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• High-strength CFS built-up beams comprising of four plain channels subjected to four-point bending were numerically investigated. • 240 FE analyses over a wide range of parametric variation (geometry, thickness, yield strength) were carried out. • The influence of aspect ratio, cross-section slenderness, flange and web slenderness on flexural strength was investigated. • A novel method to determine the elastic critical buckling stress of cold-formed HSS built-up beams was proposed. • Two modified design rules for high-strength CFS built-up beams based on DSM and CSM have been proposed and confirmed through a reliability analysis. The adoption of high-strength steel in the construction sector can provide potential advantages, such as supporting large-scale structures with small cross-sectional sizes leading to decreased self-weight and improved space availability. In this paper, detailed numerical investigations are presented to investigate the nonlinear behaviour of cold-formed high-strength steel (HSS) built-up beams subjected to in-plane flexure along with their bending moment capacities, deformed shapes, and moment-curvature curves. Finite element (FE) models incorporating the initial geometric imperfections of cold-formed sections and material nonlinearities were established and validated against the experiments presented in the literature by comparing the moment-curvature curves, deformed shape, and ultimate bending moment capacities. Following validation, the calibrated FE models were utilized to perform extensive parametric studies to generate further numerical data by varying three different parameters: cross-sectional yield strengths (S700, S900 and S1100), geometries (such that the local slenderness, λ l values varied from 1.07 to 4.65) and cold-formed steel (CFS) sheet thicknesses (1.0, 1.5, 2.0, and 2.5 mm). The specimens considered in the present study were restrained to inhibit lateral - torsional buckling and demonstrated failure owing to local buckling. The applicability of the design principles for predicting bending capabilities was assessed using numerical data in accordance with direct strength method (DSM) of AISI codal provisions and continuous strength method (CSM). The obtained numerical results demonstrated that the existing standards lack precise design procedures for cold-formed HSS built-up members and additional research is still required to provide accurate design procedures. Therefore, an improved rational extension of DSM of AISI codal provisions and CSM is recommended to predict the ultimate bending moment resistance. [ABSTRACT FROM AUTHOR]

• Cruciform timber-encased steel composite columns were proposed and experimentally evaluated. • The lateral restraint of timber contributed to the full utilization of the steel strength. • The reduction of extensive deformation of cruciform steel components by timber was quantitatively analyzed by 3D laser scanning. • A new empirical formula for compressive strength was proposed. Timber-encased steel composite (TESC) columns have garnered increasing attention owing to their high mechanical performance. However, limited studies have focused on the compressive performance of cruciform TESC columns and accurate evaluations of the full-field deformation of embedded steel components. In this paper, a novel cruciform TESC column embedded with a thin-walled cruciform steel component was proposed. 22 specimens including TESC columns, bare steel columns and bare glulam columns were tested under axial compression. Parameters such as the width and thickness of the cruciform steel component were considered. 3D laser scanning technologies were applied to measure the full-field deformation of 20 steel members, thus quantitatively assessing the reduction in the deformation of steel components resulting from the lateral restraint of timber. Finally, a nonlinear fitting equation was established to predict the load-carrying capacity. The results showed that the TESC columns exhibited significant enhancements in stiffness and load-carrying capacity. The lateral restraint of timber caused the buckling modes of the steel to change from torsional buckling to mainly local buckling. Moreover, the high post-yield stiffness of the steel components before reaching the maximum load indicated that the timber offered sufficient lateral restraint to make full use of the steel strength. The 3D laser scanning method accurately measured the full-field deformation of the steel at the failure state. Compared to bare steel columns, the torsional rotation of the steel components decreased by up to 83.14 %, while the maximum absolute lateral deflection decreased by up to 80.89 %. The suggested strength formula offered sufficient accuracy in predicting the load-carrying capacity of short TESC columns, with ratios between the calculated and experimental values ranging from 0.908 to 1.120. [ABSTRACT FROM AUTHOR]

• A series of compression tests to investigate member buckling behaviour and ultimate strengths of cold-rolled aluminium alloy channel columns are performed. • The aluminium alloy 5052-H36 materials are used to fabricate the cold-rolled aluminium structural channel columns. • The observed failure modes are flexural, flexural-torsional and local-global interaction buckling failure modes. • The experimental results are compared with predictions by current Australian/New Zealand, North American and European design specifications. Cold-rolled aluminium alloy sections have been recently introduced in Australia as newly developed thin-walled products. To fabricate these sections, the roll-forming process used in cold-formed steel production has been employed, which has proven to be more cost-effective than the conventional extrusion process. This paper describes a series of compression tests to investigate member buckling behaviour and ultimate strengths of cold-rolled aluminium alloy 5052-36 channel columns. Twenty-eight specimens of three commercially available sections (C10030, C25025 and C40030) were tested at the University of Sydney. Two configurations of end boundary conditions were specially designed to capture flexural, flexural-torsional and local-global interaction buckling failure modes. Prior to testing, initial geometric imperfections were measured using a laser scanning method, and flat/corner coupons were tested to determine compressive and tensile strengths of the aluminium alloy material. The experimental results are compared with ultimate column strength predictions by current Australian/New Zealand, North American and European design specifications for aluminium structures. Additionally, the test results provide data for calibration of finite element models of cold-rolled aluminium structural members for use in parametric and similar studies. A companion paper describes such parametric study and the derivation of new design guidelines for member buckling of cold-rolled aluminium channel columns based on the numerical parametric data and the experimental data presented herein. [ABSTRACT FROM AUTHOR]

• Experiments on the member buckling and ultimate strengths of cold-rolled aluminium alloy channel columns are performed. • The aluminium alloy 5052-H36 materials are used to fabricate the cold-rolled aluminium structural channel columns. • Non-linear FE models are developed using ABAQUS to simulate laboratory experiments and calibrated against the test results. • A parametric study based on FE models is performed to extend the data by varying cross-section dimensions and member lengths. • Experimental and numerical results are ued to calibrate the new design equations for cold-rolled aluminium alloy columns. The paper first presents the development of detailed finite element (FE) models for investigating the member capacity of cold-rolled aluminium alloy 5052-36 channel columns. The numerical non-linear FE models are developed using the commercial FE software package ABAQUS to simulate laboratory experiments and calibrated against the test results. The experimental program was performed by the authors at the University of Sydney and the detailed test results are fully described in a companion paper. The calibrated numerical FE models with actual mechanical properties and measured geometric imperfections in analyses accurately predict the experimental results and behaviours, including flexural and flexural-torsional buckling as well as local-global interaction buckling failure modes. A parametric study is subsequently performed to extend the data range by varying cross-section dimensions and member lengths. The effects of loading eccentricity positions and initial geometric imperfections are also considered in the parametric study. The experimental and numerical results are compared with design strength predictions from current Australian/New Zealand, American and European specifications for aluminium structures in the companion paper. In this paper, the Direct Strength Method (DSM) for the design of compression members as per the Australian/New Zealand standard AS/NZS 4600 for cold-formed steel structures is adopted for comparison. The DSM design rules for cold-formed steel compression members are found to provide more accurate predictions than those of current specifications for aluminium structures and therefore used to propose improved design equations for cold-rolled aluminium alloy columns. Finally, a reliability analysis is performed to evaluate the safety level of current design specifications and the proposed design rules. [ABSTRACT FROM AUTHOR]

• Introduced a novel formula for helical spring buckling under combined loads. • Experimental and numerical analyses confirm the formula's effectiveness. • Higher preload and prestretching enhance spring buckling torque resistance. A new formula is introduced to analytically determine the critical torsional load or angle of rotation that confers instability in a tension spring under combined tension and torsion load using the theoretical framework of Greenhill's problem applied to an elastic bar as a starting point. The formula's effectiveness is evaluated with experimental torsion tests and finite element method simulations in Abaqus. The results demonstrate the formula's accuracy in predicting instability within specific stretched operating ranges, and achieving a relative error in correlation below 10 % for most operating points. The study underscores the significance of preload and pre-stretching in enhancing the spring's resistance to buckling. [ABSTRACT FROM AUTHOR]

