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Reduced beam section (RBS) connections are ductile connections that have been widely used in steel structures. Because of the reduction of web resistance, local buckling usually occurs under large deformations and is associated with decreased strength. In addition, the complex deformation of beams prevents determining the residual strength, hence posing a challenge in postearthquake repairs. In this study, a buckling-restrained system (BRS) including steel channels and a mortar was proposed for deformed RBS regions to provide lateral support on buckled plates so as to recover the connection strength. Two full-scale RBS connections with various cutting ratios were first tested, and then the connection was repaired with BRS loaded again. The test results indicated that the repaired connections were loaded at a drift angle of up to 4% without fracture or strength deterioration. The negative strength increased by approximately 18%, and the maximum strength was similar to that of the original connection, indicating that the column-to-beam flexural strength ratio of the connection did not change. The strain at the heat-affected area also did not increase and rather decreased because of the additional support of the restraint. The dissipated energy capacities of the repaired specimens were approximately 92% and 87% of the values of the original specimens. These results confirmed that BRS provided sufficient lateral resistance and helped recover the connection performance. • This paper proposed a new postearthquake repair method for recovering the performance of the locally buckled reduced beam section connections. • Two full-scale connection specimens with different cutting ratios were prepared and tested. • The results indicated that the method notably enhanced the strength of the locally buckled connection, and the maximum strength was similar to that of the original connection, indicating that the column-to-beam flexural strength ratio of the connection did not change. • The strain at the heat-affected area also did not increase, and the dissipated energy capacities of the repaired specimens were closed to the values of the original connections. • The repair method does not require field cutting, welding works, and temporally support structures. [ABSTRACT FROM AUTHOR]

This paper studied buckling of parallel Z - and C-purlin systems inter-braced by sag-rods at mid-span under pure hogging moment. The purlins are connected to metal sheeting by self-drilled screws and the lateral movement of the top flange is prevented. The paper studied first in detail the buckling of a single purlin, and then buckling of parallel purlin systems. The alternate offset of the sag-rods in adjacent bays and the local deformation of the purlin web have been taken into consideration in parallel purlin systems. For one-purlin system, the buckling moments are given, valid for different combinations of sag-rod and distributed rotational stiffness. The threshold stiffness of the sag-rod, at which the buckling mode changes from symmetrical buckling to anti-symmetrical buckling, is also given. For parallel purlin systems, the buckling moments are calculated by the formulas of one-purlin system, but with a reduced equivalent sag-rod stiffness used in the calculation. Numerical examples for the reduced sag-rod stiffness reveal that an astonishingly large reduction of the sag-rod effective stiffness occurs when the purlin number and the sag-rod offset increase, and the sag-rod stiffness is maximum if the sag-rod is set as close to the bottom flange as possible. And finally some strengthening practices and details are recommended. [ABSTRACT FROM AUTHOR]

Buckling behavior and hysteretic performance of a new type of buckling-restrained brace (BRB), namely core-separated buckling-restrained brace (CSBRB), are theoretically and experimentally investigated. The material utilization efficiency of the CSBRB is significantly improved compared with common BRB, since its cross-section spreads outwards by spacing two cores, thus improving the flexural rigidity of the restraining system. On the basis of the elastic buckling loads of pin-ended CSBRBs, a design procedure involving two design parameters, namely normalized slenderness and buckling factor, is firstly established. Then, hysteretic behavior of CSBRBs is investigated by FE nonlinear analysis to obtain the critical normalized slenderness. Finally, test results of four specimens with different normalized slenderness values are presented to reveal the hysteretic characteristics and the energy-dissipation abilities, concluding that a CSBRB with adequate restraining rigidity can provide stable hysteretic performance. The test results coincide well with the results obtained from refined FE numerical analyses. [ABSTRACT FROM AUTHOR]

A novel buckling-restrained brace comprising three circular steel tubes with different diameters is proposed. The three tubes overlap, and the inner and outer tubes restrain the out-of-plane deformation of the middle tube. Slotted holes are arranged on the middle tube. This BRB has a much larger energy dissipation area and can be conveniently fabricated. The size and number of slotted holes on the middle tube were adopted as test parameters. Five different specimens were tested by using quasi-static cyclic loading schemes to investigate the strength, deformation capacity, hysteretic behavior and failure mode of the new buckling-restrained brace. Nonlinear finite element analyses using ABAQUS were carried out in detail to explain the load-deflection hysteresis curves and modes of failure obtained in all five experiments. According to the tests and finite element analyses results, the structure of the novel buckling-restrained brace is reasonable and effective. When the opening-hole ratio is 0.2 and 2 × 2 slotted holes are arranged on the middle tube, the buckling-restrained brace exhibits excellent performance in terms of its deformation capacity and low-cycle fatigue behavior. The hysteresis curves of the braces are stable and saturated, and correspond to an equivalent ratio of critical viscous damping of 0.40 at the loading amplitude of 1/100L. [ABSTRACT FROM AUTHOR]

In this study, cyclic tests of a buckling-restrained brace (BRB) subassemblage with an all-steel web-restrained brace (WRB) were conducted to investigate hysteretic behavior under combined axial and rotational demands. Four full-scale WRB frame subassemblages were subjected to the quasi-static displacement protocol used for BRB qualification described in the AISC 341–10 Seismic Provisions for Steel Buildings . Three different sizes of steel core plates were examined. One specimen used a nominal 7.9-mm thick by 152-mm wide plate, two WRB specimens used a nominal 12.7-mm thick by 152-mm wide plate, and one specimen used a nominal 12.7-mm thick by 229-mm wide plate. All specimens successfully completed the cyclic testing up to 2% story drift without experiencing brace instability, brace end connection failure, or rupture. Specimens with a 12.7-mm thick core plate survived additional cycles at 1.5% story drift before rupture. The test results also showed that the maximum compression forces were less than 1.3 times the maximum tension forces for each cycle corresponding to a deformation greater than the yield displacement, demonstrating that compression overstrength of the WRB was comparable with typical BRBs. [ABSTRACT FROM AUTHOR]

