Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.     

Ein Bemessungsansatz für zweiachsig durch Querkräfte beanspruchte Stahlbetonbalken mit Rechteckquerschnitt

Design of Reinforced Concrete Beams with rectangular Cross Sections against biaxial Shear Forces An approach is presented to design reinforced concrete beams with rectangular cross sections and usual stirrups against shear forces that act inclined to the principal axes of the cross sections. It basis on the “truss model with crack friction” and adds supplementary terms to the equations of the shear resistances acc. to DIN 1045‐1 to take account for shear force inclinations. Verifications to experimental as well as numerical data are given. An example shows that resistances evidently decrease – or higher amounts of stirrup reinforcement become necessary –, if shear forces deviate from principal axes.     

Thin-walled cold-formed sections subjected to compressive loading

The weakening effects of local buckling on the compressive load carrying capability of thin-walled cold-formed sections is examined and discussed. Theoretical results are presented for the pin-ended support condition and a study is made of the local buckling and overall bending interaction behaviour of compression members with different cross-sectional shapes. It is shown that singly symmetric plain channel sections exhibit considerably different interactive equilibrium characteristics to those of I-sections for which the shear centre and section centroid are coincident.

The theoretical results given have been obtained through the solution of a differential equation which governs, approximately, the overall bending behaviour of a locally buckled compression member. Both local and overall imperfections are considered in the theoretical approach and it is shown that the effect of these is to reduce the ultimate compressive carrying capacity of cold-formed sections.

An experimental investigation of the behaviour of concentrically loaded pin-ended I-section struts and columns is reported and the findings from this are compared with theoretical predictions. The theoretical predictions of load-deflection equilibrium behaviour and stress variations with load are shown to be in good agreement with those obtained from test.

The provisions made in the UK Code of Practice and the American Specification pertaining to the design of cold-formed compression members are briefly outlined and compared. It is shown that with regard to I-section struts and columns the American design procedure gives, in general, more conservative estimates of collapse.     

普通荷载作用下的薄壁构件截面屈曲分析

分析了普通加载条件下薄壁构件截面的屈曲性能。使用半解析有限条法进行分析。结论主要适用于均布荷载作用下的截面,如均布压力、均布弯矩和均布荷载,都施加在截面的剪力中心。在普通荷载作用条件下,首先采用线性分析得到截面的纵向应力。刚度矩阵也采用标准的表达形式。每一个有限单元条带都分割成单元,并对这些单元上的纵向应力进行记载。每一个单元都是一个完整的个体,最后将其全部汇总,便可得到带状的几何矩阵。     

Buckling analysis of thin-walled sections under general loading conditions

This paper presents an investigation of the buckling behaviour of thin-walled sections subjected to general loading conditions. The semi-analytical finite strip method is used. The existing results are only for sections subjected to a uniform loading, namely: uniform compression, uniform bending and uniform distributed loads, which are applied at the shear centre. For a general loading condition, we proposed the realizing linear analysis first to give longitudinal stresses. The stiffness matrix is provided in the standard manner. Each strip is divided into cells and longitudinal stresses are recorded in these cells. The integrations are performed on each cell domain and the sum of them provides the geometric matrix of the strip.     

A theoretical investigation of the collapse of multi-cellular structures under lateral loading

This paper describes the development of the grillage method to take into account the effects of shear, as well as bending, upon the non-linear and collapse behaviour of multi-cellular structures under lateral loading. The modified theory is outlined and the results obtained from the analysis of eleven girders are presented. In each case, the mode of failure is discussed together with the predicted ultimate load capacity. The results show the influence of varying structural proportions, including the addition of flange stiffeners, and of different support and loading conditions upon the girder behaviour.     

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.     

Lateral–torsional buckling of cold-formed channel sections subject to combined compression and bending

This paper presents an analytical study of the flexural buckling and lateral–torsional buckling of cold-formed steel channel section beams subject to combined compression and bending about their major and minor axes. For channel section beams a bending about the minor axis creates a non-symmetric pre-buckling stress distribution, which has a significant influence on the lateral–torsional buckling of the beams. This kind of feature has not been discussed in the existing literature. The focus of this present study is the interaction between the compression load and the bending moments about the major and minor axes. It has been found that for a section subject to combined compression and the major-axis bending the bending moment will decrease the critical compression load, although the critical value of the largest compressive stress in the section actually increases with the applied bending moment. However, for a section subject to combined compression and the minor-axis bending the effect of the bending moment on the critical compression load depends on the direction of bending applied. For bending that creates a compressive stress in the lips the bending moment will reduce the critical compression load. However, for bending that creates a compressive stress in the web the bending moment has almost no influence on the critical compression load.     