• Behaviour of laser-welded stainless steel slender I-section beam-columns under major-axis combined loading was studied. • Eight laser-welded stainless steel slender I-section beam-column tests were conducted. • FE models were developed and validated against the test results, and then used to perform parametric studies. • The American and European interaction curves were evaluated, based on the test and FE results. • A new interaction curve was proposed and shown to offer improved design accuracy and consistency. This paper presents testing and modelling investigations on laser-welded stainless steel slender I-section beam-column members under combined compression and major-axis bending moment, which are susceptible to torsional-flexural buckling interacting with local buckling. A testing programme was firstly conducted, including material tests, imperfection measurements and beam-column tests. Upon completion of laboratory tests, a numerical modelling programme was carried out, in which finite-element models were developed and validated based on the test results. The numerical models were then used to perform parametric studies to derive more beam-column data. The obtained test and numerical data were adopted to conduct a design analysis, in which the relevant interaction curves in the American and European standards were evaluated. The analysis results show that the American and European standards lead to inaccurate resistance predictions, especially for beam-column members subjected to eccentric compression with large eccentricity, due to the conservative bending end-points that are specified for the design of beams prone to lateral-torsional buckling. A new interaction curve was proposed based on the continuous strength method and found to provide improved design accuracy and consistency over the current American and European standards. [ABSTRACT FROM AUTHOR]

• New method to determine the lateral-torsional buckling coefficient for steel plate girders under fire conditions is presented. • Proposed lateral-torsional buckling curves depend on initial load level and the reduction degree of section bearing capacity. • Impact of an uneven temperature distribution is taken into account. The results of experimental tests and computer simulations pertaining to the bearing capacity of unevenly heated girders made of slender thin walled class 4 sections are presented in this paper. It has been shown, that for the analyzed group of elements the value of lateral-torsional buckling coefficient depends on the initial load level applied to the considered element and the cross section bearing capacity reduction level under fire conditions. It has been determined as well that the influence of steel grade used on the value of buckling coefficient is negligible. Based on the research conducted, a new proposal for calculation of the lateral-torsional buckling coefficient for considered group of elements has been prepared. A simplified method to determine the bearing capacity of non-uniformly heated class 4 sections is proposed in this paper as well. It has been shown that both proposed methods exhibit sufficient convergence of results with the results of computer simulations, and satisfy appropriate acceptance criteria as well. [ABSTRACT FROM AUTHOR]

• An orthotropic coating is used to strengthen a hollow cylinder bar that has cracks. • Fourier transform is used to find the stress field of a hollow circular bar. • Using the distributed dislocation approach, the issue is reduced to a set of integral equations. • Dynamic stress intensity factor exhibits an upward trend as the length of the fracture increases. • Dynamic torsional stiffness increase in dimensions as the fracture length increases. In this study, an analytical solution is used to strengthen a hollow cylinder bar with an orthotropic coating and is subjected to short-term torsional loading. First, the Fourier transform is used to find the stress field of a hollow circular bar with an orthotropic coating and a Volterra-type screw dislocation. Next, using the distributed dislocation approach, the issue is reduced to a set of integral equations with a Cauchy singularity in the domain. By analyzing the integral equations, the elements influencing stress intensity at the solitary fracture points and torsional rigidity are found. Lastly, a number of examples are provided to show how the orthotropic coating affects the domain under consideration's torsional rigidity and dynamic stress intensity characteristics. [ABSTRACT FROM AUTHOR]

It is found for the first time that, as the applied torque attains a critical value, a freely twisted highly elastic tube may jump from one to another state over large strain range. Unlike usual approximate buckling analyses of thin shell structures with Hooke's law for small strain, such large strain snap-through effect needs to be studied with a large strain model that can accurately simulate nonlinear elastic behaviors of soft materials. As such, nonlinear coupling issues have to be treated both in large strain kinematics and in hyper-elastic constitutive formulation. It appears that exact results would be rare even for buckling analyses with small strain but large deflections. Here, the above coupling issues are treated with a novel and decoupled approach. To this end, explicit and decoupled forms of the dual potentials for hyper-elastic stress–strain and strain–stress relationships are constructed with well-designed invariants of the Hencky strain and the deviatoric Cauchy stress and, hence, multiple data sets from benchmark tests are accurately matched with these forms in a decoupled sense. It is then shown that the nonlinear coupling equations for large torsion of elastic thin tubes can be worked out to produce exact closed-form solutions for the average radius ratio, the axial length ratio and the thickness ratio as well as the applied torque. With these solutions, the large strain snap-through effect is disclosed with an explicit criterion. Furthermore, numerical examples are provided with comparison to test data and, in particular, the large torsion response features with the snap-through effect are discussed with reference to possible correlations to certain symptoms in vascular abnormalities of blood vessels, etc. • A dual and decoupled formulation is established toward characterizing hyper-elastic behaviors of soft materials. • New elastic potentials are presented toward accurately matching large strain data from three benchmark tests. • Exact closed-form solutions for large torsion responses of soft tubes are obtained for the first time. • The large strain snap-through effect in torsion is disclosed. • Torsion response features are discussed with correlations to vascular abnormalities of blood vessels. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is to analyze the impact of the periodic resonators on the wave dispersion phenomenon of a thin-walled asymmetric beam. An analytical framework has been developed to study the triply coupled flexural and torsional wave propagation in an asymmetric metabeam. The resonators are modeled as a beam with a lumped mass at the center and placed eccentrically from the shear center. Their periodicity allows them to generate a subwavelength attenuation band in the beam. The governing equations for the coupled bending-bending-torsion vibration of a metabeam having an asymmetric cross-section are considered for generating the dispersion phenomenon, including the warping effect. Applying the Bloch-Floquet principle, the dispersive characteristics of the asymmetric metabeam are obtained by using the transfer matrix method. The modal characteristics of an asymmetric beam without a resonator are computed using the spectral element method and are validated with previously published results. Subsequently, the attenuation band is investigated due to the presence of a resonator and followed by the transmittance spectrum to verify the suppression of the elastic waves in the attenuation band. The experimental analysis is carried out to validate the analytical framework by obtaining the modal frequencies from the frequency response function. The detailed parametric investigation reveals that the resonator's position and characteristics significantly impact the occurrence of the band gap. A substantially wide attenuation band gap is attained by considering a continuous beam-mass resonator instead of a discrete spring-mass type resonator. This type of novel structure has the potential for the application of vibration control and acoustics. • Triply coupled wave propagation analysis of thin-walled asymmetric metabeam. • Analytical study on coupled bending-bending-torsion wave propagation. • Experimental validation of the modal characteristics of the beams. • Generation of band gap due to periodicity of the beam-mass resonator. [ABSTRACT FROM AUTHOR]

• A strain gradient quadrature element for geometrically exact beam with torsion warping effects is proposed. • All high order strain and strain gradient terms are retained. • Fewer degrees of freedom are needed in the present approach. • Influences of strain gradient effects and Wagner effects on nonlinear behaviors of beams are numerically demonstrated. Based on the weak form quadrature element method, this paper proposes a geometrically exact strain gradient beam formulation incorporating torsion warping effects. This formulation provides a computationally efficient numerical scheme for analyzing size dependent arbitrarily cross-sectional beams undergoing large displacements and rotations. By accommodating all high order strain and strain gradient terms in the formulation, the Wagner effects that crucial to the model's accuracy are taken into account. The warping functions determined by cross-sectional governing equations involving strain gradients are obtained using a C 1 quadrilateral quadrature element procedure. Five numerical tests are presented to demonstrate the validity and accuracy of the proposed formulation, while investigating the influences of size effects and Wagner effects on nonlinear behaviors of beam structures. [ABSTRACT FROM AUTHOR]

