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The direct strength method (DSM) has become an alternative to the effective width method (EWM) to compute the bending moment capacity of cold-formed channel sections. The traditional EWM examines the nominal moment capacity by the PURLIN program. DSM uses a signature curve from tests on many Australian channel sections to obtain design moment capacity for local and distortional buckling modes. Moreover, the non-linear analysis performed by Strand7 will be compared with the current DSM curve. In general, these comparisons of results are in good agreement: the THIN-WALL program results and the linear static analysis results in Strand7; the moment capacity calculated by the PURLIN program (EWM) and the DSM curve in the local buckling mode; the non-linear analysis results in Strand7 and the DSM curve for each buckling mode. The outcome of this study will benefit structural engineers by providing them with design methods analysis. [ABSTRACT FROM AUTHOR]

Buckling-restrained braces (BRBs) featuring flat steel core plates can be susceptible to local bulging failures when the restrainer lacks the necessary stiffness and strength. These failures arise from outward forces generated by high-mode buckling waves within the steel core. However, the methods for evaluating these high-mode buckling waves and the associated outward forces have remained elusive. This study addresses this gap by conducting cyclic loading tests on five BRB specimens with all-steel restrainers. These tests allow for direct observation of high-mode buckling waves during loading. Among the specimens, three have core segment lengths of 300 mm, each with varying debonding layer thicknesses (0.6 mm, 2 mm, and 4 mm). The remaining two specimens have approximately 900 mm core segments with a 2 mm thick debonding layer. All five specimens displayed stable hysteretic responses until the steel core fractured. Load cells were used to directly measure the outward forces induced by the steel core plate during testing. Strain gauges attached to the steel core surface provided insights into the distribution of strain variations at the high-mode buckling waves. The results indicate that adopting the tangent modulus theorem is a suitable method for estimating high-mode buckling wavelengths. Furthermore, this study establishes relationships between the outward forces and gap dimensions, including their growth over time. This research proposes a method to estimate outward forces, accounting for bending moments developed at the crests of high-mode buckling waves and considering restrainer stiffness. This method can serve as a valuable tool for assessing the risk of local bulging failure in BRBs. [ABSTRACT FROM AUTHOR]

• The results of more than 4 000 non-linear shell F.E. computations are presented, detailed and analysed. • Prior to the numerical parametric studies, the numerical models were validated against test data on full-scale specimens, as detailed in the companion paper. • Various parameters such as the base cross-section profile, the bending moment distribution, the size and position of the openings, the steel grade and member slenderness have been studied. • Besides, a dedicated design model is presented. Systematic comparisons with the results of software ACB+, which is by far the most highly used tool in design practice, are described. • A significantly improved performance of the proposed design approach in terms of accuracy, consistency and reliability is demonstrated. The present paper investigates the lateral torsional buckling resistance of cellular steel beams numerically. Such beams are quite sensitive to lateral instability owing to a substantial increase in depth of the cross-section with respect to the base profile. While a companion paper was dedicated to (i) characterising experimentally the behaviour of cellular and Angelina beams and to (ii) validating dedicated non-linear shell F.E. models, this paper details the results of extensive numerical studies. Several key parameters in the structural response are investigated, such as the base cross-section profile, bending moment distribution, size and position of the openings, steel grade and member slenderness. The results have further been used to assess an original design proposal for the lateral torsional buckling resistance of such girders. The improved design rules are shown to provide accurate yet safe ultimate load predictions. Also, in comparison with existing and available design rules, the proposal is seen to allow for substantially higher design loads – still safe-sided –, potentially leading to significant material savings. [ABSTRACT FROM AUTHOR]

