Partially braced inelastic beam buckling experiments

An experimental study of the inelastic buckling behaviour of partially braced I-beams is described. Eleven rolled 250UB37 steel beams, of lengths 7, 9 and 11·2 metres, each having different types of intermediate partial bracing were tested. A specially designed bracing box provided either rotational bracing or lateral bracing to the beam cross section at mid-span. Measurements of initial geometrical imperfections and residual stresses of the test beams were made. Experimental results obtained are in good agreement with the theoretical predictions from a geometrical and material non-linear finite element analysis. The results confirmed that a lateral brace placed at the tension flange is virtually ineffective, while a rotational brace or a lateral brace placed at the shear centre is fully effective. It was found that design loads predicted by the BS5950 and the AISC specifications provided good lower bound estimates to the failure loads of the test beams.     

Inelastic buckling of torsionally braced I-girders under uniform bending: I. Numerical parametric studies

This study examines inelastic buckling of discretely braced I-girders by diaphragm bracings and torsional stiffness requirements to attain nominal flexural design strengths. To simulate the torsionally braced multi-girders, 2-girder and 4-girder systems interconnected with I-shaped cross-beams were numerically modeled by using 3D finite elements. Incremental nonlinear analyses considering the initial imperfections and residual stresses were conducted, and the effect of torsional bracing stiffness on inelastic lateral torsional buckling was evaluated. Based on the parametric analysis results, the torsional stiffness required attaining the inelastic buckling strengths specified by the AASHTO LRFD and Eurocode 3 was examined. It was found that the current design provisions suggested by AISC and SSRC overestimate the required torsional stiffness and may lead to an excessively conservative design. Improved information on the design criteria for the torsional bracings is provided.     

Q460高强钢焊接工字形截面简支梁整体稳定性能与设计方法研究

为研究Q460高强钢焊接工字形截面简支梁的整体稳定性能,对跨中无侧向支撑的3个双轴对称和6个单轴对称焊接工字形截面简支梁进行了整体弯扭屈曲试验。实测了试件的截面残余应力和初始几何缺陷,并分析其整体弯扭屈曲变形特征和稳定承载力。建立考虑残余应力和初始几何缺陷的有限元模型对简支梁受力进行了模拟,模拟结果与试验结果吻合良好,基于试验验证的有限元模型计算了大量不同截面尺寸和跨度的Q460高强钢焊接工字形截面简支梁的整体稳定承载力。将试验和有限元参数分析结果与GB 50017—2017《钢结构设计标准》、JGJ/T 483—2020《高强钢结构设计标准》、欧洲规范EN 1993-2005和美国规范ANSI/AISC 360-2016的简支梁整体稳定系数公式的计算结果进行比较,结果表明GB 50017—2017和ANSI/AISC 360-2016的计算结果偏于不安全,EN 1993-2005的计算结果过于保守,JGJ/T 483—2020的计算结果偏于安全且最为接近。最后,在JGJ/T 483—2020的简支梁整体稳定系数计算公式基础上引入增大系数,并根据截面高宽比的不同,取用不同的长细比指数对该公式予以修正,修正后的公式更适用于Q460高强钢焊接工字形截面简支梁的设计计算。     

Inelastic buckling capacity of beams considering load height effect,stepped flanges,and compact or noncompact sections

This study aims to investigate the effects of load height, stepped beam configuration and section compactness on the inelastic lateral buckling strength of doubly and singly stepped I-beams. To study the effects of load height, the loads are situated at three points: at the center of the top flange, at the shear center and at the center of the bottom flange. To check for the effect of stepped beam configuration, beams were stepped either at both top and bottom flanges or at top flange only. Meanwhile, to investigate the effects of section compactness, two sections are analyzed: one section with compact flanges and web and another section with non-compact flanges and a compact web. The loadings are limited to those having an inflection point of zero. To also check the effect of steps, stepped parameters α, β and γ are varied. The buckling strengths of the beams investigated are obtained by conducting nonlinear analysis using the finite element program, ABAQUS. In conducting the nonlinear analysis, the residual stresses and geometric imperfections are taken into consideration to clearly simulate the inelastic behavior of the beams. The results of the analysis would then determine if the location of the loads, configuration of stepped flanges and compactness of flanges have significant effect on the inelastic buckling strength of the stepped beams.     