• Experiments on FTB of steel arches at elevated temperature are conducted. • The technique of importing nonuniform temperature field into the FEM of structural analysis is proposed. • The influence of the load ratio and geometrical imperfections on the critical temperature of FTB is analyzed. • Thermal expansion plays a dominant role on the FTB behavior of arches. This article reports the fire resistance experiments conducted on I-section circular steel arches, as well as the observed out-of-plane flexural–torsional buckling (FTB) behavior and in-depth finite element numerical simulation results. The test was carried out using a large fire test furnace to provide a real fire environment with a nonuniform temperature field. A specially designed loading device allowed for unconstrained out-of-plane deformation of the specimens inside the furnace, thereby achieving effective load conditions and noncoupled response of the components. Numerical analyses were performed using a combination of the general codes Fluent and Abaqus, with the former used for heat transfer analyses, and a structural FE model including the loading device and complex geometric imperfections was established based on the measured data. Thus, accurate simulation of the out-of-plane behavior of the steel arches at elevated temperature was achieved. On this basis, an in-depth parametric study was carried out to investigate the effects of temperature field variations, load ratio (LR), and geometric imperfection. The analysis results show that FTB occurs at nonuniform temperatures for the arches under concentrated load, and the difference in temperature distribution in fire has a minimal effect on the FTB behavior. LR is negatively correlated with critical temperature; the smaller the LR, the more significant the weakening of critical loads by fire. The effect of initial geometrical imperfections on FTB at elevated temperatures is similar to that at ambient temperatures, and the effect on the critical temperature of FTB can almost be ignored when the imperfection amplitude is less than S/400. [ABSTRACT FROM AUTHOR]

• Numerical models of HSS CHS under torsion were developed and validated against test data. • Ultimate torsional capacities of 318 cold-formed HSS members were generated. • Applicability of current design rules including CSM and DSM were assessed by comparing with 318 member capacities. • Most of design predictions outlined in European and American Standards, as well as CSM and DSM were found unsuitable. • Two modified design rules based on CSM and DSM have been proposed. The paper presents a detailed numerical investigation on the performance of high strength steel (HSS) circular hollow section (CHS) member subjected to pure torsion. Three grades of HSS, viz., S700, S900 and S1100, were considered in the study. Finite element (FE) models were initially developed and validated against the available test results. Further, the validated FE models were used for parametric study. Cross-sections of varying thickness and diameters, as well as HSS grades, were considered for the parametric study. The results generated from the parametric study were then utilised to assess the effect of steel grades on the torsional capacities and deformed shapes at ultimate and post-ultimate capacities. The effect of ratio of yield strength to ultimate ratio on the normalised member capacities has also been studied. Furthermore, the applicability of existing design equations for members subjected to pure torsion have been assessed against the FE generated member capacities. Based on the analysis, most of design predictions outlined in European and American Standards, as well as those proposed by various researchers were found unsuitable for design of HSS CHS under torsion. Hence, two modified design equations based on continuous strength method and direct strength method has been proposed. The modified design methods were found to predict more accurate and reliable torsional capacities. [ABSTRACT FROM AUTHOR]

• The symmetric and anti-symmetric distortion modes are introduced for I-sections. • All the nine DOFs of the connected elements at a common joint can be straightforwardly transformed to the global coordinates for stiffness assembly. • The warping-distortion compatibility problem in frames and curved beams can be naturally resolved. • The results obtained by the present beam element agree excellently with those by the shell element. Warping-distortion coupling is common in frames and curved beams made of I-sections, which tends to decrease significantly the lateral and torsional resistance of structures. Traditionally, it has been difficult to consider such effects in structural analysis, because the warping and distortional degrees of freedom (DOFs) of two connected elements at a common joint cannot be easily transformed to a common coordinate system for global stiffness assembly. The purpose of this paper is to conquer such a problem. By introducing the symmetric and anti-symmetric distortion modes, in addition to the warping and conventional six DOFs, this paper develops a new theory that consists of nine DOFs per node for the two-node I-beam element. The three deformational DOFs of the cross-section, i.e., the symmetric distortion, anti-symmetric distortion and warping, can be regarded as three mechanical couples relating to the twisting, shearing and bending , respectively, of the two flanges in the opposite sense. This allows all the DOFs of the connected elements at a common joint to be easily transformed to the global coordinates for stiffness assembly. As a result, the warping-distortion compatibility problem that occurs in frames and curved beams is resolved. In the exemplar studies, the present beam element has been demonstrated to be capable of producing results that are in excellent agreement with those of the shell element for the lateral deformation of angled frames with unstiffened and stiffened joints and of curved beams with various boundary conditions. It is also observed that the cross-sectional distortion effect becomes more manifest in curved I-beams of high curvature or of high flange-to-web rigidity ratio. [ABSTRACT FROM AUTHOR]

• Sectional properties of RCTCs are calculated theoretically and numerically. • Torsional buckling with more than 1 wave is observed in both RCTCs and RBCs. • The elastic torsional buckling load of RCTCs and RBCs is accurately predicted. • Design methods for RBCs undergoing torsional buckling are proposed. • A limit dimension of RBCs is presented to prevent their torsional buckling. The built-up radially battened column (RBC) has found its promising application in public buildings due to its aesthetical form and good load-bearing capacity. Like the X-shaped column, torsional buckling may be the major failure mode of the RBC under axial compression. However, current specifications lack rational design methods for the torsional buckling strength prediction of this innovative column. This paper will focus on the torsional buckling behaviour of the RBC and propose its corresponding strength design formulas. At first, the key sectional properties of the radially continuous-web tube columns (RCTC) are derived theoretically and are proven to be consistent with the numerical calculation result. Then, a finite element model (FEM) using the shell element of RCTC is established, accordingly, the elastic torsional buckling behaviour of RCTCs is investigated, and an expression for accurately estimating the elastic torsional buckling load of RCTCs is proposed. Afterward, the FEM of built-up RBCs is established to conduct the elastic buckling analysis and elastoplastic bearing capacity prediction. The elastic torsional buckling load of built-up RBCs is predicted by modifying the expression for RCTCs via the number of battens and the proportion of the area of battens. A key design parameter, the normalized slenderness ratio, is also obtained. Finally, the strength design recommendation of the RBCs for torsional buckling is presented on the ground of numerous elastoplastic FEM results by changing the normalized slenderness ratio, and a limit RBCs' dimension that can prevent the built-up RBC from the torsion buckling is further proposed. These results are expected to guide the design of the RBC and promote its application in engineering. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract A finite element formulation is developed to predict the lateral torsional buckling resistance of plane frames with moment connections. The solution focuses on the simple characterization the elastic warping behavior of moment connections in a manner that allows them to interface seamlessly with existing beam buckling finite elements, thus providing means for realistically modelling the lateral torsional buckling of plane frames. Special attention is devoted to the joint rotation effects. The technique successfully captures the interaction between beams and columns of frames, an effect that is neglected in present design methodologies based on individual member checks. The solution is shown to provide lateral torsional buckling resistance predictions in very good agreement with shell based finite element solutions at a fraction of the modelling and computational effort. For typical frames that are laterally supported at the joints, the study suggests that present design methodologies that isolate the member from the rest of the structure provide conservative buckling resistance predictions. Conversely, for frames with no lateral restraints at some of the joints, the present solution predicts lateral torsional buckling resistances that are significantly different from those based on design standard equations, suggesting the need to account for interaction effects in such situations. Highlights • An analysis technique is developed for lateral-torsional buckling analysis of plane frames. • Solution captures joint rotation effects and partial warping restraints provided by joints. • Solutions agree well with shell finite element analysis and is computationally efficient. • Present design methodologies that separate members from the structure are critically assessed. [ABSTRACT FROM AUTHOR]

The present study investigates the lateral-torsional buckling of wide flange steel members strengthened by a Glass Fiber Reinforced Polymer (GFRP) plate bonded to one of the flanges through an adhesive layer. A variational formulation and two finite elements are developed for the problem. The formulation captures global and local warping effects, shear deformation due to bending and twist, and partial interaction between the steel and GFRP provided by the flexible layer of adhesive. The destabilizing effects due to strong axis bending, axial force and load height effect are incorporated into the formulation. The first element involves two nodes and 16 buckling degrees of freedom (DOFs) while the second element involves three nodes and 14 DOFs. Comparisons of present model results against those based on 3D finite element analysis based on solid elements demonstrate the ability of the present models to accurately predict the buckling loads and mode shapes at a fraction of the modelling and computational efforts. Practical examples quantify the gain in elastic buckling strength achieved by GFRP strengthening, and characterize the moment gradient factors and load height effects. Elastic buckling interaction diagrams are developed for beam-columns and comparisons are provided to interaction diagrams of un-strengthened beams. [ABSTRACT FROM AUTHOR]