The present paper describes a theoretical study on the effect of pre-buckling displacements on the elastic instability of U-shaped members. Expressions for the elastic critical bending moments under mono-axial bending and the elastic critical load amplification factor for the case of bi-axial bending are derived and validated through elastic geometrically non-linear analysis including a geometric imperfection. It will be shown that pre-buckling displacements have a non-negligible influence on the behaviour of U-shaped members, especially when subjected to minor-axis and bi-axial bending. It will be shown that, contrariwise to the natural feeling, U-shaped members under minor-axis bending may, in some cases, be sensitive to elastic instability (lateral-torsional buckling). Moreover, the validated analytical expressions show that shorter members are more sensitive to elastic instability under minor-axis bending than their longer counterparts! [ABSTRACT FROM AUTHOR]

This paper presents the design and experimental investigation of a miniature buckling-restrained brace (MBRB) which can act as a hysteretic damper to dissipate energy when subjected to inelastic axial deformations. The MBRB is similar to a buckling restrained brace (BRB) with a yielding steel core plate restrained from buckling by a grouted restraining tube. The MBRBs, however, are designed to have shorter lengths, smaller steel core dimensions, and smaller yield capacity as compared to a typical BRB. As a result, careful consideration is required for the detailing at the ends and the stability of the MBRB. Small capacity BRBs can be useful in a range of applications as a primary energy dissipating structural fuse or supplementary axial hysteretic damper in seismic force resisting systems. The design, construction, and testing of six MBRB specimens with nominal axial yield forces between 30 kN and 95 kN are reported. Issues related to global stability of the MBRBs are discussed and a stability criterion to prevent global buckling was adopted to design the MBRB end connection pieces. The MBRBs exhibited cumulative plastic deformations between 181 and 400 times the yield deformation and cumulative plastic strain between 46% and 106%. Conclusions about the behavior and recommendations for the design of the MBRB are presented. [ABSTRACT FROM AUTHOR]

Abstract: The majority of the existing literature on castellated members is focused on beams. Very little work has been done on the stability of castellated columns although they have been increasingly used in buildings in recent years. This paper presents a new analytical solution for calculating the critical buckling load of simply supported castellated columns when they buckle about the major axis. This analytical solution takes into account the influence of web shear deformations on the buckling of castellated columns and is derived using the stationary principle of potential energy. The formula derived for calculating the critical buckling load is demonstrated for a wide range of section dimensions using the data obtained from finite element analyses published by others. It was found that the influence of web shear deformations on the critical buckling loads of castellated columns increased with the cross-sectional area of a tee section and the depth of web opening, but decreased with the length and the web thickness of the column. It is shown that the inclusion of web shear deformations significantly reduces the buckling resistance of castellated columns. Neglecting the web shear deformations could overestimate the critical buckling load by up to 25%, even if a reduced second moment of area is used. [Copyright &y& Elsevier]

The effect of distortional deformation on the elastic lateral buckling of thin-walled box beam elements under combined bending and axial forces is investigated in this paper. For the purpose, an analytical model is developed for the stability of laterally unrestrained box beams according to higher order theory. Ritz and Galerkin's methods are applied in order to discretize the governing equilibrium equations and then the buckling loads are obtained by requiring the singularity of the tangential stiffness matrix. The different solutions are discussed and then compared to the finite element simulation using Abaqus software where shell elements are used in the mesh process. The numerical results reveal that classical stability solutions as those adopted in Eurocode 3 overestimate the real lateral buckling resistance of thin-walled box beam members, particularly for the ones with high ratios between the height and the thickness of the cross-section. Numerical study of incidence of compressive forces on lateral buckling resistance of thin-walled box beam is investigated. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a method of inelastic buckling analysis of thin-walled sections to study buckling characteristics of single span and two-span composite T-section beams in the inelastic range of structural response. The method is based on a bubble-augmented spline finite strip method, developed elsewhere by the authors, and confirmed as both accurate and efficient for the elastic buckling analysis of thin-walled structural members and plates. The method admits both flexural and membrane buckling deformations and it allows for consideration of structures with intermediate supports and a variety of boundary conditions that may be prescribed at the ends of plate assembly. The analysis includes the so-called Tendon Force Concept developed at Cambridge University for residual stresses caused by the process of fabrication, and the non-linear stress–strain properties of the structural steel from which the joist section is made. The inelastic restrained distortional buckling (RDB) of continuous composite T-section beams under transverse loading and moment gradient is investigated, and conclusions are drawn that address the influence of geometry, residual stresses, member length, the rigid restraint provided by the concrete and the degree of reinforcement in the concrete element. [Copyright &y& Elsevier]

Abstract: This paper presents a study of the inelastic local buckling of flange outstands in thin-walled steel beams at elevated temperatures. A spline finite strip method of buckling analysis is modified in order to model the properties of the steel section at elevated temperatures, so that slenderness limits can be proposed. These limits are needed in describing the behaviour of members under fire loading, since the development of benign catenary action in a restrained beam that has received widespread research attention in fire engineering design is reliant on the formation of plastic hinges, and of the influence of local buckling on the formation of these hinges. A sensitivity analysis is undertaken in order to propose plasticity and yield slenderness limits at elevated temperature, and it is shown that these limits depend on the parameters describing the uniaxial stress–strain relationship at the elevated temperature. The local buckling temperature is predicted for two different boundary conditions for a flange outstand, and it is shown that at high temperatures the local buckling of the beam is highly significant in accelerating the favourable development of catenary action. [Copyright &y& Elsevier]