对预装体外钢筋的钢-混凝土组合梁弹塑性屈曲的数值分析

连续组合梁的极限承载力由侧向畸变屈曲、局部屈曲,或者由两者的相互作用决定,这一点与纯钢梁的扭转屈曲破坏模式完全不同。利用有限元模型对负弯矩区的组合梁进行了弹塑性有限元分析,其中考虑了初始几何缺陷和残余应力,最终发现有限元分析结果与试验结果吻合良好。另外,对负弯矩区的预装体外钢筋的组合梁进行了参数研究。分析了影响组合梁承载能力和屈曲弯矩抗力的因子,如初始几何缺陷、钢梁的残余应力、力比值、预应力范围、负力矩钢筋、板、翼缘和梁的宽厚比。利用有限元法对负弯矩作用下的25组共200根具有不同截面参数、初始几何缺陷、残余应力和不同力比值的组合梁进行了分析。将计算出的屈曲弯矩率与改进宽厚比的曲线与中国规范中钢柱设计曲线进行了对比。结果证实:对于改进了的宽厚比值,本文依据中国规范的设计曲线推导出来的设计方法可以用于对组合梁屈曲强度的评估。     

Numerical investigation of inelastic buckling of steel–concrete composite beams prestressed with external tendons

The ultimate resistance of a continuous composite beam is governed by either distortional lateral buckling or local buckling, or an interactive mode of the two which is sharply different from the torsional buckling mode in a bare steel beam. A finite element model is developed and based on the proposed FE model, inelastic finite element analysis of composite beams in negative bending is investigated, considering the initial geometric imperfection and the residual stress patterns and the FE results are found agree well with the test results. Parametrical analysis is carried out on the prestressed composite beams with external tendons in negative bending. Factors that influence load carrying performance and buckling moment resistance of prestressed composite beams are analyzed, such as initial geometric imperfection, residual stress in steel beams, force ratio, which is defined as the extent of prestressing force and negative reinforcement in the beams, as well as the slenderness ratios of web, flange, and beams. By varying cross-section parameters, 25 groups of composite beams under negative uniform bending with initial geometric imperfection, residual stress as well as different force ratios, 200 beams in total are studied by means of the FE method. The computed buckling moment ratios are drawn against the modified slenderness proposed by the authors and compared with the Chinese Codified steel column design curve. It is demonstrated that the tentative design method based on the Chinese Codified design curve can be used in assessment of buckling strength of composite beams in a term of the modified slenderness defined.     

Bracing requirements for inelastic castellated beams

Lateral-torsional buckling can be avoided by properly spaced and designed lateral bracing. Bracings are usually assumed to be elastic, and so may be characterized by their elastic stiffnesses. It is well known that an elastic lateral brace restricts partially the lateral buckling of slender beams and increases the elastic buckling moment. However, a full study of the effect of lateral braces on inelastic buckling has not been made especially for castellated beams, and it is not known whether the limiting stiffness for elastic buckling can be applied to castellated beams that buckle inelastically. This paper develops a three dimensional (3-D) finite-element model using a finite-element program and uses it to investigate the effect of elastic lateral bracing stiffness on the inelastic flexural-torsional buckling of simply supported castellated beams with an elastic lateral restraint under pure bending. It was found that for inelastic castellated beams, the effect of bracing initially is increased to some extent as the lateral unbraced length increases and then decreased until the beam behaves as an elastic beam. In other words, the effect of bracing depends not only on the stiffness of the restraint but also on the modified slenderness of the beam. Also, the results show that Winter’s simplified method to determine full brace requirements cannot be applied to inelastic castellated beams. Therefore, a general equation is proposed to determine the value of optimum stiffness in terms of the beam’s slenderness, applicable to all castellated beams under pure bending.     

Lateral buckling strengths of cold-formed rectangular hollow sections

Code rules for designing steel beams against lateral buckling which are based on data for hot-rolled I-sections are unnecessarily conservative when used for cold formed rectangular hollow section beams.Cold-formed rectangular hollow section beams have different stress-strain curves, residual stresses, and crookedness and twist. The effects of residual stress on the inelastic buckling of I-section beams are not nearly as pronounced for hollow sections with two webs, while the strengthening effects of pre-buckling deflections are greater for hollow sections. Simplistic code rules for top flange loading are very conservative when applied to hollow sections.This paper reviews elastic lateral buckling behaviour and the strength rules used to design steel beams. It develops realistic models for cold-formed rectangular hollow beams which are analysed to predict the effects of moment distribution, load height and yield stress on their strengths. The results of the analyses are used to develop improved design rules which remove much of the conservatism of present design rules.     

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.     