Spatial truss beams are an extremely efficient typological solution for covering large spans, especially in the cases where members do not have lateral restraints capable of preventing flexural–torsional buckling phenomena In this study the structural behaviour of innovative steel 3D lattice beams in combination with structural glass slabs, used as roof decks, is investigated for protection of historical assets and archaeological sites. After a brief description of the novel structural system, the attention is focused on the experimental activities carried out for the mechanical characterization of both material and structure. In particular, four-point bending tests are carried out on full-scale prototypes in order to both validate the design procedure and calibrate numerical models useful to extend the achieved results through Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA analysis). • Four-points bending tests on innovative 3D built-up lattice beams were performed under monotonic loads. • The prototypes showed a ductile behaviour with full yielding of the bottom chord. • The experimental response evidenced the robustness of the design criteria developed by the authors for sizing purposes. • The experimental study allowed for the evaluation of the reliability of some capacity models implemented in Eurocode 3 to predict the elastic and plastic behaviours of systems like those under investigation. [ABSTRACT FROM AUTHOR]

This paper presents the experimental and numerical studies on the full torsional behavior of single-box multi-cell box-girders with corrugated steel webs (BGCSWs) under pure torsion. Two specimens of BGCSWs with double cells and triple cells are tested under pure torsion using a new apparatus. Then the accuracy and efficiency of finite element analysis (FEA) models are validated by comparing with the experimental results, including the overall torque-twist curves, crack patterns of concrete slabs and shear strains in concrete slabs and corrugated steel webs (CSWs). Next, a parametric study is carried out, which shows that the torsional capacity is in linear proportion to the compressive strength of concrete, the thickness, yield strength and transverse position of CSWs and the number of cells in the given ranges. Besides, this study demonstrates that the CSW located at the torsional center of multi-cell BGCSWs has little effect on the torsional responses and the other inner CSWs in the multi-cell BGCSWs have little contribution to the cracking torques but have significant effects on the yield and ultimate torques. At last, a new fitted formula for the relations of smeared shear strains between the inner CSWs and the outermost CSWs is obtained from a series of case studies. [ABSTRACT FROM AUTHOR]

Cold-formed steel haunched portal frames are popular structures in industrial and housing applications. They are mostly used as sheds, garages, and shelters, and are common in rural areas. Cold-formed steel portal frames with spans of up to 30 m are now being constructed in Australia. As they are relatively new to the market, current design recommendations are fairly limited. In the specific frame system analyzed herein, the column is partially restrained against twist rotation at an intermediate point where the knee brace joining the column and rafter is connected. An experimental program was carried out on a series of portal frame systems composed of back-to-back channels for the columns and rafters. It was found that changing the knee brace and knee brace-to-column connection bracket significantly affected the buckling capacity of the column, however this was not captured in design calculations. In order to correctly predict frame behavior and ultimate loads for design purposes, the column buckling capacity must be accurately calculated. This paper presents an energy method approach to calculate the buckling load of a column with an intermediate elastic torsional restraint. Various end conditions of the column are considered including column base semi-rigidity, as well as multiple loading conditions. Displacement functions are determined based on measured experimental data. The Southwell and Meck plot methods to determine column buckling loads are discussed. The column buckling loads determined from the plot methods and calculated by the energy analysis are compared to the experimental column buckling loads. It is shown that the energy method outlined herein predicts the buckling load within 6% for columns with an intermediate elastic torsional restraint. [ABSTRACT FROM AUTHOR]

In this paper the constrained finite element method is applied for the buckling analysis of thin-walled members with holes. The method is basically a shell finite element method, but constraints are applied which enforce the member to deform in accordance with specific mechanical criteria, e.g., to force the member to buckle in flexural, or flexural-torsional or distortional mode. The method is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape functions, and longitudinal discretization is used, which transform the finite strip into multiple finite elements. As the method has already been presented in earlier papers, here it is just briefly summarized. More detailed discussion of the secondary cross-section modes is provided, since the presence of holes might have important consequences on these secondary modes. Two basic approaches for handling the holes are discussed. Numerical examples are also presented. Comparison of linear buckling results to available results from the literature fully validates the proposed constrained finite element method. Further numerical examples illustrate the difficulties and uncertainties involved in regular unconstrained buckling analysis of members with holes, and also show that the proposed constrained finite element method eliminates the uncertainties in assessing the effect of holes on the critical loads, as well as, in general, helps to understand the effect of holes on the buckling behavior. [ABSTRACT FROM AUTHOR]

This paper presents a study of the formulation of nonlinear beam elements for spatial thin-walled frame structures. A formulation based on the geometrically exact beam theory is developed first, which includes transverse shear deformation, torsion-related warping and all major nonlinear strain terms. A comprehensive investigation is then made on different terms in the nonlinear strain expressions and their effects on the solution accuracy in nonlinear stability and post-buckling analyses. It is found that some nonlinear terms in the strain expression for the Wagner effect, quadratic shear deformation and torsion-shear coupling may have a significant impact on the solution accuracy, and hence must be included in an element formulation. A simplified strain expression is proposed, and a new thin-walled beam element is developed for physically and geometrically nonlinear analyses by using the proposed expression and formulation. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed formulation and element. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of maximum torsional moment for multicorner tubes under torsional loading was investigated using nonlinear FE analysis. The effects of tube geometries and strain-hardening coefficient on the torsional behaviour were discussed. The maximum torsional moment was due to the occurrence of sectional collapse of the tubes, and the mechanism of sectional collapse could be classified into three physical phenomena, elastic buckling, plastic yielding and plastic flattening of the cross section. Moreover, based on our numerical results, analytical solution for estimating the maximum torsional moment for each phenomenon was proposed. [ABSTRACT FROM AUTHOR]

This paper aims to present the flexural, torsional and flexural-torsional buckling of axially loaded thin-walled functionally graded (FG) open-section beams with various types of material distributions. Properties of metal-ceramic materials are described by a monotonic function of volume fraction of particles that varying across blade thickness according to a power law. The problem is formulated by using a two-noded 14-degree-of-freedom beam element. Governing buckling equations has been developed. Warping of cross-section and all the structural coupling coming from anisotropy of material are taken into account in this study. The critical load is obtained for thin-walled FG mono-symmetric I- and channel-sections with arbitrary distributions of material. As a special case, a numerical comparison is carried out to show the validity of the proposed theory with available results in the literature. In addition, effects of gradual law, ceramic core and skin, span-to-height on the buckling parameters of an axially loaded thin-walled FG open-section beam are also investigated. [ABSTRACT FROM AUTHOR]

This paper presents the first study of its kind on the torsional moment behavior of a new dumbbell-shape concrete-filled steel tube (DCFST) system. Experiments were conducted to investigate the effect of the dimensions of the web connecting the two circular CFSTs, in terms of its width-to-diameter ( b/D ) and its minimum depth-to-diameter ( h/D ) ratios, on torsional strength ( T u ). Torsion tests were also conducted on circular CFSTs (CCFSTs), on hollow tubes and on plain concrete, as control specimens. It was shown that T u of DCFSTs ranged from 1.3 to 2.2 that of the CCFST, depending on ( b/D ) and ( h/D ) ratios. Increasing ( b/D ) from 0.31 to 0.54 resulted in only 7% increase in T u . However, a further increase from 0.54 to 1.0 resulted in an additional 31% increase in T u . The effect of ( h/D ) on T u was more pronounced at higher ( b/D ) ratios. In general, increasing the web width appears to be more effective than web height. A rigorous nonlinear finite element model was developed and a simple mechanics-based design equation have been proposed to predict T u of CCFSTs and DCFSTs and resulted in an average predicted-to-experimental T u of 0.98. [ABSTRACT FROM AUTHOR]