Lateral buckling of thin-walled beam-column elements under combined axial and bending loads

Based on a non-linear stability model, analytical solutions are derived for simply supported beam-column elements with bi-symmetric I sections under combined bending and axial forces. An unique compact closed-form is used for some representative load cases needed in design. It includes first-order bending distribution, load height level, pre-buckling deflection effects and presence of axial loads. The proposed solutions are validated by recourse to non-linear FEM software where shell elements are used in mesh process. The agreement of the proposed solutions with bifurcations observed on non-linear equilibrium paths is good. It is proved that classical linear stability solutions underestimate the real resistance of such element in lateral buckling stability especially for I section with large flanges. Numerical study of incidence of axial forces on lateral buckling resistance of redundant beams is carried out. When axial displacements of a beam are prevented important tension axial forces are generated in the beam. This results in important reduction of displacements and for some sections, the beam behaviour becomes non-linear without any bifurcation.     

Buckling analysis of buildings braced by frameworks,shear walls and cores

A simple hand method is presented for the three‐dimensional stability analysis of buildings braced by frameworks, coupled shear walls, shear walls and cores. Sway buckling behaviour is characterized by three types of deformation: the full‐height ‘local’ bending of the individual columns, wall sections, shear walls and cores, the full‐height ‘global’ bending of the frameworks and coupled shear walls, which is associated with the axial deformations of the column and wall sections, and the shear deformation of the frameworks and coupled shear walls. Based on the stiffnesses associated with these three types of deformation, a closed formula is derived for the calculation of the sway critical load. An analogy between bending and torsion is used to carry out the pure torsional buckling analysis. The interaction between the bending and shear modes as well as among the basic buckling modes (sway in the principal directions and torsion) are taken into account. A worked example with step‐by‐step instructions shows the easy use of the method. The results of a comprehensive accuracy analysis involving 73 multistorey buildings are also given together with comparisons with other analytical methods. Copyright © 2002 John Wiley & Sons, Ltd.     

Berechnung dünnwandiger Stäbe mit offenem Querschnitt bei Beanspruchung durch Längskraft,zweiachsige Biegung und Torsion – ohne Bestimmung von Schwerpunkt,Schubmittelpunkt und Hauptachsen

Analysis of thin‐walled bars with open cross‐section loaded by normal force, biaxial bending and torsion without use of centroid, shear centre and principal axis. For a generally loaded prismatic bar an analysis is presented, where the relations between stress resultants and deformations are not normalized, but written in a coupled form. This means that any system of coordinates y, z in the section can be chosen and is then maintained for all calculations. On this basis the equation of transfer matrix is developed, which allows the calculation of all stress resultants and displacements for a beam with arbitrary support. Finally at any point of the sections normal and shear stresses can be determined.     

Simulation of the behaviour of stiffened box girders with and without shear lag

A finite element program with large deformations and plasticity is used to analyse the behaviour of stiffened compression flanges of box girders. Simulations are performed for pure bending and for bending with shear in order to investigate the diminishing of the shear lag effect at collapse. It is concluded that at the actual ultimate load, shear lag has largely disappeared but that a design at ultimate load without consideration of the shear lag may entail an inelastic behaviour under service load. First yielding occurs in the centre of the stiffened panel for pure bending and in the middle of the unloaded edges when elastic shear lag becomes important. A substantial increase of the ultimate load can be expected from an increase of the stiffener rigidity.     