Proposed residual stress model for roller bent steel wide flange sections

The manufacturing process of structural wide flange steel sections introduces residual stresses in the material. These stresses due to hot-rolling or welding influence the inelastic buckling response of structural steel members and need to be taken into account in the design. Based on experimental data standardized residual stress models have been proposed for inclusion in inelastic buckling analyses. By incorporating these residual stress models their effect on the resistance of beams and columns can be obtained. Residual stress models for roller bent steel sections are currently not available. Roller bent wide flange sections are manufactured by curving straight members at ambient temperature. This manufacturing technique, which is also known as roller bending, stresses the material beyond its yield stress, thereby overriding the initial residual stresses prior to bending and generating an entirely new pattern. This paper proposes a residual stress model for roller bent wide flange sections, based on earlier conducted numerical investigations which were validated by experimental research performed at Eindhoven University of Technology. The proposed residual stress model can serve as an initial state of a roller bent steel section in fully non-linear finite element analyses to accurately predict its influence on the inelastic buckling response.     

Semi-empirical design of complex metal beams by buckling analysis

Structural elements with complex geometries, boundary conditions and load patterns cannot be designed against buckling using empirical formulae because of uncertain elastic buckling moments or unknown buckling effective lengths, which are basic parameters for these equations. This article proposes a shell finite element procedure for buckling design of metal beams of complex configurations with codified initial imperfections assumed in the Perry–Robertson formula. The advantage of the proposed method lies in the use of elastic buckling moment with empirical design formulae for determination of design moment capacity of a beam; thereby eliminating the uncertainty of modelling initial imperfections. More importantly, the moment modification factor and assumption of effective length can be avoided because all second-order and yield effects have been considered in the computer model. Numerical examples demonstrate that the simplified method has a high level of accuracy, versatility and flexibility for the design of complex beams.     

连续组合梁侧向失稳的弹性地基压杆稳定解

连续组合梁负弯矩区的侧向稳定可等效为弹性地基上的压杆稳定问题。为研究这一问题，分析了变轴力分布对压杆稳定解的影响，探讨采用变轴力弹性地基压杆稳定理论连续组合梁形变侧向失稳的实用设计方法。     

多孔钢梁在组合屈曲模态下的非线性分析

讨论了一般强度和高强度多孔钢梁在组合屈曲模态下的非线性分析。建立一个考虑腹板和翼缘初始几何缺陷、残余应力和材料非线性等情况的多孔钢梁的三维有限元模型。用具有不同长度,不同截面,不同荷载条件和不同失效模态的多孔梁的试验结果验证了此有限元模型。该模型能计算多孔梁的失效荷载,跨中荷载-挠度关系和失效模态。用120根多孔梁的有限元计算数据进行了参数分析,研究截面几何尺寸,梁长和钢材料强度对多孔梁强度和屈曲性能的影响。参数研究结果显示:由于组合腹板的扭转和腹板后屈曲引起的多孔梁失效对承载力有很大的影响。对于长细比较小的多孔梁,应用高强度钢材料将能显著提高失效荷载值。将有限元计算得到的失效荷载与利用澳洲规范计算的多孔梁平面外屈曲计算结果进行了对比,发现规范的计算结果对于平面外屈曲的一般强度多孔梁是不保守的,而对于组合腹板扭转和腹板后屈曲的高强度多孔梁的失效则非常保守。     

卷焊圆管、方管轴压杆的脆性屈曲

钢管截面构件受压时为脆性屈曲,可靠指标β与普通压杆理应有所不同,但目前国内有关设计规范(程)对此都没有反映。本文采用弹塑性梁柱理论、数值积分法计算了卷焊圆管、方管截面轴压杆完整的荷载-位移曲线,分析了纵向焊接残余应力、初弯曲、板件宽厚比(径厚比)对钢管压杆屈曲及屈曲后性能的影响,提出了圆管、方管截面轴压杆稳定承载力计算方法。     

残余应力分布对焊接不锈钢工字形截面梁整体稳定性能的影响

焊接残余应力导致不锈钢梁截面纤维过早达到屈服,并严重降低不锈钢梁的抗弯刚度。为了研究残余应力对焊接工字形不锈钢梁侧扭屈曲的影响,根据目前被广泛采纳的不锈钢工字形截面残余应力分布模型,采用有限元方法,对残余应力分布模型的主要因素进行参数化分析,研究这些因素对不锈钢梁侧扭屈曲的影响,使对焊接工字形不锈钢梁的整体稳定性能的研究更加完善。结果表明:翼缘残余压应力峰值对不锈钢梁侧扭屈曲的影响最为显著。     

Torsional and flexural torsional buckling — A study on laterally restrained I-sections