The buckling behaviour and design of aluminium alloy single-angle members connected by one leg are investigated in this study. Buckling tests were carried out on eight simply supported aluminium alloy single-angle members with the load applied on one leg only. Finite element models were established and validated against test results in this study and previous literature. A comprehensive parametric study was then performed to investigate the reduction in buckling resistance due to the single-side connection, which was shown to be related to the normalised slendernesses, buckling modes and material nonlinearity. The tests and numerical results were employed to assess the applicability of existing design rules for steel single-angle members, including GB50017, EN1993-3-1, EN50341-1, and ASCE 10-15. The comparisons show that these existing design rules could not be directly used for aluminium alloy single-angle members, especially for angle members undergo torsional–flexural​ buckling in axial compression. New design equations are proposed to predict the reduction in buckling resistance caused by the single-side connection and are shown to possess good accuracy. • Buckling tests were performed on single-side connected aluminium alloy angles. • A comprehensive parametric study was conducted using the validated finite element model. • The effects of slenderness, axial buckling mode and material nonlinearity are presented. • The obtained results were used to assess the applicability of four design codes. • New design equations were proposed for single-side connected aluminium alloy angles. [ABSTRACT FROM AUTHOR]

The design of thin-walled cold-formed steel members must consider various forms of buckling. The Direct Strength Method simplifies strength prediction with a common approach utilizing adaptations of the Winter plate buckling formula. Recent modifications to the Direct Strength Method were developed for flexural members not symmetric about the axis of bending, which introduced a new general form to the direct strength equation. The versatility of this form provides one strength curve for the entire range of slenderness, including inelastic reserve strength. This new form was investigated for local and distortional buckling of compression members, members with holes, beam–columns, and beam–columns with holes. The proposed formulas for members without holes gave strength predictions nearly identical to the current AISI expressions. For members with holes, the proposed strength predictions were compared to test data and showed improvement over the current AISI expressions. Shear buckling strength was also investigated using the new direct strength equation form which gave equivalent predictions. Enhancement to the global buckling strength curve for flexural members was explored for alignment with column buckling and to facilitate further consistency for global buckling of beam–columns. The proposed enhancements provide improvements with a consistent set of simpler equations, advancing a new cleaner appearance to the Direct Strength Method. • A new form of DSM equation is investigated for a variety of limit states. • Proposed DSM for members with holes provides smooth transition from yielding to buckling. • Proposed DSM equations are more accurate for flexure, compression, shear, and beam–columns. • This new DSM form can be leveraged for other limits states such as torsion and web crippling. • Improvements to DSM lateral-torsional buckling strength are also proposed. [ABSTRACT FROM AUTHOR]

This article investigates the elastic lateral buckling of unrestrained beams. According to the design code, the beam strength is function of the lateral buckling moment. In literature, the buckling moment is function on bending distribution, load height position and the monosymmetry cross section shape. The coefficients C 1 − C 3 are affected to these parameters in the solution. However, no formula or table is available for the case of beams subjected to nonsymmetrical loading. This article proposes an analytical formulation for the critical moment for lateral–torsional buckling of steel beams under asymmetrical loading. The expression of the critical buckling moment, which is based on the Galerkin method, as well as the coefficients (3C) that affect the intensity of the critical moment for asymmetric loading cases, are then proposed. The present method is compared to numerical simulations and available solutions in literature. The results obtained allowed concluding that in the case of asymmetrical loading, the application of the loading cases proposed by the CCM 97 remains unsafe. • An analytical formulation for the critical moment of steel beams under asymmetrical loading is developed. • The moment gradient factor for beams under linear moment gradient is presented. • The obtained results are discussed and compared to available solutions. • Different design codes may give different results. [ABSTRACT FROM AUTHOR]

The paper presents the development of new design guidelines for cold-rolled aluminium alloy 5052-H36 channel beams subject to global buckling. The validation data are obtained from the experimental and numerical Finite Element (FE) results as performed in previous studies by the authors. The failure modes in the experiments were observed as flexural–torsional buckling modes, and good agreement was achieved between the experimental and FE results. Based on the reliable and calibrated FE models, a parametric study is carried out in this paper to extend the data range by varying section dimensions and member lengths. Subsequently, all experimental and FE ultimate strengths of the parametric study are compared with nominal member capacities of aluminium beams as predicted by the current Australian/New Zealand, American and European aluminium design standards. Additionally, the Direct Strength Method (DSM) design rules from the Australian and New Zealand standard - AS/NZS 4600 for cold-formed steel structures are applied to predict member bending capacities for comparisons. Finally, reliability analyses are performed to evaluate the efficiency of the abovementioned design methods. It is found that the design guidelines for nominal member bending capacities to the AS/NZS 4600 standard provide accurate predictions and are therefore proposed to be used for the design of cold-rolled aluminium alloy channel beams as investigated in this paper. • New design guidelines for cold-rolled aluminium alloy H36-5052 channel beams subject to global buckling are developed. • The 5000-series high magnesium alloy, 5052-H36, is used for fabricating cold-rolled aluminium channels. • Detailed finite element (FE) models using the software ABAQUS are developed for a parametric study. • Experimental and FE ultimate strengths are compared with nominal member capacities of aluminium beams in the current aluminium design codes. • Design rules for member bending capacities to the AS/NZS 4600 standard are proposed for design of cold-rolled aluminium channel beams. [ABSTRACT FROM AUTHOR]

As shown in the companion paper, innovative tests of corrugated web girders (CWGs) were performed followed by validation of the finite element (FE) model. Accordingly, this paper continues investigating the lateral–torsional buckling of small-scale corrugated web girders through parametric studies. This is to expand the available data required to unveil their behaviour and strength. The layout of the tested girders is considered herein, where the webs of small corrugation dimensions are under pure bending moment with symmetrical boundary conditions. This study deals with the linear and nonlinear buckling analyses of the lateral–torsional buckling (LTB) of CWGs using ABAQUS software. Accordingly, 108 models are conducted, considering the effects of the girder length, web overall dimensions, corrugation dimensions, flange dimensions and different steel grades. The results show that increasing the girder length decreases consequently the ultimate flexural strength and stiffness of CWGs. With regard to the web overall dimensions, increasing the web depth is found to have a significant effect on the strength of CWGs in contrast to the effect of the web thickness value, which has insignificant effect on strength. Furthermore, the results revealed that increasing the flange dimensions increases subsequently the strengths of CWGs. In addition, it is noted that the lower the steel grade, the more effectively the material is used especially for girders failing elastically. Additionally, the critical and design LTB strengths of small-scale CWGs with small corrugation dimensions are evaluated. The comparisons show that the critical LTB stress requires modifications to accord well with FE results. Furthermore, comparisons of the ultimate FE strengths with those of Lindner's equation (1990), EC3 (2004) and AISC (2010) are provided. The comparisons exhibit that the predictions of Lindner's equation (1990) are suitable, while the predictions of EC3 (2004) and AISC (2010) are highly conservative. Therefore, modifications are made for EC3 (2004) and AISC (2010) design models to provide more appropriate design strengths for CWGs with small corrugation dimensions for use in buildings. • Small-scale CWGs under LTB are evaluated numerically to extend the companion paper. • Parametric studies are generated for different variables. • The critical stresses available in the literature are evaluated and modified. • EC3 and AISC have been checked and modified to predict well the strengths of CWGs. [ABSTRACT FROM AUTHOR]

This article presents the assessment of axial preloading impact on lateral stability capacity of a size-dependent I-section beam–column element with axially varying material properties under transverse load. Material properties of the axially/transversely loaded micro beam obey the power-law function along the longitudinal direction. Nonlocal elasticity theory, which also is identified as Eringen's theory, is employed in conjunction with Vlasov's model for non-uniform torsion to extract the governing equations for the lateral displacement and the twisting angle with the aid of energy approach. Then, the endurable buckling load is predicted using the semi-analytical power series technique. To examine the correctness of the present methodology, a comparison between the attained outcomes with those existing in the literature is made. Eventually, in the presence of a prescribed axial force, the interaction between micro beam lateral stability strength and column flexural buckling is examined and discussed. Additionally, the impact of important parameters such as nonlocal and load height ones, power-law index, and axial force is perused on the aforementioned size-dependent structure's lateral buckling resistance. • Axial preloading impact on lateral stability capacity of a size-dependent I-section beam–column have been analyzed firstly. • Material properties of the axially/transversely loaded micro beam obey the power-law function along the longitudinal direction. • Vlasov's model has been used for non-uniform torsion to extract the governing equations for the lateral displacement and the twisting angle. • The endurable buckling load is predicted using the semi-analytical power series technique. [ABSTRACT FROM AUTHOR]

