Lateral buckling of beams analysed as elastically supported columns subject to a varying axial force

The stability problem for an elasticallu supported column subject to a varying axial force has been solved by means of a general numerical procedure based on Galerkin's method. Apart from the intrinsic value of the solution itself, its possible value modelling some complex stability problems in the area of restrained lateral-torsional stability problems is demonstrated and specific numerical solutions are applied to the case of lateral buckling of the free flange of a composite girder. The results obtained are discussed and suggestions for additional investigations are presented.     

Buckling of elastically restrained beams with web distortions

An energy method is developed for studying the distortional buckling of monosymmetric I-section beams subjected to elastic restraints. The buckling solution is developed in terms of an eigenproblem for four by four symmetric matrices. The distortional buckling of monosymmetric I-beams with translational, minor axis rotational and twisting restraint applied to the smaller tension flange is considered, and the solutions are compared with predictions which assume non-distortion of the cross-section.     

Buckling and post buckling of thin-walled composite columns with intermediate-stiffened open cross-section under axial compression

The thin-walled composite columns with an open cross-section reinforced by intermediate stiffener under axial compression have been considered. The finite element method is employed to study the buckling behaviour of the thin-walled composite column. Eigenvalue analyses are carried out first to predict the buckling load and buckling mode shapes of the column, and then the geometric nonlinear analyses are performed to investigate the nonlinear buckling properties and post-buckling behaviour of the thin-walled structures. The type of angle ply symmetric laminate is used. The investigation is performed over several values of ply arrangement angle and various values of stiffener parameter. The numerical results show a significant effect of the intermediate stiffeners and composite ply angle on loading capacity and buckling behaviour of the thin-walled composite column. The research provides insight into the thin-walled structure and composite laminate, which is employed to enhance the loading capacity of thin-walled composite structures.     

Elastic buckling of cold-formed steel columns and beams with holes

Simplified methods for approximating the global, distortional, and local critical elastic buckling loads of cold-formed steel columns and beams with holes are developed and summarized. These methods provide engineering approximations appropriate for design, but are intended to be general enough to accommodate the range of hole shapes, locations, and spacings common in industry. The simplified methods are developed as a convenient alternative to shell finite element eigen-buckling analysis, which require laborious and subjective visual identification methods as well as commercial software not generally accessible to the engineering community. Global buckling of cold-formed steel beams and columns, including the influence of holes, is predicted with approximate “weighted average” cross-section properties formulated from classical energy-based stability solutions. Distortional and local buckling of a cold-formed steel member with holes are determined with the semi-analytical finite strip method, considering appropriate modifications to the element thickness and choice of buckling half-wavelength. The proposed methods are verified with shell finite element eigen-buckling studies. Unambiguous, simple methods for elastic buckling prediction of members with holes is central to the extension of the Direct Strength Method (DSM) for cold-formed steel member ultimate strength determination.     

Experimental tests of slender reinforced concrete columns under combined axial load and lateral force

The use of high strength concrete (HSC) in columns has become more frequent since a substantial reduction of the cross-section is obtained, meaning that slenderness increases for the same axial load and length, producing higher second order effects. However, the experimental tests in the literature of reinforced concrete columns subjected to axial load and lateral force focus on shear span ratios, according to Eurocode 2 (2004), clause 5.6.3., (M/(V⋅h)) lower than 6.5. This gap in the literature limits technological development for the construction of these structural elements. This paper presents 44 experimental tests on reinforced concrete columns subjected to constant axial load and monotonic lateral force. The aim of this is to gain greater knowledge of the types of elements which will also be of use in calibrating the numerical models and validating the simplified methods. The test parameters are strength of concrete (normal- and high-strength concrete), shear span ratio, axial load level and longitudinal and transversal reinforcement ratios. The strength and deformation of the columns were studied, and an analysis of the simplified methods from Eurocode 2 (2004) and ACI-318 (2008) concluded that both are very conservative.     