Featured Application: The research results included in the paper can be widely used in designing thin-walled steel elements for use in construction. The use of the presented calculation model for the calculation of continuous beams allows for more optimal and economical design of sections of this element class under resistance conditions. In this model, the real behavior of thin-walled beams under load was taken into account much more precisely in relation to the Eurocode. This made it possible to use the resistance reserves resulting from the effect of longitudinal stress variation and the elastic restraint of the thin-walled cross-section walls. In modern steel construction, thin-walled elements with Class 4 cross-sections are commonly used. For the sake of the computation of such elements according to European Eurocode 3 (EC3), simplified computational models are applied. These models do not account for important parameters that affect the behavior of a structure susceptible to local stability loss. This study discussed the effect of local buckling on the design ultimate resistance of a continuous beam with a thin-walled Class 4 I-shaped cross-section. In the investigations, a more accurate computational model was employed. A new calculation model was proposed, based on the analysis of local buckling separately for the span segment and the support segment of the first span, which are characterized by different distributions of bending moments. Critical stress was determined using the critical plate method (CPM), taking into account the effect of the mutual elastic restraint of the cross-section walls. The stability analysis also accounted for the effect of longitudinal stress variation resulting from the varied distribution of bending moments along the continuous beam length. The results of the calculations were compared with the numerical simulations using the finite element method. The obtained results showed very good congruence. The phenomena mentioned above are not taken into consideration in the computational model provided in EC3. Based on the critical stress calculated as above, "local" critical moments were determined. These constitute a limit on the validity of the Vlasov theory of thin-walled bars. Design ultimate resistance of the I-shaped cross-section was determined from the plastic yield condition of the most compressed edge under the assumptions specified in the study. Detailed calculations were performed for I-sections welded from thin metal sheets, and for sections made from two cold-formed channels (2C). The impact of the following factors on the critical resistance and design ultimate resistance of the midspan and support cross-sections was analyzed: (1) longitudinal stress variation, (2) relative plate slenderness of the flange, and (3) span length of the continuous beam. The results were compared with the outcomes obtained for box sections with the same contour dimensions, and also with those produced acc. EC3. It was shown that compared with calculations acc. EC3, those performed in accordance with the CPM described much more accurately the behavior of the uniformly loaded continuous beam with a thin-walled section. This could lead to a more effective design of structures of this class. [ABSTRACT FROM AUTHOR]

Buckling resistance predictions resulting from flexural and flexural–torsional buckling of double tee section members subjected to compression and bending are considered. A novel analytical model is developed for establishing design criteria based on decomposition of the member buckling behaviour into in-plane and out-of-plane resistance. The former is based on second-order bending relationships of load effects of structural members with in-plane equivalent imperfections, while the latter is based on the stability theory of thin-walled open sections. First part of this study presents an analytical formulation of the in-plane buckling resistance of beam–columns. In this regard, further decomposition is postulated for the in-plane first-order bending moment diagram that results in the loading state to be the superposition of two components. The first component is related to symmetrical loading and the second to antisymmetric loading. To consider the second-order effects, prebuckling displacements generated by the abovementioned loading components are amplified with regard to the inversion of the residuum of the buckling force utilisation ratio in order to obtain approximate values of second-order displacements and internal moments. As a result, the in-plane interaction curve, expressed in dimensionless coordinates, that describes the beam–column in-plane flexural buckling resistance without considering lateral–torsional buckling effects, is obtained. The results of nonlinear finite element simulations are used for the verification of the developed analytical formulation. It is concluded that this proposal yields less conservative predictions than those based on the interaction relationships of clause 6.3.3 of Eurocode 3, Part 1–1. • The study discusses design criteria for in-plane buckling and bending behaviour. • The proposed analytical model has only one design condition. • The model is based on a linear combination of elementary resistance utilisation ratios. • The model is verified by the results from finite element simulations. • The results are compared with those from EC3 interaction equations. [ABSTRACT FROM AUTHOR]

Highlights • Buckling mechanism of steel core of BRBs with fixed ends is revealed. • The design criteria as well as the buckling half wavelength were validated by the quasi-static tests of five BRBs. • Compared to existing methods, the proposed design approach can ensure a proper safety margin of the stiffening part. Abstract Based on theoretical analyses, the development of buckling mode of steel core is revealed for buckling restrained braces (BRBs) with fixed ends. The formulae are derived for the bending moments of the stiffening part of the core and restraining member of BRBs. Then a global stability design method of fixed-end BRBs is proposed. The results of the contact force, flexural response and buckling half wavelength with finite-element analysis agree with the theoretical analysis. The design criteria as well as the buckling half wavelength were validated by the quasi-static tests of five BRBs. Compared to existing methods, the proposed design approach can ensure a proper safety margin of the stiffening part. [ABSTRACT FROM AUTHOR]

