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Studies on buckling of steel tubular truss arches are lacking in contrast to steel arches with solid web sections, although they have been widely applied in long-span structures. This paper deals with the in-plane elasto-plastic buckling and strength design of circular steel tubular truss arches with triangular sections by using finite element analyses (FEA). Firstly, the in-plane buckling failure modes are explored to reveal the buckling mechanics of truss arches. By introducing the normalized slenderness of the entire arch and the chord tube, as well as the interactive coefficient that accounts for the effect of chord tube buckling, the unified buckling curve for truss arches in uniform compression are obtained. Lastly, an interactive equation is proposed for in-plane buckling resistance of steel tubular truss arches under combined compressive and bending actions. It is found that, the buckling of diagonal web tubes greatly reduces the load-carrying capacity and deformation ability of truss arches hence should be prevented in design. The chord tube deformation always exists during the buckling failure of the truss arch and its effect on the buckling resistance is inevitable. The buckling curve b in the codes can used for truss arches in uniform compression, and the interactive equation can provide satisfactory lower bound predictions for truss arches under general loading. [ABSTRACT FROM AUTHOR]

Buckling instability refers to a significant limit on the structures with I-section members, which causes severe decreasing of critical buckling load. Many mechanisms and techniques have been developed to increase the loading capacity of I-section structures, e.g., using composite materials or changing web geometry. This study aims at theoretically investigating the effect of geometry on the buckling capacity of wood composite I-beams with sinusoidal corrugated web. Experiments and numerical simulations are carried out to validate the theoretical predictions. The presented model is also reduced to flat web to validate with an existing study. Good agreements are observed from the validations. Parametric study is conducted to indicate the effects of web geometry on the critical buckling load. A significant increasing of buckling load (minimum 17.7%) is obtained between flat and sinusoidal web I-beams. Sensitivity study is carried out to evaluate the influences of web thickness, beam length and beam height on the loading capacity of sinusoidal I-beams. Optimal design is conducted to investigate the impact of the ratios of wavelength-to-beam length ( a L ) and wave amplitude-to-flange width ( A T ) on the critical buckling load and volume of wood corrugated I-beams. The findings in this study can be further used as guidance for the design of composite I-beams with sinusoidal corrugated web. [ABSTRACT FROM AUTHOR]

The exact consideration of the global buckling behaviour of HSS steel structures is very important in the design because due to the higher yield strength smaller cross sections can be used, which might be more sensitive to stability failure. According to the previous research results, the flexural buckling behaviour of HSS and NSS columns can be significantly different, however, these differences are not considered in the current design methods. The application range of the current EN 1993-1-1 [1] is limited for steel grades up to S460. The EN 1993-1-12 [2] gives design rules for materials up to steel grades of S700, however, for the determination of the flexural buckling resistance of welded box section members there are no improved design guidelines for HSS structures. Therefore, the purpose of the current study is to investigate the column buckling behaviour of HSS welded box section columns based on previous and current experimental investigations and on numerical simulations. This paper focuses on the effect of the different material properties, imperfections and residual stresses on the global buckling behaviour of HSS members and gives design proposal for the applicable column buckling curves for steel grades between S420 and S960. [ABSTRACT FROM AUTHOR]

Presence of flaws or cracks may cause substantial decrease in the strength of a component or structure. This kind of structural damage will accumulate over time, leading to significant decrease in ultimate load carrying capacity of structural members and premature brittle failure. In this paper, a coupled analytical and numerical study is implemented in order to evaluate buckling load of cracked cylindrical shells which is often encountered in the fields of civil engineering, offshore engineering and mechanic engineering. In the first phase of the study, buckling load of cylindrical shells with circumferential crack is investigated by treating the symmetric model as a cracked rectangular beam-column on an elastic foundation. The cracked beam-column is modelled as two beam elements on elastic foundation connected by an equivalent rotational spring and governing characteristic equation is obtained. Finite element models are used to verify analytical results and assess their accuracy, based on which good agreement is observed between analytical and numerical results. Effect of different parameters such as the length of cylinder, radial stiffness of cylinder, crack location and crack severity is studied on the axial load carrying capacity of such members. A simplified equation is proposed in order to calculate buckling load of tall cylindrical shells with a circumferential crack. In the second phase, the buckling load of cylindrical shells with a partial crack is studied using the results of finite element analysis on models with varying crack length. Based on the results of numerical analysis, an empirical equation is proposed to interpolate buckling load of these members between two limiting values, namely the buckling loads of same uncracked cylinder and the cylinder with circumferential crack. [ABSTRACT FROM AUTHOR]

This paper presents results of a numerical parametric study on elastic shear buckling of cold-formed steel channels with flat slotted webs. The study was performed on finite element models developed in ANSYS and validated against test data. The effects of perforation pattern, channel flange width, flange lip length, and aspect ratio on the elastic shear buckling load were investigated on the models with realistic and test setup boundary conditions. Equations for predicting the elastic shear buckling load of slotted channels were developed. The equations account for the effects of the studied parameters on the elastic shear buckling load of cold-formed steel channels with flat slotted webs and showed a good agreement with the finite element analysis results. [ABSTRACT FROM AUTHOR]

In practical engineering, the measured differential settlement can be gained by monitoring the points beneath the tank wall and it can induce the buckling of the tank even with a small amplitude. In general, Fourier series is adopted to decompose the measured differential settlement into harmonic components with various wave numbers. However, the question that which harmonic components should be considered is a main challenge for buckling investigations of the tank under measured differential settlement. In this work, a recommendation for harmonic components needed for consideration was proposed when decomposing measured differential settlement into harmonic components in terms of Fourier series. Moreover, the effects of the harmonic components considered on buckling behavior of floating roof tanks and conical roof tanks were discussed. The results presented that three monitoring points can make a first estimate of ovalling and the harmonic components considered should be smaller than and equal to [ N ]/3 ([] is the rounding function and N is the number of the monitoring points). The introduction of the harmonic component with a high wave number can cause the change of the buckling modes of the tanks under differential settlement, including floating roof tanks and conical roof tanks. Meanwhile, it can decrease the buckling strength of the floating roof tank more significantly than that of the conical roof tank. [ABSTRACT FROM AUTHOR]