Torsional and torsional–flexural buckling of columns under axial compression–as defined in the Eurocode 3-1-1(2005)–may practically occur in axially compressed I-sections, which are laterally restrained so that weak axis flexural buckling is prevented and buckling is initiated by torsional deformation about the axis of lateral restraint. The present study is focussed on the development and representation of specific buckling curves for this type of buckling mode. This is based on numerical simulations taking into account material nonlinearities as well as geometric imperfections and residual stresses. The study not only illustrates the typical buckling curves for torsional buckling, but also the transition from torsional buckling to main axis flexural buckling when the column length increases. It also shows that the use of weak-axis buckling coefficients for torsional buckling–as given in the rules of Eurocode 3-1-1–may lead to rather conservative results in many cases.     

Flexural strength of tubular flange girders

A tubular flange girder is an I-shaped steel girder with either rectangular or round tubes as flanges. A tubular flange girder has a much larger torsional stiffness than a conventional I-shaped plate girder of similar weight, which results in a much larger lateral-torsional buckling strength. Finite element (FE) models of tubular flange girders with hollow tubes (HTFGs) are developed in this paper, considering material inelasticity, instability, initial geometric imperfections, and residual stresses. A parametric study is performed using the FE models to study the effects of stiffeners, geometric imperfections, residual stresses, cross section dimensions, and bending moment distribution on the lateral-torsional buckling flexural strength of HTFGs. These analytical results are used to evaluate formulas for determining the flexural strength of HTFGs.     

Inelastic restrained distortional buckling of continuous composite T-beams

This paper develops a method of inelastic buckling analysis of thin-walled sections to study buckling characteristics of single span and two-span composite T-section beams in the inelastic range of structural response. The method is based on a bubble-augmented spline finite strip method, developed elsewhere by the authors, and confirmed as both accurate and efficient for the elastic buckling analysis of thin-walled structural members and plates. The method admits both flexural and membrane buckling deformations and it allows for consideration of structures with intermediate supports and a variety of boundary conditions that may be prescribed at the ends of plate assembly. The analysis includes the so-called Tendon Force Concept developed at Cambridge University for residual stresses caused by the process of fabrication, and the non-linear stress-strain properties of the structural steel from which the joist section is made. The inelastic restrained distortional buckling (RDB) of continuous composite T-section beams under transverse loading and moment gradient is investigated, and conclusions are drawn that address the influence of geometry, residual stresses, member length, the rigid restraint provided by the concrete and the degree of reinforcement in the concrete element.     

Local buckling of steel plates in concrete-filled thin-walled steel tubular beam-columns

The availability of high strength steels and concrete leads to the use of thin steel plates in concrete-filled steel tubular beam-columns. However, the use of thin steel plates in composite beam-columns gives a rise to local buckling that would appreciably reduce the strength and ductility performance of the members. This paper studies the critical local and post-local buckling behavior of steel plates in concrete-filled thin-walled steel tubular beam-columns by using the finite element analysis method. Geometric and material nonlinear analyses are performed to investigate the critical local and post-local buckling strengths of steel plates under compression and in-plane bending. Initial geometric imperfections and residual stresses presented in steel plates, material yielding and strain hardening are taken into account in the nonlinear analysis. Based on the results obtained from the nonlinear finite element analyses, a set of design formulas are proposed for determining the critical local buckling and ultimate strengths of steel plates in concrete-filled steel tubular beam-columns. In addition, effective width formulas are developed for the ultimate strength design of clamped steel plates under non-uniform compression. The accuracy of the proposed design formulas is established by comparisons with available solutions. The proposed design formulas can be used directly in the design of composite beam-columns and adopted in the advanced analysis of concrete-filled thin-walled steel tubular beam-columns to account for local buckling effects.     

钢梁稳定性再研究:国际上的试验研究和理论分析(2)

介绍国际上对钢梁进行试验研究的试验数据以及理论分析,表明如下几个现象和结论:1)焊接梁的稳定系数低于热轧梁;2)焊接梁试验结果的离散性比热轧梁的大;3)早期热轧梁的试件较多,而且为了验证切线模量法,试件的制作和对中比较严格,试验结果偏高;后期随双非线性分析技术和手段的发展,相关试验结果下降;4)初弯曲对稳定系数影响巨大,无法采用残余应力来等效;5)截面的高宽比越大,稳定系数越小;6)荷载形式对稳定系数有不能忽略的影响;7)正则化长细比1.0处的试验结果中,热轧梁稳定系数的下限约为0.6,焊接梁约为0.5。