Strength design curves and an effective width formula for cold-formed steel columns with distortional buckling

Distortional buckling mode of cold-formed steel thin-walled member is an unstable behavior, and in some cases it may govern the load-carrying capacity of the member. The source, evolution and performance of the formulas and test data for the two strength design curves developed by Hancock are studied, for predicting the load-carrying capacity in the distortional mode. A proposed strength design curve based on available test data and Hancock׳s strength design curves are then compared with the current design methods, the Direct Strength Method and the Effective Width Method, which are incorporated in the “North American specification for the design of cold-formed steel structural members” (AISI-NAS: 2007), “cold-formed steel structures” (AS/NAS 4600: 2005), and the Chinese “Technical specification for low-rise cold-formed thin-walled steel buildings” (JGJ 227-2011). The results indicate that the current design standards adopted the two strength design curves for the DSM and EWM, but they have some differences at the partial extent. A novel formula is proposed for dealing with this problem. The range of applicability of the proposed strength equation is extended from that in AS/NZS 4600 and is shown to be more accurate than AS/NZS 4600 when compared with that in the NAS S100.     

Elastic flexural-torsional buckling of steel beams with rigid and continuous lateral restraints

A simple model of the elastic buckling of steel beams with rigid and continuous lateral restraints has been developed. It is based on a method of displacements that associate lateral restraint conditions. A numerical procedure for resolving the resulting partial differential equations is proposed in which rotations are approximated by trigonometric functions. The effects of moment distribution and continuous restraints on the elastic flexural-torsional buckling of beams are also studied and design approximations and procedures developed. This study also highlights that the restraint of the tensioned part of the beam is not sufficient to limit lateral buckling. The use of these solutions is demonstrated by two examples.     

Iterative system buckling analysis,considering a fictitious axial force to determine effective length factors for multi-story frames

Traditional elastic buckling analysis, based on the system buckling approach, is a convenient tool for the evaluation of effective length factors of columns, in the stability design of multi-story frames. This method is superior to other analytical approaches, such as the isolated subassembly and story-based approaches, in that the inter-story and inter-column interactions are inherently taken into account. Nevertheless, use of the conventional critical load expression, in combination with results of elastic buckling analysis, may yield an excessively large effective length in members having relatively small axial forces. The present paper proposes an iterative elastic buckling analysis to determine reasonable effective length factors of columns in multi-story frames. In this paper, numerical procedures for an iterative buckling analysis using a modified geometric stiffness matrix, are described to obtain the effective length factors of the columns in multi-story frames. The axial force term in the geometric stiffness matrix is modified by adding a fictitious axial force to make the columns buckle along with the overall buckling of the frame. Iterative eigenvalue analysis is performed using the modified geometric stiffness matrix, to obtain the effective length factors of each column using the critical load expression. Example frames presented in this paper demonstrate that the proposed method not only provides excellent outcomes by amending the weakness associated with traditional elastic buckling analysis for determining the effective length factor, but is also a competitive alternative in the design of multi-story frames.     

焊接不锈钢工字形截面梁整体稳定性试验研究

不锈钢材料在建筑结构中已得到广泛应用。为研究焊接不锈钢梁的整体稳定性能,进行了纯弯状态下的静力试验研究。试验包括10个试件,材料类型为奥氏体型316。截面类型采用了双轴对称和单轴对称工字形截面,试件的端部约束采用夹支,试验过程持续加载,直至达到试件的承载力峰值。基于试验结果,研究了焊接不锈钢梁的失稳破坏形态和极限承载力;对比了试验极限弯矩与理论弹性弯矩、塑性弯矩的差异,并将试验结果与有限元分析结果进行了对比。结果表明：试件的承载能力随着跨度的增大而减小,有限元分析能够准确预测试件的承载力,与试验结果吻合良好。     

Limit of axial force ratio and requirement for stirrups of RC columns with special shape

