基于修正Rayleigh-Ritz法的工字钢梁预弯阶段侧向失稳分析
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摘要
为精确分析工字钢梁在预弯阶段的侧向失稳规律,对施加可变位置的双集中荷载并布置不同个数侧向支撑的工字钢梁建立计算模型,用Rayleigh-Ritz法求解.考虑侧向支撑分段布置引起的梁段约束效应,对Rayleigh-Ritz法的求解结果进行修正.选取不同工字钢梁尺寸及加载参数作为分析指标,采用ABAQUS有限元进行大量模拟分析,验证修正公式的精确性.结果表明:随着侧向支撑个数的增多,传统Rayleigh-Ritz法的求解误差逐渐增大,提出的修正Rayleigh-Ritz法可将传统Rayleigh-Ritz法求解结果的相对误差最大减小约13%,有良好的精确性和适用性.参数研究表明:预弯加载阶段,工字钢梁侧向失稳临界弯矩随着集中荷载作用点参数的增大而减小,随着侧向支撑个数的增多呈增幅逐渐减小的增大趋势;侧向稳定安全系数随着侧向支撑个数和上下翼缘板对称度的增大而增大.
In order to accurately analyze the law of lateral-torsional buckling(LTB) of steel I-beams in the pre-bending stage, a mathmatical model of a steel I-beam, which was subjected to two movable concentrated loads and with different numbers of lateral braces, was established. The restraint effect of beam segments caused by the segmental arrangement of lateral braces was considered, and the solution of the Rayleigh-Ritz method was modified. Additionally, different sizes and loading parameters of steel I-beams were selected as analysis indexes, and a large number of simulation analyses were carried out by the finite element method ABAQUS to verify the modified Rayleigh-Ritz method. The comparison results show that as the number of lateral braces increases, the error of the traditional Rayleigh-Ritz method increases gradually. The modified Rayleigh-Ritz method can minimize the relative error of solution results of the traditional Rayleigh-Ritz method by about 13%, and the modified Rayleigh-Ritz method has proved to be of good accuracy and applicability. The results of the parameter study show that in the pre-bending stage, the LTB critical moments of steel I-beams decrease with the increase in the value of concentrated loading location parameter, and increase slowly with the increase in the number of lateral braces. The safety factor of LTB increases with the increase in the number of lateral braces and the degree of monosymmetry.
In order to accurately analyze the law of lateral-torsional buckling(LTB) of steel I-beams in the pre-bending stage, a mathmatical model of a steel I-beam, which was subjected to two movable concentrated loads and with different numbers of lateral braces, was established. The restraint effect of beam segments caused by the segmental arrangement of lateral braces was considered, and the solution of the Rayleigh-Ritz method was modified. Additionally, different sizes and loading parameters of steel I-beams were selected as analysis indexes, and a large number of simulation analyses were carried out by the finite element method ABAQUS to verify the modified Rayleigh-Ritz method. The comparison results show that as the number of lateral braces increases, the error of the traditional Rayleigh-Ritz method increases gradually. The modified Rayleigh-Ritz method can minimize the relative error of solution results of the traditional Rayleigh-Ritz method by about 13%, and the modified Rayleigh-Ritz method has proved to be of good accuracy and applicability. The results of the parameter study show that in the pre-bending stage, the LTB critical moments of steel I-beams decrease with the increase in the value of concentrated loading location parameter, and increase slowly with the increase in the number of lateral braces. The safety factor of LTB increases with the increase in the number of lateral braces and the degree of monosymmetry.
引文
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[19] American Institute of Steel Construction.ANSI/AISC 360-10 Specification for structural steel buildings [S].Chicago,Illinois,USA:American Institute of Steel Construction,2005.
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[2] 中华人民共和国住房和城乡建设部.CJJ/T 276—2018 预弯预应力组合梁桥技术标准[S].北京:中国建筑工业出版社,2018.