To simplify the construction of traditional self-centering buckling-restrained braces (SC-BRBs) and achieve efficient recovery function, an innovative type of single-tube self-centering buckling-restrained braces (ST-SC-BRBs) is proposed. The ST-SC-BRBs only require one outer tube for the prestressed system. The detailed structure and working principle of the ST-SC-BRBs are described, and it is emphasized that the restrained steel tube should be checked as a compression-bending member to ensure its overall stability. Low-cycle fatigue tests are conducted on scaled models of one traditional BRB and two ST-SC-BRBs. The results show that the residual deformation of the ST-SC-BRBs is significantly reduced compared to that of the traditional BRB, with comparable energy dissipation capacity. The ST-SC-BRB works stably with a full hysteresis curve and an obvious "flag-shaped" pattern within the inter-story drift ratio of 2%. The self-centering ratio is the key factor affecting the recovery effect of the ST-SC-BRB. To achieve smaller residual deformation, the self-centering ratio is suggested to be greater than 1. Overall, the ST-SC-BRB presents a more simplified and effective approach to constructing a recoverable functional structure. • A new type of single-tube self-centering buckling restrained brace (ST-SC-BRB) is proposed. • Axial low-cycle tests show that the ST-SC-BRB structure achieves significantly reduced residual deformation. • The self-centering ratio of the ST-SC-BRB is the key factor affecting its self-centering effect. [ABSTRACT FROM AUTHOR]

Abstract: At present, there are only a few studies concerning the application of different types of buckling strength verification according to Eurocode 3 at combined loading. Besides the stress design as classical hand calculation method of checking cylindrical steel shells against buckling failure, the new Eurocode 3 also offers two global numerical analyses at different modelling levels. The linear buckling analysis (LBA) combined with a materially nonlinear but geometrically linear analysis (MNA) is the simpler concept from the perspective of the modelling and calculation effort. The more sophisticated method is a geometrically and materially nonlinear analysis of the imperfect structure (GMNIA). This paper presents the application of both numerical concepts to the cantilevered shell subject to a transverse load at the free edge. The results are compared to those from stress design. There are specific features at both types of numerical analysis: As the determination of the plastic reference resistance and the buckling parameters is the main focus at MNA/LBA, the choice of proper equivalent geometric imperfections demands special diligence at GMNIA. The presented analyses show that the GMNIA concept in connection with consistent equivalent geometric imperfections may lead to a safe and economic design of cylinders subject to combined loading. At the particular load case the MNA/LBA concept currently suffers from the lack of proper regulations concerning the determination of the overall buckling reduction factor. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to propose a simplified approach to the evaluation of the critical buckling load of multi-story frames with semi-rigid connections. To that effect, analytical expressions and corresponding graphs accounting for the boundary conditions of the column under investigation are proposed for the calculation of the effective buckling length coefficient for different levels of frame sway ability. In addition, a complete set of rotational stiffness coefficients is derived, which is then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, featuring semi-rigid connection at their near end as well as the eventual presence of axial force, are considered. Examples of sway, non-sway and partially-sway frames with semi-rigid connections are presented, where the proposed approach is found to be in excellent agreement with the finite element results, while the application of codes such as Eurocode 3 and LRFD leads to significant inaccuracies. [Copyright &y& Elsevier]

Abstract: Tanks with a conical roof are studied in this paper under wind load, for a roof which is supported by rafters and columns. Buckling occurs in the form of deflections in the cylindrical shell and the buckling mode is localized in the windward region. Both bifurcation analysis and geometrically nonlinear analysis have been performed using finite element discretizations of the structure. The wind pressures have been obtained from wind tunnel experiments performed as part of the research, and have been obtained for tank geometries for which information was not previously available. The results show high imperfection sensitivity of tanks with a conical roof, and buckling loads for wind velocities in the same order as those expected to occur in the Caribbean region. [Copyright &y& Elsevier]

Abstract: The behaviour of unrestrained steel I-beams has been studied by means of numerical analysis and published experimental results. The numerical model was developed using a commercial finite element program, MSC.MARC Mentat. A series of different UB and UC sections and different spans, subjected to both uniform moment and midspan point loads, are considered. The numerical predictions of the buckling moments are then compared with published experimental results. Consequently, a new approach is proposed to provide more accurate and safe predictions of the fire resistance of unrestrained beams, as well as to overcome certain weaknesses in the EC3:1.2 [European committee for standardization (CEN). Eurocode 3: Design of steel structures, Part 1.2: General rules — structural fire design, EN 1993-1-2. Brussels (Belgium); 2005] design formula. In addition, to provide a quick and simple design approach for engineers, a straightforward and rational method known as the Rankine method is introduced to predict the LTB failure load of steel beams in fire. It is shown that the Rankine approach generally provides a good lower bound value for numerical predictions. [Copyright &y& Elsevier]

Abstract: Doubly symmetric steel I-section members with thin webs and stocky flanges that have their tension flange restrained fully against translational and lateral rotational buckling deformations and elastically against twist rotation during buckling by the flexibility of a continuous restraint have been shown in previous studies to buckle in a so-called restrained distortional buckling (RDB) mode, involving distortion of the web of the I-section in the plane of its cross-section. These bifurcative buckling modes must necessarily occur in the negative moment region of composite T-beams and in half-through girder bridges. The present paper describes the elastic RDB analysis of a simply supported doubly symmetric I-section beam–column subjected to combined uniform axial force and moment gradient. The study adopts an energy method of analysis. The numerical solutions are used to develop a simple method of predicting the elastic RDB loads of beam–columns for use in design. [Copyright &y& Elsevier]

Abstract: This paper summarises and presents main results of an in-depth numerical analysis dealing with the shear buckling resistance of stainless steel plate girders. The studies conducted have permitted the development of a simple design expression to determine the critical shear buckling stress in steel web panels. This expression takes into account the effects of the material nonlinearity together with the actual boundary conditions of the web panel given by the geometry of the plate girder by two defined parameters: and , which is the shear buckling coefficient. Expressions given to obtain will quantify mainly the effect of the material nonlinearity whereas the proposed analytical expression of will reproduce principally the influence of the real boundary conditions in a web panel. [Copyright &y& Elsevier]

Abstract: The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling. [Copyright &y& Elsevier]

