Torsion in thin-walled cold-formed steel beams

Thin-walled cold-formed steel members have wide applications in building structures. They can be used as individual structural framing members or as panels and decks. In general, cold-formed steel beams have open sections where centroid and shear center do not coincide. When a transverse load is applied away from the shear center it causes torque. Because of the open nature of the sections, torsion induces warping in the beam. This paper summarizes the research on the behavior of cold-formed steel beams subject to torsion and bending. The attention is focused on beams subject to torque, because of the effect of transverse loads not applied at the shear center. A simple geometric nonlinear analysis method, based on satisfying equilibrium in the deformed configuration, is examined and used to predict the behavior of the beams. Simple geometric analyses, finite element analyses and finite strip analyses are performed and compared with experimental results. The influence of typical support conditions is studied and they are found to produce partial warping restraint at the ends. This effect is accounted for by introducing hypothetical springs. The magnitude of the spring stiffness is assessed for commonly used connections. Other factors that affect the behavior of cold-formed steel members, such as local buckling, are also studied.     

Wölbkrafttorsion von Durchlaufträgern mit konstantem Querschnitt unter Berücksichtigung sekundärer Schubverformungen

Warping torsion of continuous beam with constant cross‐section considering shear deformation. The analogy between the theory of warping torsion and second order theory of a bending member with tensile force is also valid, if shear‐deformations in both cases are additionally included. On the basis of this analogy the three‐moment equation for continuous beam with constant cross‐section is given. It is demonstrated, that shear‐deformations for open sections can normally be neglected but must be encluded in the case of hollow‐sections. It is also shown, that for these sections warping‐torsion occurs only in ranges of discontinuity, but causes stresses which are in the same order as the stresses of primary torsion.     

Elastic lateral buckling of cantilever Litesteel Beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.     

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.     

The effect of the warping deformation on the structural behaviour of thin-walled open section shear walls

Thin-walled open section beams are carefully analysed by Vlasov׳s theory of the sectorial areas. It allows to take into account their peculiar warping deformation which appears in the presence of torsional actions. This behaviour determines a further stress state along the axis of the element which is rarely considered in structural analyses. The aim of the present paper is the evaluation of the warping deformation of thin-walled open section beams subjected to torsion. Firstly, the analytical theory proposed by Vlasov is verified through an experimental test on a steel specimen defined by a U profile. Specific analyses are performed with the aim of a sophisticated optical device in order to assess the transverse distortion of the section. Then, the results obtained experimentally and confirmed by a Finite Element (FE) programme permit to validate a computer programme based on the analytical theory and devised to study the structural behaviour of high-rise buildings stiffened by thin-walled open section shear walls. In order to evaluate the effectiveness of the programme, an example which highlights the benefits provided by the present method compared to FE programme is carried out.     

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.     

Section moment capacity tests of LiteSteel beams

The LiteSteel beam (LSB) is a new cold-formed hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. In addition to this unique geometry, the LSB sections also have unique characteristics relating to their stress–strain curves, residual stresses, initial geometric imperfections and hollow flanges that are not encountered in conventional hot-rolled and cold-formed steel channel sections. An experimental study including 20 section moment capacity tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. The presence of inelastic reserve bending capacity in these beams was investigated in detail although the current design rules generally limit the section moment capacities of cold-formed steel members to their first yield moments. The ultimate moment capacities from the tests were compared with the section moment capacities predicted by the current cold-formed and hot-rolled steel design standards. It was found that compact and non-compact LSB sections have greater moment capacities than their first yield moments. The current cold-formed steel design standards were found to be conservative in predicting the section moment capacities of compact and non-compact LSB sections, while the hot-rolled steel design standards were able to better predict them. This paper has shown that suitable modifications are needed to the current design rules to allow the inclusion of available inelastic bending capacities of LSBs in design.     

Bestimmung der Wölbspannungen von doppeltsymmetrischen Kastenquerschnitten mit Diagrammen

Determination of warping stresses of box sections by diagrams. For determination of warping torsion for beams with box section it is sufficient to examine only points with external torsional moments. Moreover in the case of statically indeterminate systems the reaction torsional moments may be calculated neglecting warping torsion completely. This contribution allows the determination of normal and shear stresses of warping torsion by diagrams or alternatively by formulae depending only of two parameters of the section. Warping moment and secondary torsional moment must then not be calculated. The applied theory encludes secondary shear deformation, which is always necessary in the case of hollow sections.     