The design of unbraced cold-formed steel beams must consider lateral-torsional buckling due to the low torsional stiffness associated with open cross-sections. The American Iron and Steel Institute incorporated design equations for the critical elastic lateral-torsional buckling stress in the North American Specification for the Design of Cold-Formed Steel Structural Members. These equations are based on elastic theory for singly-symmetric and doubly-symmetric sections. However, the equation for point-symmetric sections is only a rough approximation. Furthermore, there are no provisions for lateral-torsional buckling of non-symmetric sections, or sections oriented to non-principal axes. This paper investigates and develops a general formulation of the lateral-torsional buckling equation to broadly cover all cold-formed steel cross-sections. [ABSTRACT FROM AUTHOR]

• The bi-modular FGMs UMAT is developed for the first time and successfully conducted to validate the perturbation solution. • The rise-to-thickness ratio and corresponding critical load are two factors influencing the snap-through buckling. • The rotation constraint and radial constraint at the shell edge have opposite effects on the snap-through buckling. • The bi-modular FGM effect may speed up or slow down the snap-through buckling. Functionally graded materials (FGMs) enable structures to achieve a smooth transition between different material properties, providing an optimized combination of functions to meet the diversity of engineering needs. However, the presence of bi-modular effect in FGMs is often neglected due to the complexity in the analysis. In this paper, the curvature correction equivalent method based on the von Kármán theory will be applied to the theoretical study for the large deformation problem and the resulting snap-through buckling of functionally graded revolutionary shallow thin shells with bi-modular effect under different boundary constraints. Furthermore, a bi-modular FGMs user material subroutine (UMAT) is developed for the first time to simulate the real material model, thus validating the theoretical solution. The results show that except for the bi-modular effect of materials, boundary constraints of shells also have important influences on the relationship of load vs. central deflection and snap-through buckling. The research of boundary constraints brings new conclusions to snap-through buckling: the rotation constraint and radial constraint at the shell edge have opposite effects on snap-through buckling. This work will contribute to the analysis of the snap-through buckling of functionally graded revolutionary shallow thin shells with an obvious bi-modular effect and under various boundary constraints. [ABSTRACT FROM AUTHOR]

An effective way for improving the global load-carrying capacity of a steel arch with a welded hollow section is to increase the height of its webs. However, the high and thin web may buckle locally, which will affect the global load-carrying capacity and should be taken into account in predicting the global strength of the arch. This paper presents a numerical investigation for the in-plane strength and design for pin-ended circular steel arches with a welded hollow section, focusing on the effects of web local buckling by the large deformation inelastic analysis in association with a finite shell element model. The circular steel arches subjected to a radial load uniformly distributed along the arch length, a load uniformly distributed over the full span of the arch, or/and over the half span of the arch and their various combinations are considered in the investigation of their failure modes and strengths. The initial global and local geometric imperfections as well as residual stresses are included in the finite element model. It is found that web local buckling influences the global strength of the steel arches significantly and needs to be accounted in formulate their strength design formulas. The parameters related to the web local buckling and global buckling of the arch are thoroughly explored. It is found that the stability coefficients of arches under the nominal uniform axial compression are related to the equivalent normalized web height-to-thickness ratio of the cross-section and the normalized slenderness of the arch, and accordingly the design formula of the stability coefficients is proposed by including their effects. In addition, a design formula for predicting the strengths of the arches under a load uniformly distributed over the full span is developed by introducing a corrective coefficient into the stability coefficient, and it is found that the corrective coefficient is related to the arch rise-to-span ratio and slenderness of the arch. Furthermore, a general interaction design formula is developed for predicting in-plane strength of the arches under general in-plane loading such as a load uniformly distributed over the half span of the arch and various combinations of a full span uniform load and a half span uniform load. Comparisons with the finite element results demonstrate the proposed design formulas can provide good predictions and/or lower bound predictions for the strengths of the steel arches with a welded hollow section [ABSTRACT FROM AUTHOR]

The compressive buckling behaviour of extruded aluminium alloy I-section columns with fixed-pinned end conditions has been experimentally and numerically investigated in this study. A total of 11 column tests, involving two heat-treated aluminium alloys – 6061-T6 and 6063-T5, were carried out to acquire the compressive buckling strengths. Prior to the column tests, material properties of the two aluminium alloys were determined from tensile coupon tests, while the initial local and global geometric imperfections were separately measured by means of experimental techniques. By using the ABAQUS software package, finite element (FE) models that could account for material non-linearity and initial geometric imperfections were developed. The FE models were further validated against the test results, enabling reliable simulation of the compressive buckling behaviour of the tested columns with fixed-pinned end conditions. Based on the obtained test and numerical results, the calculation methods in the current design standards, including the European, Chinese, American and Australian/New Zealand specifications, were all assessed. It was shown that the design provisions in all the four standards provided relatively conservative strength predictions, especially for the aluminium alloys with more pronounced strain hardening capacity. [ABSTRACT FROM AUTHOR]

The present paper deals with the interactive buckling of thin-walled C-beams with imperfections, subjected to the bending moment in the web plane when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) was adopted for the C-beams. The structures were assumed to be simply supported at the ends. Two kinds of cross-sections in the C-beams were considered: channels and lip channels. A method of the modal solution to the coupled buckling problem within Koiter's asymptotic theory, using the semi-analytical method (SAM) and the transition matrix method, was applied. The calculations were carried out for C-beams of different lengths – from short through medium-long to long beams. [ABSTRACT FROM AUTHOR]