Abstract: This study aims to develop a concise formula for the critical buckling stresses of a simply supported plate under biaxial compression and shear. The critical stresses are obtained for different aspect ratios using classical plate theory and the Ritz method. The four-dimensional critical stress formula, which is expressed in terms of the three in-plane stresses and the aspect ratio, is developed empirically according to the two-dimensional relationships between the in-plane stresses. The findings that are of interest are: (1) the critical stress relationship is linear for the aspect ratios within the range 1 to and nonlinear for the aspect ratios within the range to 5; and (2) as shear stress approaches its critical value, the critical stress relationship becomes increasingly linear and less dependent on aspect ratio. [Copyright &y& Elsevier]

Abstract: Steel design codes do not provide sufficient information for the efficient design of steel structures against out-of-plane failure, and what is provided is often overly conservative. The method of design by buckling analysis (DBA) specified in one code corrects this situation for beams, but the extension of this method to columns is only referred to, while there is no guidance on how to apply this method to the design of beam–columns and frames. Beam DBA uses the design code formulation for the member nominal design strengths in terms of the section moment capacities and the maximum moments at elastic buckling, accurate predictions of which may be determined by computer programs. Column DBA is similar, in that it uses the design code formulation for the column nominal design strengths in terms of the section compression capacities and accurate predictions of the elastic buckling. However, design codes do not provide formulations for the direct buckling design of beam–columns, but instead use the separate results of beam design and column design in interaction equations. The further extension to frames is not directly possible, because frames are not designed as a whole (except through the rarely used methods of advanced analysis), but as a series of individual members. This paper shows how the method of DBA can be used to design beam–columns and frames as well as beams and columns. Two example frames are designed and very significant economies are demonstrated when the DBA method is used. [Copyright &y& Elsevier]

Abstract: Cross-section classification is an important concept in the design of metallic structures, as it addresses the susceptibility of a cross-section to local buckling and defines its appropriate design resistance. For structural stainless steel, test data on cross-section capacity have previously been relatively scarce. Existing design guidance has been developed based on the limited experimental results and conservative assumptions, generally leading to unduly strict slenderness limits. In recent years, available test data for stainless steel cross-sections have increased significantly, enabling these slenderness limits to be re-assessed. In this paper all available stainless steel test data have been collected and additional moment–rotation curves have been presented. The study covers both cold-formed and welded plated elements as well as CHS. Following analysis of the test results, new slenderness limits for all loading conditions have been proposed and statistically validated. In addition to re-assessment of the current slenderness limits, a new approach to the treatment of local buckling in structural elements–the Continuous Strength Method–has been outlined. The Continuous Strength Method (CSM) is based on a continuous relationship between cross-section slenderness and deformation capacity and is applied in conjunction with accurate material modelling. The method enables more rational and precise prediction of local buckling than can be achieved with the traditional cross-section classification approach, thus allowing better utilization of material and more economic design. [Copyright &y& Elsevier]

Abstract: The buckling behavior of a new ductile bracing concept for steel structures is examined. The system makes use of cast components introduced at the ends and the center of the brace to produce a special bracing detail with reliable strength, stiffness and deformation capacity. The system takes advantage of the versatility in geometry offered by the casting process to create configurations that eliminate non-ductile failure modes in favor of stable inelastic deformation capacity. This paper presents analytical research performed to determine the buckling strength and buckling direction of the bracing element based on the geometries of the cast components. Limiting geometries are determined for the cast components to control the buckling direction. Design formulas for buckling strength are proposed. [Copyright &y& Elsevier]

Abstract: This paper presents the results of a research project analysing some aspects of the stability failure of thin-walled compression members that are likely to exhibit combined global and local buckling. In particular, the influence of various imperfections, namely residual stresses due to welding and local as well as global geometrical defects, on the load-carrying capacity was subjected to detailed experimental and numerical investigations. The insights obtained into the structural behaviour led to a proposal for modification of the non-dimensional slenderness used in the global buckling verification, and to the recommendation of a shift from the currently applied European buckling curve to a more favourable one in the case of non-stiffened members with welded box sections subjected to pure compression. [Copyright &y& Elsevier]

A novel assembled steel double-stage yield buckling restrained brace (DYB) was experimentally studied. The DYB core plate comprises one small core plate and one large core plate connected in series. The deformation capacity of the small core plate is restricted by a stopper mechanism. The deformation of the DYB is first concentrated at the small core plate and then shifted to the large core plate once the stopper mechanism is triggered, resulting in double-stage yield behavior of the DYB. Three specimens were fabricated with core plates of different size to study the main influencing factors in the design of DYBs. Quasi-static tests were conducted. Results from a comprehensive experimental study demonstrate that the DYB has a ductile, stable, and repeatable hysteretic behavior. It is a reliable and practical alternative to conventional framing systems in that it can enhance the earthquake resistance of existing and new structures and provide the rigidity needed to satisfy structural drift limits while delivering a stable and substantial energy absorption capacity. The proposed hysteretic model of the DYB was calibrated with the test results, showing good agreement and the capacity to capture characteristic points of hysteresis curves. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a general formulation for the analysis of steel hollow structural beams subjected to biaxial bending. The model has been developed within the framework of lumped damage mechanics. In this approach, the models are based on methods of continuum damage mechanics and the concept of plastic hinge. The model was implemented in a commercial finite element program. In order to calibrate the model, a set of experimental tests were carried out in the Structural Mechanics Laboratory at the Lisandro Alvarado University. The model was evaluated by the numerical simulation of these tests finding a good agreement between the experimental tests and the numerical simulations. [Copyright &y& Elsevier]

Abstract: This paper investigates the influence of weld rotation stiffness on the global bifurcation buckling strength of laser-welded web-core sandwich plates. The study is carried out using two methods, the first is the equivalent single-layer theory approach solved analytically for simply supported plates and numerically for clamped plates. First-order shear deformation theory is used. The second method is the three-dimensional model of a sandwich plate solved with finite element method. Both approaches consider the weld through its rotation stiffness. The weld rotation stiffness affects the transverse shear stiffness. Plates are loaded in the web plate direction. Four different cross-sections are considered. Weld stiffness is taken from experimental results presented in the literature. The results show a maximum of 24% decrease in buckling strength. The strength was affected more in plates with high reduction of transverse shear stiffness and high bending stiffness. Furthermore, clamped plates were influenced more than simply supported. The intersection between buckling modes shifted towards higher aspect ratios, in the maximum case by 24%. The results show the importance of considering the deforming weld in buckling analysis. [Copyright &y& Elsevier]