The behaviour and design method of 7A04-T6 high-strength extruded aluminium alloy lipped angle columns in axial compression are investigated. First, compressive tests on 27 pin-ended lipped angle columns of various dimensions were conducted. Measurement on initial geometric imperfections and tensile coupon tests were also performed. Second, the finite element (FE) models were developed to simulate the compressive behaviour of the tested specimens. The validated FE models were then used to carry out a parametric study covering a wide range of cross-sectional dimensions and column slendernesses. The obtained ultimate compressive strengths were compared with existing design codes in Europe, China, America and Canada for aluminium alloy structures. Furthermore, the direct strength method (DSM) codified in AISI S100-16 was also considered. In predicting the ultimate compressive strength, the elastic global buckling stress was determined from classical column buckling theory, while the elastic sectional buckling stress was given by energy method. The comparisons show that the compressive strengths of columns failing in flexural buckling are generally well predicted by existing design methods. For torsional–flexural buckling, the Eurocode 9 (EC9) generally gives more accurate predictions and the other design rules are relatively conservative, because an independent strength curve is adopted in EC9 and the interaction with local buckling is excluded. Finally, modified equations are proposed to improve the accuracy of DSM in predicting the compressive capacities of columns failing in distortional buckling and torsional–flexural buckling. • 7A04-T6 high-strength aluminium alloy lipped angle columns were tested. • An extensive parametric study was conducted using the validated finite element model. • The obtained results were compared with four design codes and direct strength method. • Modified strength curves were proposed to improve the accuracy of direct strength method. [ABSTRACT FROM AUTHOR]

Recent developments in the high-output wind turbine have heightened the need for CFDST support towers. Tapered Concrete-Filled Double Skin Steel Tubular columns with Large Hollow Ratios (TLHR-CFDSTs) are the typical members in the wind turbine towers, which are usually subjected to torsion during the life cycle. It is necessary to pay more attention to these members under torsion due to their tapered shapes and thin-walled cross sections. This paper thus presents an experimental study on the torsional behaviour of the TLHR-CFDST column. Specimens with different tapered angles, hollow ratios, tubes' thicknesses and axial compression ratios were tested under pure torsion and compression–torsion. The typical failure modes, torque versus deformation relations, strain distributions and the influence of important parameters are revealed. Based on the experimental results, the mechanism of TLHR-CFDST columns under torsion is discussed. The applicability of existing torsional capacity calculation methods is evaluated and finally a simplified method for predicting the torsional capacity of TLHR-CFDST columns is proposed. • Tests on TLHR-CFDST columns under pure torsion and compression–torsion​ are reported. • Behaviour and parametric effects of TLHR-CFDST columns under torsion are revealed. • Torsional mechanism of TLHR-CFDST columns is discussed. • Theoretical method for predicting the torsional capacity of TLHR-CFDST columns is proposed. [ABSTRACT FROM AUTHOR]

The protective characteristics of novel bionic structures inspired by turbulent energy dissipation are studied. From the perspective of small-scale turbulent energy dissipation, the reentrant design of structures is carried out, and combined with rotation characteristics of the chiral structure and bending characteristics of the Euler beam, novel bionic reentrant chiral structures with multi-direction torsional energy dissipation characteristics are further designed and constructed: Single Reentrant Chiral Cubic Structure (SRCCS), Double Reentrant Chiral Cubic Structure (DRCCS), Single Reentrant Chiral Honeycomb Structure (SRCHS), Double Reentrant Chiral Honeycomb Structure (DRCHS), Single Reentrant Chiral Negative Poisson Structure (SRCPS), Double Reentrant Chiral Poisson Structure (DRCPS). The relative elastic modulus, yield stress, and plastic failure stress of novel reentrant chiral structures are analyzed theoretically, and the relationship between the relative density and relative elastic modulus, yield stress, and plastic failure stress of novel reentrant chiral structures are compared. The mechanical properties of novel bionic structures in the quasi-static compression process are analyzed from experiments and simulations. The results show that bionic double torsion reentrant structures have the most excellent properties. Energy absorption and load-carrying capacity of novel bionic reentrant structures are 30 % higher than traditional bionic structures. To better determine the excellent performance of the reentrant chiral structures, the reentrant chiral structures are further studied in combination with the crash of the protective helmet of motorcycle racers. It is obvious from the results that the protective effect of helmets with bionic reentrant chiral structures' sandwich is 25 % higher than the safety helmet with the corrugated sandwich. • From the perspective of small-scale turbulent energy dissipation, the reentrant design of the structures is carried out. • The relative elastic modulus, yield stress, and plastic failure stress of novel reentrant chiral structures are analyzed theoretically. • The excellent mechanical properties of novel reentrant chiral structures are compared. • The reentrant chiral structures are studied in combination with the crash of the protective helmet of motorcycle racers. [ABSTRACT FROM AUTHOR]

In recent years, with the application of filament wound composite (FWC) materials in shaft structures, the mechanical behavior study of this material under related loads is urgently needed. This paper presented the experimental study on the mechanical behavior of filament wound carbon fiber reinforced polymer under uniaxial tensile loading, torsional loading, and multi-axial loading. To alleviate the stress concentration effect caused by clamping, an improved filament wound specimen was designed and produced by reinforcing each end. A new method of analysis from the inside of a winding pattern was used to investigate failure modes and behavior under different loading conditions. To further describe the mechanical behavior, the strength, stiffness, and failure mechanisms were evaluated by the stress analysis and the measurement techniques, such as the extensometer, the strain gauge, and the scanning electron microscope (SEM). The results show that the pipe is nonlinearly progressively damaged until final failure under tensile load. Brittle failure is dominant under pure torsional load. Under tension–torsional load, the pipe is progressively damaged with slight nonlinearity and the final failure strength is much lower than the pure tension or torsion load condition. • The improved FWC pipe is integrally processed as a dumbbell shape to reduce stress concentration. • The inside of a winding pattern is used to investigate failure modes and behavior. • The stains of different areas are measured by different measurement techniques. • The failure mechanisms of FWC under different the loading conditions are compared. [ABSTRACT FROM AUTHOR]

This article studies the influence of the bimoment on the buckling of thin-walled beams with open cross section subjected to axial loading. In the case of torsional and torsional-flexural buckling of thin-walled Z-section beam, it is shown that influence of the bimoment could be of importance in the assessment of buckling loads. In order to verify the accuracy and validity of this analysis, the obtained results are compared with those calculated by ANSYS software. [ABSTRACT FROM AUTHOR]

The practical design of single steel angle members in compression has to cover multiple effects. Due to the commonly eccentric connection on only one angle leg (bolted or welded), additional bending moments are acting on the member, leading to a complex load carrying behaviour with flexural and/or lateral torsional buckling phenomena. Furthermore, type and size of rotational restraints at the member's ends (provided by the adjacent structure) significantly influence the compression member capacity of these members. Within this paper, a recently developed design approach for hot-rolled angle members in compression is introduced. The presented method allows for calculating the internal forces based on elastic second order theory for an individual member with eccentricities and rotational spring stiffness at both ends. This calculation can be carried out by means of conventional structural analysis software. Detailed analytical models for the estimation of appropriate spring stiffness values for several practical applications in buildings with two-bolt connections have recently been presented by the authors. The proposed design method is now enhanced by means of additional formulae for angle members welded to the adjacent structure. Detailed background information on the derivation of these newly developed spring stiffness formulae is given. Finally, the accuracy of the design model for this enlarged range of application for angle members with welded joints is shown through comparison with sophisticated finite element calculations, code provisions (AISC 360 and EN 1993-1-1) and experimental tests from literature. • A design model for hot-rolled angle columns with welded end-joints is presented. • Boundary conditions are considered via rotational spring restraints. • The resistances are compared with tests, codes and finite element results. [ABSTRACT FROM AUTHOR]