In this work, the development of rational explicit equations for distortional buckling critical stress of lipped channel columns subject to uniform compression is presented. An energy-based approach is adopted along with two different assumed buckled shapes (models) to obtain the analytical expressions. In Model 1, stiffened flange is assumed rigid, i.e., transverse wall bending is neglected, whereas in Model 2 the flange plate flexibility is taken into account. An analytical procedure to determine warping stresses based on cross-section displacements and considering that flange-stiffener assembly rotation center does not coincide with web-flange fold-line is described. To validate proposed equations, a parametric analysis is carried out for lipped channels with flange-to-web width ratio, b f / b w , ranging from 0.2 to 1.0 and lip-to-web width ratio, b s / b w , from 0.1 to 0.4. Results are compared to those obtained with a generalized beam theory (GBT) software for ‘pure’ distortional mode and it is shown that, within the range of typical geometries used in industry, average differences are approximately 1.062 ± 0.073 and 0.998 ± 0.001 for Models 1 and 2, respectively. The linear (natural) coupling of pure distortion and local/global deformation modes is also briefly described and its influence on the critical loads is discussed. Finally, comparison is made to benchmark methodologies currently used in design standard and specifications. The obtained results indicate that proposed equations are reliable and valuable for practical design applications. [ABSTRACT FROM AUTHOR]

An analytical study to investigate the local buckling capacity of steel I-section beams under elevated temperatures is presented. The study is based on an inelastic local buckling stability model that was developed by the author. The study is focused on I-section beams loaded in pure bending and subjected to either uniform or linear temperature gradient through the section depth. A parametric study is presented to investigate the effect of section geometry, steel type, and temperature gradient on local buckling capacity. The parametric study results are used to propose a new method to estimate the local buckling capacity of I-section beams under elevated temperatures. A numerical example is presented to illustrate the use of the proposed method. [ABSTRACT FROM AUTHOR]

The thermal buckling of the shells is among the popular topics in solid mechanics. To date, most studies adopt the linear constitutive equation method. However, the non-linear temperature is important when studying thermal buckling. In this study, the non-linear constitutive equation of isotropic materials is derived using the tensor method to obtain the stability equation of axisymmetric spherical shells. Moreover, quadratic non-linear constitutive equations are applied to study the thermal buckling of spherical shells, and the heat stability equations of spherical shells expressed by displacements are obtained. Considering the common function of external pressure and temperature, the potential energy function of the spherical shell expressed in displacement is obtained using the principle of least potential energy. Moreover, the Ritz method is used to study the thermal buckling of simple, supported shells. The changing trend of the critical pressure caused by the temperature change of the thin spherical shells is analyzed, as well as the influence of the temperature nonlinearity on the critical pressure. [ABSTRACT FROM AUTHOR]

The paper introduces a generalisation of the Ayrton-Perry formula for thin-walled members, covering uncoupled and coupled instabilities of global, distortional and local type. This semi-analytical solution is based on the Generalised Beam Theory (GBT) and it provides the maximum carrying capacity in elastic domain for simply-supported thin-walled members with initial geometric imperfections, under various loading conditions. Direct generalised Ayrton-Perry formulae are developed for the buckling described by one or a combination of two pure imperfection/deformation modes; for more than two coupled modes, a simple incremental procedure is provided. [ABSTRACT FROM AUTHOR]

In this paper, a mode identification technique in the context of spline finite strip method (SFSM) is presented to compute the contribution of primary (global, distortional and local) and secondary (shear/transverse extension) buckling modes. The base vectors corresponding to individual buckling modes are developed based on the principles of generalized beam theory. The buckling mode shape in SFSM is approximated as a linear combination of these orthonormal base vectors to evaluate the participation of individual buckling mode. The proposed mode identification technique is able to successfully quantify the participation of different buckling modes and the mode participation is comparable with mode identification using finite strip method (FSM) and generalized beam theory (GBT). Illustrative examples are presented to calculate the participation of individual modes in cold-formed steel sections under different loading and boundary conditions. Also the specific application of mode identification in SFSM is demonstrated. [ABSTRACT FROM AUTHOR]

A novel layerwise theory based on the first order shear deformation theory (FSDT) has been proposed to evaluate the buckling and post-buckling behavior of delaminated composite plates with multiple through-the-width delaminations. The Rayleigh–Ritz Method has been adopted and displacement fields are obtained by incorporating simple and complete polynomial series which result in much less computational cost. The proposed layerwise theory provides a more realistic description of the kinematics of composite laminates when compared to Equivalent Single Layer theories. Both local buckling of the delaminated sublaminates and global buckling of the whole plate can be handled. The method is capable of predicting response of thick delaminated composite plates. Presence of multiple delaminations can also be handled. In order to prevent unacceptable penetration, contact constraints are imposed on the delaminated area. The three dimensional finite element analysis is performed using ANSYS5.4 commercial software. The results show a very good agreement with those obtained by the analytical Model. [ABSTRACT FROM AUTHOR]

In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of DP500 and DP980 dual-phase steels, and AZ31B magnesium composite under tension–compression cyclic loading. The advantage of the device lies in the possibility of monitoring friction between the specimen and supporting blocks during the test. In consequence, it allows to avoid an error during stress determination. The full cyclic loading capacity for each material can be executed at the displacement amplitude within the range ± 2.5 mm which corresponds to the maximum strain amplitude of ± 0.2 for the specimen with the gauge length of 21.5 mm. It is concluded, that the technique proposed is promising since the thin sheet material can be tested under tension–compression in a wide range of deformation without the buckling effect. Furthermore, useful data for modelling cyclic deformation behaviour for shell structures can be obtained. [Display omitted] • Proposed fixture enables to avoid buckling during thin metal sheet compression. • The friction force is continuously registered during the test. • Complex characteristics could be successfully and precisely determined. • Useful data for modelling cyclic deformation can be obtained. [ABSTRACT FROM AUTHOR]