New design rules for the shear strength of LiteSteel beams

The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section produced using dual electric resistance welding and automated continuous roll-forming technologies. The innovative LSB sections have many beneficial characteristics and are commonly used as flexural members in building construction. However, limited research has been undertaken on the shear behaviour of LSBs. Therefore a detailed investigation, including both numerical and experimental studies, was undertaken to investigate the shear behaviour of LSBs. Finite element models of LSBs in shear were developed to simulate the nonlinear ultimate strength behaviour of LSBs, including their elastic buckling characteristics, and were validated by comparing their results with experimental test results. Validated finite element models were then used in a detailed parametric study into the shear behaviour of LSBs. The parametric study results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs. Significant improvements to web shear buckling occurred due to the presence of torsionally rigid rectangular hollow flanges, while considerable post-buckling strength was also observed. This paper therefore proposes improved shear strength design rules for LSBs within the current cold-formed steel code guidelines. It presents the details of the parametric study and the new shear strength equations. The new equations were also developed based on the direct strength method. The proposed shear strength equations have the potential to be used with other conventional cold-formed steel sections such as lipped channel sections.     

Nonlinear analysis of composite beams with concrete-encased steel truss

Composite beams constituted by a concrete-encased steel truss welded to a continuous steel plate are analyzed using a nonlinear finite element formulation based on Newmark's classical model. The web member of the steel truss is made by deformed or structural steel rebars and behaves like a deformable shear connection. In order to avoid slip locking, finite elements based on second-order interpolation of longitudinal displacements and flexural rotations are employed. Simply supported composite beams subjected to a uniformly distributed transverse load are considered. The bending capacity is evaluated for short up to long spans, taking the nonlinear behavior of concrete, steel and shear connection into account. The effects of the shear connection ductility are put in evidence, showing that, for short spans, the interfacial stress transfer resulting from the yielding of connection may be penalizing. In fact, the high slip gradient arising in sections near the supports may lead to a premature concrete failure. In this case, the exact solution to the linear elastic problem for steel–concrete composite beams can be used for design purposes.     

Behaviour,failure and DSM design of cold-formed steel beams: Influence of the load point of application

This work presents and discusses the results of an ongoing numerical investigation on the buckling, post-buckling, collapse and design of cold-formed steel beams subjected to non-uniform bending due to transverse loadings acting away from the shear centre (either at the top or bottom flange). These results consist of (i) elastic buckling loads and modes, obtained through analyses based on Generalised Beam Theory (GBT), and (ii) elastic–plastic equilibrium paths and collapse loads, yielded by Ansys geometrically and materially non-linear shell finite element analyses. The numerical ultimate strength values are compared with their estimates provided by the current Direct Strength Method (DSM) strength curves and, on the basis of this comparison, it is possible to assess the merits of the DSM approach to design beams subjected to transverse loadings acting away from the shear centre – moreover, novel features that may improve the performance of this approach are identified.     

开口截面钢-混凝土组合梁弯扭性能非线性分析

在钢筋混凝土变角软化桁架模型的基础上,提出了适于分析开口截面钢-混凝土组合梁弯扭性能的三维桁架模型。在弯扭作用下,组合梁截面各单元分别处于一维应力状态(体系1)和二维应力状态(体系2),体系1用来抵抗由弯矩和扭矩引起的截面纵向应力,体系2用来抵抗由扭矩引起的截面剪应力,两者通过截面的纵向应变协调和内力平衡条件联系起来。分析充分满足平衡条件、变形协调条件和材料本构方程。通过对部分试件的计算验证,结果表明该模型不仅可以用于预测组合梁的极限强度,而且为混凝土翼板开裂后组合梁全过程分析,提供了有效途径。     

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.     