Beams with sinusoidal web opening are alveolar beams manufactured from a single web cut, which lead to the production of higher I-sections and with a better strength-to-weight ratio when compared to the I-sections from which they originated. There are few studies in the literature about this I-section type, especially in relation to their behavior regarding global stability and Lateral Torsional Buckling (LTB) strength. Bearing in mind the importance of understanding the behavior of alveolar beams with sinusoidal openings in relation to LTB, an extensive parametric study was carried out through numerical analysis in the commercial finite element software ABAQUS. The study was performed with 10 I-sections of the IPE type, with lengths ranging from 6 m to 32 m. In addition, initial imperfections were considered, such as residual stresses and geometric imperfections. With the parametric study results, it was possible to evaluate the main existing analytical procedures, both for the determination of the LTB elastic critical moment, as well as the LTB ultimate moment. The adequacy of standard procedures (AISC; Eurocode 3 and AS4100) was evaluated, as well as analytical procedures present in the scientific literature for determining the LTB ultimate moment. Through the achieved results, it was possible to analyze the behavior of different adaptation methods for the calculation of the elastic critical moment in sinusoidal alveolar beams, as an alternative to the traditional double-T approach. Furthermore, it was found that the AISC-360 standard is unsafe in the case of actions applied to the upper flange, even though this is the most common condition in engineering projects. • Buckling and Post-buckling numerical analyses are performed in AngelinaTM beams. • Several approaches to determining the I-section geometric properties were evaluated. • Alternative approaches to double T section were verified. • The average section approach can be a good alternative. • The LTB behavior of standard procedures for AngelinaTM beams was studied. [ABSTRACT FROM AUTHOR]

Shear lag effect and torsional and distortional warping can significantly affect the performance of thin-walled curved box girders used in modern bridge engineering. The structural behaviour of these bridges exhibits complexity due to coupled bending and torsion together with warping effects of non-uniform torsion, distortion and shear lag. A practical method of analysis, based on the symplectic approach, with the same perspective as the Higher Order Beam Theories, is presented for overcoming the difficulties of numerical approaches via the Finite Element Method. In this paper, the Hamiltonian Structural Analysis method implements the analysis of the shear lag effect together with non-uniform torsion and distortion, for curved box girder bridges. The examples given can allow engineers to evaluate the effects of the negative shear lag phenomenon and the distribution of axial stresses in box slabs and webs, due to different warping effects, which strongly influence thin-walled box sections subjected to point loads and restrained areas. • The analysis of thin-walled curved beams is carried out via symplectic approach. • The contribution to axial stress of torsion, distortion and shear lag is showed. • A method of analysis for curved bridges with box or T sections is developed. • Positive and negative shear lag effects are investigated. • Applications to straight and curved girders are presented. [ABSTRACT FROM AUTHOR]

The paper presents analytical solutions for the buckling of single beams as well as two- and three-member frames subjected to torques at the supports. The governing equations and their solutions are stated, including boundary conditions and continuity conditions at connections between members, and buckling solutions are provided for a wide range of support conditions and frame geometries. The cross-section is assumed to be solid or hollow and accordingly, warping effects are ignored. The presented solutions are for a solid rectangular cross-section, and different aspect ratios are analysed to investigate the effect of changing the ratio between the minor and major second moments of area on the buckling torque and associated buckling mode. Solutions are provided for both the critical mode and higher-order modes, allowing mode-changes between symmetric and asymmetric modes to be identified. [Display omitted] • Buckling analyses of frames subjected to end torsional moments are carried out. • Single beam and symmetric two- and three-member frames are considered. • The solutions are obtained by solving the governing equations. • The solutions apply to members with doubly symmetric sections and arbitrary length. • Numerical examples illustrate the applicability of the proposed methods. [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]

Abstract: This technical note addresses a surprising result concerning the lateral-torsional buckling of monosymmetric I-section beams: amongst all bending moment diagrams caused by any combination of applied end moments and transverse loads acting at the shear centre, the lowest critical moment does not necessarily correspond to uniform bending, which is at odds with the “intuitive expectation” of most engineers that such bending moment distribution is the most unfavourable with respect to lateral-torsional buckling. It is shown, by means of several illustrative examples, that this may not be the case for I-section beams with unequal flanges (monosymmeric cross-section – symmetry with respect to the minor axis). Moreover, the critical inspection of the terms (i) associated with the cross-section monosymmetry and (ii) appearing in the beam potential energy expression and differential equilibrium equation provides the mechanical/mathematical explanation for this surprising behavioural feature. [Copyright &y& Elsevier]

Recently, Dinis et al. (2019,2020) reported in-depth numerical investigations showing that the current Direct Strength Method (DSM) global design curve may severely underestimate the flexural–torsional (FT) failure loads of fixed-ended cold-formed steel (CFS) columns with slenderness above 1.5. This finding was based on the analysis of columns exhibiting various cross-section shapes and geometries, and covering wide slenderness ranges. Moreover, these authors used the failure load data gathered to develop, and propose a novel DSM column strength curve set that was shown to improve considerably the FT failure load prediction for those columns. The purpose of this work is to extend the scope of the previous investigations to fixed-ended CFS cold-formed columns failing in FT modes under elevated temperatures (up to 800 °C). The results presented and discussed consist of column FT post-buckling equilibrium paths and failure loads, obtained through geometrically and materially non-linear A nsys shell finite element analyses — to ensure covering wide FT slenderness ranges, several room-temperature yield stresses are considered. The model prescribed in Part 1–2 of Eurocode 3, for cold-formed steel, is adopted to describe the temperature-dependence of the steel material properties. Lastly, the numerical failure loads assembled in this work, together with numerical and experimental ones collected from the literature, are used to propose a modification of the DSM-based FT strength curve set developed by Dinis et al. (2020), making it capable of handling FT failures under elevated temperatures. Since the merit assessment of the modified strength curve set shows a visible improvement in FT failure load prediction quality, it is fair to argue that it constitutes a good starting point to search for an efficient general DSM-based design approach for CFS columns failing in FT modes at elevated temperatures. • Response and DSM design of CFS columns failing in FT modes at elevated temperatures. • 8400 FE columns simulation for many cross-sections, yield stresses and temperatures. • Buckling and post-buckling behaviour of columns at elevated temperatures. • Failure loads under steady-state loading for the EC3:1.2 constitutive steel model. • Proposal of DSM design curves for CFS fixed-ended columns at elevated temperatures. [ABSTRACT FROM AUTHOR]

Highly flexible thin-walled beams with complex open cross-sections are sensitive to torsional and warping effects. The analysis of higher-order vibration modes in these structures needs more accurate and precise methods in order to achieve reliable results and detect the cross-sectional deformations in the structures' free vibration response. This paper analyzes higher vibration modes in a series of thin-walled beams, which were proposed by Chen as benchmark problems. These are all open-section thin-walled beams with complex geometries. Global vibration modes, such as bending and torsion, related to the rigid cross-sectional deformations can be detected via classical and shear refined theories. However, cross-sectional deformations appear at higher frequencies, and these modes are mixed with the global ones. To highlight this fact, this paper compares classical beam theories with refined ones based on the Carrera Unified Formulation (CUF) and the shell results using the commercial finite element (FE) software and the data available from the literature. The CUF FEs based on the power of cross-sectional deformation coordinates (x, z) and those based on the Lagrangian polynomials are implemented and compared using Modal Assurance Criterion. A number of interesting conclusions are drawn about the effectiveness of classical and CUF-based results. The need for models capable of detecting cross-sectional deformations is outlined. In fact, many modes are lost by classical beam theories; on the other hand, they show rigid cross-section modes that do not really exist. This fact is also confirmed by the shell models, which are more expensive in terms of computational costs regarding the efficient CUF ones proposed here. [ABSTRACT FROM AUTHOR]

