轴向压力和均布载荷作用下压杆的屈曲研究

采用摄动法研究了压杆在轴向压力和轴向均布载荷联合作用下的弹性屈曲问题,推导出了压杆弹性屈曲模态函数和屈曲载荷的特征方程,并讨论分析了轴向压力与轴向均布载荷对压杆弹性屈曲的影响.实例计算证明,摄动法计算的结果与Bessel函数法计算的结果相差较小.     

初始扭转轴压杆弹性弯曲屈曲性能研究

初始扭转杆在工程设计中有着广泛的应用.通过对初始扭转轴压杆弹性弯曲屈曲性能的研究表明,初始扭转轴压杆弹性弯曲屈曲位移在两截面主轴平面上相互耦合.初始扭转角使得强轴对压杆绕弱轴的屈曲位移产生"抵抗"作用,从而提高了杆的弹性弯曲屈曲临界荷载.同时,提出基于初始扭转轴压杆弹性弯曲屈曲变形后的位移曲线是平面位移曲线的假定,提出需进一步验证分析.     

初始扭转轴压杆弯曲屈曲性能有限元验证分析

通过对初始扭转轴压杆弹性弯曲屈曲性能的研究表明:初始扭转轴压杆弹性弯曲屈曲位移在两截面主轴平面上相互耦合.初始扭转角使得强轴对压杆绕弱轴的屈曲位移产生"抵抗"作用,从而提高了杆的弹性弯曲屈曲临界荷载.以有限元法对初始扭转角不同的轴压杆进行参数分析表明,弹性弯曲屈曲变形后,其位移曲线是一条空间曲线,随着初始扭转角的增加,屈曲后位移曲线偏离同一平面的幅度变大.     

初始扭转轴压杆弹性扭转屈曲性能研究

初始扭转杆在工程设计中有着广泛的应用。通过对初始扭转轴压杆弹性扭转失稳性能的研究表明:初始扭转轴压杆弹性扭转屈曲承载力与初始扭转角ω无关,与一般无初始扭转轴压杆扭转失稳承载力相等。同时,还以有限元法对初始扭转角不同的轴压杆进行参数分析,验证了初始扭转轴压杆弹性扭转失稳的理论值的正确性。     

开口薄壁截面悬臂压杆的稳定问题研究

根据能量泛函变分原理,推导开口薄壁杆件在杆端压力P和沿杆轴向均匀分布压力q共同作用下的控制方程,并采用伽辽金法求解,研究开口薄壁截面悬臂压杆的稳定问题,计算荷载P和ql不同比例情况下的临界荷载和P-ql临界荷载包络线。     

薄壁截面杆件的自由扭转变形能力比较

近些年建筑行业对薄壁杆件的应用在迅猛增加,冷弯形成的各种杆件以及焊接、热轧薄壁杆件在钢结构中比比皆是。本文进行对比研究相同材料用量下工字形、T形开口薄壁截面杆和圆形、箱型、三角形闭口薄壁截面杆在自由扭转时的变形能力,分析了相同材料用量下工字形、箱形和三角形薄壁截面杆高宽比对截面扭转变形能力的影响。     

轴心受压开口薄壁构件弹塑性屈曲荷载的统一计算方法

通过分析构件截面上应变与轴向力间的关系，以构件轴向应变为基本参数，提出了轴心受压开口薄壁构件的弹塑性屈曲荷载统一计算方法，给出了轴压构件的弯曲屈曲、扭转屈曲、弯扭屈曲等屈曲荷载的弦截法迭代格式，可应用于H形、T形、L形、十形截面等不同开口形式的轴压构件屈曲荷载计算，并可考虑具有残余应力的弹塑性本构关系。该方法以无残余应力的弹性屈曲荷载对应的轴向应变作为初始值，根据不同屈曲形式对应的非线性方程计算弦截区间点的函数值，进行弦截法迭代计算，得到弹塑性构件的临界轴向应变，进而获得屈曲荷载等信息。该方法采用的弦截法收敛速度快、计算量小、无需嵌套循环，可有效解决两端铰接轴心受压开口薄壁构件的弹塑性屈曲快速计算问题，便于工程应用。     

