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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]

Abstract: In this paper we revisit an elastic constitutive equation proposed in two previous works and extend it in order to include all higher-order terms on the deformations. Our purpose is to assess the influence of these terms on the elastic buckling of thin-walled rods. The resulting material model was incorporated into a geometrically exact rod formulation and implemented into a nonlinear finite element code. By means of simple numerical examples we show that the higher order terms may play a significant role on the values of the buckling loads and on the post-buckling behavior of thin-walled beams and columns. [Copyright &y& Elsevier]

Abstract: A long, thin, inextensible cylindrical tube made of Hollomon's power-law material acted upon by a uniform normal pressure is considered. The nonlinear boundary value problem that governs the equilibrium states of such a tube is formulated as a differential system of equations. Perturbation solutions are obtained for the cases of small pressure values in the neighborhood of the critical buckling pressures. Numerical solutions based on a special initial value problem Matlab solver, Newton's and shooting methods are obtained. The results show that a high strength material tube deforms similarly to an elastic material tube for values of strain hardening exponent. [Copyright &y& Elsevier]

Abstract: Large steel silos are typical kinds of thin-walled structure which are widely used for storing huge quantities of granular solids in industry and agriculture. In the present analyses, buckling design of large steel silo subject to wind pressure is demonstrated in accordance with Eurocode (EN1990, 1991, 1993) and the proposed combinational Load Case WE (wind and empty silo) and WF (wind and full silo). The finite element model is established by using the commercial general purpose computer package ANSYS. Five types of buckling analyses are carried out for the geometrically perfect and imperfect models with and without the consideration of the material plasticity, which are designated as LBA, GNA, GMNA, GNIA, and GMNIA in EN 1993 Part 1–6. The geometrical imperfections are known to have a large impact on the buckling behavior of steel silo structure, in which the magnitude and distribution of the weld depression during construction process is adopted to account for fabrication quality. The buckling behavior of a reference silo with a diameter of 40m and an aspect ratio of 0.9 is first investigated, which shows that the buckling behaviors from Load Case WE and WF are much different. The material nonlinearity shows little influence on buckling resistance in Load Case WE, while the buckling resistance and buckling mode is much sensitive to weld imperfection. In Load Case WF, both material nonlinearity and geometrical nonlinearity effect is strong and detrimental to buckling behavior of steel silos, resulting in decrease of buckling resistance. The buckling deformation corresponding to the critical point in Load Case WE is governed by the circumferential compression which is generated in the windward region of the shells localized at the top part of silo wall. The buckling mode in Load Case WF takes the form of the well-known elephant-foot deformation at the bottom part of the shell wall, which is induced by the meridional compressive stress. It is also indicated from the parametric analyses that the buckling resistance of steel silo is closely correlative with the loading conditions involving the wind velocity, the patch load, and the geometrical parameters including the aspect ratio, the radius-to-thickness ratio, the type of wall thickness, and the wall openings. [Copyright &y& Elsevier]

Abstract: Post-buckling of a stiffener beam subjected to single shear load was experimentally investigated. The results were analysed using Wagner theory and non-linear finite elements. A new method was proposed to study the postbuckling behaviour. Each panel is divided into two zones. A central zone where an orthotropic material with a damage law is used and a surrounding zone with the initial material. The results obtained with this analysis were found to agree well the experimental results. The method is less time consuming than classical non-linear finite elements so it can be used for studying complex structures in optimisation procedures. [Copyright &y& Elsevier]

Abstract: In a companion paper, a variational principle based on the principle of stationary complementary energy was developed for the buckling analysis of thin-walled members with open cross-sections. In this paper, the variational principle is adopted to formulate a finite element buckling solution. The formulation successfully incorporates shear deformation effects, a feature that is neglected in most available buckling solutions. By adopting a non-orthogonal coordinate system, the solution successfully captures the transverse load position effect relative to the shear center. A series of examples demonstrate the validity of the finite elements formulated and their applicability to a wide variety of buckling problems. Examples include column flexural and torsional buckling, lateral torsional buckling of beams with a variety of end conditions and subjected to a variety of moment gradients. The formulation is shown to be applicable to beams with mono-symmetric sections. In all cases, the validity of the new solution is assessed and established through comparisons to well-established closed-form and/or numerical solutions. [Copyright &y& Elsevier]

