Lateral–distortional buckling of monorails

This paper is concerned with the elastic lateral–distortional (LD) buckling of single span steel monorail I-beams and its influence on their design strengths. The distortion of a slender web reduces the elastic buckling resistance of an intermediate length beam below its flexural–torsional (FT) resistance. A finite element computer program was used to study the elastic LD buckling of single span beams. The LD to FT buckling moment ratios were generally higher for simply supported beams with bottom flange central concentrated loads than for uniform bending, and lower for shear centre concentrated loads. For beams with bottom flange loading and unrestrained bottom flanges, there were very significant reductions in these ratios, but they increased when rigid web stiffeners or top flange torsional restraints were provided at the supports. For beams with bottom flange loading and unrestrained bottom flanges, the reductions in the elastic buckling resistance were greater for beams with stocky flanges than for slender flanges. Approximations were found for estimating the reduced resistances which were generally of high accuracy or conservative, and for estimating the increased resistances caused by elastic and rigid top flange end torsional restraints. A method of designing steel beams against LD buckling was proposed and its use demonstrated by a worked example.     

A study on local buckling behavior of hybrid beams

In this paper, the local buckling behavior of hybrid beams, with high-strength steel webs and mild steel flanges, is investigated. A wide-flange shaped member is essentially an assemblage of plate elements and then the plate buckling has a significant effect on the plastic deformation capacity of a beam, while the web provides the flange with some degree of rotational restraint against local buckling. The torsional restraint of the web against the flange inelastic buckling depends on the web stiffness, namely, the length of the plastic region in the web. A hybrid beam with high-strength steel webs and mild steel flanges is considered to be effective in carrying loads after the flange local buckling. The results of investigation are presented herein.     

Stability of web plates in W-shape columns accounting for flange/web interaction

North American, British and European codes of practice provide design equations for local buckling limit state of W-shape columns, by assuming the web and the flanges are either simply supported or clamped along their lines of junctions. In doing so, the geometric interactions between the web and flange are ignored. In practice, the column webs rarely have simply supported or clamped edges but are rather elastically restrained against rotation. In addition, the in-plane boundary conditions of the web, which is dictated by geometric properties of the flanges, have a great influence on its buckling and post-buckling stiffness. The paper highlights the influence of the flange/web geometric proportions on the stability of web plates in W-shape columns under uniform compression. Results are obtained showing the influence of the flange/web thickness (t_f/t_w) on the buckling and post buckling stiffness of the web. Also, the influence of the flange/web width (b_f/b_w) on the web stability is highlighted. Graphs are presented showing the transitions between various “theoretical” boundary conditions by adjusting the flange/web geometric proportions. These graphs are useful to use in practice in order to achieve economical design of column section.     

剪切作用下冷弯槽钢的弹性屈曲

研究与腹板平行的纯剪切荷载作用下包含翼缘和卷边的整个槽钢截面的弹性屈曲,并给出了解决方案。采用样条有限条法(SFSM)对纯剪切作用下的薄壁槽钢进行弹性屈曲分析,以获得截面的弹性屈曲载荷(Vcr)。利用剪切屈曲载荷计算用于截面设计的腹板的剪切屈曲系数(KV)。主要变量为翼缘宽度、构件长度和卷边尺寸。边界条件为两端简支。根据分析结果绘制交互作用曲线,可作为设计指南,使得设计人员不用样条有限条法(SF-SM)软件也能够预测弹性屈曲剪切系数(KV)。给出了不同的翼缘宽度、构件长度和卷边尺寸下构件的典型屈曲模态。包括局部屈曲和翼缘屈曲,畸变屈曲和截面扭曲。     