A pre-stressed stayed steel column (PSSC) can effectively enhance the buckling behaviour of compression columns. In the past, researchers have primarily concentrated on examining the behaviour of PSSCs with single-bay crossarms. However, research focused on PSSCs with multiple crossarms is limited. This article aims to investigate the stability behaviour of PSSCs stiffened with multiple crossarms according to geometric analysis in conjunction with finite element (FE) studies. The results show that the critical buckling modes can be complicated due to the introduction of multiple crossarms. Critical buckling deformation similar to three half sine waves can be observed. It has also been demonstrated that interactive buckling can be ignored when determining the actual buckling strength of PSSCs stiffened by multiple crossarms, though it must be considered for PSSCs with single-bay crossarms. The effects of stay diameter and pretension in the stay have been separately investigated, and the results show that the buckling strength of a steel column can be obviously enhanced even if the pretension in stays is quite small, because the stiffness of the stays can be automatically activated by column deformation. [ABSTRACT FROM AUTHOR]

Abstract: The critical buckling load of a structure undergoing lateral buckling can be determined experimentally by using the extrapolation or plotting techniques, without having to subject the structure to loading in the vicinity of critical. To achieve this, it is only necessary to have data relating load to a deformation characteristic. A search of the literature reveals that only certain and just a few deformation characteristics such as lateral displacement and/or twist have mostly been used by researchers in this regard. In this paper, the feasibility of application of various deformation variables for experimental determination of the critical buckling load is investigated in case of I-beams with different initial geometrical imperfections undergoing the elastic lateral–distortional mode of buckling. It is demonstrated that lateral displacement of the I-beams is directly coupled with different deformation variables such as web transverse and longitudinal strains, vertical deflection, and angles of twist of top and bottom flanges. Based on these key findings, the Southwell, Massey, Modified, and Meck Plot methods are applied on these various deformation variables, and consequently satisfactory and reliable estimates are obtained for the critical buckling loads. Finally, it may be concluded that the application of the extrapolation techniques does not actually need to be limited to some certain deformation variables. [Copyright &y& Elsevier]

Abstract: Buckling-restrained braces (BRBs) permit exploiting the hysteretic properties of their core material both in tension and compression. However, the global behaviour of the BRB does not fully replicate the local behaviour of the core material and important differences have been observed in experimental tests, such as a higher bearing capacity in compression and a significant role of isotropic hardening. These observations have thus promoted the use of specific constitutive models for BRBs. Besides a proper description of behavioural aspects, a BRB model should include some highly desired requirements: explicit computation of the plastic component of the deformation as required in BRB capacity models, smoothness of the elastic–plastic transition to improve convergence rate, simple implementation and limited number of input data parameters to facilitate its implementation and use. In order to address the above behavioural and modelling issues, an elastoplastic model for steel BRBs is presented in this paper following a consistent approach based on a rheological scheme that leads to a quite simple constitutive law involving only one internal variable. The adopted formulation allows a straightforward physical interpretation and identification of the constitutive parameters of the model as well as explicit computation of response quantities related to failure and dissipated energy. Response results obtained using the proposed model are compared to the outcomes of experimental tests available in the literature and involving different BRBs under various strain histories, showing good predictions of the experimental behaviour. [Copyright &y& Elsevier]

Abstract: This work conducts compression tests and finite element analyses for steel dual-gusset-plate connections used for buckling-restrained braced frames (BRBFs). Compared to a single-gusset-plate connection, dual gusset plates sandwiching a BRB core reduce gusset plate size, eliminate the need for splice plates, and enhance connection stability under compression. The experimental program investigated ultimate compression load by testing ten large dual-gusset-plate connections. Out-of-plane deformation of the gusset plate in the test resembled that of a buckled gusset plate with low bending rigidity provided by the BRB end. The general-purpose nonlinear finite element analysis program ABAQUS was applied for correlation analysis. A parametric study of the dual-gusset-plate connection was performed to study the effects of plate size, presence of centerline stiffeners, and beam and column boundaries on ultimate compression load. The ultimate compression load of the dual-gusset-plate connection could not be predicted based on the AISC-LRFD approach due to beam flange out-of-plane deformation. The ultimate compression load of the dual-gusset-plate connection was reasonably predicted using a column strip length from the Whitmore section to the workpoint of the beam and column centerlines and a buckling coefficient of K =2. [Copyright &y& Elsevier]

This paper presents an experimental investigation into locally unstable ultra-light-gauge steel storage rack frames that are prone to flexural-torsional buckling. The aim of the research was to understand how local instabilities and interactive buckling affect the strength of ultra-light gauge frames and to create reliable data through a controlled experimental investigation. A total of twelve full scale tests were conducted in the Civil Engineering Structures Laboratory at the University of Sydney. Prior to testing, the geometric imperfections of each member were measured, as were the material properties of the cold-rolled sections and the virgin steel from which the sections were formed. The cross-sectional deformations, ultimate loads and observations regarding failure modes were accurately captured and documented. The tests were also successful in capturing the post-ultimate response of the frames as well as the rotational stiffness of the beam-to-upright connections. Results from nominally identical tests were in good agreement. The tests provide comprehensive data for assessing the effects of interactive buckling and the extent to which cross-sectional deformations amplify the second-order deformations in locally unstable storage rack frames. [ABSTRACT FROM AUTHOR]