弹性支承上简支约束长矩形薄板面内剪切作用下屈曲行为分析

近年来,钢-混组合结构在工程中广泛应用,薄壁钢板在组合结构承载过程中易发生局部屈曲。矩形钢管混凝土作为结构梁时,薄壁钢板易发生弯剪局部屈曲;薄壁钢-混凝土组合墙在抵抗水平作用时,钢板也易发生剪切屈曲。组合结构中充当支承的材料除了刚性混凝土,还有轻质弹性材料。论文采用Rayleigh-Ritz法,对弹性支承上简支约束长矩形薄板面内剪切受力条件下的屈曲行为进行分析研究,建立了满足上述边界条件的板的弹性屈曲计算公式。计算结果表明:该理论计算方法对于长矩形薄板(长宽比大于2)的屈曲具有广泛适用性。     

薄壁槽形截面压杆弹性整体屈曲数值计算研究

为研究薄壁槽钢整体屈曲下的数值算法的适用性,以4种不同杆端约束下的薄壁槽形截面压杆为研究对象,根据广义梁理论确定其发生弹性整体屈曲的有效长度及临界荷载,与开口薄壁理想压杆的线性及非线性解析解进行对比,得到一致的临界荷载。利用ABAQUS有限元分析软件建立壳体有限元模型,采用杆端截面形心集中加载,依据约束情况确定杆端约束,以及根据有效长度施加不同初始缺陷的计算模型,开展特征值算法和隐式弧长法数值计算分析。计算结果表明:当开口薄壁压杆的有效长度足够大时,临界荷载的特征值数值解与理论解一致,弧长法计算得到的非线性解误差相对较大。当有效长度不够大时,弧长法计算得到的极限荷载与理论解基本一致,且弧长法可有效追踪后屈曲路径。     

采用遗传算法编程的公式计算冷弯型钢构件的扭转屈曲应力

研究的主要目的是开发一种基于遗传算法编程的计算公式,用于计算压力作用下冷弯型钢构件的弹性扭转屈曲应力。计算和试验中所采用的数据,是从各类文献中收集而来的。提出2个基于遗传算法的公式,用以预测冷弯C型钢的弹性扭转屈曲。将计算结果与其他研究人员和其他方法的分析结果相对比,证实这种计算公式是准确的。结果显示在预测冷弯C型钢截面的弹性屈曲应力方面,遗传算法编程非常具有发展前景。     

Torsional vibrations and buckling of thin-walled beams on elastic foundation

The problem of free torsional vibration and buckling of doubly symmetric thin-walled beams of open section, subjected to an axial compressive static load and resting on continuous elastic foundation, is discussed in this paper. An analytical method based on the dynamic stiffness matrix approach is developed, including the effects of warping. The resulting transcendental equation is solved for thin-walled beams clamped at one end and simply supported at the other. A computer program is developed, based on the dynamic stiffness matrix approach. The software consists of a master program to set up the dynamics stiffness matrix and to call specific subroutines to perform various system calculations. Numerical results for natural frequencies and buckling load for various values of warping and elastic foundation parameter are obtained and presented.     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

Lateral torsional stability analysis of large order space frame systems

In this paper the elastic stability of rigid space frames is investigated with the aid of the finite element method. The element stiffness matrix for second order (stability) analysis is formulated on the basis of open thin-walled element theory considering the coupling of torsional and flexural behaviour in three dimensions under the assumption of small deformations. A first order (static) analysis is done first in order to calculate the axial force distribution in the members, and the vanishing of the determinant of the global stability stiffness matrix is the criterion used to obtain the critical load of the structure. The rigid space frames investigated here by the proposed methodology consist of commonly used steel joists with horizontal or X-bracing connecting them. The effects of the support conditions and bracing configuration on the buckling loads of various steel joist systems are studied. Useful conclusions are drawn and comparisons with existing experimental results are made.     