A non-linear theory for the behaviour of thin-walled sections subject to combined bending and torsion

Thin-walled steel sections are extensively used in modern building either as purlins or as sheeting rails. Comparatively little is known about the effects of position and orientation with respect to the shear centre of the loading on the stability of such sections. The governing differential equations for the non-linear elastic behaviour of thin-walled sections subject to combined bending and torsion are developed in the paper. They include the non-linear contribution resulting from the movement of the point of application of the load. This is shown to have a significant influence on the behaviour of the member when the loads are inclined to the principal axes, as in the case of an asymmetrical section subject to gravity loading. Furthermore, it is shown that load resultants which pass through the shear centre but which are inclined to the principal axes of the section do not produce pure bending. They induce torsional moments in the section which are not accounted for in traditional theories. A finite-difference method is used to solve the equations, and the validity of the theory is assessed by comparing the results with those obtained from experiment.     

Experimental study of web crippling behaviour of hollow flange channel beams under two flange load cases

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel beam (LSB) subject to web crippling under End Two Flange (ETF) and Interior Two Flange (ITF) load cases. The LSB sections with two rectangular hollow flanges are made using a simultaneous cold-forming and electric resistance welding process. Due to the geometry of the LSB, and its unique residual stress characteristics and initial geometric imperfections, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending, predominant shear and combined actions. To date, however, no investigation has been conducted on the web crippling behaviour and strength of LSB sections. Hence an experimental study was conducted to investigate the web crippling behaviour and capacities of LSBs. Twenty-eight web crippling tests were conducted under ETF and ITF load cases, and the ultimate web crippling capacities were compared with the predictions from the design equations in AS/NZS 4600 and AISI S100. This comparison showed that AS/NZS 4600 and AISI S100 web crippling design equations are unconservative for LSB sections under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of LSBs based on experimental results. Suitable design rules were also developed under the direct strength method (DSM) format.     

Influence of shear deformation on restrained torsional warping of pultruded FRP bars of open cross-section

Pultruded FRP bars of open cross-section possess relatively low transverse shear moduli in relation to their axial and flexural moduli. This can result in shear deformation constituting a significant proportion of the total deformation induced by non-uniform bending, and a reduction in the buckling loads of members subjected to axial compression and bending. Herein an approximate theory for quantifying the influence of shear deformation on the restrained torsional warping of pultruded FRP bars of open cross-section is presented. Contrary to expectations the theory indicates that the influence of shear deformation on the restrained warping torsional stiffness of such members is not significant. The theory is validated by a series of bending and torsion tests on three pultruded FRP I-beams.     

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。     

Torsions‐Querschnittswerte für rechteckige Hohlprofile nach EN 10210‐2:2006 und EN 10219‐2:2006

The new European Standards EN 10210‐2:2006 and EN 10219‐2:2006 contain the necessary cross‐section values for calculation of primary torsion (St. Venant‐torsion). In the following paper all cross‐section values for secondary torsion are additionally given, so that calculation of normal and shear stresses of the warping torsion is possible. These stresses cannot be neglected, but occur only at certain points of disturbance. For hollow sections it is always necess‐ary to take into consideration the shear deformations of warping torsion.     

Global optimization of cold-formed steel channel sections

Cold-formed steel sections have an important advantage which is the great flexibility of cross-sectional profiles and sizes available to structural steel designers. However, this flexibility makes the selection of the most economical section difficult for a particular situation. This paper presents a global optimization method for designing the cross-section of channel beams subjected to uniformly distributed transverse loading. The optimization of the cross-section is performed using the trust-region method (TRM) based on the failure modes of yielding strength, deflection limitation, local buckling, distortional buckling and lateral–torsional buckling. Numerical examples include the comparisons of the optimized sections obtained based on the applications of BS 5950-5 standard and the recently developed ENV-1993-1-3.     

Shear buckling characteristics of cold-formed steel channel beams

Cold-formed steel members are increasingly used as primary structural elements in the building industries around the world due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. For the shear design of LCB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of LCB web panels are determined by assuming conservatively that the web panels are simply supported at the junction between their flange and web elements. Hence finite element analyses were conducted to investigate the elastic shear buckling behavior of LCBs. An improved equation for the higher elastic shear buckling coefficient of LCBs was proposed based on finite element analysis results and included in the ultimate shear capacity equations of the North American cold-formed steel codes. Finite element analyses show that relatively short span LCBs without flange restraints are subjected to a new combined shear and flange distortion action due to the unbalanced shear flow. They also show that significant post-buckling strength is available for LCBs subjected to shear. New equations were also proposed in which post-buckling strength of LCBs was included.