复合荷载作用下钢梁弯扭屈曲临界弯矩研究
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摘要
基于由完备的复合荷载作用下钢梁弯扭屈曲总势能方程推导的平衡微分方程,采用Galerkin法推导了考虑横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式,建立了等效弯矩系数的计算理论。依据等效弯矩系数的计算理论确定了7种常见工况的等效弯矩系数理论计算式并给出了6种特殊工况的C_b实用计算式,从C_b计算式的计算精度、适用范围和形式三个方面对国内外文献的C_b计算式进行对比,验证了等效弯矩系数理论的正确性并提出了C_b计算式的选用准则,最后通过2个数值算例验证了复合荷载作用下钢梁临界弯矩M_(cr)计算式的正确性和C_b计算式选用准则的合理性。结果表明:考虑了横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式形式简单、物理意义明确且便于计算;C_b实用计算式的适用范围广且精度高;等效弯矩系数的选用准则合理、有效。
Based on the complete total potential energy of flexural-torsion buckling for steel beam subjected to combined loads,the equilibrium differential equation is obtained. The closed-formed formula of critical moment,considering both the height of load and the monosymmetry section constants,is deduced by employing Galerkin method. The theory of equivalent moment factor is also proposed. Based on the proposed equivalent moment factor theory,theoretical formulas of C_b for seven conventional load conditions and practical formulas of C_b for six special load conditions are derived. The practical C_b formulas are compared,about accuracy,application range and form,with those formulas in current literatures. The theory of equivalent moment factor is verified and the criteria on C_b formula is proposed. Two numerical examples are presented to verify the proposed M_(cr) formula and the criteria on C_b formulas. The results shown that the closed-formed formula of critical moment,considering both the height of load and the monosymmetry section constants,is of simple form,clear physical significance and easy application. The practical C_b formula is of wide application range and high accuracy. The criteria on C_b formula is reasonable and effective.
Based on the complete total potential energy of flexural-torsion buckling for steel beam subjected to combined loads,the equilibrium differential equation is obtained. The closed-formed formula of critical moment,considering both the height of load and the monosymmetry section constants,is deduced by employing Galerkin method. The theory of equivalent moment factor is also proposed. Based on the proposed equivalent moment factor theory,theoretical formulas of C_b for seven conventional load conditions and practical formulas of C_b for six special load conditions are derived. The practical C_b formulas are compared,about accuracy,application range and form,with those formulas in current literatures. The theory of equivalent moment factor is verified and the criteria on C_b formula is proposed. Two numerical examples are presented to verify the proposed M_(cr) formula and the criteria on C_b formulas. The results shown that the closed-formed formula of critical moment,considering both the height of load and the monosymmetry section constants,is of simple form,clear physical significance and easy application. The practical C_b formula is of wide application range and high accuracy. The criteria on C_b formula is reasonable and effective.
引文
[1]Clark J W,Hill H N.Lateral buckling of beams[J].Journal of the Structural Division,1960,86(7):175-196
[2]童根树,张磊.薄壁钢梁中的横向正应力及其对强度和稳定性的影响[J].土木工程学报,2003,36(4):59-64(Tong Genshu,Zhang Lei.Transverse normal stresses in thin-walled beams and its effect on strength and stability[J].China Civil Engineering Journal,2003,36(4):59-64(in Chinese))
[3]罗小丰,李国强,孙飞飞,等.焊接楔形波纹腹板工字钢梁整体稳定性能研究[J].土木工程学报,2013,46(2):88-99(Luo Xiaofeng,Li Guoqiang,Sun Feifei,et al.Investigation in the stability of welded tapered I-beams with corrugated webs[J].China Civil Engineering Journal,2013,46(2):88-99(in Chinese))