Abstract: The governing equations for determining thermal buckling of imperfect sandwich plates are developed using the large deflection theory and considering first shear deformation principles. The equations are then solved via an analytical method comprising infinite summation of trigonometric series and defining in-plane and out-of-plane displacement. After verification of the proposed method and convergence studies, the effects of parameters like plate aspect ratio, material properties and layer setting angles on buckling stress and the post-buckling path are studied. Numerical results show that the number of trigonometric terms does not affect the buckling thermal stress or the post-buckling path of sandwich plates having face layer setting angles less than 15°. Results also show that the buckling stress and post-buckling path for complementary layer setting angles are similar and that the rate of variation of bifurcation points for different face layer setting angles of sandwich panels strongly depend on material properties, especially on the face and core stiffness. Furthermore, for aspect ratios greater than five, buckling thermal stress remains about constant. [Copyright &y& Elsevier]

Abstract: This paper studies the buckling behaviour of simply supported square plates, which have weakening or strengthening bands. The weakening/strengthening bands are equally spaced and their thickness is either decreased or increased. The analysis assumes that the stress state in the plate before and during the buckling process remains in the elastic range. Two cases of plate loading are studied, one with compressive forces and one with tangential forces. The buckling coefficients are calculated for different numbers and thicknesses of strengthening/weakening bands. The thickness of strengthening/weakening bands and the thickness of the remaining plate is varied so that the volume/weight of the plate remains constant. In one case it is found that the buckling load at constant weight of the plate can be increased by 118% if an optimal ratio of the thickness of strengthening bands and the thickness of the remaining plate is used. [Copyright &y& Elsevier]

Abstract: Fuselage panels are commonly fabricated as skin-stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post-buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the Finite Element method and employing non-linear material and geometric analysis procedures it is possible to model the post-buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Previous work has demonstrated that using a commercial implicit code, the Finite Element method can be used successfully to model the post-buckling behaviour of flat riveted panels subjected to uniform axial compression. This paper expands the compression modelling procedures to flat riveted panels subjected to uniform shear loading, investigating element, mesh, idealisation and material modelling selection, with results validated against mechanical tests. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform shear loading, highlighting subtle but important differences between shear and compression modelling requirements. [Copyright &y& Elsevier]

Abstract: This paper presents an original method based on the Generalised Beam Theory (GBT) capable to decompose the elastic buckling modes from a shell finite element analysis (FEA) of an isotropic thin-walled member, into pure buckling modes of global, distorsional or local nature. The main novelty lies in using only the GBT cross-sectional deformation modes instead of member base mode shapes. The contribution of each pure buckling mode can be calculated, allowing a better understanding of the member post-buckling behaviour and strength reserve. Following the GBT classical assumptions, the membrane shear strains and transverse extensions are neglected. The modal participations obtained from FEA are in good agreement with the values calculated via classical GBT approach. [Copyright &y& Elsevier]

Abstract: An experimental investigation on the behavior of steel storage rack columns subjected to compression is presented. Members of different lengths are tested, but special attention is focused on the behavior of the specimens having lengths that make them subject to distortional buckling. This mode of buckling can be observed in moderately long specimens; namely, longer than the stub columns used for the determination of the local buckling strength, but short enough to avoid the effects of global buckling. The deformation experienced by these specimens is measured, and it is observed that there is a range of member lengths where the failure mode is a combination of distortional buckling and global buckling modes. Furthermore, it is verified that, although the effect of the interaction between these modes on the member strength is not large, the accuracy of the current design procedures improves if it is considered in the calculations. [Copyright &y& Elsevier]

Abstract: The variational principle developed in a companion paper is adopted to formulate a new finite element for the buckling analysis of members of doubly symmetric cross-sections. A series of examples demonstrate the convergence characteristics of the element and its applicability to a wide variety of problems. The examples include column flexural buckling, lateral–torsional buckling of beams subjected to moment gradients, buckling of members under combinations of axial force and bending moment, and eccentrically supported structural members. In all cases, the validity of the solutions is assessed through comparisons to well-established closed-form and/or other established numerical solutions. [ABSTRACT FROM AUTHOR]