Buckling analysis of thin-walled members with closed cross sections

In this paper, an analytical procedure for the elastic buckling problems of thin-walled members with closed cross sections by the transfer matrix method is presented. The transfer matrix is obtained from the differential equations for a plate subjected to axial load, and the extended transfer matrix for closed cross sections is derived from that for branched panels. The analytical local and overall elastic buckling loads for thin-walled members with closed cross sections can be obtained simultaneously. Furthermore, a technique to estimate the buckling mode shapes of these members is also shown. To investigate the accuracy and efficiency of this method, some numerical examples are presented.     

Buckling analysis of thin-walled open members—A finite element formulation

In a companion paper, a variational principle based on the principle of stationary complementary energy was developed for the buckling analysis of thin-walled members with open cross-sections. In this paper, the variational principle is adopted to formulate a finite element buckling solution. The formulation successfully incorporates shear deformation effects, a feature that is neglected in most available buckling solutions. By adopting a non-orthogonal coordinate system, the solution successfully captures the transverse load position effect relative to the shear center. A series of examples demonstrate the validity of the finite elements formulated and their applicability to a wide variety of buckling problems. Examples include column flexural and torsional buckling, lateral torsional buckling of beams with a variety of end conditions and subjected to a variety of moment gradients. The formulation is shown to be applicable to beams with mono-symmetric sections. In all cases, the validity of the new solution is assessed and established through comparisons to well-established closed-form and/or numerical solutions.     

单角钢压杆的屈曲及稳定计算

在钢结构工程中经常采用等边或不等边单角钢作为轴心受压构件,现行钢结构设计规范(GB50017—2002)提供了等边单角钢压杆的截面类别及稳定计算方法,但对不等边单角钢压杆的规定相对粗糙。本文根据弹性稳定理论和角钢截面特征规律,推导了等边及不等边单角钢轴心受压构件的屈曲条件和长细比简化计算方法,并给出了稳定设计方法。扭转屈曲换算长细比仅与角钢肢宽与肢厚的比值有关,这使得弯扭屈曲换算长细比的计算也进一步简化。经过验证,该方法简单实用,可供工程设计参考。     

板件中间加劲的复杂卷边槽钢轴压构件弹性畸变屈曲应力的实用计算法

为了研究板件中间加劲的复杂卷边槽钢轴压构件畸变屈曲临界应力的简便计算方法,应用有限条分析软件CUFSM对冷弯薄壁板件中间加劲的复杂卷边槽钢以及腹板中间V型加劲的复杂卷边槽钢共90个轴压构件进行数值模拟,分析各参数对构件弹性畸变屈曲临界应力的影响。经拟合分析,得出针对板件中间加劲的复杂卷边槽钢、腹板中间V型加劲的复杂卷边槽钢轴压构件的弹性畸变屈曲临界应力的简化计算公式,并验证该公式的有效性。     

Performance-based analysis of concrete-filled steel tubular beam-columns, Part I: Theory and algorithms

This paper presents a performance-based analysis (PBA) technique based on fiber element formulations for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam-columns with local buckling effects. Geometric imperfections, residual stresses and strain hardening of steel tubes and confined concrete models are considered in the PBA technique. Initial local buckling and effective strength/width formulas are incorporated in the PBA program to account for local buckling effects. The progressive local buckling of a thin-walled steel tube filled with concrete is simulated by gradually redistributing normal stresses within the steel tube walls. Performance indices are proposed to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam-columns under axial load and biaxial bending. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral axis in a thin-walled CFST beam-column section to satisfy equilibrium conditions. The analysis algorithms for thin-walled CFST beam-columns under axial load and uni- and biaxial bending are presented. The PBA program can efficiently generate axial load-strain curves, moment-curvature curves and axial load-moment strength interaction diagrams for thin-walled CFST beam-columns under biaxial loads. The proposed PBA technique allows the designer to analyze and design thin-walled CFST beam-columns made of compact or non-compact steel tubes with any strength grades and normal and high-strength concrete. The verification and applications of the PBA program are given in a companion paper.