For compression members with primarily axial forces, steel angles with bolted connections are often used. Due to the eccentric connection on only one leg additional bending moments are acting on the member, leading to a complex load carrying behaviour with flexural and/or lateral torsional buckling phenomena. The paper mainly focuses on the presentation of the influence of realistic end support conditions at the gusset plates on the member capacity in compression. In the first part of the paper, about 300 existing test results for steel angles in compression with bolted connections are prepared in such a way that they can be compared with different design rules. This was achieved through the common representation of all test results as a function of the normalized slenderness λ ¯ v about the weak axis. In the second part, systematic numerical calculations are conducted for limit cases of the stiffness of the boundary condition of the load-introducing gusset plates (rigid/hinged). The results are also presented in dependency of the relative slenderness λ ¯ v . The consolidation of all tests and numerical results shows (besides the well-known difference between one-bolt and two-bolt connections) a very high influence of the end support of the gusset plate. [ABSTRACT FROM AUTHOR]

This paper presents a design proposal for the out-of-plane buckling resistance of prismatic beam-columns subject to axial compression and uniaxial major-axis bending that was developed based on the well-known Ayrton-Perry format. Firstly, the relevant theoretical background is summarized, closely following the theoretical derivation performed by Szalai and Papp (2010). Secondly, the required transformations for the engineering application of the design procedure are detailed and extended to arbitrary bending moment distributions. Appropriate generalized initial imperfection factors for the out-of-plane buckling of beam-columns are defined so as to achieving complete consistency across the stability verifications for columns, beams and beam-columns. The proposed procedure is subsequently validated against a large set of advanced numerical simulations. A good agreement was found between the numerical results and the estimates provided by the proposed design procedure, both in terms of the overall trend and the specific quantitative results. Based on a statistical assessment, the comparison with the interaction expression of Eurocode 3 (2005) (method 2) showed that this proposal slightly outperforms the Eurocode procedure, both in terms of average values and dispersion of results. [ABSTRACT FROM AUTHOR]