Abstract: In this article, the bucking of cylindrical shells with longitudinal joint has been investigated through the experimental and numerical analysis. It was clarified that the buckling behavior of cylindrical shells with longitudinal joints under lateral external pressure is not only related to its dimension, but also longitudinal joint and an imperfection. The buckling of cylindrical shells with rigid joint buckles only once and in multi-lobe buckling, whereas one with flexible joints buckles twice and firstly in single-lobe buckling in the vicinity of the joint, secondly in multi-lobe buckling in remaining un-deformed area. And the more flexible the longitudinal joint, the lower the critical pressure, with respect to the same dimension of jointed cylindrical shells and imperfection condition. Moreover the numerical analysis approaches were also presented and verified, by which the imperfection can greatly enlarge the effect of joint on buckling has been demonstrated. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to demonstrate an approximate method whereby eigen buckling modes from a shell finite element method (FEM) analysis of a thin-walled member can be quantified in terms of the fundamental buckling classes, namely, global, distortional, local, or other. The buckling classes are defined using the mechanical definitions employed in the constrained finite strip method (cFSM). The cFSM base vectors are used to approximate an arbitrary FEM buckling mode. The resulting identification and its associated error is investigated, including dependency on FEM discretization, the number of cFSM functions considered, boundary conditions, and loading. The long-term goal of the work is to provide a generalized method for identification of local, distortional, and global buckling modes for arbitrary thin-walled members modeled in general purpose finite element codes. [Copyright &y& Elsevier]

Abstract: The effect of an friction stir weld (FSW) on the buckling behavior of an integrally stiffened panel (ISP) structure was investigated. For proper consideration of the buckling modes, the Riks method based on geometric imperfection was introduced. The Ramberg–Osgood deformation plasticity model was used for the elasto-plastic material behavior. A basic buckling benchmark test with a simple square plate was performed to verify the effect of the element type, Ramberg–Osgood model and the Riks method on the critical buckling load. Buckling analyses with two different sectional shapes were conducted corresponding to 400 and 600kN buckling loads. After confirming that the predicted results without FSW were in excellent agreement with known analytical solutions, finite element (FE) analyses for 2- and 3-stiffener ISP sections joined by FSW were performed. The simulated results with and without FSW were compared to each other. The presence of the weld reduced the maximum buckling load from 3% to 10% depending on the sectional shape as a result of the reduction in material strength in the weld zone. The reduction in buckling load was greater for the 2-stiffener ISP section than for the 3-stiffener ISP configuration, due to the closer spacing of the welds. For both ISP configurations, the percentage decrease in the buckling load for the higher load case (600kN) was less than that for the lower load case (400kN). [Copyright &y& Elsevier]

Abstract: The effect of pre-buckled nonlinearity on the bifurcation point of laminated cylindrical shells is examined on the basis of Donnell''s shell theory. The eigenvalue problem is solved iteratively about the nonlinear equilibrium state up to the bifurcation point. An algorithm is presented for the real buckling behavior, dispensing with the need to cover the entire nonlinear pattern. This algorithm is very important for structures characterized by a softening process in which the pre-buckled nonlinearity depresses the buckling level relative to the classical one. The procedure involves nonlinear partial differential equations, which are separated into two sets (using the perturbation technique) for the pre-buckled and buckled states, respectively, and solved with the variable expanded in Fourier series in the circumferential direction, and by finite differences in the axial direction. A special purpose computer code NBLCS (Nonlinear Buckling of Laminated Cylindrical Shells) was developed, for calculating the bifurcation point of laminated cylindrical shell. [Copyright &y& Elsevier]

Abstract: Thin shell torispherical pressure vessel heads are known to exhibit complex elastic–plastic deformation and buckling behaviour under static pressure. In pressure vessel Design by Analysis, the designer is required to assess both of these behaviour modes when specifying the allowable static load. The EN and ASME boiler and pressure vessel codes permit the use of inelastic analysis in design by analysis, known as the direct route in the EN Code. In this paper, plastic collapse or gross plastic deformation loads are evaluated for two sample torispherical heads by 2D and 3D FEA based on an elastic-perfectly plastic material model. Small and large deformation effects are considered in the 2D analyses and the effect of geometry and load perturbation are considered in the 3D analysis. The plastic load is determined by applying the ASME twice elastic slope criterion of plastic collapse and an alternative plastic criterion, the Plastic Work Curvature criterion. The formation of the gross plastic deformation mechanism in the models is considered in relation to the elastic–plastic buckling response of the vessels. It is concluded that in both cases, design is limited by formation of an axisymmetric gross plastic deformation in the knuckle of the vessels prior to formation of non-axisymmetric buckling modes. [Copyright &y& Elsevier]

