Lateral bracing of I-girder with corrugated webs under uniform bending

Lateral-torsional buckling may occur in an unrestrained beam where its compression flange is free to displace laterally and rotate. This paper presents the results of the theoretical and finite element analyses of the lateral-torsional buckling of I-girders with corrugated webs and lateral bracing, under uniform bending. 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 lateral-torsional buckling has not been made especially for I-girder with corrugated webs. This paper develops a three-dimensional finite element model using ANSYS [User’s manual, version 10.0] for the lateral-torsional buckling analysis of I-girder with corrugated webs and uses it to investigate the effects of elastic lateral bracing stiffness on the critical moment of simply supported I-girders with corrugated webs under pure bending. It was found that for plastic and inelastic I-girder with corrugated webs, 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 I-girder. Also, the results show that Winter’s simplified method to determine full brace requirements cannot be applied to I-girders with corrugated webs. Therefore, a general equation is proposed to determine the value of optimum stiffness (K_opt) in terms of the I-girder’s slenderness.     

Inelastic buckling and strengths of steel I-section arches with central torsional restraints

The elastic flexural–torsional buckling behaviour of arches with a central elastic torsional restraint has been reported elsewhere by the authors, and it was found that a central elastic torsional restraint restricts the buckling shape of an elastic arch and increases its elastic buckling resistance. However, both the inelastic buckling and strength of arches with a central elastic torsional restraint have hitherto not been investigated. It is not known whether the threshold stiffness for elastic buckling can be applied to arches which buckle inelastically, nor is it known how to determine the strength of steel arches with a central elastic torsional restraint. This paper modifies a finite element model for the nonlinear inelastic flexural–torsional analysis of steel I-section arches by including the effects of elastic restraints, and uses it to investigate the influence of central elastic torsional restraints on the inelastic flexural–torsional buckling and strength of steel I-section arches. It is found that a central elastic torsional restraint increases the strength of steel arches, but that the increase in strength decreases as the modified slenderness of the arches decreases. The threshold value of the stiffness of a central elastic torsional restraint at which the inelastic strength of an arch is equal to that of the corresponding arch with a rigid restraint is related to both the modified slenderness and included angle of the arch. For an arch with a low modified slenderness and with a small included angle which buckles inelastically, the threshold restraint stiffness is much smaller than that for an arch which buckles elastically. Design formulae for the strengths of steel I-section arches in uniform bending and in uniform compression with a central elastic torsional restraint are proposed. Comparisons with finite element results show that the proposed formulae provide good predictions for the strength of thin-walled steel I-section arches with a central elastic torsional restraint.     

圆孔蜂窝梁的弯扭屈曲分析

为了对纯弯状态下圆孔蜂窝梁的弯扭屈曲进行研究,将蜂窝梁翼缘和腹板分离,采用有限元软件ANSYS对蜂窝梁开圆孔腹板进行侧向纯弯分析,由挠度-刚度关系反算侧向刚度,得出开孔腹板相对于实心腹板的刚度折减系数ky。考虑开孔腹板的径高比和距高比,经拟合给出了刚度折减系数ky的计算公式,用该系数对蜂窝梁的自由扭转刚度进行修正,代入实腹工字截面梁弯扭屈曲临界弯矩计算公式,得到蜂窝梁的相应计算公式。最后利用该公式分别对不同跨度、不同孔况的简支蜂窝梁在纯弯状态下的弯扭屈曲临界弯矩进行计算,并与有限元分析结果进行对比。分析结果表明,修正后的临界弯矩计算公式具有较高精度。     

Experiments on elastically braced castellated beams

Castellated beams are widely used as flexural members in steel construction. The economical and structural advantages of these elements have prompted many researchers to investigate the failure behavior of such structures. Despite numerous reported researches on the buckling stability of castellated beams, no experimental study is found on lateral–torsional buckling of these elements with elastic bracing. In this paper, the experimental study of nine full-scale castellated beams is reported with the aim of investigation of the performance as well as effect of elastic bracing on the buckling stability of these structural elements. In addition to the presentation of the experimental observations and findings, the current test results are compared with the results of other reported experimental, analytical and numerical studies. Ultimately, the experimental findings and results are evaluated by considering the AISC 360–05 code requirements and predictions.     

