压杆轴力与轴向位移全过程曲线的近似表达式
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摘要
考虑了几何缺陷、残余应力和材料塑性,采用大变形理论自编程序3D-Steel-Struct对工字形压杆屈曲前后的变形曲线进行了研究。对非完善双轴对称工字形截面压杆进行了二阶弹性和二阶刚塑性的理论分析,推导了相应阶段的轴压力与变形之间的关系,构造了轴压力与跨中挠度和轴压力与轴向位移之间的解析表达式,并与数值解非常吻合。研究了压杆轴压延性随长细比的变化规律,提出了一个延性与长细比的近似表达式,并具有良好的精度。
This paper investigates the deformation of compressed bars with I-section.A finite-element program of 3D-Steel-Struct developed by authors is used in the analysis.Initial geometric crookedness,residual stress and material inelasticity are considered in the investigation.Second order elastic and second order rigid-plastic analysis are carried out for imperfect members,and relations between axially compressive force and deformation are deduced.Analytical expression for axially compressive force and deflection at mid-span are presented,as well as that for axially compressive force and axial shortening.A comparison shows the excellent agreement between the proposed explicit expressions and the numerical results.The axial ductility of compressed member is also studied in the paper.A formula relating the ductility to the slenderness is proposed.
This paper investigates the deformation of compressed bars with I-section.A finite-element program of 3D-Steel-Struct developed by authors is used in the analysis.Initial geometric crookedness,residual stress and material inelasticity are considered in the investigation.Second order elastic and second order rigid-plastic analysis are carried out for imperfect members,and relations between axially compressive force and deformation are deduced.Analytical expression for axially compressive force and deflection at mid-span are presented,as well as that for axially compressive force and axial shortening.A comparison shows the excellent agreement between the proposed explicit expressions and the numerical results.The axial ductility of compressed member is also studied in the paper.A formula relating the ductility to the slenderness is proposed.
引文
[1]Timoshenko S P,Gere J M.Theory of elastic stability[M].2nd ed.New York:McGraw Hill Book Company,Inc.,1961.
[2]伯拉希F.金属结构的屈曲强度[M].同济大学钢木结构教研室,译.北京:科学出版社,1965.Bleich F.Buckling strength of metal structures[M].Translated by Staff Room of Steel and Timber Structureof Tongji University.Beijing:Science Press,1965.(inChinese)
[3]吕烈武,沈世钊,沈祖炎,胡学仁.钢结构构件稳定理论[M].北京:中国建筑工业出版社,1983.Lu Liewu,Shen Shizhao,Shen Zuyan,Hu Xueren.Theory for stability of steel member[M].Beijing:ChinaArchitecture&Building Press,1983.(in Chinese)
[4]谢道清.罕遇地震下考虑压杆屈曲的网壳弹塑性分析[D].杭州:浙江大学,2010.Xie Daoqing.Elastic-plastic analysis of lattice shellsunder rare earthquake considering compression barpost-buckling[D].Hangzhou:Zhejiang University,2010.(in Chinese)
[5]Tremblay R,Timler P,Bruneau M,Filiatrault A.Performance of steel structures during the 1994Northridge earthquake[J].Canadian Journal of CivilEngineering,1995,22(2):338―360.
[6]Tremblay Robert.Inelastic seismic response of steelbracing members[J].Journal of Constructional SteelResearch,2002,58(5/6/7/8):665―701.
[7]Loov R.A simple equation for axially loaded steelcolumn design curves[J].Canadian Journal of CivilEngineering,1996,23(1):272―276.
[8]童根树.钢结构的平面内稳定[M].北京:中国建筑工业出版社,2005.Tong Genshu.In-plane stability of steel structure[M].Beijing:China Architecture&Building Press,2005.(inChinese)
[9]张磊.考虑横向正应力影响的薄壁构件稳定理论及其应用[D].杭州:浙江大学,2005.Zhang Lei.A theory of stability for thin-walled membersconsidering the effects of transverse stresses and itsapplications[D].Hangzhou:Zhejiang University,2005.(in Chinese)
[10]Yang Y B,Shieh M S.Solution method for nonlinearproblems with multiple critical points[J].AIAA Journal,1990,28(12):2110―2116.
[11]Powell G,Simons J.Improved iteration strategy fornonlinear structures[J].International Journal forNumerical Methods in Engineering,1981,17:1455―1467.
[12]沈永欢.实用数学手册[M].北京:科学出版社,1992.Shen Yonghuan.Handbook of mathematics for utility[M].Beijing:Science Press,1992.(in Chinese)
[2]伯拉希F.金属结构的屈曲强度[M].同济大学钢木结构教研室,译.北京:科学出版社,1965.Bleich F.Buckling strength of metal structures[M].Translated by Staff Room of Steel and Timber Structureof Tongji University.Beijing:Science Press,1965.(inChinese)
[3]吕烈武,沈世钊,沈祖炎,胡学仁.钢结构构件稳定理论[M].北京:中国建筑工业出版社,1983.Lu Liewu,Shen Shizhao,Shen Zuyan,Hu Xueren.Theory for stability of steel member[M].Beijing:ChinaArchitecture&Building Press,1983.(in Chinese)
[4]谢道清.罕遇地震下考虑压杆屈曲的网壳弹塑性分析[D].杭州:浙江大学,2010.Xie Daoqing.Elastic-plastic analysis of lattice shellsunder rare earthquake considering compression barpost-buckling[D].Hangzhou:Zhejiang University,2010.(in Chinese)
[5]Tremblay R,Timler P,Bruneau M,Filiatrault A.Performance of steel structures during the 1994Northridge earthquake[J].Canadian Journal of CivilEngineering,1995,22(2):338―360.
[6]Tremblay Robert.Inelastic seismic response of steelbracing members[J].Journal of Constructional SteelResearch,2002,58(5/6/7/8):665―701.
[7]Loov R.A simple equation for axially loaded steelcolumn design curves[J].Canadian Journal of CivilEngineering,1996,23(1):272―276.
[8]童根树.钢结构的平面内稳定[M].北京:中国建筑工业出版社,2005.Tong Genshu.In-plane stability of steel structure[M].Beijing:China Architecture&Building Press,2005.(inChinese)
[9]张磊.考虑横向正应力影响的薄壁构件稳定理论及其应用[D].杭州:浙江大学,2005.Zhang Lei.A theory of stability for thin-walled membersconsidering the effects of transverse stresses and itsapplications[D].Hangzhou:Zhejiang University,2005.(in Chinese)
[10]Yang Y B,Shieh M S.Solution method for nonlinearproblems with multiple critical points[J].AIAA Journal,1990,28(12):2110―2116.
[11]Powell G,Simons J.Improved iteration strategy fornonlinear structures[J].International Journal forNumerical Methods in Engineering,1981,17:1455―1467.
[12]沈永欢.实用数学手册[M].北京:科学出版社,1992.Shen Yonghuan.Handbook of mathematics for utility[M].Beijing:Science Press,1992.(in Chinese)
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