EN 1993-1-1 gives stability design rules for columns, beams and beam–columns up to S460, whereas EN 1993-1-12 gives additional guidance for S500 up to S700. Recent studies show that high strength steel members may be designed using improved buckling curves, where the enhanced behaviour is usually attributed to the improved material properties but mainly due to the more favourable residual stress distribution. The behaviour of unrestrained beams in HSS has not been widely studied. At present in EN 1993-1-1, the design rules for lateral-torsional buckling of beams are not dependent on the steel grade, meaning that the code does not distinguish between beams in conventional strength steel or HSS. In pursuit of an answer to the mentioned shortcomings, the present research is based on the experimental programme covering 12 full-scale tests, residual stress measurements, advanced numerical models and analytical derivations. The experiments cover different steel grades up to S690, welded and hot-rolled sections, homogeneous and hybrid (flanges in HSS and web in mild steel), double and mono-symmetric sections as well as variations in the cross-section class. This paper provides an overview of the experimental programme, discusses the results for lateral-torsional buckling of beams, and presents an advanced numerical model that was calibrated to the experimental results including the measured residual stress distribution and geometrical properties of the members. The numerical model was explored to assess various assumptions for the member imperfections, and these are further compared with code recommendations. • Full-scale experimental tests on high strength steel beams hybrid and homogeneous. • Lateral-torsional buckling of beams with doubly and monosymmetric cross-section. • Residual stresses and geometrical imperfection measurements. • Non-linear analyses with imperfections for welded I-section beams in high strength steel. • Comparison with design resistance according to Eurocode 3. [ABSTRACT FROM AUTHOR]

Unequal-leg angles can be used to provide more efficient design in specific cases, but the behaviour of unequal-leg angles has received much less attention than equal-leg angles. This paper studies the flexural and torsional buckling modal participation and investigates the structural behaviour of aluminium alloy unequal-leg angle columns. The experimental programme, which was carried out on two unequal-leg angle cross-sections, included material coupon tests, initial geometric imperfection measurements and a total of eight column tests. The test setup, procedure and results are fully reported. Following the experimental investigation, numerical models were developed and validated against the test results. Upon validation, a series of parametric studies were carried out to analyse the influence of width-to-thickness ratio and aspect ratio on the flexural and torsional buckling modal participation. The ultimate resistances obtained from simulations were used to assess the accuracy of the current design provisions given in the European standard for aluminium alloy structures. The result comparison shows that the existing design provisions yield inaccurate predictions for unequal-leg angle columns. Considering mode interaction, a more accurate and convenient design method was proposed for unequal-leg angle columns. • Results of tests on aluminium alloy unequal-leg angle columns were presented. • Existing design provisions in EC9 for unequal-leg angle columns were assessed. • Buckling modal participation for unequal-leg angle columns was investigated. • A revised design method with accuracy and convenience was proposed. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional mixed beam element formulation for fully nonlinear distributed plasticity analysis of members composed of sections with no significant torsional warping such as steel angles and tees. This formulation is presented using a corotational total Lagrangian approach and implemented in the OpenSees corotational framework. In this context, a basic coordinate system is lined up with the element chord and translates and rotates as the element deforms. The element tangent stiffness matrix and resisting forces in the basic system are derived through linearization of the two-field Hellinger-Reissner variational principle. The displacement shape functions are cubic Hermitian functions for the transverse displacements and a linear shape function for the axial and torsional deformation. The generalized stress resultant shape functions are linear for moments and constant for axial force and torque with the P - δ effect considered, which are developed from equilibrium equations. The fiber section method with uniaxial constitutive laws is adopted to account for material nonlinearity. Since the degrees-of-freedom in the basic system are defined with respect to different reference points, all element responses are transformed to acting about the shear center before conducting the corotational transformation. The mixed element is validated through a number of experimental and numerical examples. • A mixed finite beam element for beams with no significant torsional warping is developed. • The corotational total Lagrangian method is used to model the axial-flexural-torsional interaction behavior. • This element is free of membrane locking. • This element can represent a nonlinear curvature field within the element. • Modeling of geometric and material nonlinearities is validated. [ABSTRACT FROM AUTHOR]

A quasi-3D finite element model (FEM) with a low computational cost is presented for coupled bending and torsional–warping analysis of thin-walled beams. The presented FEM converts the problem of 3D analysis of thin-walled beams into separated 2D cross-sectional and 1D modeling. The warping function over the cross-section of the thin-walled beams is firstly approximated, via a 2D FEM. Then, a 1D FEM is developed for computing the axial variations of the displacement field variables. For describing the kinematic of the thin-walled beam due to axial extension and bending, the concept of hypothetical equivalent layered composite cross-section (HELCS) is employed. Using the HELCS, the non-classical effects like transverse shear flexibility can be easily incorporated into the formulation. A refined sinus theory is employed to describe the displacement fields of the equivalent layered cross-section. In contrast to other refined models of literature, the present model does not require the calculation of any geometric, torsional and warping constants. For validation of the proposed model, comparisons are made with the results of 2D/3D finite element analysis as well as the numerical and analytical results reported by other researchers. The proposed model not only gives accurate results but also reduces the number of involved degrees-of-freedom (DOFs) significantly. Considering the effects of the restrained warping due to torsion, no need to use the shear correction factor, satisfaction of zero-conditions of shear stresses on the exterior surfaces of beams are other advantages of the proposed FEM. • A new FEM is developed for flexural–torsional analysis of thin-walled beams. • The formulation is based on the concept of equivalent layered composite section. • The shear strains due to bending are modeled using a Cosine shape function. • The proposed FEM reduces the number of degrees-of-freedom significantly. [ABSTRACT FROM AUTHOR]

Substantial research has been conducted in the last years into the structural responses of cold-formed and hot-rolled stainless steel equal-leg angle columns, whereas there is no experimental data on laser-welded stainless steel angle columns despite these sections being increasingly used in the modern construction industry. To fill this gap and provide benchmarks for design, a comprehensive experimental investigation into the structural strength and stability of laser-welded austenitic stainless steel equal-leg angle columns under pure axial compression was performed and described in this paper. A series of laboratory tests, performing on two test groups of specimens with nominal dimensions of 60 × 60 × 6 mm and 100 × 100 × 10 mm and different lengths, involved 6 stub column tests and 20 global buckling tests together with measurements on material properties, initial geometric imperfections and residual stresses. The experimental observations reveal that the column ultimate capacity and prevalent failure mode – major-axis flexural–torsional buckling and minor-axis flexural buckling – are highly dependent on the column slenderness and initial imperfections. The full load-lateral displacement, load-torsional rotation and load-axial strain responses of the specimens were fully reported and discussed. The results were employed to evaluate the accuracy of the current European and North American stainless steel design standards. The evaluation results revealed that the codified design procedures yield conservative resistance predictions of laser-welded stainless steel equal-leg angle columns, showing a prospective for their modification and improvement by providing more optimized and realistic results in design considering the actual residual stress distributions, material nonlinearity and strain hardening. • Residual stress distribution in laser-welded angles found using the sectioning method. • Twenty-six laser-welded stainless steel equal-leg angle columns were tested. • Different buckling responses were systematically examined. • Buckling loads conservatively predicted by European and North American design codes. [ABSTRACT FROM AUTHOR]

This paper presents the dynamic analysis extension of the Generalized Beam Theory (GBT) formulation developed in [1] for curved thin-walled pipes. The new proposed dynamic curved GBT element formulation goes beyond the current GBT's analysis of straight pipes, not only concerning the coupling and behavior of pipe bends or toroidal shells, but also concerning the effects of the transverse shear modes. In the preceding paper, the stresses and the deformations of a pipe bend under static conditions have been determined through the potential energy formulation for different loading and support conditions. In this paper, the formulation of the kinetic energy is presented to determine the inertia of the GBT element. The consistent element mass matrix derived from the GBT dynamic formulation involves the coupling of certain types of GBT deformation modes resembling that of the element stiffness matrix. Here, to illustrate the application and capabilities of the developed GBT formulation, numerical examples concerning undamped free vibration analysis of truncated and closed toroidal shells with different support conditions are considered involving a combination and coupling of bending, warping, torsional, axisymmetric and local deformation modes. For the purpose of validation, these examples are compared with refined shell finite element models. • Dynamic GBT formulation of toroidal shells is presented and validated. • Coupled GBT deformation modes are identified. • Numerical examples of truncated and closed toroidal shells are presented. • Modal Assurance Criterion (MAC) analysis is used to validate the mode shapes. [ABSTRACT FROM AUTHOR]