Abstract: The flexural capacity of cellular steel beams is influenced by both local and global instabilities. In the current paper, the finite element method is employed to investigate the inelastic behavior of cellular steel beams under combined buckling modes. A three-dimensional non-linear finite element model, that takes into consideration possible interaction between lateral torsional/distortional buckling modes and localized deformations of the cross section is developed and validated against available results in the literature. The study considers simply supported beams subjected to three different load configurations; mid-span load, uniformly distributed load and end moments. An extensive parametric analysis is conducted to assess the impact of various geometrical parameters on the inelastic stability of cellular steel beams. These parameters include the dimensions of the beam cross-section; flange width and thickness, web height and thickness, and hole size and spacing. The moment gradient factors that correspond to various buckling modes experienced by the wide range of dimensions considered in the simulation study are reported. The outcomes of the this study are expected to provide more insight into the behavior of cellular steel beams and enable accurate prediction of the moment gradient factor and consequently the flexural capacity of this special type of steel beams. [Copyright &y& Elsevier]

Abstract: Proposed in this paper is an approach of evaluating the elastic buckling loads for multi-storey unbraced steel frames subjected to variable loading or non-proportional loading. In the case of variable loading, the conventional assumption of proportional loading is abandoned, and different load patterns may cause the frame to buckle at different levels of critical loads. In light of the use of the storey-based buckling concept to characterize the lateral sway buckling of unbraced framed structures, the problems of determining the lower and upper bounds among all of the frame buckling loads associated with different load patterns are presented as a pair of minimization and maximization problems subjected to elastic stability constraints. The problems take into account the semi-rigid behaviour of beam-to-column connections and the lateral stiffness reduction of columns due to the presence of an axial compressive load. The minimization and maximization problems are then solved by a linear programming method; thus, the lower and upper bounds of the frame buckling loads subjected to variable loading are obtained. Parametrical studies on the influence of the connection rigidity to the lower and upper bounds of critical loads and the comparisons to the conventional proportional loading are also presented in this paper. [Copyright &y& Elsevier]

Abstract: During the procedure of manufacturing structural steel profiles the considerable temperature changes cause residual stresses in the material. These stresses can have a significant effect on the stability resistance of structures consisting of such profiles. Therefore engineers have paid special attention to the consideration and modelling of residual stresses in the comprehensive research into column buckling. They developed several stress distribution forms based on experimental and/or theoretical results, which worked well in column buckling problems. However, when the member has twisting displacements–e.g. in the case of lateral–torsional buckling–these stress distributions can lead to malfunction, because they do not satisfy certain equilibrium equations connected with torsion and warping of the profile. In order to avoid this problem a new stress pattern is proposed which satisfies all the equilibrium equations, thus being applicable in stability problems including torsional and warping effects. [Copyright &y& Elsevier]

This study proposes a novel type of metallic yielding damper called block slit damper or BSD. This damper is a slit damper with very low height to thickness ratio. This device has high shear capacities, and is more economical than SSD devices with high height to thickness ratios. Based on theoretical analysis the formulation for the BSD device's main parameters is derived. Then to investigate the hysteretic behavior of the proposed devices, 5 specimens with different aspect ratios (height-width ratios) were manufactured and tested in a quasi-static manner. The tests revealed that by reducing the aspect ratios, the shear and energy dissipation capacity increases while the displacement capacity decreases. The experimental analysis is compared to analytical analysis which showed a good agreement between them. Based on the buckling analysis conducted on the BSD, it was determined that by increasing the thickness of SSD devices, the device becomes buckle resistant while the unit material's dissipated energy remains the same. [ABSTRACT FROM AUTHOR]

In the construction of single layer domes and vaulted structures manufactured ball-node type connections are widely used. These ball-nodes deform due to the action of a three-dimensional state of stress while offering their resistance. These deformations result in a loss of connection stiffness, which influences the overall stability of these domes, and is usually ignored in the analysis. This work presents an investigation on the effect of ball-node deformations in the inelastic post-buckling behavior of domes and vaulted structures. A model for the load-deformation properties of the ball-nodes has been proposed in this study, in the lines of EC3-8. This connection flexibility model is integrated into a corotated–updated Lagrangian finite element formulation. Results for single layer domes and a braced barrel vault are presented. Although the present investigation deals with ball nodes only, the computational framework is still relevant for other type of connections of space structures, with modifications. [ABSTRACT FROM AUTHOR]

Abstract: The study presents a numerical approach to first-hinge stability design of open thin-walled steel members with arbitrary internal forces including nonuniform torsion. A generally applicable numerical method for the evaluation of plastic cross-section resistance is presented. The applied optimization formulation allows for yielding due to the simultaneous action of normal and shear stresses according to the von Mises yield criterion. Specific considerations are necessary to account for shear stresses from uniform torsion. Unlike in the case of two-dimensional beam problems, the load-carrying behaviour of thin-walled beams under lateral buckling loading changes significantly when yielding starts. This leads to restrictions and specific procedures in the application of second-order beam theory with a first-hinge criterion, to the solution of 3-D stability problems. [Copyright &y& Elsevier]

Prediction of the column strength, associated with buckling and material yielding, is vital in a successful design. In this paper, a completely numerical analysis technique is employed for simulating the compressive behavior of Q690 high-strength steel columns with box- and H-sections, and its accuracy is verified by the experimental results as presented in the part 1 of the companion papers. To this, the curved Pointwise-Equilibrating-Polynomial (PEP) is introduced for representing the column deformations with an explicit simulation on the member initial imperfection. Further, the refined plastic hinge model combined with the use of sectional yield surfaces is employed to reflect inelastic yielding at the critical location. A cross-sectional analysis approach allowing for residual stresses modeling is also incorporated into the numerical method. Sequentially, a parametric study is conducted extensively for the Q690 high-strength steel welded columns. At last, the buckling curves from Chinese (GB 50017-2003), European (Eurocode 3), and American (ANSI/AISC 360-10) codes are examined, and some recommendations for design of Q690 high-strength steel columns are presented. [ABSTRACT FROM AUTHOR]