Inelastic behaviour and design of slender I-sections in minor axis bending

Slender steel sections in bending are generally designed by taking the maximum moment as the yield moment. The assumption for the ultimate condition is thus the point at which first yield is reached in the section. Certain types of slender sections, however, have shown significant post-elastic behaviour in attainment of the ultimate moment. Experiments on I-sections in minor axis bending have shown this to be the case, where significant plastic stress distributions are attained in the tension flanges after the compression flanges have locally buckled. Current international steel specifications are unduly conservative when estimating the bending strength of these sections as the yield moment. This paper quantifies this conservatism and presents inelastic design methods whereby the post-elastic strength may be captured. Design equations are proposed for Australian, American and European hot-rolled and cold-formed steel specifications.     

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.     

剖分T型钢压杆的屈曲性能和应用

剖分T型钢由热轧H型钢一分为二得来,属单轴对称截面。在承受轴线压力时,它的屈曲性能有两个特点。其一是绕对称轴屈曲时必然伴随有扭转,从而降低其承载力。另一方面,当压力移至截面剪心时,屈曲不再出现扭转,承载力达到弯曲屈曲荷载。杆件承载力的这种提高,只有在绕另一主轴屈曲有多余承载力,足以承担压力移至剪心产生的偏心力矩时才能加以利用。本文分析表明,截面高宽比不小于1．25的剖分T型钢满足或部分满足这一条件。有时,荷载作用在形心与剪心距离的一半处较为有利。第二个特点表现在压杆腹板局部屈曲承载力和宽厚比限值。本文揭示出腹板的临界应力总是高于杆件弯扭屈曲的临界应力,因此,只要杆件通过弯扭屈曲验算,就不必顾虑腹板屈曲。然而,在工程实践中有些杆件扭转受到约束,从而不去验算其弯扭屈曲。此时,腹板有可能作为一纵边嵌同、另一纵边自由的板件屈曲。建议的腹板宽厚比限值就是为保证在这种情况下的稳定性而给出的。     

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.     

陶粒砼剪力墙的试验研究

本文介绍8片陶粒砼剪力墙试件与4片普通砼剪力墙试件的对比试验研究结果,讨论了在低周反复荷载下单肢剪力墙的破坏形态、变形能力、构件延性,斜截面抗剪强度及水平和竖向分布钢筋的配筋构造等,证实了在低轴压比下的陶粒砼剪力墙可以满足延性要求,最后对轻砼剪力墙斜截面承载力计算与其配筋构造提出了一些设计建议。     

轻骨料混凝土抗剪性能研究

在大量试验的基础上研究了桥梁用轻骨料混凝土的抗剪能力，得出钢筋轻料混凝土受弯构件斜截面抗剪剪承载力的计算公式。     

The design of perforated cold-formed steel sections subject to axial load and bending

The uprights in a typical pallet rack are typically singly-symmetrical cold-formed sections subject to axial load together with bending about both axes. They usually contain arrays of holes in order to enable beams to be clipped into position at heights that are not pre-determined prior to manufacture. Their slenderness is such that their behaviour may be influenced by the three generic forms of buckling, namely local, distortional and global (lateral torsional). In practice, these members have generally been designed on the basis of expensive test programmes. This paper addresses the problem of how they might be designed analytically. The basis of the investigation is a comprehensive set of test results on upright sections in compression which embraces both stub column tests, in which the load position was varied along the axis of symmetry, and longer columns. The test results were analysed using both finite elements and a version of “Generalized Beam Theory” (GBT) which incorporated systematic imperfections. Consideration was also given to the design procedures proposed by the “Federation Europeene de la Manutention” (FEM) and recent research into the influence of perforations on the performance of cold formed steel sections. It is shown that GBT can be modified to take account of perforations so that the lower bound results give a sufficiently accurate column design curve, which takes account of local, distortional and global buckling, thus making extensive testing unnecessary.     

Tragverhalten von Stahlbetonbalken bei geneigter Querkraft

Bearing Behaviour of RC Beams Subjected to Biaxial Shear Forces The shear bearing behaviour of RC beams is still subject of expert's discussion and intensive research. Most investigations focus on uniaxial loading conditions parallel to one principal axis. More recently, biaxial shear – leading to inclined shear forces – was theoretically considered and integrated into new design concepts. However, its experimental basis is rather limited. Thus, extensive biaxial shear tests are carried out and analysed. Their main findings are presented in the paper. The design concept is elaborated to introduce inclination effects into all partitions of the resistances provided by the tensile and the compressive shear struts. Designs become more precise and more economic.