The behaviour of monosymmetric steel sections when they become fully plastic under the action of an axial force P and a bending moment M applied in the plane of symmetry is considered. Attention is focused on the cross sectional strength, the possibility of local buckling occurring being ignored. The interaction curve that relates the co-existing values of P and M when the section becomes fully plastic is derived. The conditions that this curve must satisfy are established and a procedure for obtaining the curve is given. Interaction curves available for some T -sections are discussed; some anomalies are found in these curves. These are investigated and it is found that they exist because of the procedure used to obtain these curves; they disappear when the procedure proposed in this paper is used instead. If the procedure used previously in the analysis of monosymmetric sections is used to analyse eccentrically loaded doubly symmetric sections, the same anomalies are encountered; these also disappear when the proposed procedure is used. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical investigations of the buckling behaviour and resistance of S960 ultra-high strength steel slender welded I-section beam–columns under combined compression and minor-axis bending moment. An experimental programme, including initial geometric imperfection measurements and eight beam–column tests, was firstly conducted. The test procedures, setups and results were fully reported. Following the experimental programme, a numerical modelling programme was carried out, with finite element models initially developed and validated against the test results and then employed to conduct parametric studies to generate further numerical data. On the basis of the test and numerical data, the relevant design interaction curves, as provided in the European code, Australian standard and American specification, were evaluated for their applicability to S960 ultra-high strength steel slender welded I-section beam–columns. The evaluation results revealed that all three codified design interaction curves lead to conservative resistance predictions, mainly owing to the conservative end points (i.e. column buckling strength and cross-section minor-axis bending resistance). Finally, a revised Eurocode design interaction curve, with improved compression end point determined from more accurate column buckling curve and bending end point determined from the direct strength method, was finally proposed, and shown to result in more accurate resistance predictions for S960 ultra-high strength steel slender welded I-section beam–columns than the codified design interaction curves. • The buckling behaviour of S960 ultra-high strength steel slender welded I-section beam–columns is studied. • Eight beam–column tests on S960 ultra-high strength steel slender welded I-sections are conducted. • FE models are developed and validated against the test results and then used to perform parametric studies. • The applicability of the relevant codified design interaction curves is assessed, revealing inaccuracy. • A new design interaction curve is proposed, resulting in more accurate failure load predictions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a proposal for the design of steel structures sensitive to lateral torsional buckling due to bending moment in order to fill the gaps in the current Standard EN 1993-1-1, guidelines for obtaining the magnitude of the imperfection. The proposal generalizes the approach provided in clause 5.3.2(11) of EN 1993-1-1 for steel structures sensitive to flexural buckling under compression. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical investigations of lateral–torsional buckling behaviour of welded Q690 steel I-beams with double lateral restraints along the length. In the experimental programme, 11 steel beams with different beam depths, load ratios and span ratios were tested under two concentrated point loads. Lateral–torsional buckling resistance of beams was obtained through experimental tests. Comparisons between experimental bending moments and calculated values suggest that existing design methods in different national codes cannot accurately predict the critical moments of beams in the selected range of slenderness. Besides, numerical models were also established and verified against test data. Parametric studies showed that the buckling factor of beams increased with increasing ratio of the middle span over the clear span and with increasing ratio of concentrated point loads on beams. It was also concluded from numerical results that the Chinese code and the American code are not safe when used for calculating the buckling factor of beams with intermediate slenderness, whereas Eurocode 3 is rather conservative. Comparisons between buckling factors of continuous and single beams also indicate that the buckling factor of beams can be substantially underestimated if only the beam segment in the middle span is considered by neglecting the restraints provided by adjacent beams. Finally, a modification factor was proposed for welded Q690 steel beams with unequal bending moments at the two ends, which can predict the buckling factor of beams with fairly good accuracy. • Welded Q690 steel I-beams with double lateral restraints along the length were tested under two concentrated point loads. • Numerical models were developed for welded Q690 steel beams and verified by using test data. • A modification factor was proposed for Q690 steel beams against lateral–torsional buckling. [ABSTRACT FROM AUTHOR]

In composite structures, the strength of different material can be fully taken advantage of due to the composite effect. In steel-encased concrete-infilled composite structures, steel plates are restrained unilaterally by infilled concrete. The contact buckling mode of steel plates differs from the bilateral buckling mode, and the buckling load is improved. Compared with flat-plates, corrugated-plates have greater out-of-plane stiffness and even larger buckling load restrained by a rigid medium and the shear connectors between them. This paper focuses on the compressive buckling behaviour of corrugated-plates in contact with a rigid medium, taking into consideration the influences of geometrical parameters and shear connector arrangement. First, through finite element (FE) analysis and theoretical derivation, we propose the bilateral and contact buckling loads of corrugated-plates. Then, based on the buckling analysis, the FE model considering material and geometrical nonlinearity is developed to investigate the load resistance of corrugated-plates and validated by existing experimental results. According to the numerical results, we propose the design formulas of the strength reduction factor of corrugated-plates and the upper limit of the normalized slenderness ratio for compact sections. The design formulas can further provide fundamental for the stability design of corrugated-plates under compression and bending moment. [ABSTRACT FROM AUTHOR]