The study presents the post-buckling behaviour of thin-walled beam of open section supported by Winkler-Pasternak foundation and it is subjected to an axial compressive load. Here, the assumptions are the strains to be small and elastic, in-plan cross-sectional deformations and the shear deformations to be negligible. The post-buckling paths are determined for clamped beam of I - cross-section which is constant. The point of bifurcation for clamped beam is calculated. It is found to be symmetric and stable for various values of Winkler-Pasternak foundation parameters and Warping parameter. [ABSTRACT FROM AUTHOR]

This work investigates the buckling behavior of circular sandwich plates with tapered cores and functionally graded carbon nanotube (FG-CNT) reinforced composite face sheets under uniform radial compression based on the first order shear deformation plate theory. The sandwich plate is assumed to be constituted of a pure polymer core and two FG-CNT reinforced composite layers with constant thickness whose material properties are assumed to be graded through the thickness direction. Different distributions of multi walled CNTs (MWCNTs) in the thickness direction of face sheets are introduced. Effective properties of materials are estimated through the modified form of rule of mixture. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudospectral method, the stability equations are numerically solved to evaluate the critical buckling load. Parametric studies are conducted for various types of CNTs distributions and geometrical parameters under different boundary conditions. The results show that the buckling behavior is significantly influenced by the CNTs distributions, the thickness variation profile, the aspect ratio and the face sheet-to-core thickness ratio. Some conclusions are drawn on the parametric studies with respect to the buckling characteristics. [ABSTRACT FROM AUTHOR]

This study presents the buckling analysis of radially loaded solid circular plate made of porous material. Properties of the porous plate, where pores are assumed to be saturated with fluid, vary across its thickness. The boundary condition of the plate is assumed to be clamped and the plate is assumed to be geometrically perfect. The higher order shear deformation plate theory (HSDT) is employed to derive the governing equations. The equilibrium and stability equations, derived through the variational formulation and based on the Sanders non-linear strain–displacement relation, are used to determine the prebuckling forces and critical buckling loads. The results are compared with the buckling loads of circular plates made of porous material and reported in the literature based on the classical plate theory (CPT) and the first order shear deformation plate theory (FSDT). [ABSTRACT FROM AUTHOR]

Anti-sag bar is frequently adopted to enhance the lateral stiffness of cold-formed steel purlins. In existing studies, the anti-sag bar is normally treated as the rigid lateral restraint of cold-formed steel purlins, while according to the previous study of the authors', the local deformation of purlin web near the location connecting the anti-sag bar may significantly reduce the efficiency of anti-sag bar for providing the lateral restraint to cold-formed steel purlins. The lateral buckling of C-section purlins with one anti-sag bar at their middle span section is investigated in this paper, where the effective stiffness of the anti-sag bar taking into account the local deformation of purlin web is adopted. Two representative total potentials for the lateral buckling of C-section purlins are discussed with the differences between highlighted. Based on the proposed total potential, a hand-calculation solution for the lateral buckling load of C-section purlins is developed. The total potential and the solution for buckling load proposed in this study are verified by comparing their results with those from the finite element (FE) analysis using the shell element modeling of ANSYS or the FE program developed. The influences of the key parameters on the lateral buckling load of the C-section purlins are discussed in the parametric study. [ABSTRACT FROM AUTHOR]

In this article, the nonlinear buckling behavior of imperfect cylinders made of isotropic, composite and functionally graded materials is studied. A continuum-based semi-analytical finite element formulation is introduced to study the nonlinear behavior of cylinders under thermal loads. A method is proposed to implement the initial geometric imperfection of the cylinder by transformation of structure due to deformation gradients. The influences of geometrical parameters, different materials and imperfection factors are investigated on pre- and post-buckling paths. A comparison is made between the classical von Kármán-based and continuum-based approaches to ensure the validation of the results and to study the applicability of the von-Kármán approximation. [ABSTRACT FROM AUTHOR]

Many authors in the literature agreed that the flow theory of plasticity either fails to predict buckling or overestimates plastic buckling stresses and strains of plates and shells while the deformation theory succeeds in forecasting buckling and provides estimates that are more in line with the experimental results. Following a previous study by the same authors focused on compressed cylinders, the present work aims to investigate the reasons for the discrepancy between the flow and deformation theory predictions in the case of cylinders subjected to combined axial tensile load and increasing external lateral pressure. To this end, geometrically nonlinear finite-element calculations of selected cylindrical shells using both the flow theory and the deformation theory of plasticity have been conducted, and the results are compared with some accurate physical test results and with numerical results obtained by other authors using the code BOSOR5. It is found, contrary to common belief, that very good agreement between numerical and test results can be obtained in the case of the flow theory of plasticity. The reasons underlying the apparent plastic buckling paradox are discussed in detail. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an experimental investigation into the behaviour of ultra light-gauge steel storage rack uprights subjected to compression. Two different types of members with varying lengths are tested and while the combined effects of local and distortional buckling are investigated, special attention is given to longer specimens that fail by flexural–torsional buckling in combination with local and distortional buckling. Deformations experienced during testing by all of the specimens were measured and observations regarding failure modes have been documented. In addition, the geometric imperfections of each member were measured before testing, as were the material properties of the cold-rolled sections and the virgin steel from which the sections were formed. This paper details the observed failure modes, the recorded ultimate strengths and the load-deflection responses. Design capacities calculated from AS/NZS 4084 (2012) [1], RMI (2012) [2] and EN 15512 (2009) [3] specifications are then evaluated and compared to the experimental results obtained.The evaluation of international specificationsdetermined that EN 15512 (2009) [3] is more accurate in predicting ultimate loads of sections undergoing interactive buckling than both AS/NZS 4804 (2012) [1] and RMI (2012) [2]. [Copyright &y& Elsevier]