Structural behavior of hybrid FRP composite I-beam

This paper presents the structural behavior of an innovative hybrid Fiber Reinforced Polymers (FRP) beam consisting of carbon/glass fibers and vinyl-ester resin. The advanced feature of this hybridization is the optimum use of carbon and glass fibers in the flanges to maximize structural performance while reducing the overall cost by using only glass fibers in the web section. A series of beam tests were conducted under four-point bending varying ratio of flange to web width (b_f/b_w) and volume content of carbon and glass fiber in the flanges. Experimental investigations revealed that the ratio of flange to web width of hybrid FRP I-shaped beams plays an important role in their structural behavior. Small flange beams (b_f/b_w = 0.43) showed stable and linear behavior under bending moment and failed in a brittle manner by delamination of the compressive flange at the interfacial layers while wide flange beams (b_f/b_w = 1.13) exhibited unstable and nonlinear behavior in the buckling and post-buckling region leading to delamination failure of the compressive flange. The experimental and analytical results discussed in this paper emphasize on the best composition of carbon and glass fibers for the optimum design of such hybrid beams. It is found that the maximum strength of hybrid FRP beams can be obtained with the volume content of carbon fiber to be 25–33%. Furthermore, the results of this study show the potential of applying hybrid FRP beams for bridge components.     

Predicting the maximum compressive beam axial force during fire considering local buckling

Local buckling in floor beams has been one of the important observations in several fire events in steel buildings such as World Trade Center Tower 7 and large-scale fire experiments such as Cardington building test in U.K. Utilizing three dimensional finite element methods for complex geometry and nonlinear behavior of such connections, local buckling of the web followed by the buckling of the lower flange is observed to occur in early stages of fire, which causes instability to the floor system, and a significant reduction in the connection strength. The observations also suggest that the maximum compression in the floor beam is limited to the buckling capacity of the web and flanges near the connection. This paper contributes to such knowledge by investigating the local buckling of floor beams for different connection types at elevated temperatures using nonlinear finite element models. Moment connections are found to be more resistant to local buckling when compared to the shear connections. The results are also compared to the AISC design equation for plate buckling under ambient and elevated temperatures. Compared to the finite element analyses of this study, it is observed that at ambient temperature the AISC curve conservatively captures the buckling capacity of webs and flanges; at higher temperatures, AISC overestimates the capacity.     

嵌套连接冷弯斜卷边Z形连续檩条的受弯性能试验研究

本文对嵌套连接的冷弯斜卷边Z形连续檩条的受弯性能进行了试验研究。试验分两部分,一是搭接段极限承载力试验,以确定常用范围内搭接负弯矩段的极限承载力;二是两跨连续檩条试验,目的是确定搭接段截面的抗弯刚度。试验分上下翼缘均有自攻钉和仅上翼缘有自攻钉两种情况。对于承载力试验,搭接长度的范围为截面高度的3～5.625倍。通过对5种不同搭接长度和方式共30个试件的破坏性试验发现,破坏都是由受压下翼缘的屈曲引起,且破坏主要发生在搭接开始处。当中间支座处弯矩是搭接开始处弯矩的两倍时破坏出现在中间支座处,此时单个截面的承载力仍然与破坏发生在搭接开始处的情况接近。在试验所用试件的搭接长度范围内,搭接长度对承载能力的影响不大;但搭接段檩条下翼缘是否有自攻钉对搭接段承载能力有约5%的影响。对两跨连续梁,分搭接长度为跨度的10%和20%的两种情况,上下翼缘均有自攻螺钉和仅上翼缘有自攻螺钉两种构造,共进行了11个试验,试验结果表明,搭接长度较长时搭接     

Comprehensive stability design of planar steel members and framing systems via inelastic buckling analysis

This paper presents a comprehensive approach for the design of planar structural steel members and framing systems using a direct computational buckling analysis configured with appropriate column, beam and beam-column inelastic stiffness reduction factors. The stiffness reduction factors are derived from the ANSI/AISC 360-16 Specification column, beam and beam-column strength provisions. The resulting procedure provides a rigorous check of all member in-plane and out-of-plane design resistances accounting for continuity effects across braced points as well as lateral and/or rotational restraint from other framing. The method allows for the consideration of any type and configuration of stability bracing. With this approach, no member effective length (K) or moment gradient and/or load height (C _b ) factors are required. The buckling analysis rigorously captures the stability behavior commonly approximated by these factors. A pre-buckling analysis is conducted using the AISC Direct Analysis Method (the DM) to account for second-order effects on the in-plane internal forces. The buckling analysis is combined with cross-section strength checks based on the AISC Specification resistance equations to fully capture all the member strength limit states. This approach provides a particularly powerful mechanism for the design of frames utilizing general stepped and/or tapered I-section members.     

