
[10]Yoo C H,Pfeiffer P A.Buckling of curved beams with in-plane deformation[J].Journal of Structural Engineering,1984,110(2):291-300
[11]Rajasekaran S,Ramm E.Discussion of“Flexural-torsional stability of curved beams”by Chai Hong Yoo[J].Journal of Engineering Mechanics,1984,110(1):144-148
[12]Yoo C H.Closure to‘Flexural-torsional stability of curved beams’[J].Journal of Engineering Mechanics,1984,110(1):148-149
[13]Yang Y,Kuo S,Yau J.Use of straight beam approach to study buckling of curved beams[J].Journal of Structural Engineering,1991,117(7):1963-1978
[14]刘磊,许克宾.曲杆结构非线性分析中的直梁单元和曲梁单元[J].铁道学报,2001,23(6):72-76Liu L,Xu K B.Curved-beam element and straight-beam element used in the nonlinear analysis of curved frame structures[J].Journal of the China Railway Society,2001,23(6):72-76(in Chinese)
[15]Yang Y,Kuo S,Cheng Y D.Curved beam elements for nonlinear analysis[J].Journal of Engineering Mechanics,1989,115(4):840-855
[16]Wen R K.Nonlinear curved-beam element for arch structures[J].Journal of Structural Engineering,1991,117(11):3496-3515
[17]许强.薄壁曲梁线弹性理论和弹塑性稳定极限承载力分析[D].杭州:浙江大学,2002Xu Q.Linearelastic theory and ultimate load carrying capacity analysis of thin-walled curved beams[D].Hangzhou:Zhejiang University,2002(in Chinese)
[18]童根树,许强.工字形截面圆弧曲梁的非线性理论[J].土木工程学报,2004,37(4):1-7Tong G S,Xu Q.Nonlinear theory for round curving beams with I-sections[J].China Civil Engineering Journal,2004,37(4):1-7(in Chinese)