有平面外支撑的工形截面圆弧钢拱弹性稳定性能及支撑刚度设计

采用有限元特征值屈曲数值方法，对平面外支撑工形截面圆弧拱弹性屈曲荷载及其刚度取值进行研究。在考虑各种荷载条件与拱脚条件下，研究了支撑刚度，约束类型、数量以及作用位置对钢拱平面外屈曲性能的影响，对于设置等间距侧向支撑的情况，给出了侧向支撑弹性门槛刚度的拟合式，并提出了支撑点间拱段不发生平面外弹性失稳的条件。研究结果表明：平面外支撑越靠近拱顶，其防止平面外失稳的工作效率越高；设置侧向支撑的钢拱屈曲时，随着支撑刚度的增大其屈曲半波数逐渐增加，而仅在拱顶设置扭转约束时始终呈现1个半波失稳模式；从均匀受压圆弧拱的情况获得的等间距侧向支撑门槛刚度，应用在其他组合荷载作用下，同样可以获得足够的支承刚度；当工形截面钢拱的支撑点间拱段长度满足所提出的要求时，钢拱平面外失稳不先于平面内反对称整体失稳。     

拱墙结构平面外失稳机理与设计研究

拱墙是一种由拱、立柱、横梁组合而成的竖向平面结构，横梁上的竖向平面内荷载通过立柱传递到大跨度拱体中。为研究拱墙结构的失稳机理，采用有限元分析方法，对拱墙模型在弹性和弹塑性条件下的稳定性能进行了研究。分析结果表明：立柱侧向刚度及横梁侧向支撑刚度是影响拱墙稳定性能的主要因素，当横梁侧向支撑刚度小于其门槛刚度时，拱墙的屈曲模式表现为拱墙整体平面外失稳；当横梁侧向支撑刚度大于其门槛刚度而立柱的侧向刚度小于其门槛刚度时，拱墙的屈曲模式表现为拱体的平面外失稳；当横梁侧向支撑和立柱的侧向刚度均大于各自的门槛刚度时，拱墙的屈曲模式表现为拱墙整体平面内失稳。结合某火车站站房工程，建立了横梁位置施加侧向弹簧支撑和带纵向桁架的两种拱墙模型，分析了该拱墙结构的平面外稳定承载力。结果表明，纵向桁架为拱墙横梁提供的平面外支撑刚度远大于拱墙的侧向支撑门槛刚度，提高拱墙的平面外稳定承载力需通过增大立柱的侧向刚度和加强立柱两端的可靠连接实现。     

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.     

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.     

偏心支撑压弯构件稳定性分析

对压弯构件在跨中设置侧向支撑和扭转支撑时的稳定性进行研究 ,先就一般情况建立平衡微分方程 ,推导出压弯构件的稳定临界方程 ,在此稳定临界方程的基础上对偏心支撑压弯构件进行详细的分析 ,得到了使压弯构件计算长度减半的扭转支撑临界刚度表达式和侧向支撑临界刚度表达式 ,导出了判断支撑是否能使压弯构件计算长度减半的临界荷载偏心。此外还分析了非完全支撑时支撑刚度和构件承载力的关系 ,以及侧向支撑、扭转支撑及两者联合作用对构件承载力的影响 ,推出了上面所有分析的解析式     

Interaction of buckling modes in castellated steel beams

This paper investigates the behaviour of normal and high strength castellated steel beams under combined lateral torsional and distortional buckling modes. An efficient nonlinear 3D finite element model has been developed for the analysis of the beams. The initial geometric imperfection and material nonlinearities were carefully considered in the analysis. The nonlinear finite element model was verified against tests on castellated beams having different lengths and different cross-sections. Failure loads and interaction of buckling modes as well as load-lateral deflection curves of castellated steel beams were investigated in this study. An extensive parametric study was carried out using the finite element model to study the effects of the change in cross-section geometries, beam length and steel strength on the strength and buckling behaviour of castellated steel beams. The parametric study has shown that the presence of web distortional buckling causes a considerable decrease in the failure load of slender castellated steel beams. It is also shown that the use of high strength steel offers a considerable increase in the failure loads of less slender castellated steel beams. The failure loads predicted from the finite element model were compared with that predicted from Australian Standards for steel beams under lateral torsional buckling. It is shown that the Specification predictions are generally conservative for normal strength castellated steel beams failing by lateral torsional buckling, unconservative for castellated steel beams failing by web distortional buckling and quite conservative for high strength castellated steel beams failing by lateral torsional buckling.     