A family of three finite elements is developed for the lateral-torsional buckling analysis of thin-walled members with doubly symmetric cross-sections. The elements are based on a recently derived variational principle which incorporates shear deformation effects in conjunction with a special interpolation scheme ensuring C1 continuity. One of the elements is developed such that it consistently converges from above while another element is intended to consistently converge from below. The third element exhibits fast convergence characteristics compared to other elements but cannot be guaranteed to provide either an upper or a lower bound solution. The formulation incorporates the ability to enforce any set of linear multi-point kinematic constraints. The validity of the solution is established through comparisons with other well-established numerical solutions. The elements are then used to solve practical problems involving simply supported beams, cantilevers and continuous beams under a variety of loading conditions including concentrated loads, linear bending moments and uniformly distributed loads. The effect of lateral and torsional restraints and the location of lateral restraint along the section height on lateral-torsional buckling capacity of beams are also examined through examples. [ABSTRACT FROM AUTHOR]

This paper reports the development, numerical implementation and practical application of a novel/improved approach to perform the buckling analysis of braced/restrained cold-formed steel members by means of Generalised Beam Theory (GBT). The novelty consists of a cross-section analysis procedure that incorporates elastic restraints and, therefore, leads to a set of constrained deformation modes with clear structural meaning for the member under consideration. The potential of the developed GBT-based approach is illustrated by presenting and discussing numerical results concerning cold-formed steel (i) purlins restrained by sheeting and (ii) studs braced by sheathing. For validation and assessment purposes, several GBT-based results are compared with values provided by the programs GBTul2.0 (conventional GBT), CUFSM (finite strip method) and/or A nsys (shell finite elements). It is shown that the proposed GBT-based approach is much more efficient than the conventional one, as it offers the possibility of obtaining accurate buckling results with very few (constrained) deformation modes – this feature makes it possible to derive semi-analytical formulae to calculate critical buckling loadings of braced/restrained members. This capability is used in this work to derive GBT-based semi-analytical formulae providing critical length and buckling loading estimates for cold-formed steel purlins and studs restrained by panels (sheeting or sheathing). • Novel approach for the buckling analysis of restrained members based on Generalised Beam Theory (GBT). • Restraints included in the GBT cross-section analysis, leading to constrained deformation modes. • Constrained deformation modes lead to improved structural interpretation and computational efficiency. • Application to the buckling analysis of purlins restrained by sheeting and studs braced by sheathing. • Semi-analytical formulae derived to estimate purlin lateral–distortional and stud distortional buckling loadings. [ABSTRACT FROM AUTHOR]

Abstract Purlins are usually connected to roof sheeting by sliding-clips, while wall sheeting is often screw-fastened to girts. This paper investigates the buckling of such two types of parallel purlin/girt systems inter-connected by multiple lines of sag rods. One single purlin braced by one sag rod at any place along the span is first analyzed, and its buckling deformation at any cross-section is seen as a flexibility coefficient which is then used to study the buckling of the purlin braced by multiple sag rods along span. A flexibility matrix is constructed, whose eigenvalues are the base of critical equations. In the case where the sag rods are placed with equal spaces along span, the eigenvalues are expressed in explicit forms, of which each represents one buckling mode. Threshold stiffness of the sag rods are presented for multiple sag rod bracings for these two types of sheet-to-purlin connection. Based on the findings of this paper, the differences of buckling behaviors between these two types of purlin systems have been revealed. The effect of local deformation of the web at the sag rod connecting points on the sag rod stiffness is also included. Parallel purlin systems are then investigated in a compact matrix form. After carrying out matrix operations and slight approximations, a key parameter is found to be used to reflect the effect of the number of purlins and zig-zag layout of sag rods in adjacent bays on the effective sag rod stiffness. Highlights • Buckling of parallel purlins braced by multiple lines of sag rods is studied. • Rotational restraints of roof sheeting to purlins are considered. • The reduced effectiveness of the sag rods are revealed systematically. • It's found parallel purlins can be analyzed as if they one single-purlin-system. • Two types of purlin-to-sheeting connections are analyzed and compared. [ABSTRACT FROM AUTHOR]

This study investigated the buckling of nontypical prolate domes subject to hydrostatic external pressure. The domes were shells of revolution with an egg-shaped configuration, with a base diameter and height of approximately 160 and 121 mm, respectively. Four laboratory-scale egg-shaped domes, cold-pressed from a 1-mm 304 steel sheet, were measured for geometry, tested to collapse, and analysed numerically. The experimental results and numerical evaluations were well consistent. Furthermore, the buckling behaviours of a perfect egg-shaped dome, a capacity-equivalent hemisphere, and a mass-equivalent hemisphere were numerically studied. The results indicate that the prolate egg-shaped dome has a relatively large load-carrying capacity that is not highly sensitive to material plasticity and geometrical imperfections. [ABSTRACT FROM AUTHOR]

In this paper, the Bree diagram is extended to consider the progressive buckling failure and a direct approach for structural progressive buckling design considering ratcheting deformation is developed. Firstly, the progressive buckling mechanism of structures subjected to the combination of constant and cyclic loadings is sufficiently discussed. Then, a two-stage direct approach is developed based on the Linear Matching Method and nonlinear buckling analysis, which can generate progressive buckling design curves in the extended Bree diagram. To illustrate the application of the direct approach to progressive buckling design, a cylindrical shell model with an opening is provided as a numerical example. Furthermore, geometrical effects, e.g. the opening size and the shell thickness, on the progressive buckling limit are investigated. Formulas for progressive buckling design of cylindrical shells with various geometrical parameters are derived by fitting curves. Compared with other methods, the direct approach could predict accurate progressive buckling load. • The Bree diagram is extended to consider the progressive buckling design. • Novel direct approach is proposed to predict progressive buckling limit. • Progressive buckling design curves and formulas for cylindrical shells are predicted. • The direct approach is confirmed to predict accurate progressive buckling load. [ABSTRACT FROM AUTHOR]

