Flexural-Torsional Capacity of Beam-Columns Beam-Columns with Box Section
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摘要: 对箱形截面压弯杆弯扭屈曲承载力验算公式进行了理论研究,主要工作如下:1)对我国、欧洲和美国的钢结构设计规范中H形截面压弯杆平面外稳定验算公式进行了比较,指出了改进的可能性;2)对有初始弯曲和扭转压弯杆的弹性弯扭变形进行了二阶分析,在引入初始弯曲和初始扭转的特定关系后,得到了二阶效应放大后的弯曲、扭转、弯矩和双力矩的简单的解析表达式;3)对箱形截面绕强轴和绕弱轴的单向压弯塑性铰状态的强度公式分别进行了单一表达式拟合,对给定压力时双向弯矩作用下的塑性铰状态的双向弯矩相关关系进行了计算,提出了精度良好略偏安全的公式,并将提出的公式进行改造,使之能够考虑双力矩的影响;4)参照压弯杆平面内稳定验算公式的推导方法,利用已知的绕弱轴弯曲屈曲的柱子稳定系数公式,反推获得了压杆绕弱轴弯曲屈曲的等效初始弯曲,该等效初始弯曲综合考虑了残余应力、初始弯曲和塑性开展过程带来的额外挠度增量;5)引入该等效初始弯曲,采用平面内二阶分析获得的二阶弯矩、平面外二阶弯矩和二阶双力矩等,代入双向压弯强度计算式,得到压弯杆弯扭屈曲承载力的上限解。为了获得更为接近实际的承载力相关关系,对弹性分析得到的平面内二阶弯矩和平面外二阶弯矩以及双力矩进行弹塑性放大,得到了箱形截面压弯杆的弯扭屈曲计算公式,画出了一系列曲线,提出了拟合公式。可知:在长细比较小时,曲线接近强度相关曲线、随长细比增大,曲线接近弹性屈曲相关公式;继续增大长细比,则曲线超越弹性屈曲相关公式。对比研究表明,现行GB 50017—2017《钢结构设计标准》中的平面内和平面外稳定计算公式共同控制着杆件的承载力,在现行平面外稳定公式看似偏不安全的地方,由平面内稳定公式保证杆件安全。Abstract: A theoretical study is carried out for the flexural-torsional buckling capacity of beam-columns with box-section. The main works and developments are as follows: 1) Comparisons are carried out between the formulae used in the codes of GB50017-2017, AISC LRFD 2016, Eurocode 3 part 1-1 and the formulae derived in the flexural-torsional theory, possible improvements are pointed out. 2) As the first step of the development, plastic interactive relations are obtained for the axial force and bending moments about the strong axis and about the weak axis respectively. Fitting curves with good accuracy are provided for interaction equations of axial force-bending moments about the strong axis and about the weak axis. For the general cases of axial force and biaxial bending moments, exact analysis is carried out for the state of spatial plastic hinges and an approximate interactive equation for biaxial bending under a given axial force is also proposed. The effect of bi-moment is incorporated into the proposed equation. 3) Second-order analysis is carried out for the beam-columns with initial deflection and initial twisting, after introducing a specific relation between the initial deflection and initial twisting, simple expressions are obtained for the lateral displacement, twisting angle, lateral bending moments and bi-moments. 4) Based on the well-accepted and codified column strength reduction factor, the equivalent initial out-of-plane deflections are obtained by taking the buckling strength of the column about the weak axis as a plastic hinge state under the axial force and the amplified bending moment due to the second order effect and initial deflection, this equivalent initial deflection includes the effect of residual stress, initial deflection and the additional deflection increment due to plasticity development. 5) Introducing this equivalent initial deflection into the second-order bending moment about the weak axis and into the bi-moment, together with the second-order in-plane bending moment, they are substituted into the spatial interactive equation of the axial force and biaxial bending moments, the interactive equation of beam-column is derived for flexural-torsional buckling. But this is an upper bound solution of the interactive equation because the process of elastic-plastic development has not been included. After amplifying the second order in-plane bending moment, and further amplifying the out-of-plane bending moments and bi-moment to consider the elastic-plastic development, the obtained equation is applicable. A series of curves are provided to show the interaction curves, the curves are close to the interactive relation of strength when the slenderness is small, and the curves are close to the interactive relation for elastic flexural-torsional buckling when the slenderness is increased, and over it when the slenderness is further increased. The paper proposes also a new formula based on the observation of the derived curves. 6) Comparison shows that the in-plane and out-of-plane stability formluae in the current national code GB 50017—2107 govern safety of the beam-columns together, in the case that the out-of-plane formula is on the unsafe side, the in-plane formula will provide the safety.
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Key words:
- flexural-torsional buckling /
- beam-column /
- box-section /
- second-order effect
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[1] 中华人民共和国住房和城乡建设部.钢结构设计标准:GB 50017-2017[S].北京:中国建筑工业出版社,2018. [2] 郭在田.薄壁箱形截面偏心钢压杆弯扭屈曲的理论和试验分析[J].西安冶金建筑学院学报,1981(2):33-47. [3] AISC. Specification for structural steel buildings:ANSI/AISC 360-10[S]. Chicago:American Institute of Steel Construction, 2010. [3] AISC. Specification for structural steel buildings:ANSI/AISC 360-10[S]. Chicago:AISC, 2010. [4] European Committee for Standardization.Eurocode 3:design of steel structures-part 1-1:general rules and rules for buildings:EN 1993-1-1[S]. Brussels:ECS, 2005. [4] European Committee for Standardization.Eurocode 3:design of steel structures-part 1-1:general rules and rules for buildings:EN 1993-1-1[S].Brussels:ECS,2005. [5] 童根树.钢结构的平面外稳定[M].2版.北京:中国建筑工业出版社,2013. [6] AISC. Specification for structural steel buildings:ANSI/AISC 360-05[S]. Chicago:American Institute of Steel Construction, 2005. [7] 童根树.钢结构的平面内稳定[M].2版.北京:中国建筑工业出版社,2015.
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