[4]刘占科,周绪红,何子奇,等.复合荷载作用下简支钢梁弹性弯扭屈曲研究[J].建筑结构学报,2014,35(4):78-85(Liu Zhanke,Zhou Xuhong,He Ziqi,et al.Study on flexural-torsional buckling of simply supported steel beam under combined loads[J].Journal of Building Structures,2014,35(4):78-85(in Chinese))
[5]Kirby P A,Nethercot D A.Design for structural stability[M].1st edtion.New York:John Wiley&Sons,1979
[6]Serna M A,López A,Puente I,et al.Equivalent uniform moment factors for lateral–torsional buckling of steel members[J].Journal of Constructional Steel Research,2006,62(6):566-580
[7]Wong E,Driver R G.Critical evaluation of equivalent moment factor procedures for laterally unsupported beams[J].Engineering Journal,2010,47(1):1-20
[8]Trahair N S,Bradford M A,Nethercot D A,et al.The behaviour and design of steel structures to EC3[M].4th edition.USA:Taylor&Francis,2008
[9]Suryoatmono B,Ho D.The moment-gradient factor in lateral—torsional buckling on wide flange steel sections[J].Journal of Constructional Steel Research,2002,58(9):1247-1264
[10]ANSI/AISC 360-16 Specification for structural steel buildings[S].Chicago:American Institute of Steel Construction,2016
[11]BS EN 1999-1-1:2007 Eurocode 9:Design of aluminium structures—Part 1-1:General structural rules[S].London:British Standards Institution,2007
[12]BS 5950—1:2000 Structural use of steelwork in building—Part 1:Code of practice for design—Rolled and welded sections[S].London:British Standards Institution,2001
[13]Load and resistance factor design specification for structural joints using ASTM A325 or A490 bolts[S].Chicago:American Institute of Steel Construction,1994
[14]Helwig T A,Frank K H,Yura J A.Lateral-torsional buckling of singly symmetric I-beams[J].Journal of Structural Engineering,1997,123(9):1172-1179
[15]陈绍蕃.有约束梁的整体稳定[J].钢结构,2008,23(8):20-25,41(Chen Shaofan.Overall stability of beams with restraints[J].Steel Construction,2008,23(8):20-25,41(in Chinese))
[16]Larue B,Khelil A,Gueury M.Elastic flexural–torsional buckling of steel beams with rigid and continuous lateral restraints[J].Journal of Constructional Steel Research,2007,63(5):692-708
[17]Khelil A,Larue B.Simple solutions for the flexuraltorsional buckling of laterally restrained I-beams[J].Engineering Structures,2008,30(10):2923-2934
[18]刘占科,周绪红.薄壁构件弯扭屈曲总势能的完备性分析[J].工程力学,2017,34(7):1-10(Liu Zhanke,Zhou Xuhong.An analysis on completeness of total potential energy of thin-walled members with flexural-torsional buckling[J].Engineering Mechanics,2017,34(7):1-10(in Chinese))
[19]Mohri F,Brouki A,Roth J C.Theoretical and numerical stability analyses of unrestrained,mono-symmetric thinwalled beams[J].Journal of Constructional Steel Research,2003,59(1):63-90
[20]周绪红,刘占科,陈明,等.钢梁弯扭屈曲临界弯矩通用公式研究[J].建筑结构学报,2013,34(5):80-86(Zhou Xuhong,Liu Zhanke,Chen Ming,et al.Study on general formula of critical moment of steel beam with flexuraltorsional buckling[J].Journal of Building Structures,2013,34(5):80-86(in Chinese))
[21]GB 50017—2003钢结构设计规范[S].北京:中国计划出版社,2003(GB 50017—2003 Code for design of steel structures[S].Beijing:China Planning Press,2003(in Chinese))
[22]Ziemian R D.Guide to stability design criteria for metal structures[M].6th edition.New York:John Wiley&Sons,2010
[23]Lim N H,Park N H,Kang Y J,et al.Elastic buckling of I-beams under linear moment gradient[J].International Journal of Solids and Structures,2003,40(21):5635-5647
[24]Nawaz R.Equivalent uniform moment factor for lateral torsional buckling of steel beams[R].Edmonton:University of Alberta,2009
[2]童根树,张磊.薄壁钢梁中的横向正应力及其对强度和稳定性的影响[J].土木工程学报,2003,36(4):59-64(Tong Genshu,Zhang Lei.Transverse normal stresses in thin-walled beams and its effect on strength and stability[J].China Civil Engineering Journal,2003,36(4):59-64(in Chinese))