This paper presents the experimental and simulation study of circular steel arches attached on the steel columns through the rigid connection, which are loaded to failure under static load. Local buckling of the top flange at the mid-span arch or the bottom flange at end of the arch occurs under the ultimate load. The deformation shape is approximately antisymmetrical with a 0.2 rise-to-span ratio and is symmetrical with a 0.1 rise-to-span ratio. A simplified model is proposed as an arch with elastic horizontal and rotational end restraints. The corresponding stiffness is determined as equivalent horizontal and rotational stiffness at each arch end under the ultimate load. Then a large amount of parameter analysis is conducted to investigate the influence of the elastic supported stiffness, load type, rise-to-span ratio, and slenderness on the ultimate resistance. The finding is that the reduction of the ultimate resistance for the arch with the horizontal and rotational elastic end restraints is maximal under the uniform full-span vertical load, minimal under the concentrated load. Finally, a design method of the steel arch with elastic horizontal and rotational end restraints is proposed taking both ultimate resistance and maximum horizontal displacement of the supports into account for engineering reference. [ABSTRACT FROM AUTHOR]

This paper reports on experiments addressing the buckling and collapse behavior of common built-up cold-formed steel (CFS) columns. The built-up column consists of two individual CFS lipped channels placed back-to-back and connected at the web using two self-drilling screw fasteners at specified spacing along the column length. The experiments aim to quantify ultimate strength, composite action, member end fixity, and buckling interactions and collapse behavior for common built-up CFS members. The testing also explicitly explores the effect of sheathing, as typically employed in cold-formed steel framing, on the response. The experiments provide benchmarks for design that include specific considerations for both thin-walled buckling and fastener behavior. A total of 17 monotonic, concentric compression tests with a column length of 1.83 m (6 ft) are completed with an array of position transducers monitoring displacements at key locations. Tests are conducted with the built-up member seated in CFS tracks. Results indicate a large range of deformation behavior, with local-global interaction and flexural-torsional modes common in many of the unsheathed specimens. Columns sheathed with oriented strand board on both flanges behave as braced against global buckling in the plane of the wall, and local buckling induced failures prevail. The end condition for the tested built-up members seated in track is determined to be semi-rigid, but generally closer to fixed than pinned. [ABSTRACT FROM AUTHOR]

Over the years a large number of works have shown that for many buckling problems of plates and shells in the plastic range the flow theory of plasticity seems to lead to a significant overestimation of the critical stress while the deformation theory seems to provide much more accurate predictions and therefore the latter has been generally recommended for use in practical applications. This fact is generally known in literature as the “plastic buckling paradox”. Possibly the simplest examples of such a circumstance is given by the torsional instability of a cruciform column. The present study examines the problem from its roots and shows that in order to overcome this apparent conundrum it is not only necessary to consider an imperfect column, as generally suggested in the past, but principally to account correctly for the effects of the imperfection up to the point where the limit load is attained. In such manner a very good agreement between the results from the flow theory of plasticity and other analytical and experimental results can be obtained on the basis of classic formulae only. [ABSTRACT FROM AUTHOR]

Suitable and fast calculation methods with sufficient accuracy are required to optimise large composite structures. The present paper introduces a progressive stiffness degradation analysis (PSDA), which computes skin buckling onset and strength failure initiation of skin fields separated by stiffeners, as well as the subsequent damage propagation using closed form solutions. This constitutes a simplified, but much faster approach compared to state of the art progressive failure analyses, which incorporate finite element simulations. Therefore, the computational effort can be reduced. This paper illustrates the process of the PSDA and then verifies this simplified approach by means of one example. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified Kirchhoff theory for analyzing thermo-mechanical static and buckling responses of functionally graded material (FGM) isotropic and sandwich plates. In comparison to the classical Kirchhoff theory, the proposed method is taken account into the shear deformation effects, then it can be applied for both moderately thick and thin plates. On the other hand, comparing to the first order shear deformation theory (FSDT) or Reissner-Mindlin plate theory, the number of independent unknowns reduces one variable and retains four degrees of freedom (Dofs) per node. The shear locking phenomenon is also negligible due to extending from the classical Kirchhoff theory. Furthermore, a new normalization of a quartic form is used to build the shape functions in the radial point interpolation method (RPIM). The novel imposing essential boundary conditions related to slopes of deflections has been proposed, then the enforcement of these gradient deflections becomes easily and directly as the same in finite element analysis. The obtained numerical results for the thermo-mechanical static and buckling problems from the proposed method are stable and well accurate prediction as comparing to the exact solutions and other published analyses. [ABSTRACT FROM AUTHOR]

The paper describes the derivation of a beam finite element method which enables the effects of local and/or distortional buckling deformations to be accounted for. The development of local/distortional buckling reduces the rigidity of the section against axial straining, minor and major axis flexure, as well as twisting. The reduction in rigidity can be determined by an analysis performed prior to the frame analysis, in which tangent rigidities (( EA ) t , ( EI z ) t , ( EI y ) t , ( EI w ) t ) and other tangential stiffness terms are obtained for increasing values of generalised strains ( ε x , κ z , κ y , κ x ). The paper sets out the tangential stiffness matrix for a locally/distortionally buckled element and discusses in detail the determination of tangent rigidities. The companion paper [1] shows that close agreement can be obtained between the beam analysis which incorporates reduced rigidities and analysis using full shell finite element discretisation. The paper is limited in scope to doubly-symmetric open sections. [ABSTRACT FROM AUTHOR]