[3] 郭赵元.预弯组合梁开裂荷载试验及理论研究[D].南京:东南大学,2017.Guo Z Y.Experimental and theoretical study on cracking load of preflexed beam[D].Nanjing:Southeast University,2017.(in Chinese)
[4] 黄侨.桥梁钢-混凝土组合结构设计原理[M].2版.北京:人民交通出版社,2017:190-193.Huang Q.Design principle of bridge steel-concrete composite structure[M].2nd ed.Beijing:China Communications Press,2017:190-193.(in Chinese)
[5] 黄侨,郑一峰,李光俊.预弯组合梁非线性全过程分析方法[J].中国公路学报,2006,19(4):88-93.DOI:10.19721/j.cnki.1001-7372.2006.04.016.Huang Q,Zheng Y F,Li G J.Nonlinear whole-course analysis method of preflex composite beam[J].China Journal of Highway and Transport,2006,19(4):88-93.DOI:10.19721/j.cnki.1001-7372.2006.04.016.(in Chinese)
[6] 祝建军.工字形受压翼缘板的宽度和侧向支撑对钢梁整体稳定的影响[D].重庆:重庆交通大学,2015.Zhu J J.The influence of compression flange width and lateral supporting condition on the overall stability carrying capacity of steel beams[D].Chongqing:Chongqing Jiaotong University,2015.(in Chinese)
[7] 周红钦.支撑位置对轻型工形钢梁侧向稳定性的影响[D].郑州:郑州大学,2009.Zhou H Q.Influence of supporting position on lateral stability of light-weight steel beams[D].Zhengzhou:Zhengzhou University,2009.(in Chinese)
[8] 王全凤,李华煜.薄壁杆件侧向稳定的近似闭合解[J].工程力学,1996,13(2):24-33.Wang Q F,Li W Y.A closely approximation of lateral buckling of thin-walled members[J].Engineering Mechanics,1996,13(2):24-33.(in Chinese)
[9] Zhang W F.Symmetric and antisymmetric lateral-torsional buckling of prestressed steel I-beams[J].Thin-Walled Structures,2018,122:463-479.DOI:10.1016/j.tws.2017.10.015.
[10] Ozbasaran H,Aydin R,Dogan M.An alternative design procedure for lateral-torsional buckling of cantilever I-beams[J].Thin-Walled Structures,2015,90:235-242.DOI:10.1016/j.tws.2015.01.021.
[11] Nguyen C T,Moon J,Le V N,et al.Lateral-torsional buckling of I-girders with discrete torsional bracings[J].Journal of Constructional Steel Research,2010,66(2):170-177.DOI:10.1016/j.jcsr.2009.09.011.
[12] Nguyen C T,Joo H S,Moon J,et al.Flexural-torsional buckling strength of I-girders with discrete torsional braces under various loading conditions[J].Engineering Structures,2012,36:337-350.DOI:10.1016/j.engstruct.2011.12.022.
[13] Mohammadi E,Hosseini S S,Rohanimanesh M S.Elastic lateral-torsional buckling strength and torsional bracing stiffness requirement for monosymmetric I-beams[J].Thin-Walled Structures,2016,104:116-125.DOI:10.1016/j.tws.2016.03.003.
[14] Dux P F,Kitipornchai S.Buckling of suspended I-beams[J].Journal of Structural Engineering,1990,116(7):1877-1891.DOI:10.1061/(asce)0733-9445(1990)116:7(1877).
[15] Tankova T,Martins J P,da Silva L S,et al.Experimental lateral-torsional buckling behaviour of web tapered I-section steel beams[J].Engineering Structures,2018,168:355-370.DOI:10.1016/j.engstruct.2018.04.084.
[16] 陈骥.钢结构稳定理论与设计[M].北京:科学出版社,2011:323-331.Chen J.Theory and design of steel structure stability[M].Beijing:Science Press,2011:323-331.(in Chinese)
[17] 李喆.预弯梁预加载失稳机理及其在不同支撑条件下的稳定性研究[D].南京:东南大学,2018.Li Z.Research on preloading instability mechanism of preflexed beam and its stability under different support conditions[D].Nanjing:Southeast University,2018.(in Chinese)
[18] 孙训方,方孝淑,关来泰.材料力学[M].北京:高等教育出版社,2001:157-176.Sun X F,Fang X S,Guan L T.Mechanics of materials[M].Beijing:Higher Education Press,2001:157-176.(in Chinese)
[19] American Institute of Steel Construction.ANSI/AISC 360-10 Specification for structural steel buildings [S].Chicago,Illinois,USA:American Institute of Steel Construction,2005.
[20] AMA Institute of Steel Construction.AISC 316-89 AISC manual of steel construction [S].Washington,DC,USA:AMA Institute of Steel Construction,2001.
[21] 曹金凤,石亦平.ABAQUS有限元分析常见问题解答[M].北京:机械工业出版社,2009:136-139.Cao J F,Shi Y P.Answers to frequently asked questions in ABAQUS finite element analysis[M].Beijing:China Machine Press,2016:136-139.(in Chinese)