This study investigates the stability of the structural systems assembled by system scaffolds. Loading tests were conducted on the indoor single-bay system scaffolds and the outdoor full-scale structural system assembled by system scaffolds. Test results were compared with the second-order inelastic analysis with semi-rigid joints to determine the reliability of various analytical parameters. The study reveals that, while the failure model of the single-bay two-storey system scaffold without diagonal braces is overall buckling failure of the structure, the failure model of the same structure with diagonal braces is buckling failure of the vertical standards between the upper and lower storeys. The critical load of the configuration with diagonal braces is about double that of the same structure without diagonal braces. At the moment of buckling failure of the outdoor full-scale two-row, two-bay, six-storey structural system assembled by system scaffolds, the vertical standards at the four corners appeared to have large horizontal displacements owing to without diagonal braces. However, the vertical standard in the center did not exhibit obvious horizontal deformation because it was reinforced with diagonal braces on four sides. In addition, the use of diagonal braces can significantly increase the load capacity of vertical standards. This study recommends that all vertical standards be reinforced with diagonal braces to ensure the load capacity of the structural systems assembled by system scaffolds. A second-order inelastic analysis with semi-rigid joints and various notional lateral forces is recommended to determine the critical loads of full-scale structural systems assembled by system scaffolds. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of shear buckling in the panel zone of beam-to-column connections is examined. In particular, following the application of the shear buckling theory for rectangular plates, both in the elastic and in the plastic field, and a critical review of American and European provisions for panel zones, a parametric FEM analysis using ABAQUS Code is carried out on beam-to-column connections. The comparison of the analysed code provisions with the numerical and experimental results shows a good agreement of the American provisions; on the contrary, some drawbacks are identified in the application of the European provisions. Thus, in order to exclude any buckling phenomena, some possible improvements are proposed in terms of panel zone slenderness limit. [Copyright &y& Elsevier]

Abstract: In this work the nonlinear in-plane behavior of circular arches with hollow circular cross-section is investigated. The influence of a number of design parameters, such as the boundary conditions, the rise-to-span ratio, and the included angle on the strength is presented. Moreover, the effect of other behavior factors, such as the geometrical and material nonlinearities and the initial imperfections, is investigated. A criterion for the prediction of the type of nonlinear behavior of arches is given, and a formula for the determination of the nonlinear buckling load is proposed. It is found that the effect of initial imperfections on the strength depends largely on the arch slenderness and the imperfection magnitude in the case of shallow arches. When arches are deep this dependence becomes less significant. The effect of geometrical nonlinearity depends significantly on the shallowness and the slenderness of the arches. Stocky arches are less influenced by the rise-to-span ratio than slender ones. The effect of boundary conditions depends significantly on the shallowness of arches and the arch slenderness. The reduction of strength is larger in slender arches than in stocky ones. [Copyright &y& Elsevier]

To investigate the mechanical deformation characteristics of the 'Segment-SCC-Steel Tube' combined bearing lining structure under internal and external pressure, the loading device and monitoring system for the stability analysis of the full-scale lining were proposed. The effect of cracked encased concrete and local external pressure on the instability mode of thin-walled steel pipes was explored by full-scale model experiment and three-dimensional FEM numerical simulation. The influence of SCC (Self-Compacting Concrete) and stiffening rings on the stability of steel pipes subjected to external pressure was discussed. The results show that SCC cracks occur and intensify with increasing internal pressure. The external water acts directly on the steel tube through cracking, resulting in wavy deformation, and the gap between the SCC and steel tube further increases. When calculating the critical external pressure for the steel pipe, the constraint of encased concrete can be ignored, and only the constraint effect of the stiffening ring can be considered. Therefore, the Von Mises formula was used to predict the critical external pressure between the stiffening rings with high accuracy. In addition, the stiffening ring can mitigate the crack propagation of nearby SCC. The steel tube remained in the elastic stage under internal pressure. In the full-scale experiment, the external pressure could not continue to rise after reaching 0.65 MPa. Nevertheless, the amplitude of the buckling wave continued to increase. It is considered that the steel pipe is in an unstable state, and the failure mode is dominated by single-lobe buckling. • According to the performance of the 'Segment-SCC-Steel Tube' lining structure, the influence of cracked encased concrete and local external pressure on the buckling mode of steel pipes is investigated. • The loading device of the full-scale model test is proposed for the external pressure stability analysis of the 'Segment-SCC-Steel Tube' lining structure, and the monitoring system combining distributed optical fiber and traditional vibrating wire sensors is established. • The mechanical deformation characteristics of the SCC and Steel Tube lining under internal and external pressure are revealed, and the influence of SCC and stiffening rings on the stability of steel pipes under external pressure is discussed. [ABSTRACT FROM AUTHOR]

Abstract: Based on the equilibrium configuration paths, this study investigates the postbuckling behaviour, including the shape recovery capability, of stainless steel (SUS304) columns after a complete loading–unloading cycle. Experiments were conducted and later numerical simulation was carried out in order to analyze the observed buckling and postbuckling behaviour. Large deflection analysis is necessary for slender columns. Moreover, comparison of the experimental critical load with analytical predictions verifies the fact that physical nonlinearity should be taken into account to analyze the column’s buckling behaviour comprehensively. Thus, based on large deflection theory as well as the nonlinear stress–strain relations, the load–deformation curves of the columns during a complete loading–unloading cycle have been predicted by using the finite element modelling (FEM) code ANSYS. Precise and quantitative analyses of the results verify the fact that the material’s stress–strain properties, both in tension and compression, attribute to the column’s buckling behaviour. [Copyright &y& Elsevier]