[3]罗小丰,李国强,孙飞飞,等.焊接楔形波纹腹板工字钢梁整体稳定性能研究[J].土木工程学报,2013,46(2):88-99(Luo Xiaofeng,Li Guoqiang,Sun Feifei,et al.Investigation in the stability of welded tapered I-beams with corrugated webs[J].China Civil Engineering Journal,2013,46(2):88-99(in Chinese))
[4]刘占科,周绪红,何子奇,等.复合荷载作用下简支钢梁弹性弯扭屈曲研究[J].建筑结构学报,2014,35(4):78-85(Liu Zhanke,Zhou Xuhong,He Ziqi,et al.Study on flexural-torsional buckling of simply supported steel beam under combined loads[J].Journal of Building Structures,2014,35(4):78-85(in Chinese))
[5]Kirby P A,Nethercot D A.Design for structural stability[M].1st edtion.New York:John Wiley&Sons,1979
[6]Serna M A,López A,Puente I,et al.Equivalent uniform moment factors for lateral–torsional buckling of steel members[J].Journal of Constructional Steel Research,2006,62(6):566-580
[7]Wong E,Driver R G.Critical evaluation of equivalent moment factor procedures for laterally unsupported beams[J].Engineering Journal,2010,47(1):1-20
[8]Trahair N S,Bradford M A,Nethercot D A,et al.The behaviour and design of steel structures to EC3[M].4th edition.USA:Taylor&Francis,2008
[9]Suryoatmono B,Ho D.The moment-gradient factor in lateral—torsional buckling on wide flange steel sections[J].Journal of Constructional Steel Research,2002,58(9):1247-1264
[10]ANSI/AISC 360-16 Specification for structural steel buildings[S].Chicago:American Institute of Steel Construction,2016
[11]BS EN 1999-1-1:2007 Eurocode 9:Design of aluminium structures—Part 1-1:General structural rules[S].London:British Standards Institution,2007
[12]BS 5950—1:2000 Structural use of steelwork in building—Part 1:Code of practice for design—Rolled and welded sections[S].London:British Standards Institution,2001
[13]Load and resistance factor design specification for structural joints using ASTM A325 or A490 bolts[S].Chicago:American Institute of Steel Construction,1994
[14]Helwig T A,Frank K H,Yura J A.Lateral-torsional buckling of singly symmetric I-beams[J].Journal of Structural Engineering,1997,123(9):1172-1179
[15]陈绍蕃.有约束梁的整体稳定[J].钢结构,2008,23(8):20-25,41(Chen Shaofan.Overall stability of beams with restraints[J].Steel Construction,2008,23(8):20-25,41(in Chinese))
[16]Larue B,Khelil A,Gueury M.Elastic flexural–torsional buckling of steel beams with rigid and continuous lateral restraints[J].Journal of Constructional Steel Research,2007,63(5):692-708
[17]Khelil A,Larue B.Simple solutions for the flexuraltorsional buckling of laterally restrained I-beams[J].Engineering Structures,2008,30(10):2923-2934
[18]刘占科,周绪红.薄壁构件弯扭屈曲总势能的完备性分析[J].工程力学,2017,34(7):1-10(Liu Zhanke,Zhou Xuhong.An analysis on completeness of total potential energy of thin-walled members with flexural-torsional buckling[J].Engineering Mechanics,2017,34(7):1-10(in Chinese))
[19]Mohri F,Brouki A,Roth J C.Theoretical and numerical stability analyses of unrestrained,mono-symmetric thinwalled beams[J].Journal of Constructional Steel Research,2003,59(1):63-90
[20]周绪红,刘占科,陈明,等.钢梁弯扭屈曲临界弯矩通用公式研究[J].建筑结构学报,2013,34(5):80-86(Zhou Xuhong,Liu Zhanke,Chen Ming,et al.Study on general formula of critical moment of steel beam with flexuraltorsional buckling[J].Journal of Building Structures,2013,34(5):80-86(in Chinese))
[21]GB 50017—2003钢结构设计规范[S].北京:中国计划出版社,2003(GB 50017—2003 Code for design of steel structures[S].Beijing:China Planning Press,2003(in Chinese))
[22]Ziemian R D.Guide to stability design criteria for metal structures[M].6th edition.New York:John Wiley&Sons,2010
[23]Lim N H,Park N H,Kang Y J,et al.Elastic buckling of I-beams under linear moment gradient[J].International Journal of Solids and Structures,2003,40(21):5635-5647
[24]Nawaz R.Equivalent uniform moment factor for lateral torsional buckling of steel beams[R].Edmonton:University of Alberta,2009