负弯矩区Π型组合梁的连接强度与刚度

研究了加肋腹板连续组合梁的横向连接刚度和强度。采用横向腹板劲肋 ,加强了组合梁刚性上翼缘 (混凝土板 )对工字梁下翼缘的横向约束 ,能有效提高组合梁的侧向失稳荷载 ,但在钢梁上翼缘与钢筋混凝土板连接区域会产生较大的横向集中力。该集中力会导致混凝土板与下部钢梁上翼缘连接区的强度破坏 ,在设计中必须予以考虑     

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.     

Optimal design of a mono-symmetrical open cross section of a cold-formed beam with cosinusoidally corrugated flanges

The paper is devoted to a thin-walled beam with a flat web and cosinusoidally corrugated flanges. Considered beam has an open cross section and is mono-symmetric. Two different types of load are taken into account, i.e. pure bending and uniformly distributed load. The authors are searching for an optimal cross section shape of the beam. The beam cross section is characterized by dimensionless parameters, which are design variables. The dimensionless objective function is so defined as to comprise both a cross section area and a maximal allowable bending moment. The constraints follow from the local buckling condition for corrugated flange and geometric restrictions. The beams with different length to height ratio are analyzed. Results of the numerical calculations are presented graphically.     

Elastic buckling of I-beam flanges subjected to a linearly varying stress distribution

Lateral forces or torsion combined with major axis bending result in a stress gradient across the compression flanges of I-shaped flexural members. Sources that cause significant stress gradient include situations where unequal reactions come to opposite sides of a girder or beams that frame into one side of a girder, skewed bridge girder supports, wind loading on facia girders, curvature induced warping, etc. In this study, three sets of support conditions are considered for evaluating the elastic buckling capacity of flanges of I-shaped beams subjected to a stress gradient. This includes a Galerkin series solution that considers the full width of the flange plate with a variable rotational stiffness along the center of the plate. For a stress gradient leading to tension over part of the flange, equations for predicting the buckling capacity are developed using finite element analyses. Simplified equations are developed for I-shaped cross sections, and numerical examples are used to demonstrate the accuracy of the solution. A definition of the noncompact limit for flanges of I-shaped beams and girders subjected to stress gradient is presented.     

Proposing two new methods to decrease lateral-torsional buckling in reduced beam section connections

Reduced web section (RWS) connections can prevent lateral-torsional buckling and web local buckling experienced by reduced beam section (RBS) connections. In RWS connections, removing a large portion of web can result in shear demand intolerance induced to plastic hinge region. The present study aims to resolve the problems of RBS and RWS connections by proposing two new connections: (1) RBS with stiffener (RBS-ST) and (2) RBS with reduced web (RW-RBS) connections. In the first connection (RBS-ST), a series of stiffeners is connected to the beam in the reduced flange region, while the second connection (RW-RBS) considers both a reduction in flanges and a reduction in web. Five beam-to-column joints with three different connections, including RBS, RBS-ST, and RW-RBS connections were considered and simulated in ABAQUS. According to the results, RBS-ST and RW-RBS connections can decrease or even eliminate lateral-torsional buckling and web local buckling in RBS connection. It is important to note that RW-RBS connection is more effective in long beams with smaller shear demands in the plastic hinge region. Moreover, results showed that RBS and RW-RBS connections experienced strength degradation at 4% to 5% drift, while no strength degradation was observed in RBS-ST connection until 8% drift.     

Elastic shear buckling characteristics of LiteSteel beams

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam. The unique LSB section is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. To date, limited research has been undertaken on the shear buckling behaviour of LSBs with torsionally rigid, rectangular hollow flanges. For the shear design of LSB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the flange and web elements. Therefore finite element analyses were carried out to investigate the elastic shear buckling behaviour of LSB sections including the effect of true support conditions at the junction between their flange and web elements. An improved equation for the higher elastic shear buckling coefficient of LSBs was developed and included in the shear capacity equations of Australian cold-formed steel codes. Predicted ultimate shear capacity results were compared with available experimental results, both of which showed considerable improvement to the shear capacities of LSBs. A study on the shear flow distribution of LSBs was also undertaken prior to the elastic buckling analysis study. This paper presents the details of this investigation and the results including the shear flow distribution of LSBs.     