This work presents the milestones of the underlying of a patented work [1] (Abdul-Latif, 2014) which aims to enhance the plastic buckling resistance of thin-walled right-circular cylindrical mild steel tubes deformed axially under the quasi-static compressive load. The proposed concept can be described by producing a metal like-composite where a hard phase incorporates in these tubes made by case-hardening of 15% of tubes outer surface with different geometrical shapes and a constant depth along the tubes thickness. To study the effect of case-hardening configurations, several forms were designed, made and tested. They were four ring forms (with 2, 3, 4 and 5 rings), two vertical strip forms (2 and 3 strips) and, six helical strip forms with three tilt angles of 30°, 45° and 60° (2H30, 3H30, 2H45, 3H45, 2H60 and 3H60). The total energy absorption of conventional tubes could be increased up to 46%. The effects of the case-hardened zone, quasi-static strain rate and the crush force efficiency were investigated. Moreover, the deformation modes of these case-hardened tubes were analyzed. The effect of the case-hardened forms could be classified into three categories by the gain percentage (low, intermediate and high gains). Especially in the high gain category, the material behavior seems to be directed by complicated local strain induced by the metal like-composite tube, where a triaxial strain state was encouraged particularly within the tube wall of 3H30. For this reason, the collapse load became the function of case-hardened forms. [ABSTRACT FROM AUTHOR]

The paper provides comparisons of sensitivity of buckling pressures to initial shape imperfections, for the case of externally pressurised steel domes. A priori defined deviations from perfect shape include: Legendre polynomials, increased-radius patch, and localised inward dimple. The latter is created by a concentrated force acting radially. In this case the effects of spring back and/or annealing of the dented patch and the surrounding area on the load carrying capacity are assessed. Some of the elastic solutions related to the lower-bound approach are compared with the available experimental data. [ABSTRACT FROM AUTHOR]

A thermal postbuckling analysis for composite laminated plates reinforced with graphene sheets is performed in this research. All of the thermomechanical properties of the composite media are assumed to be temperature dependent. Volume fraction of the graphene in each layer is assumed to be different which results in a piecewise functionally graded plate. Based on the third order shear deformation plate theory of Reddy, the total strain energy of the plate is obtained. Composite laminated plate is assumed to be under uniform temperature rise. Properties of the graphene reinforced composite media are estimated by means of a refined Haptin-Tsai approach which contains efficiency parameters to capture the size dependency of the constituents. Afterwards, a non-uniform rational B-spline (NURBS) based isogeometric finite element method is implemented to study the thermal postbuckling response of the graphene reinforced composite laminated plates. Thermally induced postbuckling curves of the composite plate reinforced by graphene are provided for different functionally graded patterns, aspect ratios, side to thickness ratios and boundary conditions. It is shown that, FG-X pattern of graphene reinforcement results in the highest critical buckling temperature and the lowest postbuckling deflection. [ABSTRACT FROM AUTHOR]

Generalised Beam Theory assumes the displacement field of a thin-walled member as a linear combination of deformation modes. The main family of deformation modes is constructed based on two simplifying assumptions: null membrane shear strain and null membrane transverse extension. If these modes are not sufficient for an accurate representation of the structural behaviour, two other families of modes are derived (from the main family) for which the two simplifying assumptions are eliminated. In this paper, for the special case of thin-walled cylinders, all three families of deformation modes are replaced by a new unified family, for which the membrane shear strain and transverse extension are not neglected. The derivation of the proposed modes is based on the stress equilibrium equations, and it involves the trigonometric series representation of the longitudinal modal amplitudes. The advantages of the proposed modes are highlighted throughout several linear buckling analyses with various loading and boundary conditions. • New GBT deformation modes are derived using the stress equilibrium equations. • Longitudinal modal amplitude functions are represented by trigonometric series. • Stiffness matrices are derived for linear buckling analysis. • Formulation is validated using shell finite element models. • Proposed formulation is compared with classical GBT. [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 practical applications, the load bearing capability of slender plates can be affected by the existence of flaws resulting from a number of material deterioration (corrosion, fatigue, etc.). In the present work, a numerical analysis on the residual strength and post-buckling behavior of flawed shear panels using FE method is performed. Using a continuum damage mechanics model, the possibility for a ductile crack to grow under loading is considered. This approach allows us to investigate the role of crack growth in materials with different capabilities to accommodate plastic deformations at the crack tip, as well as geometry effect on the material crack resistance, due to loss of constraint. The effect on the buckling load, ultimate load and postbuckling response of shear panels varying both geometry characteristics and materials (such as initial crack length, slenderness ratio, panel boundary conditions, material properties, etc..) is investigated. Results indicate that crack growth can play a relevant role in the response of shear panels, especially for those materials in which ductile tearing can occur in the early stages of loading. The damage mechanics model used in this work offered the possibility to simulate the occurrence of ductile crack growth based on material properties, without the need of arbitrary assumptions on the crack advance process. [ABSTRACT FROM AUTHOR]

Modeling and analysis for the postbuckling of FGM doubly curved panels resting on elastic foundations and subjected to lateral pressure under heat conduction are presented. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The temperature-dependent material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction based on Mori–Tanaka micromechanics model. The formulations are based on a higher order shear deformation theory with von Kármán strain–displacement relationships. The panel-foundation interaction and thermal effects are also included. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling deformations and initial geometric imperfections of the panel. These equations are then solved by means of a singular perturbation technique along with a two-step perturbation approach. The effects of volume fraction index, temperature variation, the panel geometric parameters as well as foundation stiffness on the postbuckling behavior of FGM doubly curved panels are discussed in detail. [ABSTRACT FROM AUTHOR]