A performance based seismic design method for eccentrically braced frames (EBFs) and buckling restrained braced frames (BRBFs) is developed herein. The method is a force-based seismic design one where the design base shear is obtained by using different modal strength reduction factors for each one of the first four modes of the frame, instead of using a constant behavior factor for all modes as in all current design codes. These modal strength reduction factors incorporate the dynamic characteristics of the structure, different soil types and different performance targets. Thus, the proposed method can automatically satisfy deformation demands at all performance levels without requiring deformation checks, as it is the case with code-based design methods. The basic concept of the method is associated with the determination of an equivalent elastic structure that retains the mass and initial stiffness of the original nonlinear one, and is characterized by high amounts of viscous damping in order to equilibrate the nonlinear energy of dissipation by the viscous one. The above mentioned factors are obtained through the use of extensive parametric studies on 98 steel plane frames subjected to 100 far-field ground motions. Empirical expressions for those modal strength reduction factors as functions of period, deformation/damage and soil types, which can be used directly in conjunction with the conventional elastic pseudo-acceleration design spectra with 5% damping for seismic design of steel EBFs and BRBFs, are provided. The proposed method is illustrated with representative numerical examples that demonstrate its advantage over code-based seismic design methods. [ABSTRACT FROM AUTHOR]

Abstract: Multi-tube latticed steel columns without diagonal tubes and the ones with diagonal tubes are two common types of prismatic latticed columns used nowadays. Instability behavior of prismatic multi-tube latticed steel columns is studied in this paper. The focus on the problem is based on the derivation of shear stiffness for multi-tube latticed steel columns. Formulas are established to express the elastic buckling loads as well as the modified slenderness ratios, in which the effect of shear deformation is taken into account. Cases are analyzed via finite element method ANSYS to calculate the ultimate load-carrying capacity of the latticed columns for comparison with the design method in different design codes for compressive members. Formulas to estimate the design resistance for axial compressive prismatic multi-tube latticed steel columns are proposed and detailed design suggestions for the component steel tubes are presented as well. [Copyright &y& Elsevier]

Abstract: This paper presents an overview of the mechanics of distortion in members which have restrained thin-walled steel sections. First, the basic features that characterize the distortion of thin-walled sections under compression and/or bending are explained and the generally adopted kinematical assumptions are presented and discussed. On the basis of these assumptions, a simple procedure to build the distortional displacement fields is proposed. Then, two illustrative examples of restrained sections are given and their distortional displacement fields are built. The I-section illustrates the case of a symmetric section having a distortional displacement field with a single d.o.f. The Z-section exemplifies the case of a non symmetric section having a distortional field with two d.o.f. Based on an energy formulation, the equilibrium equation for buckling analysis of simply supported thin-walled members is derived. For two illustrative examples, the distortional displacement field is used to obtain distortional analytical formulae. Finally, some results (buckling loads and moments) were determined and validated by means of comparison with fully numerical obtained from finite strip analysis. [Copyright &y& Elsevier]

Abstract: The development of design procedures based on inelastic advanced analysis is a key consideration for future steel design codes. In advanced analysis the effect of imperfections has to be modelled in such a way that the incremental analysis fully captures this effect in the process of moment redistribution. In modelling the influence of imperfections on the behaviour of individual members of real structures, different approaches have been used to globally represent this effect in the overall analysis of structural systems. They are referred to as the initial bow imperfection approach or as the equivalent transverse load approach. When using the abovementioned approaches in analysis of multiple member structural systems, the designer is required to arrange the directions of bow imperfections or equivalent transverse loads in such a way that the imperfection arrangement leads to the least constrained solution, i.e. the lowest ultimate load predicted from all possible sets of member initial imperfection arrangements. Since there is still ongoing research on the development of simple application rules ensuring that the designer obtains a unique solution when choosing a certain set of member initial imperfections, there is at the same time interest in the development of alternative approaches to modelling the influence of member imperfections on the behaviour of structural systems. This paper provides the necessary background information as well as describes the formulation and modelling techniques used in the development of a new approach to modelling the influence of imperfections on the stability behaviour of structural components and systems. This new approach, called hereafter an equivalent stiffness approach, has an advantage over the previously described approaches since an imperfect member is treated as a hypothetically straight element, flexural and axial stiffnesses of which at each load level are predicted in a continuous fashion dependent upon the actual force and deformation states. This type of modelling does not require any explicit modelling of equivalent geometric imperfections or equivalent forces and their directions in advanced analysis; therefore also it does not require any buckling mode assessment. Moreover, the effects of strain hardening and section class may conveniently be included in modelling. Finally, European buckling curves are used to estimate the values of parameters of the developed model that can be immediately used in advanced analysis conducted according to Eurocode 3. [Copyright &y& Elsevier]

Abstract: This paper describes the study of the low-yield-point (LYP) steel plate shear walls under in-plane load. In the LYP steel plate shear wall system, LYP steel was selected for the steel plate wall while the boundary frame was constructed by the high strength structural steel. A series of experimental studies examined the inelastic shear buckling behavior of the LYP steel plate wall under monotonic in-plane load. The effects of width-to-thickness ratio on the shear buckling of LYP steel plates were examined. The stiffness, strength, deformation, and energy dissipation characteristics were investigated by performing cyclic loading tests on the multistorey LYP steel plate shear walls. Excellent deformation and energy dissipation capacity were obtained for all specimens tested. The LYP steel plate shear wall system is able to exceed 5% of storey drift angle under lateral force. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of determining the stiffness and strength of steel storage rack base plate assemblies. Base plate assemblies are usually bolted to an upright and to a concrete floor, and they are used to provide resistance against the flexural buckling of the upright and/or the overall down-aisle buckling of the frame. The semi-rigid stiffness is usually determined by means of a test of two pre-loaded uprights connected to a concrete block in a dual-actuator set-up. Guidance for conducting the test is provided in the European Standard EN 15512. However, several aspects of the test need clarification, notably the test set-up and the transducer arrangement for measuring the rotations of the base plate. This paper provides recommendations for how best to conduct the test, and proposes an alternative test method to that given in the EN 15512 Specification. The paper also identifies the contributions to the deformations of base plate assemblies, including the deformations of the supporting floor, the base plate assembly itself and the upright, and proposes simple expressions for calculating the stiffness associated with each contributing deformation where applicable. Furthermore, the paper proposes a deformation criterion for determining the ultimate design moment for base plate tests which do not attain a peak moment. [Copyright &y& Elsevier]