Buckling of interbraced beam systems

Analyses of parallel beam floor support systems under both uniform beam moment and uniform spread load are carried out. The beams are braced by lines of braces which provide torsional and lateral support and which may be attached eccentrically. Charts illustrate the variation of the buckling load of this interconnected structure under different brace stiffnesses and eccentricities and, in particular, show the levels of stiffness at which ‘full bracing’ is achieved. The matrix equation which allows the uniform moment calculations to be quickly made is presented. Other cases employ a beam-column finite element.     

Practical formulas towards distortional buckling failure analysis for steel–concrete composite beams

As the most predominant type of failure for steel–concrete composite beams (SCCBs) in negative moment area, distortional buckling is significantly impacted by the interaction effect between the applied loading and the torsional–lateral restraint stiffness of the bottom flange, which is termed as loading–restraint interaction here for short. Recently, a modified elastic foundation beam method capable of considering the interaction effect properly was proposed to calculate critical buckling moment for SCCBs under negative uniform moment. As a sequel to such development, a functional relationship between two dimensionless auxiliary parameters (i.e. equivalent slenderness ratio and equivalent moment coefficient) is discovered in this study. On the basis of the close association between the pair of dimensionless parameters, empirical formulas are derived in a remarkably simply explicit form to evaluate the critical buckling moment for SCCBs under negative uniform moment or moment gradient. These formulas are simple, user‐friendly and of practical use. Compared with conventional approaches without considering the loading–restraint interaction effect, the practical approach developed in this paper can achieve higher accuracy and is more easy‐implemented. The study lays a foundation for determining the ultimate bearing capacity of SCCBs considering moment gradient effect rapidly. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Plastic design of CB-frames with reduced section solution for bracing members

The seismic behaviour of concentrically braced frames (CBFs) designed according to the current European provisions is unsatisfactory due to the premature out-of-plane buckling of columns. For this reason, a new design methodology, based on a rigorous application of “capacity design” criteria has been recently proposed. In addition, aiming at a reduction of the plastic out of plane deformations of gusset plates due to brace buckling and at the prevention of sudden impact load affecting connections at the end of the straightening phase, Eurocode 8 requires the limitation of the brace slenderness. This limitation leads to the oversizing of diagonals and, consequently, of beams and columns. Therefore, to avoid this problem a new design strategy for bracing members is suggested: the Reduced Section Solution (RSS). It allows the calibration of the diagonal yielding resistance, leaving the brace slenderness practically unchanged.The results of dynamic inelastic analyses carried out with reference to braced frames designed according to the proposed procedure, both with and without RSS, are compared with those obtained with reference to the same structural schemes designed according to Eurocode 8. The obtained results show that the proposed design approaches are able to assure a significant improvement of the seismic performance.     

Seismic performance of floor-by-floor assembled steel braced structures with stiffened connections

This paper presents an overview of a full-scale testing on a tension-only concentrically braced beam-through frame (TCBBF). The implementation of TCBBF facilitates the construction of low-rise industrialised residential steel houses by means of floor-by-floor assembling. This type of TCBBF system features cold-formed hollow structural section columns connected to H-section through beams by end plate with bearing-type high-strength bolts. A two-storey, four-span by one-span TCBBF subjected to vertical loads was cyclically loaded horizontally to examine the seismic behaviour. Stable behaviour was observed up to a storey drift angle of 1/10. The cyclic behaviour was characterised by a linear response, a slip range and a significant hardening response. Deteriorating pinched hysteretic behaviour was notable for cyclic loading primarily because of cyclic brace compression buckling and tension yielding. TCBBF incorporates very slender bracing members that are unable to bear much axial load when subjected to compression. Alternating brace compression buckling and tension yielding induce unrecoverable plastic deformation, which results in a sharp decrease in the lateral system stiffness of TCBBF when lateral displacement becomes zero or around zero. Additionally, bracing members and frame members share different proportions of horizontal force although the dual systems bear the lateral forces collaboratively. The variation philosophy of distribution proportion of bracing and frame members is evaluated. Pushover analysis is undertaken to duplicate the test results and develop an analytical model, which is able to predict the elastic stiffness and the strength reasonably.     

