反对称横向荷载作用下钢梁的弹性弯扭屈曲研究
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摘要
为了建立反对称横向荷载作用下双轴对称截面简支钢梁弹性弯扭屈曲的设计理论,考虑荷载比例系数ψ的影响,推导了反对称横向荷载作用下钢梁的弯扭屈曲总势能方程。采用Rayleigh-Ritz法得到了反对称横向荷载作用下钢梁弹性临界弯矩M_(cr)的通用计算式以及系数C_1、C_2的计算式,并总结了荷载比例系数ψ对临界弯矩的影响规律。采用有限元法对本文理论公式进行了验证,当0≤ψ≤4时,临界弯矩M_(cr)的理论解与有限元解吻合良好;当ψ>4时,临界弯矩收敛于ψ=4时的值。在此基础上,通过线性回归分析,拟合出了等效弯矩系数C_b与荷载比例系数ψ以及跨长影响系数ξ之间的近似关系式,C_b的近似解与有限元解吻合较好,最大误差为6.5%,大部分工况下误差控制在5%以内。该拟合公式适用性较强,精度较高。
In order to establish the design theory for elastic flexural-torsional buckling of simply supported symmetric I-section steel beams under antisymmetric transverse loads, the total potential energy equation considering the influence of the load proportional coefficient ψ is derived. The general calculation formula for critical moment M_(cr) and for the coefficients C_1 and C_2 are derived by employing Rayleigh-Ritz method. The effects of coefficient ψ for the M_(cr) are summarized. A review of critical moment values given by using theoretical formula and their comparison with results presented by FEA shows that both of the two results are in goodagreement while 0≤ψ≤4 and are convergent while ψ>4. In addition, the approximate formula for the relationship between the equivalent moment factor C_b and the coefficient ψ and the influence coefficient of span length ξ is obtained through linear regression analysis, the maximum error of the formula is 6.5% and the errors are less than 5% for most loading conditions, which shows a preferable calculation accuracy comparing with the FES results.
In order to establish the design theory for elastic flexural-torsional buckling of simply supported symmetric I-section steel beams under antisymmetric transverse loads, the total potential energy equation considering the influence of the load proportional coefficient ψ is derived. The general calculation formula for critical moment M_(cr) and for the coefficients C_1 and C_2 are derived by employing Rayleigh-Ritz method. The effects of coefficient ψ for the M_(cr) are summarized. A review of critical moment values given by using theoretical formula and their comparison with results presented by FEA shows that both of the two results are in goodagreement while 0≤ψ≤4 and are convergent while ψ>4. In addition, the approximate formula for the relationship between the equivalent moment factor C_b and the coefficient ψ and the influence coefficient of span length ξ is obtained through linear regression analysis, the maximum error of the formula is 6.5% and the errors are less than 5% for most loading conditions, which shows a preferable calculation accuracy comparing with the FES results.
引文
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[11]尹凌峰,葛艳丽,唐敢,等.基于直接强度法的冷弯薄壁开口多次卷边槽钢立柱截面形式研究[J].应用力学学报,2016,33(1):137-142.(YIN Lingfeng,GE Yanli,TANG Gan,et al.Research on cross-sections of cold-formed multi-roll lipped channel column based on DSM[J].Chinese journal of applied mechanics,2016,33(1):137-142(in Chinese)).
[12]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)).
[13]郭兵,管海龙,褚昊.复杂荷载作用下单向受弯简支钢梁的弹性临界弯矩[J].建筑结构学报,2017,38(11):166-173.(GUO Bing,GUAN Hailong,CHU Hao.Elastic critical moment of simply-supported steel beams under unidirectional bending with complex loads[J].Journal of building structures,2017,38(11):166-173(in Chinese)).
[14]陈绍蕃.双轴对称工形截面无支撑简支梁的整体稳定[J].钢结构,2008,23(8):6-13.(CHEN Shaofan.Overall stability of unbraced simply-supported beams with doubly symmetric I-section[J].Steel construction,2008,23(8):6-13(in Chinese)).
[15]中华人民共和国行业标准编写组.钢结构设计标准:GB50017-2017[S].北京:中国建筑工业出版社,2017.(The Professional Standard Complication Group of People’s Republic of China.Standard for design of steel structures:GB 50017-2017[S].Beijing:China Architecture&Building Press,2017(in Chinese)).
[2]ВЛАСОВВЗ.Тонкостенныеупругиестержни[M].Москва:ГосударственноеИздательствоСтроительнойЛитературы,1959.
[3]TIMOSHENKO S P,GERE J M.Theory of elastic stability[M].2nd ed.New York:McGraw-Hill,1961.
[4]CLARK J W,HILL H N.Lateral buckling of beams[J].Journal of the structural division,2015,86(7):175-196.
[5]KIRBY P A,NETHERCOT D A.Design for structural stability[M].Suffolk,England:Constrado Monographs,1979.
[6]TRAHAIR N S,BRADFORD M A.The behavior and design of steel structures[M].2nd ed.New York:Chapman and Hall,1988:203.
[7]ANDRADE A,CAMOTIMB D,COSTA P Providencia E.On the evaluation of elastic critical moments in doubly and singly symmetric I-section cantilevers[J].Journal of constructional steel research,2008,63(7):894-908.
[8]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.
[9]KHELIL A,LARUE B.Simple solutions for the flexural-torsional buckling of laterally restrained I-beams[J].Engineering structures,2008,30(10):2923-2934.
[10]高英华,席丰.受火作用单对称截面钢梁的侧向弯扭屈曲分析[J].应用力学学报,2013,30(1):130-135.(GAO Yinghua,XI Feng.The lateral torsional buckling of mono-symmetric cross-section steel beam sunder fire conditions[J].Chinese journal of applied mechanics,2013,30(1):130-135(in Chinese)).
[11]尹凌峰,葛艳丽,唐敢,等.基于直接强度法的冷弯薄壁开口多次卷边槽钢立柱截面形式研究[J].应用力学学报,2016,33(1):137-142.(YIN Lingfeng,GE Yanli,TANG Gan,et al.Research on cross-sections of cold-formed multi-roll lipped channel column based on DSM[J].Chinese journal of applied mechanics,2016,33(1):137-142(in Chinese)).
[12]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)).
[13]郭兵,管海龙,褚昊.复杂荷载作用下单向受弯简支钢梁的弹性临界弯矩[J].建筑结构学报,2017,38(11):166-173.(GUO Bing,GUAN Hailong,CHU Hao.Elastic critical moment of simply-supported steel beams under unidirectional bending with complex loads[J].Journal of building structures,2017,38(11):166-173(in Chinese)).
[14]陈绍蕃.双轴对称工形截面无支撑简支梁的整体稳定[J].钢结构,2008,23(8):6-13.(CHEN Shaofan.Overall stability of unbraced simply-supported beams with doubly symmetric I-section[J].Steel construction,2008,23(8):6-13(in Chinese)).
[15]中华人民共和国行业标准编写组.钢结构设计标准:GB50017-2017[S].北京:中国建筑工业出版社,2017.(The Professional Standard Complication Group of People’s Republic of China.Standard for design of steel structures:GB 50017-2017[S].Beijing:China Architecture&Building Press,2017(in Chinese)).