Abstract: This paper presents some results of an extensive investigation on the failure of the pressurized double-piping system (pipe-in-pipe system) being one of the main structural elements of the thermo-conditioning installation in the sewage treatment plant. The investigation included the survey of the failed piping, checking of the design and manufacturing against the standards of various types, theoretical analysis employing the results of works carried out on buckling propagation. As an useful and highly informative element of the investigation three tests have been designed to expose the phenomena, which lead to an explanation of the cause of the failure under consideration. They also verified the results of the theoretical analysis performed. [Copyright &y& Elsevier]

Abstract: Effects of the lateral pressure on the FEM and reduced stiffness lower bound buckling strength of axially loaded sandwich cylindrical shell are examined. Further, a reduced stiffness lower bound buckling strength for the axially loaded sandwich cylindrical shell under lateral pressure is proposed. The effect of the lateral pressure on the FEM and reduced stiffness lower bounds are corresponding; it causes them to reduce slightly. However, reduced stiffness buckling mode shape remains the same. In addition, the proposed reduced stiffness lower bound buckling strength is shown to provide effective and valid for cores having different shear stiffness. It provides comparatively close lower bounds to short axially loaded sandwich cylindrical shells under lateral pressure. Further, it provides a safe lower bound that does not depend on precise geometrical imperfection spectra and lateral pressure and it is simple and easy to employ. [Copyright &y& Elsevier]

Abstract: This paper deals with distortional buckling in monosymmetric propped cantilever I-beams under two types of load: a central point load and a uniformly distributed load. Top-flange and bottom-flange load positions are considered. ABAQUS is used for the investigation. Moment modification factors are obtained and are compared with those based on Structural Stability Research Council Guidelines, which take into account lateral–torsion buckling only. It is seen that provisions in SSRC Guidelines seriously overestimate the critical load, especially for short beams. [Copyright &y& Elsevier]

Abstract: The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes are essential for reliable and lightweight structural design. This paper presents some parametric studies on simply supported laminated composite blade-stiffened panels subjected to in-plane shear loading. A total of 450 models were analyzed using ANSYS 7.1 and a database is prepared for different plate and stiffener combinations. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and extensional stiffness to shear stiffness ratio of the plate. Based on the studies, few important parameters influencing the buckling behaviour are identified and guidelines for better stiffener proportioning are developed, which will be helpful for the designer. [Copyright &y& Elsevier]

Abstract: A solution for the elastic buckling of flat rectangular plates with centerline boundary conditions subjected to non-uniform in-plane axial compression is presented. The loaded edges are simply supported, the non-loaded edges are free, and the centerline is simply supported with a variable rotational stiffness. The Galerkin method is used to establish an eigenvalue problem and a series solution for plate buckling coefficients is obtained by using combined trigonometric and polynomial functions that satisfy the boundary conditions. It is demonstrated that the formulation approaches the classical solution of a plate with a clamped edge as the variable rotational stiffness is increased. The variation of buckling coefficient with aspect ratio is presented for various stress gradient ratios. The coupling between plate aspect ratio, centerline rotational stiffness, and gradient of applied compressive stress is illustrated and discussed. The solution is applicable to stiffened plates and I-shaped beams that are subjected to biaxial bending or combined flexure and torsion, and is important to estimate the reduction in elastic buckling capacity due to stress gradient. [Copyright &y& Elsevier]

Abstract: A reduced stiffness lower bound method for the buckling of laterally pressure loaded sandwich cylindrical shell is proposed. Also, an attempt is made to assess the validity of the proposed reduced stiffness lower bound with FEM numerical examples. In addition, the proposed method is compared with classical and Plantema''s approaches of the buckling of the laterally pressure loaded sandwich cylindrical shell. Comparison of the proposed reduced stiffness lower bound with that obtained from non-linear FEM analysis verifies that it indeed provides a safe lower bound to the buckling of laterally pressure loaded sandwich cylindrical shells. The attractive feature of the proposed reduced stiffness method is that it can be readily used in designing laterally pressure loaded sandwich cylindrical shells without being concerned about geometrical imperfections. [Copyright &y& Elsevier]

Abstract: The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed. [Copyright &y& Elsevier]