Ultimate behaviour of continuous steel beams with discrete lateral restraints

Through a programme of experiments, numerical modelling and parametric studies, the implications of allowing for strain-hardening in the design of laterally restrained continuous steel beams are investigated with particular emphasis on the performance of the bracing elements. A total of six tests were performed on continuous beams considering two basic scenarios: discrete rigid restraints and discrete elastic restraints of varying stiffness. In the latter case, the forces developed in the restraints were measured and compared to the design forces specified in EN 1993-1-1 (2005) for members containing rotated plastic hinges. Two different restraint spacings were considered in the tests to give non-dimensional lateral torsional slenderness values of 0.3 and 0.4 for the unrestrained lengths. In all tests, bending resistances predicted by the deformation-based continuous strength method (CSM) were exceeded. Using a standardised numerical model validated against the laboratory test data, a series of parametric studies were conducted; it was concluded that elastic restraints for members containing rotated plastic hinges should be designed to sustain higher forces than required for traditional plastic design if the full CSM collapse load is to be achieved.     

Inelastic seismic response of steel bracing members

A survey of past experimental studies on the inelastic response of diagonal steel bracing members subjected to cyclic inelastic loading was carried out to collect data for the seismic design of concentrically braced steel frames for which a ductile response is required under earthquakes. The parameters that were examined are the buckling strength of the bracing members, the brace post-buckling compressive resistance at various ductility levels, the brace maximum tensile strength including strain hardening effects, and the lateral deformations of the braces upon buckling. Equations are proposed for each of these parameters. In addition, the maximum ductility that can be achieved by rectangular hollow bracing members is examined.     

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.     

Lateral-torsional buckling of I-girders with discrete torsional bracings

Discrete torsional bracing systems are widely used in practice to increase the lateral-torsional buckling (LTB) strength of I-girders. However, only limited studies are available on the LTB strength of I-girders with mid-span torsional bracing. In addition, equivalent continuous brace stiffness concept is adopted for general discrete torsional bracing problems. This article presents an analytical solution for LTB strength and stiffness requirements of I-girders with discrete torsional bracings under a uniform bending condition. Firstly, the critical moment and torsional stiffness requirement are derived by using an energy method for an arbitrary number of bracing points. The proposed equations are then compared with the results of finite element analyses and those obtained by previous researchers. From the results, it is found that the proposed solutions agree well with the results of finite element analyses regardless of the number of bracing points, while the results for the equivalent continuous brace stiffness concept are not suitable for multiple discrete torsionally braced beams. Finally, reduced formula for the total stiffness requirement is proposed for the purpose of design, and effects of linear moment gradient loading and geometric imperfections on critical moments and stiffness requirement are also observed.     

Analytical study on seismic behavior of proposed hybrid tension‐only braced frames

The first intention of this study is to enable tension‐only bracing (TOB) as the main lateral load resisting system. In order to attenuate deteriorating of the TOB hysteretic behavior, a simple mechanical device, called slack‐free connection (SFC), is proposed by which buckling/slacking would not occur in the TOB. Using the TOB‐SFC system in parallel with a wire rope brace, an innovative bracing system, called hybrid tension only brace (HTOB), is proposed, which has a non‐deteriorating hysteretic behavior with tunable post‐yield stiffness. Adopting the so called Incremental Dynamic Analyses, sensitivity of the HTOB on its post‐yield stiffness is explored and also seismic behavior of the proposed HTOB is compared to other representative lateral load resisting systems. Obtained results indicate that a minor increase in post‐yield stiffness can substantially reduce maximum and residual deformations of the HTOB. However, compared to other representative systems, HTOB still tends to experience higher residual deformations. This is due to the fact that the elastic‐to‐inelastic transition in hysteretic behavior of the HTOB is very sharp. Meanwhile HTOB would generally result in less maximum deformations compared to other representative systems because of its large energy dissipation capability.