• A novel prefabricated beam-to-column steel joint for precast concrete structures was proposed. • Damper with buckling energy-dissipation segments was used in the proposed joint. • Three prefabricated joints and a monolithic joint were cyclically tested. • Plastic hinge location of the beam was controlled. A novel prefabricated beam-to-column steel joint (PSJ) for precast concrete structures was proposed in this study. The joint had the advantages of easier to fabricate and more environmentally friendly than existing monolithic joint (MJ) cast on site. Low-yield-point steel 100 was used to fabricate the dampers of the joint to provide a high energy dissipation capacity. In addition, the plastic hinge location of the beam can be controlled in the dampers by the buckling energy-dissipation segments (BEDS) of the dampers. Cyclic loading experiments were conducted on three PSJs and an MJ to investigate their seismic performance. The effects of the BEDS' slenderness ratio on the seismic behaviour of the joints were studied. According to the test results, the PSJs exhibited higher ductility and energy dissipation capacity than the MJ. The BEDS used in the proposed joint were beneficial for concentrating the plastic deformation in the damper, thus preventing the damage to the concrete beams. The decreased slenderness ratio of the BEDS increased the strength of the PSJ. An analytical model that considering the buckling effect was proposed to evaluate the bending moment capacity of the PSJ. [ABSTRACT FROM AUTHOR]

• New lateral-torsional buckling theories are formulated and analytically solved for the PS H-beam system having no deviator, one deviator, two deviators, and multiple deviators. • For the validity of the proposed analytical theories, numerical examples for the PS system are given, and compared with analysis results by FE models. • Un-bonded deviators restrain the lateral and torsional deformations of the buckled beam pre-stressed by cables without any external loadings so strongly that its buckling strength is greatly improved. • Conclusively, it is emphasized that the deviators in the self-anchored PS system are fully activated as lateral bracing during the out-of-buckling. The out-of-plane buckling characteristics of a pre-stressed (PS) system that consists of a steel H-beam, rectilinear tendon cable, anchorages and deviators is newly reported, in which the girder is subjected to combined compressive force and bending moment introduced by the tendon. For this, new lateral-torsional buckling theories were analytically formulated and solved for the PS system having no deviator, one intermediate deviator, two deviators at regular intervals and multiple deviators. In order to verify the validity of the proposed theories, numerical examples for the PS system are given and compared with the analysis results by ABAQUS models, which are composed of thin-walled beam, rigid beam and truss cable elements. The results showed that un-bonded deviators installed externally restrain lateral and torsional deformations of the steel beam sufficiently strongly to greatly improve its lateral-torsional buckling strength. [ABSTRACT FROM AUTHOR]

• Cantilevers are very different from simply supported beams. • Cantilevers have different restraints and moment and yielding patterns. • Yielding in steel cantilevers varies with moment distribution and residual stresses. • Yielding reduces out-of-plane section rigidities. • Lateral buckling resistance is affected by moment distribution and reduced rigidities. • Beam buckling design rules are inappropriate for cantilevers. Steel cantilevers are very different from the simply supported beams under uniform bending which provide the basis for designing steel members against lateral buckling. Cantilevers have different end restraint conditions, while the most critical loading condition for cantilevers is one of concentrated end load leading to a linear moment distribution. Thus the elastic lateral buckling formulations for uniform bending of simply supported beams used more generally for design are inappropriate for cantilevers. The mono-symmetric yield patterns in simply supported beams with residual stresses in uniform bending are of opposite sense to those of cantilevers because of the opposite sense of the bending moments. Thus formulations which take account of the effect of mono-symmetry on the inelastic lateral buckling of simply supported beams are inappropriate for cantilevers. Further, the linear cantilever moment distribution leads to very localised yielding instead of the uniform yielding of beams under uniform bending. This paper studies the inelastic lateral buckling of cantilevers in order to produce better design guidance than that currently based on the inelastic buckling of simply supported beams in uniform bending. The effects of mono-symmetry on the elastic buckling of beams and cantilevers are first investigated, and then the effects of the mono-symmetric non-uniform yielding patterns which complicate the prediction of the inelastic buckling resistances of cantilevers are studied. Cantilevers with reduced (instead of rigid) end warping restraints occur in overhanging beams, and so the effects of yielding on overhanging segments are also studied. These studies are used to develop simple approximate methods for designing cantilevers and overhanging segments against inelastic lateral buckling. [ABSTRACT FROM AUTHOR]