Thousands of columns with special shape are analyzed by nonlinear numerical methods. The ductility is calculated to investigate the limit of the axial force ratio and circumstantial requirement for stirrups of an reinforced concrete (RC) column with special shape, in the point of view of the characteristic value for providing stirrup. The limit of the axial force ratio of columns with special shape in relation to the characteristic value of the stirrup is obtained. Then, the effect of stirrup arrangement on the ductility of the RC column is discussed in case of buckling of the longitudinal reinforcement and constraint concrete columns. The complete requirement for stirrups of RC column with special shape is given. Translated from Journal of Tianjin University (Natural Science Edition), 2006, 39(3): 295–300 [译自: 天津大学学报 (自然科学版)]     

Inelastic buckling analyses of beams, columns and plates using the spline finite strip method

A method of inelastic buckling analysis of thin-walled structural members and plates is described. The method is based on the spline finite strip method of structural analysis. The analysis takes into account the non-linear material stress-strain properties, strain hardening and residual stresses. The plastic theories used in the study are the flow theory of plasticity and the deformation theory of plasticity. The method of inelastic buckling analysis is applied to a variety of instability problems including plates, cold-formed columns, hot-rolled columns and welded tee section beams. The buckling modes and loads computed are compared with theoretical values and test results.     

Proposed design methods for lateral torsional buckling of unrestrained steel beams in fire

The behaviour of unrestrained steel I-beams has been studied by means of numerical analysis and published experimental results. The numerical model was developed using a commercial finite element program, MSC.MARC Mentat. A series of different UB and UC sections and different spans, subjected to both uniform moment and midspan point loads, are considered. The numerical predictions of the buckling moments are then compared with published experimental results. Consequently, a new approach is proposed to provide more accurate and safe predictions of the fire resistance of unrestrained beams, as well as to overcome certain weaknesses in the EC3:1.2 [European committee for standardization (CEN). Eurocode 3: Design of steel structures, Part 1.2: General rules — structural fire design, EN 1993-1-2. Brussels (Belgium); 2005] design formula. In addition, to provide a quick and simple design approach for engineers, a straightforward and rational method known as the Rankine method is introduced to predict the LTB failure load of steel beams in fire. It is shown that the Rankine approach generally provides a good lower bound value for numerical predictions.     

轴压比超限时框架柱的恢复力模型研究

根据收集到的28根轴压比超限时框架柱在固定轴向荷载和水平反复荷载作用下的试验结果,分析回归出试验柱的各位移角和刚度与剪跨比、轴压比、配箍特征值等之间的关系。根据轴压比超限时框架柱屈服的截面平衡条件推出的屈服柱顶水平位移和荷载、按《混凝土结构设计规范》(50010—2002)计算的柱顶水平峰值荷载及有关试验回归公式确定出框架柱的恢复力模型。研究表明:轴压比超限时试验骨架曲线强化段在水平轴上的投影长度和屈服位移的比值与配箍特征值成正比,与轴压比和剪跨比成反比;框架柱的强化刚度与弹性刚度的比值随着轴压比增大而逐渐减小,而随着配箍特征值增大和剪跨比增大而逐渐增大。框架柱最大荷载时的刚度及退化刚度与弹性刚度比值的绝对值随着配箍特征值增大而逐渐减小,而随着轴压比增大和剪跨比增大而逐渐增大;框架柱的卸载刚度和再加载刚度随位移幅值增加而退化,且在不同位移幅值下卸载刚度和再加载刚度的退化率与轴压比有关。本文建议的恢复力模型既可     

960 MPa高强度钢材轴压构件整体稳定性能试验研究

为研究960 MPa高强度钢材轴压构件的整体稳定性能,对6个焊接工字形和等边箱形截面试件进行了静力试验研究,测量了试件的几何初弯曲、荷载初偏心以及截面残余应力分布等初始缺陷,分析了试件的失稳破坏形态,得到了整体稳定承载力,并与规范设计曲线进行了对比分析。利用试验结果验证了有限元分析模型,并进行参数分析。研究结果表明：试件的破坏模态均为整体弯曲失稳,除两个几何初始缺陷过大的试件外,其他试件的整体稳定系数试验值均明显高于规范设计值;参数分析结果表明,960 MPa钢材焊接截面轴压构件的整体稳定系数较普通钢材显著提高,建议采用GB 50017-2003中的a类柱子曲线设计此类轴压构件,同时拟合了960 MPa高强度钢材的柱子曲线公式。     