Post-Northridge connection with modified beam end configuration to enhance strength and ductility

In order to enhance the strength and ductility of post-Northridge connections with beam depths varying from 450 mm to 912 mm, two parallel horizontal long voids were opened on their beams web. Results showed that the proposed beam end configuration (BEC) is effective in moving the plastic hinge away from the column face. Adding web stiffeners and two tubes at the center of voids were effective in preventing excessive beam flange/web buckling. Based on the analytical results a step by step design procedure is proposed to determine the most suitable geometry for the BEC to achieve adequate connection strength and ductility.     

Effect of moment of inertia on elastic stability of rectangular webs for thin-walled beams under a transverse load

So far, the equations for buckling capacity of web panels focus on thin-walled beams with very strong flanges. In this paper, elastic buckling behavior of web panels of thin-walled beams with weak flanges is further studied, aiming at a buckling coefficient formula unifying the effect of both weak and strong flanges. A new parameter, the flange-to-web ratio of moment of inertia, is proposed to characterize the effect of flanges. Then, a semi-analytical method is applied to investigate the buckling behavior of simply supported web panels, in two cases, inclusive or exclusive of effect of the moment of inertia of flanges. It is revealed that elastic buckling load, in particular, the buckling coefficient of web panel is a function of two key parameters, web aspect ratio and flange-to-web ratio of moment of inertia. Meanwhile, a finite element analysis (FEA) model allowing for the sensitivity of boundary conditions is validated by comparing with the semi-analytical solution to the case exclusive of effect of the moments of inertia of flanges. Next, numerical results are utilized to illustrate the influence of the previous parameters, which verify the increase of buckling coefficient with flange-to-web ratio of moment of inertia or the decrease of buckling coefficient with web aspect ratio. Besides, it also verifies that for the same flange-to-web ratio of moment of inertia, the buckling behavior of square web panels is closer to the uniform shear buckling than other rectangular web panels. Finally, an accurate design formula is proposed to calculate buckling coefficient of web panel.     

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.     

Plastic mechanism analysis of unstiffened steel I-section beams strengthened with CFRP under 3-point bending

This paper presents experiments and theoretical analysis of 16 steel I-section beams strengthened using externally bonded CFRP under quasi-static large deformation 3-point bending. The main parameters examined in this paper were the section and member slenderness and the location of the CFRP plates. The member slenderness examined in this paper was in the range of L_e/r_y=40–92. The section slenderness examined in this paper was in the range of b/t_f=6.25–16.67. The CFRP plates were added either to the tension flange or both compression and tension flanges or even to the whole section including the web. An expression for the yield and plastic moments of the composite section were obtained by means of an equivalent thickness approach for the web and flange. The newly obtained strength results were compared against the present design rules in steel specifications. The CFRP increased the strength by up to 32% for compression and tension flange strengthening whereas the strength increased only by 15% for tension flange strengthening. The per cent increase in strength for short specimens was mostly affected by the section slenderness where the maximum gain was obtained for the semi-compact section. Plastic mechanism analysis was performed to predict the collapse curves. Good agreement was found between the theoretical and experimental post buckling load–deflection curves.     

Lateral buckling resistance of inelastic I-beams under off-shear center loading

Lateral-torsional buckling (LTB) strength of steel I-beams subjected to moment gradient loading is scaled by the moment gradient factor, C_b. The C_b factor depends on the non-uniformity of moment diagram, the height of the applied transverse loads within the unbraced length and end conditions. Generally, the C_b factors given by codes have been derived from elastic LTB analysis theory. However, the same C_b factors are used for beams that buckle inelastically. This paper develops a three dimensional finite element model using ANSYS for the inelastic nonlinear flexural-torsional analysis of I-beams and uses it to investigate the effects of unbraced length and central off-shear center loading (located at center, top flange and bottom flange) on the moment gradient factor in inelastic behavioral zone. It is found that the C_b factors given by AISC-LRFD in Specification for structural steel buildings (AISC 360-05) and Structural Stability Research Council Guidelines are not accurate for the point load cases applied at center and bottom flange in which I-beam buckles inelastically. It is seen also that the AISC-LRFD flexural resistance equations overestimate the actual moment capacity of inelastic I-beams under moment gradient. Therefore, a simple equation is proposed to be used instead of the code equation in inelastic zone for the investigated load cases in this paper.