This work reports numerical results concerning cold-formed steel simply supported beams buckling and failing in distortional modes under uniform bending and exhibiting three cross-section shapes, namely (i) lipped channels bent about the major-axis, (ii) zed-sections under skew bending causing uniform flange compression (worst case), and (iii) hat-sections subjected to either major-axis or minor-axis bending (compressed lips in the latter case). Two end support conditions are considered, differing in the warping and local displacement/rotation restraints, which are either completely free or fully prevented. The beams analysed have several cross-section dimension ratios and lengths, in order to assess their influence on the distortional post-buckling behaviour and ultimate strength – particular attention is paid to the influence of (i) the flange-web and lip-flange width ratios, and (ii) the critical (distortional) half-wave number. In addition, the beams exhibit different yield stresses, making it possible to cover wide distortional slenderness ranges. After presenting and discussing the numerical elastic and elastic-plastic post-buckling results obtained, consisting of equilibrium paths, deformed configurations, plastic strain distributions, failure moments and collapse mechanisms, the paper shows that the currently codified Direct Strength Method (DSM) design curve fails to predict adequately the failure moments of some of the beams analysed and addresses the development/proposal of novel DSM strength curves, providing better quality predictions of all the numerical failure moments available. [ABSTRACT FROM AUTHOR]

This technical note discusses aspects related to the combination of standard Reissner–Mindlin shell and GBT-based (beam) finite elements, with the purpose of modelling, efficiently (with degree-of-freedom economy) and accurately, the structural behaviour of thin-walled members and frames with complex geometry, undergoing global-local-distortional deformation. Following the approach previously proposed by the authors (Manta et al., 2020 [1] ; 2021 [2] ; 2020 [3]), each element type is employed where it is most efficient: (i) GBT-based elements in the prismatic zones and (ii) shell elements in the geometrically complex zones (e.g., tapered, joints, etc.). While lack of compatibility obviously leads to over-flexible solutions, it is shown that full compatibility can lead to locking. Consequently, a well-balanced compatibility statement is proposed. Several numerical examples are presented to show the advantages of the proposed approach over the previous one, in linear static and buckling (bifurcation) analyses. [ABSTRACT FROM AUTHOR]

In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained. During optimization procedure, a cubic polynomial spline interpolating on a finite number of design variables is considered as porosity distribution function. Solving the multi-objective optimization problem using bio-inspired genetic algorithm (NSGA II), leads to a set of optimal porosity distributions known as Pareto optimal solutions. To show the validity of the proposed formulation, we compare results with those reported (1D and 2D porosity distributions) in the literature as well as finite element simulations. We also compare Pareto solutions with optimization result of one dimensional porosity distribution which clearly demonstrates the importance of the presented optimization procedure. In general, optimum porosity distributions are different in each boundary condition. However, in most of the optimum solutions, middle line of the beam is composed of the material with higher values of porosity and outer corners have lower values of porosity. Pareto optimal solutions also indicate that, sharp decreasing of the mass makes a slight decline in critical buckling load when it has large values. The proposed approach can be used for design of porosity distribution in FGP structures. [ABSTRACT FROM AUTHOR]

Elastic instabilities (such as buckling) have been recognized as a promising phenomenon to design smart materials and mechanical systems. Thin-walled cylindrical shells under axial compression can attain multiple bifurcation points in their postbuckling regime due to the natural transverse deformation restraint provided by their geometry; but harnessing such behavior for smart purposes is lacking extensive study due to its notoriously high imperfection sensitivity. In this paper, the concept of seeded geometric imperfection (SGI) design is proposed to modify and control the elastic postbuckling behavior of cylindrical shells. Eigenvalue-based mode shapes were used as basic geometric forms to generate a seeded imperfection. Prototyped SGI cylindrical shells were fabricated through 3D printing and tested under loading–unloading cycles. Numerical and experimental results suggest that the SGI cylindrical shells are less sensitive to initial imperfections and load variation than uniform ones. Cylindrical shells with seeded geometry can be potentially used in the design of smart devices and mechanical systems such as energy harvesters and self-powered sensors. [ABSTRACT FROM AUTHOR]

The present paper deals with a dynamic interactive response of FG beam-columns subjected to in-plane pulse loading when the shear lag phenomenon and distortional deformations are taken into account. The structures are assumed to be simply supported at the ends. In order to obtain the equations of motion of individual plates, the classical laminate plate theory (CLPT) has been modified in such a way that it additionally accounts for all components of inertial forces. Thin-walled trapezoidal FGM beam-columns are considered. A dynamic interaction of the global mode with the lowest primary local buckling mode and the secondary local mode has been analysed. Attention has been drawn to some unexpected aspects related to the fact that a two- and three-modal approach has been assumed in the analysis of dynamic interactive buckling. [ABSTRACT FROM AUTHOR]

Typical methods of analysis and modelling of measured geometric imperfections make use of the Fourier transform to represent the imperfections as summations of sinusoids. The reconstruction of the imperfection usually consists of only a few harmonics, chosen with half-wavelengths equal to the half-wavelengths of the critical elastic buckling modes. This modelling of geometric imperfections is well suited for slender prismatic structures which buckle elastically and for which the buckling modes are harmonic in the longitudinal direction. However, when buckling occurs inelastically, buckling deformations are frequently confined to a relatively small part of the structure and associated with the formation of a spatial plastic mechanism. For this case, the accurate reconstruction of localised imperfections using sinusoids requires the summation of a wide range of frequencies. Further, the Fourier transform cannot explicitly give information on the positioning of localised components. This paper explores the application of the wavelet transform to the analysis and modelling of localised geometric imperfections. Seeing the similarity between various wavelets and the longitudinal variation of typical inelastic buckles, wavelet transforms are expected to be more suitable for modelling the geometric imperfections of non-slender thin-walled structures than the Fourier transform. The theory of the wavelet transform is briefly covered including methods by which practical issues that arise in evaluating the transform, and reconstructing the analysed imperfection, may be resolved. Three imperfection schemes are developed and compared to numerical models incorporating detailed longitudinal and transverse geometric imperfection measurements. These schemes represent the pertinent imperfection components via Fourier series, via wavelet frames, and via a few empirically selected wavelets. The scheme utilising wavelet frames produces excellent results, as does that utilising Fourier series, although it requires a great number of component wavelets due to their finite length. As such, it is worth noting that, in addition to those covered herein, many more methods of reconstruction utilising wavelets are possible. [ABSTRACT FROM AUTHOR]