高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲控制试验研究

针对屈服强度550MPa高强冷弯薄壁型钢轴压构件提出了一种控制畸变屈曲的构造措施--在卷边间设缀板,并通过试验对其有效性进行了验证。试验结果表明：屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件易发生畸变屈曲,通过构造措施能有效地阻止翼缘的转动,试件的畸变屈曲荷载和极限承载力都有很大的提高;随着缀板布置间距的不同,构件承载力的提高幅度也不同;缀板间距越小,试件承载力提高越多,但当缀板间距大于畸变屈曲半波长时,缀板不能起到提高承载力的作用。最后,在此基础上提出了构件不考虑畸变屈曲影响的若干条件,供实际设计参考。     

Elastic, full plastic and lateral torsional buckling analysis of steel single-angle section beams subjected to biaxial bending

Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account.     

Free vibration of partially supported piles with the effects of bending moment, axial and shear force

The pile parts above the soil and embedded in the soil are called the first region and the second region, respectively. The fourth order partial differential equations of both regions for free vibration of partially supported pile subjected to bending moment, axial force and shear force are obtained using the small-displacement theory and the Winkler model. It is assumed that the behavior of the material is linear-elastic, and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the partial differential equations by the second derivative of the elastic curve function with respect to shear deformation. Natural circular frequencies and relative stiffness of the pile are calculated for non-trivial solution of linear homogeneous system of equations obtained due to the values of axial forces acting on the pile, the shape factors, and the boundary conditions of the pile with both ends free and both ends simply supported; the results are presented in graphs.     

Strength of cold-formed lipped channel beams under interaction of local,distortional and lateral torsional buckling

Cold-formed thin-walled lipped channel steel beams may undergo buckling modes such as short half-wavelength local buckling, intermediate half-wavelength distortional buckling and long half-wavelength lateral-torsional buckling or a combination of these before failure. ABAQUS software based on finite element analysis is used to analyse the interaction behaviour of these buckling modes in this study. The finite element model, after calibration with experimental results available in the literature, is used to perform parametric studies, to evaluate the behaviour and strength of such beams under different types of interactions due to variation of material and member properties. The large volume of synthetic data thus generated over a range of failure modes along with the available test results are used to evaluate different equations for calculating the strength of such cold-formed lipped channel beams. Based on the comparison, a method for the design of lipped channel beams failing under the interaction of local, distortional and overall lateral torsional buckling is recommended.     

纵向变厚度钢板焊接工字形截面受压短柱的局部稳定试验研究

纵向变厚度(LP)钢板是一种沿轧制方向具有不同厚度钢板的钢材,可用于优化结构的力学性能和提高材料利用率。为研究其局部稳定性能,设计了6根LP翼缘焊接工字形截面短柱,6根LP腹板焊接工字形截面短柱和4根传统等厚度焊接工字形截面短柱,并进行了轴向受压试验。试验研究中确定板临界屈曲荷载的两个主要屈曲准则,同时分析了破坏模式、荷载-侧向变形曲线、荷载-应变曲线和极限荷载,研究LP短柱的局部屈曲行为,得到试件更容易在LP钢板的薄端发生屈曲破坏。将试验结果与现有等厚度板设计规范计算结果进行比较可得,现有等厚度板的设计规范预测腹板变厚度短柱的极限荷载偏于危险,而对于翼缘变厚度短柱欧规EN 1993-1-5能较为准确预测,但需要进一步的数值模拟去验证,从而进一步提出修正公式或者修正系数来指导设计。     

Analysis of equal leg single-angle section beams subjected to biaxial bending and constant axial compressive force

Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure.