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This paper presents an analytical and numerical investigation of the relationship between the compressive load level and the natural frequency variation toward a vibration correlation technique for the buckling load calculation of imperfection-sensitive isotropic cylindrical shell structures. Firstly, a back-to-basic s study is proposed and the linear equation between the applied load and the square of the loaded natural frequency is revisited. Such review considers the Flügge-Lur'e-Byrne's linear shell theory for the free vibrations of an isotropic unstiffened cylindrical shell under uniform axial loading. The demonstrated linear equation is rearranged for expressing the square of the applied load as a quadratic function of the square of the loaded natural frequency. The suggested formulation provides the analytical support to a novel vibration correlation technique that has been empirically proposed and experimentally validated for unstiffened cylindrical shells. Aiming a numerical verification based on finite element models, two cylindrical shells are defined. At first, the critical buckling load and the fundamental natural frequency for different load levels are determined and compared to the analytical results for validation of the numerical models. The finite element models are extended considering geometric nonlinearities, more realistic boundary conditions and three magnitudes of a benchmark measured initial geometric imperfection. The numerical results are considered for analyzing the variation of the natural frequency in the surroundings of buckling and for verifying the vibration correlation technique. • The free vibration of an axially loaded simply supported cylinder is revisited to verify an existing VCT. • A new insight to define a VCT which does not depends on the similarities between buckling and vibration modes is proposed. • The capability of the VCT to provide conservative estimations is corroborated through detailed numerical models. [ABSTRACT FROM AUTHOR]

Abstract Experimental study is carried out to investigate the behavior and strength of square hollow structural section (SHS) columns, strengthened with an innovative polymer-mortar system. Thirteen specimens of cold-formed SHS columns with different variables are chosen. Three short-column and ten long-column SHS specimens were experimentally tested. The local and overall buckling of specimens are measured in the laboratory. The tested specimens are subjected to an axial compressive load. The effect of the thickness of polymer-mortar applied directly to the well-prepared steel surface was studied. The effect of slenderness ratio (kL/r) and width-to-thickness ratio (b/t) on the effectiveness of mortar strengthening was also discussed. Different failure modes are discussed as well as complete axial strength curves are drawn for different cross-sections and member lengths. A maximum axial strength gain of 31.6% was achieved for SHS short columns strengthened with 6 mm thickness polymer-mortar layer. For long columns, a maximum strength gain of 76.7% was achieved with 6 mm thickness polymer-mortar layer applied on four sides. In all mortar-strengthened SHS short and long columns, the axial and lateral deflection, and the axial strain were reduced. The axial strength of SHS long slender columns increased greatly as the overall slenderness ratio increases. Highlights • Cold-formed steel members is an economical alternative in design for low-rise buildings compared to hot-rolled. • Buckling is an important phenomenon to be considered by designers for steel members under compression. • Effectiveness of polymer-mortar strengthening system in increasing the axial strength of slender columns increases greatly as the overall slenderness ratio increases. • The axial strength of HSS columns increases as the plate slenderness ratio (b/t) increases. • Polymer-mortar strengthening system has a great effect on reducing axial, lateral displacement, and axial strain of the strengthened specimens. [ABSTRACT FROM AUTHOR]

• A competitive-failure analysis framework of composite cylinder was proposed. • The material degradation model was adapted to judge the failure mode of composites. • The effectiveness and precision of the proposed framework were validated. • The effects of several design parameters on the competitive-failure were examined. When thin-walled composite cylindrical shells are subjected to combined loads, not only will they buckle, but they could fail under overstressing. Buckling-failure and stress-failure are two types of failure that compete mutually, and if one of them occurs, the structure loses its ability to carry the load. However, there is a lack of study, and very little attention was paid to the competitive-failure of the composite cylindrical shells under combined loads. To bridge this research gap, a competitive failure analysis framework of degraded composite cylindrical shells exposed to combined axial compression and external pressure loads was developed, considering the nonlinear buckling-failure interacting curve approach for buckling-failure analysis and the Tsai-Wu failure criterion for stress-failure analysis. The material degradation model was adopted to modify the properties of the failed ply based on two degrading philosophies. The proposed framework agrees well with the published results. Extensive parametric studies are accomplished and presented to detect the failure mode of composites. For material parametric study, the variation of material properties does not significantly affect the shape of the normalized buckling-failure interacting curve, while it appreciably affects the behavior of the stress-failure interacting curve. Moreover, it is found that as the proportions of the longitudinal compressive strength to longitudinal modulus and transverse tensile strength to transverse modulus of composite materials increase, the tendency for buckling-failure increases; otherwise, stress-failure happens. For a geometric parametric study, decreasing the radius-to-thickness ratio leads to an increase in the shape of the buckling-failure interacting curve and the possibility of stress-failure. [ABSTRACT FROM AUTHOR]

Buckling behavior of cylindrical shells with measured settlement under axial compression has been researched and analyzed in this paper. Using the method of Fourier series expansion, the measured settlement data is transformed into differential settlement. Applying the finite element simulation method, the differential settlement is applied to bottom of the cylindrical shell in order to simulate behavior of the cylindrical shell under differential settlement. Based on the deformed cylindrical shell caused by settlement, the finite element simulation method is applied to research buckling behavior of the cylindrical shell under axial compression considering the geometric nonlinearity and large deformation. The meridional membrane stress distribution in the circumferential direction of the cylindrical shell under differential settlement is obtained and compared with the differential settlement distribution. Effects of liquid storage on buckling behavior of the cylindrical shell are researched by applying hydrostatic pressure to the inner surface. Parametric analysis is carried out to research the effects of diameter-thickness ratio and height-diameter ratio of the cylindrical shell on the axial buckling capability. Results show that the cylindrical shell will be subjected to deformation and meridional membrane stress because of the differential settlement and the critical axial buckling load will be decreased then. Liquid storage is helpful for the cylindrical shell to remain stable. The cylindrical shell with larger height-diameter ratio and smaller diameter-thickness ratio is more capable to resist buckling under axial compression following differential settlement. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a refined model for local buckling of rectangular concrete-filled steel tubular (CFST) columns with binding bars under axial compression due to a deficiency in the previous model i.e. the influences of horizontal spacing and diameter of binding bars were not considered. The influences of longitudinal spacing, horizontal spacing and diameter of binding bars on the critical local buckling stress can be reasonably considered in the proposed model, which is applicable to both elasto-plastic phase and elastic phase. The refined model is verified against the experimental results, showing better agreement than the previous model. Then, the proposed model is employed to investigate the influences of longitudinal spacing, horizontal spacing, diameter of binding bars and cross-sectional aspect ratios on the critical local buckling stress. It is found that the critical local buckling stress increases considerably with the decrease of the spacing of binding bars. Furthermore, the influence of longitudinal spacing of binding bars on the critical local buckling stress is more significant than that of horizontal spacing. It is also found that the critical local buckling stress increase modestly with the increase of diameter of binding bars in the case of small spacing of binding bars. In addition, the cross-sectional aspect ratio have little influence on the critical local buckling stress, which can be ignored. Aiming at delaying the occurrence of local buckling of steel plates in rectangular CFST columns with binding bars, it is suggested that decreasing longitudinal spacing as an efficient measure has priority over other measures. Highlights • A refined model for local buckling of rectangular CFST columns with binding bars is proposed. • The influences of horizontal spacing and diameter of binding bars are considered in the model. • The previous model has been extended to elasto-plastic phase. [ABSTRACT FROM AUTHOR]

Thin-walled cylindrical shell is a fundamental engineering structure which has efficient load-carrying capacity. In practical application, this structure is more easily subjected to localized axial compression loads and is prone to buckling. However, until now there is only limited studies on the buckling problems of multi-region localized axial compression loaded cylindrical shells. To elucidate the buckling behaviors of cylindrical shell under such kind of non-uniform loading condition, experimental and numerical studies are carried out in this paper. Twenty cylindrical shell test specimens with different types of localized axial compression loads are fabricated and tested. The corresponding finite element model considering the measured initial geometric imperfections is established for buckling analysis, and good agreement between the numerical and experimental results is validated. Then the buckling failure mode and axial load-carrying capacity of cylindrical shells are investigated in details. Finally, the imperfection sensitivity of thin-walled cylindrical shell under multi-region localized axial compression is discussed. It is found that the number of loading regions and the total loading area have significant effects on buckling failure mode and axial load-carrying capacity of cylindrical shells. The results obtained from experimental and numerical studies can provide some important guidance or suggestions for the design of thin-walled cylindrical shell structures in actual engineering. • Buckling tests of 20 metallic thin-walled cylindrical shell specimens under multi-region localized axial compression loads were performed. • Finite element model for studying buckling behaviors of cylindrical shell were established. • Buckling failure mode and axial load-carrying capacity of cylindrical shell were systematically investigated for the first time. • Imperfection sensitivity of cylindrical shell under multi-region localized axial compression loads was discussed. [ABSTRACT FROM AUTHOR]

Following the bifurcation approach, a generalized closed form buckling solution for clamped-pinned anisotropic laminated composite columns under axial compression is developed using the energy method. The effective axial, coupling, and flexural rigidity coefficients of the anisotropic layups are determined following the generalized constitutive relationship using dimensional reduction by static condensation of 6×6 rigidity matrix. The presented analytical explicit formula reproduces Euler buckling expression in the case of isotropic or specially-orthotropic materials once the effective coupling term vanishes. On the other hand, the analytical formula furnishes two extra terms which are functions of the effective coupling, flexural and axial rigidity. The analytical buckling formula is confirmed against finite element Eigen value solutions for different anisotropic laminated layups yielding high accuracy for a wide range of stacking sequences. A parametric study is then conducted to examine the effect of ply orientations, material properties including hybrid carbon/glass fiber composites, FE element type, and column size. Relevance of the numerical and analytical results is discussed in comparison to previous results in literature for cross ply laminates. [ABSTRACT FROM AUTHOR]

Lateral buckling is a main failure mode controlling the strength of C- and Z-section purlins under wind suction, as the compressive flange of cross-section is laterally free in this case. The lateral buckling of roof purlins is different from the normally considered simply supported beams, because the top flange of cross-section of these purlins is laterally restrained due to the bracing of the above roof sheeting. To reveal the lateral buckling of C- and Z-section purlins with their top flanges horizontally restrained, two representative buckling theories for the lateral buckling of thin-walled beams, the traditional buckling theory and a new theory recently proposed by the authors of this paper, are adopted in this study. Comparisons made in this study indicate that the total potentials derived from these two theories have different expressions for the considered purlins. Subsequently, the finite element (FE) analysis using the shell element modeling is adopted to examine the buckling loads of purlins based on these two buckling theories, which indicates that the buckling theory proposed by the authors of this paper is more reasonable for this problem. Simple solutions are also proposed for buckling loads of C- and Z-section purlins with their top flange horizontally restrained, and very good agreements are achieved in the comparisons between the predictions of the proposed solutions and FE results. [ABSTRACT FROM AUTHOR]

• Galvanization mostly led to higher compressive load capacity. • Distinct yielding pattern was detected depending on the galvanization. • Unlike standards, ultra-high-strength samples did not experience local buckling. This article reports on an extensive experimental study on galvanized and ungalvanized cold-formed circular hollow sections (CFCHS). All samples were produced by cold-forming thermomechanically rolled steels (TM-steels) in S355, S550, S600, S700, and S960 with high-frequency induction welding (HFI). The test specimens were examined without galvanization, with a pre-galvanization and a post-galvanization. Hardness measurements and microstructural analysis were conducted on seven samples, while the mechanical behavior was examined through 82 tensile and 78 stub-column tests with corresponding imperfection measurements. Despite being classified as prone to local elastic buckling according to international standards, the S960 samples in this study did not exhibit such failure. This suggests that the classification by the codes was conservative. The effects of pre-galvanization on CHS have not been investigated so far, and current findings from literature regarding the impact of post-galvanization on load-bearing behavior suggest a severe capacity decrease for CFCHS in high steel grades. Contrary to previous findings, the current study reveals capacity-enhancing effects resulting from galvanization. Both galvanization types enhanced the stiffness and the cross-section capacity under compression. Galvanization induces changes in material properties, including yield and tensile strength, ductility, and the characteristics of the stress-strain curve. This study serves as a validation base for less conservative yet reliable approaches for the cross-section design of high-strength steel CHS and the utilization of beneficial effects due to galvanization. [ABSTRACT FROM AUTHOR]

In the paper the post-buckling behaviour of thin-walled channel cross-section columns made of Fiber Metal Laminate subjected to an axial compressions is considered. The main interest is focused on the initial imperfection influence on the post-buckling response and thus the sensitivity analysis with application of Monte Carlo simulations is performed. A different shapes and amplitudes of geometrical imperfections – all corresponding to a particular buckling mode or to a few superimposed, have been applied in numerical models. The numerical simulations have been performed using developed FEM software based on Koiter's asymptotic theory for hundreds of buckling mode cases. The obtained results of numerical calculation have been compared with results of experimental investigations. Both - the numerical computations and laboratory experiments were performed on short FML channel section columns with four different layer arrangements. The strain-gauge technique, laser measurement and digital image correlation system were employed to determine deformation modes in laboratory tests. A comparison of the results shows that geometrical imperfections have substantial impact on the post-buckling response of considered columns. [ABSTRACT FROM AUTHOR]

This study aimed to investigate axisymmetric post-buckling behavior of a circular plate made of porous material under uniformly distributed radial compression with simply supported and clamped boundary conditions. Pores are saturated with fluid and plate properties vary continuously in the thickness direction. Governing equations are obtained based on classical plate theory and applying Sanders nonlinear strain-displacement relation. Shooting numerical method is used to solve the governing equations of problem. Effects of porosity coefficient, pore distribution, pore fluid compressibility, thickness change and boundary conditions on the post-buckling behavior of the plate are investigated. The results obtained for post-bucking of homogeneous/isotropic plates and critical buckling load of porous plates are compared with the results of other researchers. [ABSTRACT FROM AUTHOR]

Experimental investigation was conducted on large-section extruded aluminum alloy columns of I-section and rectangular hollow section (RHS). Altogether seven columns with different slenderness ratios were comprised. The failure modes and stability resistance as well as load-displacement responses were identified. It was found that all tested specimens failed in flexural buckling. An extensive parametric analysis on 180 specimens was carried out with general FEA software ANSYS to evaluate the reliability level of the current design specifications including American aluminum design manual, Eurocode 9 and Chinese code GB 50429. The design stability resistance advised by Eurocode 9 and Chinese code GB 50429 is conservative, while that of American aluminum design manual slightly overestimates the practical stability resistance. Based on the parametric analysis results, a new design method was proposed to improve the design accuracy. [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 manuscript employed experimental and numerical procedures to investigate the effects of initial geometric imperfection on the buckling behavior of the perfect and perforated composite cylinders. In the numerical part, linear eigenvalue analysis of the perfect cylinder showed a large discrepancy in comparison to the NASA SP-8007 guideline from 1968. However, results were considerably enhanced by performing a nonlinear analysis where initial geometric imperfection was simulated using Single Perturbation Load Imperfections (SPLI) and Linear Buckling Mode-shaped Imperfections (LBMI) techniques. Numerical analyses were performed for three different groups of the perforated cylinders to evaluate the effect of the growing cutout size on the buckling behavior. In addition, the mutual effect of the cutout and the initial geometric imperfection on the buckling analysis were investigated. Results confirmed that cutout effect is dominant, for the cylinder under consideration, so considering initial geometric imperfection has a negligible effect on the predicted buckling load. In the experimental part, perfect and perforated glass/epoxy composite cylinders with a stacking sequence of [90/+23/−23/90] were manufactured using filament winding technique and tested under compressive axial loading. Buckling test data of the perfect and perforated cylinders showed an acceptable correlation with the numerical results obtained using the nonlinear analyses methods. [ABSTRACT FROM AUTHOR]

The concept of local buckling of compressed isotropic cylindrical shells is developed in this paper. Buckling of axially compressed cylindrical shells under different types of local perturbations has been studied in many theoretical and experimental researches. Different methodologies, based on these studies, were suggested for design buckling load estimation. However, in most calculations and experiments only two classical boundary conditions were considered: fixed displacement of the shell edges in the axial direction or fixed and uniformly distributed compressive load. Both of them are hard or even impossible to realize in practical applications. In the present paper we studied the shell behaviour with 6 different types of boundary conditions, which included the above mentioned two types. We considered shell loading through rigid plates with different types of possible displacements (degrees of freedom) and through stiffening ribs at the edges of the shell. Two theoretical methods were applied: numerical (finite element method) and analytical (Pogorelov's geometrical method). Lateral force was applied as a perturbation and stability of the shell under load combination was studied. The results of calculations were compared with obtained experimental data for validation of numerical solutions. Then metastability and post-buckling behaviour of the structure was studied using theoretical and experimental methods. In particular the interval of existence and stability of post-buckling equilibrium states of the shells with one or several buckles was studied systematically. The post-buckling equilibrium paths and corresponding energy barriers for all mentioned types of boundary conditions were analyzed. Parametric analysis of boundary value problem allowed to establish the main (Batdorf) structure parameter. Formula for design buckling load was suggested and discussed. • The effect of boundary conditions on stability of compressed cylindrical shells under local perturbations is studied. • Results obtained by numerical method are validated by comparison with experimental data. • Post-buckling behaviour and metastability of the structure was studied using analytical, experimental and numerical methods. • Analysis of boundary value problem allowed to establish the main (Batdorf) structure parameter. • Formula for design buckling load is suggested and discussed. [ABSTRACT FROM AUTHOR]

Buckling collapse of thin-walled structures under compression is one of the critical type of failures. These structures also may be locally buckled under tensile load with special conditions. In this paper, compressive and tensile buckling of thin cracked cylindrical panels are investigated. Effects of various factors such as the position, length and direction of crack, length, width and thickness of the panel and boundary conditions on the compressive and tensile buckling loads are determined. The results show that the dimensions of panels have lowest while characteristics of crack and closing to edges have greatest effects on the buckling load. [ABSTRACT FROM AUTHOR]

The issue of buckling load determination in composite channel section beams subjected to pure bending and channel section columns subjected to uniform compression is considered. Some selected problems with determination of buckling load on the basis of the collected and processed experimental data are discussed. The data necessary to determine buckling load (applied load and the corresponding displacement, strains at chosen points of beam-columns and displacements in three perpendicular directions of all visible points of the considered beam-columns) were collected with a strain gauge system, an Aramis ® 3D optical system and a universal testing machine. Buckling load was determined by means of the following well-known methods: the mean strain method, the method of straight-lines intersection on the graph of load vs. mean strains, the curve inflection point method, the load-square of deflection curve method and Koiter’s method. All results were obtained during the experimental investigations and the numerical FEM analysis of the channel section profile made of a GFRP laminate with the symmetrical eight-layer arrangement [45/-45/90/0] s . The profiles under consideration were subjected to compression or pure bending (four-point bending test). The rules for each methods of buckling load determination are proposed on the basis of the obtained results. [ABSTRACT FROM AUTHOR]

In practical engineering, cutouts in thin-walled cylindrical shells are usually welded with ringed stiffeners for the purpose of connect and seal. In this paper, experimental and numerical studies have been conducted to investigate the effects of ringed stiffener on the buckling behavior of perforated cylindrical shells under axial compression. Three test specimens with ringed stiffener and three specimens without ringed stiffener are manufactured and tested. The mid-surface imperfections of all specimens are measured and introduced into the finite element model. The finite element method using static analysis with artificial damping is used to simulate the displacement controlled compression tests. Good agreement is found between the numerical and experimental results. It is found that the global buckling loads of perforated shells are improved by ringed stiffener. The larger the cutout size is, the more obvious improvement shows. In addition, effects of ringed stiffener on axial stiffness and imperfection sensitivity of perforated shells are studied in details. The relationship between ringed stiffener thickness and global buckling load of perforated shell is also discussed. Meanwhile, a critical thickness parameter k of approximately 15% is proposed. [ABSTRACT FROM AUTHOR]

Abstract: An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. A formulation combining the Rayleigh–Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments. [Copyright &y& Elsevier]

Abstract The present research is aimed at verifying design rules for cold-formed steel (CFS) members under axial compression when local-distortional buckling modes (LD) is achieved. Sets of experimental results previously available were applied to calibrate a shell finite element model addressed to survey the structural behavior of CFS lipped channels under LD bucking interaction. A large range of distortional-local slenderness ratio was considered in order to obtain numerical results of LD interaction including strong and weak interaction conditions. Based on both experimental and numerical results, the nature of LD interaction was assessed and the column strength variation was observed according with the representative slenderness variables, λ L , λ D and R λDL , respectively local and distortional slenderness factors and distortional-local slenderness ratio λ D / λ L. The column strength variation was established based on the Winter-type equation, conceived to cover the complete range of LD interaction. The proposed solution follows the direct strength method concept, is easy to apply and accurate enough for the structural design of lipped CFS columns. Additional research is under way to include other CFS types in the proposed design approach. Highlights • Local-distortional interaction buckling mode of CFS lipped channel columns. • Original direct strength method-based approach for structural design of columns. • Original experimental results of columns affected by LD buckling interaction. [ABSTRACT FROM AUTHOR]

This paper considers local buckling of perforated square aluminium plates. Plates of various slenderness with simply supported edges and subjected to uniaxial compression are studied using the finite element method. Different perforation patterns are investigated, from a single circular hole to 25 circular holes distributed over the plate. A number of aluminium alloys are considered and compared to steel grade A36. Results show that the resistance of the plates containing a single central cut-out is higher than that of plates with more holes and of equal total cut-out size. A further refinement beyond 5 holes does not influence the resistance. [ABSTRACT FROM AUTHOR]

This paper examines the buckling of short mild steel cylindrical shells subjected to axial compression. Cylinders were joined together using Metal Inert Gas (MIG) welding process with radius-to-thickness ratio, R / t , ranging from 25 to 100. The axial length of the specimens were assumed to be 111.8 mm. Past result on axially compressed cylinder machined using Computer Numerically Controlled (CNC) machining is compared with fresh experimental results on MIG manufactured axially compressed cylinder. The paper contains a comparison between theoretical predictions, ABAQUS FE results and experimental data for axially compressed cylinder. Details about material testing and collapse test are provided. As compared to the CNC machined specimen, results indicates that there is a good agreement between theoretical prediction, ABAQUS FE results and experimental data for MIG manufactured cylinder with radius-to-thickness ratio, R / t ranging from 25 to 100, with difference ranging between −7% and +2%. [ABSTRACT FROM AUTHOR]

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members. [ABSTRACT FROM AUTHOR]

Abstract: To date, despite the significant development in the field of structural mechanics, there still remains a paradox in the solutions available for a classical shell buckling problem. The difference in strength between a cylindrical shell under uniform axial compression and that under pure bending is not quite well investigated. This lack of research is reflected in the wide variations in the elastic bending strength and the slenderness limits given in current international design standards. The discrepancies in the available classical solutions and hence the design rules have initiated the current research. The main aim of this paper is to present a closed-form solution for the elastic buckling strength of unstiffened circular cylinders under pure bending using a new simplified energy approach employing the well-known Ritz method. Two types of analyses are presented for cylinders with large (D/t>200) and medium (100

Lateral–torsional buckling (LTB) resistance of an I-beam depends on the minor axis moment of inertia of its compression flange and torsional rigidity of the section. A practical solution to increase lateral buckling of I-beams is to add two Delta stiffeners between the compression flange and web plates to form a hollow compression flange. Although these beams known as Delta hollow flange beams (DHFBs) have been introduced about half a century ago for bridge construction, however, their LTB behavior has not been investigated, yet. This paper develops a three dimensional finite-element model using ABAQUS for the inelastic nonlinear flexural–torsional analysis of DHFBs and uses it to investigate the effects of unbraced length and central off-shear center loading (located at center, top flange and bottom flange) on their moment gradient factor in different behavioral zones. It was found that the C b factor and moment resistance curve given by AISC-LRFD in Specification for structural steel buildings [2] are not accurate for intermediate (inelastic) and short plastic DHFBs leading to an unconservative design. Therefore, a modified moment resistance equation is proposed to be used instead of the code equation in inelastic zone for the investigated load cases in this paper. [ABSTRACT FROM AUTHOR]

In this work, experimental and numerical studies are conducted to explore the buckling behaviours of cylindrical–conical–cylindrical assembly shells under axial compression at elevated temperature. Firstly, bucking experiments of six test specimens at 600 °C are carried out. Then, numerical method considering initial geometric imperfection is used to predict buckling behaviours of these assembly shells. Furthermore, the effects of key factors on buckling behaviours of cylindrical–conical–cylindrical shells are also discussed. Results indicate a good agreement between experimental data and numerical result based on the model with measured geometric imperfection, and the shell model with measured outer surface imperfection is adequate for buckling analysis. Comparatively, the buckling load predicted by the model with eigenmode imperfection is reasonably conservative compared with experimental result only when the amplitude of imperfection is close to the measured imperfection amplitude. In addition, the effects of material properties and geometry parameters, e.g., yield stress, ratio of radius to shell thickness and semi-vertex angle, on the load-carrying capacity and buckling mode of cylindrical–conical–cylindrical shells are investigated systematically. Finally, a strategy for buckling analysis of cylindrical–conical–cylindrical shells is proposed. • Buckling mechanism of cylindrical–conical–cylindrical shells under axial compression at elevated temperature is elaborated. • Shell model with measured outer surface imperfection or eigenmode imperfection is recommended for buckling analysis. • Key factors effects on load-carrying capacity and buckling mode of cylindrical–conical–cylindrical shells are discussed systematically. • A strategy for buckling analysis of cylindrical–conical–cylindrical shells is proposed. [ABSTRACT FROM AUTHOR]

The axial compressive buckling loads of shape memory polymer composite (SMPC) cylindrical shells are very sensitive to geometric imperfections and temperatures, but few studies have been conducted on this phenomenon. In this study, the buckling loads and geometric imperfection sensitivities of SMPC cylindrical shells at different temperatures are determined by means of numerical simulations and experimental analyses. The single perturbation displacement imperfection (SPDI), multiple perturbation displacement imperfection (MPDI) and linear buckling mode imperfection (LBMI) techniques are used to simulate the initial geometric imperfections and calculate the corresponding buckling loads and knock-down factors (KDFs) of SMPC cylindrical shells at different temperatures. In the experimental part, the [ 0 / 90 / ± 45 ] s SMPC cylindrical shells are manufactured through the autoclave molding process. The load-bearing capacities at different temperatures are tested and compared with the numerical results. The results demonstrate that the buckling loads of the SMPC cylindrical shell obtained by numerical techniques are sensitive to temperature, while the KDFs are insensitive to temperature. Meanwhile, results indicate that brittle fracture is the main failure mode instead of buckling at low temperature, so there is a risk when using any numerical technique to design SMPC cylindrical shells in low-temperature region. At high temperatures, the SPDI method overestimates the KDFs, while the KDFs calculated by the MPDI and LBMI techniques are in good agreement with the experimental results. However, only the LBMI method can distinguish the influence of temperature on the post-buckling patterns, and the corresponding post-buckling pattern is more consistent with the experiment. In addition, the shape-recovery properties and repeatability of the SMPC cylindrical shells are good. • The buckling loads of the SMPC cylindrical shell obtained by numerical techniques are sensitive to temperature, while the KDFs are insensitive to temperature. • In the low-temperature region, the SMPC cylindrical shell is more prone to brittle fracture than buckling deformation during the axial compressive experiment. In the high-temperature region, the SMPC cylindrical shell buckles before being destroyed. • An assumption of the potential application of SMPC cylindrical shells is proposed. [ABSTRACT FROM AUTHOR]

Based on the Galerkin method, a semi-analytical solution for the shear buckling of composite laminated plates with all four edges elastically-restrained against rotation is presented. The considered laminated plates are loaded in pure shear or combined shear and compression. The deformation shape function is constructed through a unique weighting combination of vibration eigenfunctions of simply-supported and clamped conditions, and it is an effective method for solving the considered eigenvalue problem. A parametric study is conducted to evaluate the effect of the rotational restraint stiffness, plate aspect ratio, material orthotropy and anisotropy on the buckling behavior of the rotationally-restrained laminated plates under pure shear or combined shear and compression action. The semi-analytical solution presented can be used to analyze the restrained laminated plates under shear-dominated loading and applied to predict the web local buckling of thin-walled composite beams. [ABSTRACT FROM AUTHOR]

Six aluminum alloy tensile coupon tests were carried out and stress–strain curves obtained from tests were compared with a Ramberg–Osgood model. Comparison showed that the Ramberg–Osgood model can precisely describe stress–strain relationship of 6063-T5 aluminum alloy. Totally, 10 axial compression tests on thin-walled aluminum alloy members with four stiffened closed-section were carried out. Local buckling occurred in all specimens eventually. The axial displacement, lateral deflection, strain development and failure modes of the tested specimens were recorded. A finite element method (FEM) model was presented to simulate local buckling behaviors of the tested columns under axial load. The ultimate strength, strain development and failure modes obtained from FEM agreed well with the test results. Current design codes on aluminum alloy structures, such as the American aluminum design manual (AA), the European code (EC9), Chinese design specifications for aluminum structures (GB50429), the North American Specification for the design of cold-formed steel structural members (AISI) and the direct strength method (DSM), were used to calculate the ultimate strength of the tested columns. Comparison showed that current design codes overestimated the ultimate strength of stiffened closed-section thin-walled aluminum alloy columns under axial compression loads. [ABSTRACT FROM AUTHOR]

The paper deals with buckling of short thin-walled lipped-channel columns, simply supported on both ends and subjected to uniformly distributed compressive load. The main objective of the study was to investigate the structure׳s work in far post-buckling state and at collapse corresponding to the moment of the column׳s stiffness loss. The following measuring devices and methods were applied: electrical strain gauges for strain measurements, a laser sensor to measure the displacements, and the Acoustic Emission method. Along with running the experimental tests, the non-linear stability of compressed composite columns was analyzed with the Finite Element Method. The numerical and experimental results showed good agreement. [ABSTRACT FROM AUTHOR]

One of the most effective nondestructive methods to estimate the buckling load of imperfection sensitive thin-walled structures is vibration correlation technique (VCT). Although this technique can determine the buckling load for several types of structures without reaching the instability point, it is still under development for composite sandwich plates and shells. In this paper, experimental and numerical verification of VCT approach are presented for the estimation of the buckling load of the composite sandwich plates with iso-grid cores loaded in compression. In the experimental section, four specimens are designed and fabricated using a new silicone rubber mold, and hand lay-up technique. The modal test is performed on the first specimen by exciting the sandwich plates using the modal hammer method in the different applied loads. Then, the variation of the natural frequency with the applied compressive load is recorded up to actual experimental buckling load. Besides, numerical models, including nonlinear effects, are created in full details to calculate the variation of the natural frequencies with the applied load, and to be compared with the experimental results. Finally, the buckling test is carried out on all specimens to validate the experimental and numerical results of VCT approach. The results demonstrate that the maximum difference between the predicted buckling load using the VCT approach on the experimental and numerical results with an experimental buckling load is less than 3%. Also, VCT provides a reliable estimate of buckling load when the composite sandwich plates with iso-grid cores have been loaded up to at least 67% of the experimental buckling load. • Experimental and numerical validation of VCT approach were presented for the estimation of the buckling load of the composite sandwich plates with iso-grid cores. • The modal analysis of the composite sandwich plates with iso-grid-cores was performed using the modal hammer method. • Finite element models, including nonlinear effects such as geometric and thickness imperfection, was performed. • The maximum difference between the predicted buckling load using the VCT approach on the experimental and numerical results with an experimental buckling load was less than 3%. • It was shown that VCT provides a reliable estimate of buckling load when the composite sandwich plates with iso-grid cores have been loaded up to at least 67% of the critical load. [ABSTRACT FROM AUTHOR]

The paper is devoted to a thin-walled rectangular frame. The frame is simply supported in the planes of symmetry and in-plane compression forces are applied in the corners. The longitudinal and transverse thin-walled beams of the frame are rigidly joint at the corners. Two buckling forms of the frame are studied. The analytical and numerical-FEM (SolidWorks) models are formulated. The results of the studies are presented in Tables and Figures. [ABSTRACT FROM AUTHOR]

Sandwich structures are important structural members in modern lightweight engineering. Accurate and effective buckling predictions are vital to the design and optimization of sandwich structures. This paper extends and validates a homogenization theory namely the mechanics of structure genome (MSG) in predicting eigenvalue buckling of sandwich structures under compressive and bending loads. Global buckling is predicted on a homogeneous plate with effective plate properties computed by MSG. Local buckling is predicted by perturbing the fluctuating function of structure gene under Bloch-periodic boundary conditions. Accuracy of buckling predictions is validated by three-dimensional finite element analysis. • Mechanics of structure genome for global and local buckling of sandwich structures. • Buckling of sandwich structures under both compressive load and bending load. • Bloch-periodic boundary conditions used in mechanics of structure genome models. • New buckling modes including type II flexural modes and torsional modes identified. [ABSTRACT FROM AUTHOR]

Abstract: The unified formulations of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) and the principle of virtual displacements (PVD) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders and laminated composite ones under combined axial compression and external pressure. In this work, the material properties of the FGM layer are assumed to obey the power-law distributions of the volume fraction of the constituents through the thickness coordinate, and full kinematic nonlinearity is also considered. The accuracy and convergence of the RMVT- and PVD-based FCLMs are assessed by comparing their solutions with both the exact 3D and accurate two-dimensional (2D) solutions available in the literature. A parametric study for variations of the lowest critical load parameters with the material-property gradient index, the load intensity, and the orthotropic, length-to-radius, and radius-to-thickness ratios is carried out. [Copyright &y& Elsevier]

Abstract: This paper presents a finite element (FE) study on fixed-ended LDSS slender hollow columns with square (SHC), and non-rectangular hollow columns (NRHCs) viz., L- (LHC), T- (THC), and +- (+HC) shaped cross-sections subjected to pure axial compression using Abaqus software. SHC columns with thicknesses of 5.25mm and 2.0mm, which lie in Class 3 (stocky) and Class 4 (slender) sections, respectively, as per EN 1993-1-4 were considered in the study as referral sections. Variations in buckling strength with changes in the cross-sectional shapes were studied by considering NRHCs having equal material cross-sectional areas (or equal material consumption) as that of SHCs over a range of column lengths. The FE results of SHC and NRHCs were then compared with the design strengths predicted by the EN1993-1-4 and ASCE 8-02 specifications. Good agreements between the FE strengths and codal predictions have been observed, except for the ASCE 8-02 prediction of LHC where it over predicts the FE strengths. At both the slenderness regime (i.e., low and high slenderness values) of Class 3 sections and high slenderness regime of Class 4, all the sections exhibit similar structural capacities. Cross-sectional shape is found to become increasingly significant with decreasing member slenderness in Class 4 sections. In Class 3 sections, compared to SHC there is a nearly linear variation in strength (increased for +HC, similar behavior for THC and decreased for LHC) up to ∼2.0, then it stabilizes out. After, ∼2.0, P u for +HC showed ∼30% higher; THC showed similar strength; and LHC showed∼20% lower than the corresponding value for SHC, indicating that +HC has an improved ultimate strength for all the ranges of . The strength enhancement as compared to that of SHC are ∼10%, 50%, and 90% higher for LHC, THC, and +HC, respectively, for Class 4 sections. Based on the reliability analyses it is recommended that both the codes can be adopted for all the design of fixed-ended LDSS columns except for LHC, wherein a suitable modification may be employed after systematic studies. [Copyright &y& Elsevier]

In this study, a detailed experimental investigation of 29 extruded columns with box-type and L-type sections made of 6082-T6 aluminum alloy, was carried out to study the stability behavior of these columns when subjected to eccentric loads. Finite element (FE) models of all tested columns under eccentric loads were developed using the ABAQUS software package. The precision and utility of these FE models were verified by experimental data. Both the stability bearing capacity and deformation performance were evaluated. Using the proposed FE models, an extensive parametric study was performed to investigate the effects of section dimensions, slenderness ratio, and eccentricity on the stability bearing capacity of the eccentrically loaded columns. The test and parametric study results were compared to the design capacity predictions in the current Eurocode 9 and the Chinese Code for the Design of Aluminum Structures, GB 50429. It was found that the predicted stability bearing capacities in the two design codes was generally conservative for the eccentrically loaded columns made of 6082-T6 aluminum alloy. Several parameters of the design formulae from the Chinese Code were modified to predict the ultimate strength of 6082-T6 aluminum alloy columns more accurately. [ABSTRACT FROM AUTHOR]

The present work investigates the elasto-visco-plastic buckling of thick plate structures. Methods to estimate the buckling of thin elasto-visco-plastic shells and plates are proposed in literature. To the knowledge of the authors, only few works present experimental results, and none treat the experimental elasto-visco-plastic buckling of thick plate. Thick rectangular plates are chosen as a structure of interest to study elasto-visco-plastic buckling. A modelling/experimental approach is followed to solve such problem. Buckling experiments at room temperature on thick elasto-visco-plastic plates subjected to compressive load are performed. 3D digital image correlation (3D-DIC) is used to measure displacement fields on plate surface during buckling experiments. The experiments are also modelled through a finite element model. Bodner 's approach is coupled to Hencky 's deformation theory to predict buckling of elasto-visco-plastic plates. Bifurcation analysis are performed to estimate buckling critical stresses and strains, and buckling modes. Geometrical and loading imperfections are also discussed. A good correlation is observed between numerical results and experiments. The limitation of Bodner 's approach is also discussed. • Original buckling criterion for thick elasto-visco-plastic plates. • Buckling experiments on plates with several shapes and strain rates. • 3D-DIC used to extract buckling modes. • Observation of mode proximity and successive bifurcations. • Numerical/experimental validation of the buckling criterion. [ABSTRACT FROM AUTHOR]

This paper presents general explicit analytical formulae to provide distortional critical stress estimates for cold-formed steel C-section columns subjected to uniform compression. These formulae are derived by employing the Lau and Hancock model and by introducing a new factor for considering the web rotational restraint reduced by web bending. The results obtained from the general explicit analytical formulae are compared with the numerical results obtained from the computer programs CUFSM or/and GBTUL. For pinned-ended columns, these values are also compared with those yielded by the formulae developed by Lau and Hancock, Schafer, and Silvestre and Camotim. In particular, the distortional critical stress of fixed-ended C-section columns is validated by comparing the corresponding ultimate load based on Schafer’s DSM expressions with numerical results from the research literature. The formulae derived here are validated and their application, accuracy and capabilities are illustrated by these comparisons and validations. [ABSTRACT FROM AUTHOR]

This paper introduces two semi-analytical models developed for the nonlinear analysis of stability of isotropic and orthotropic plates under uniaxial compression. The possibility of considering fully free in-plane displacements at longitudinal edges (or unloaded edges) is the innovation of these models over existing models, where these displacements are always assumed constrained to remain straight. Contributions for the large deflection theory of plates related to the derivation of analytical solutions for the Airy stress function which satisfy Marguerre?s equations for isotropic and orthotropic plates are presented. Namely, the extension of the Coan and Urbana solution for isotropic plates in order to consider all the terms of the unknown amplitudes of the out-of-plane displacements and the derivation of a solution for orthotropic plates. Comparisons between the semi-analytical model and nonlinear finite element model results are presented in order to discuss the effect of in-plane displacement boundary conditions on behaviour and strength of plates similar to bottom flanges used in steel box girder bridges. This study shows that the semi-analytical models have a clear potential to provide accurate solutions, requiring only a short computer time. It is also shown that the in-plane displacement boundary conditions for the unloaded edges significantly influence the behaviour and strength of plates and this problem cannot be neglected in the definition of the design rules. [ABSTRACT FROM AUTHOR]

Abstract: A recently developed inelastic large displacement isoparametric spline finite strip method was used to investigate the inelastic stress distributions, load transfers and failure modes for a range of hole shapes, sizes and spacings. While such study is available for elastic material behaviour, the influence of yielding on the load transfers in and failure modes of perforated plates and sections is not well understood. This study considers perforated simply supported plates under compression and perforated C-section columns in compression failing by local buckling. Several inelastic material models were included in the study, including elastic perfectly-plastic and linear hardening models, and a model with nonlinear yielding and isotropic hardening. Comparisons are made with elastic analyses and conclusions are drawn about the influence of yielding and strain hardening on the stress distributions, load transfers and failure modes of typical thin-walled metallic plates and structural sections. [Copyright &y& Elsevier]

An imperfection sensitivity analysis of thin-walled cold-formed steel members in compression is presented. The members under investigation are perforated steel pallet racks in compression of different lengths. The analysis is based on a finite element implementation of the Koiter method coupled with Monte Carlo simulation. It is based on an intensive experimental study carried out at the Politehnica University of Timisoara, which showed a strong interaction of the buckling mode with a significant reduction in the load carry capacity. Using Koiter's method the limit load is evaluated statistically analysing thousands of geometrical imperfections. Based on this, the worst combination of imperfections is detected and the erosion of the critical buckling load due to imperfections and modal interaction, is evaluated. A critical discussion of the results is presented with reference to some aspects of Koiter's analysis and how to use these in subsequent GMNIA analysis to account for the nonlinear effects of the material due to plasticity. [ABSTRACT FROM AUTHOR]

This work proposes a new generation of energy dissipating system based upon an original patented mechanical assembly: the Absorption par Compression–Torsion Plastique (ACTP) presented in Abdul-Latif and Baleh (2005). 1 1 Patent no. WO 2005090822. In fact, the ACTP transforms a uniaxial external loading into biaxial compression–torsion, where several degrees of biaxial loading paths complexity can be created within the loaded tubes. Such a concept which aims to enhance the strength properties of material is now extended to study the biaxial plastic buckling of different materials, and different cross sections under further severe loading conditions. The intention of this comprehensive experimental study is to further investigate a new severe loading configuration under quasi-static strain regime. Thus, five inclination angles (30°, 37°, 45°, 53° and 60°) are tested using circular and square tubes made from copper and aluminum alloy, respectively. An integrity measure of the mean collapse load and the corresponding energy absorbed shows that the higher the inclination angle (i.e., the higher loading complexity), the greater the rates of change of torsional component, and the greater the mean collapse load, and the corresponding energy absorbed in copper and aluminum tubular structures. [ABSTRACT FROM AUTHOR]

The buckling and post-buckling behaviour of thin-walled Fibre Metal Laminate (FML) profiles subjected to axial loading is discussed. Study concerns open cross-section profiles which consist of alternating thin layers of aluminium and fibre-reinforced unidirectional prepreg. Laboratory tested specimens were manufactured by autoclaving technique. Depending on fibres alignment, various 3/2-layer stacking were considered and subjected to axial compression in buckling tests. Carrying out an experiment allowed one to determine buckling load and equilibrium paths in buckling and post-buckling state. The results of substantial experimental investigations were compared with FML panel/columns modelling in FEA and with analytically examined based on Koiter's asymptotic theory. In conducted experiments the careful design of simply support boundary conditions of loaded edges of thin-walled columns is examined and discussed. Detailed analysis was also performed to assess the influence of the various fibres alignment on the specimen buckling and post-buckling response. [ABSTRACT FROM AUTHOR]

Multi-celled concrete filled steel tubular wall (MCFSTW) is an innovative shear wall member which is formed by welding multiple U-shaped cold-form steels together and filled with concrete. The global buckling performance of composite walls is of great concern, especially with the increasing wall height in engineering practice. In this research, the global buckling behavior of MCFSTWs with four simply-supported edges is studied. A refined finite element (FE) model was established and validated by comparing it with previous test results. Then, a numerical parametric study was conducted to investigate global buckling behavior influenced by various parameters including: geometrical dimensions, initial imperfection and material strengths. Based on an orthotropic plate model, an analytical study was performed to derive the theoretical formulas for predicting the elastic buckling loads of MCFSTWs with four simply-supported edges. According to FE eigenvalue buckling analysis results, the obtained theoretical formulas were further modified to fit well with the FE results, thus providing better predictions of the elastic buckling loads of MCFSTWs. Finally, a design curve in a form of φ - λ n relationship was proposed on the basis of the results obtained from numerous FE models with an imperfection amplitude of w 0 = a /500. The design curve is capable of conservatively predicting the ultimate resistance under axial compressive load, thus it could provide valuable references for designing MCFSTWs with four simply-supported edges. • Global buckling behavior of MCFSTWs with four simply-supported edges is studied. • Refined FE model is established and validated against tests. • Parametric study is conducted and b/h < 40 is required to prevent global buckling. • Analytical study is performed to derive the elastic buckling formulas of orthotropic plates. • A φ - λ n design curve is proposed for designing MCFSTWs subjected to global buckling failure. [ABSTRACT FROM AUTHOR]

Beetle elytron plate (BEP) is a biomimetic sandwich structure inspired by the internal architecture of beetle elytra and characterisedby trabeculae in the core. This type of structure has been shown to possess superior mechanical properties to conventional sandwich plates; however, there are no studies that evaluate its structural bending resistance. This paper develops an analytical method to calculate the key component of bending resistance of BEPs: the elastic local buckling load of the compression skin. It assumes that the compression skin of BEPs is simply supported by the trabecular core. After eliminating local buckling in the edges of the compression skin outside the trabeculae, two buckling zones, depending on the ratio (η) of trabecular radius to the distance between two adjacent trabeculae, are identified. At low η values (η ≤ 0.25), elastic buckling occurs in the space of the compression skin surrounded by four adjacent trabeculae. Beyond the critical value of η (η >0.25), buckling occurs in the compression skin enclosed by individual trabecula. Guided by finite element simulation results, this paper identifies a new suite of deformation shape functions and derives local elastic buckling load for the compression skin according to the principle of minimal total potential energy. Afterwards, a convenient quadratic polynomial regression equation is proposed to modify the elastic buckling coefficient of the compression skin of equivalent conventional grid honeycomb sandwich plates, with the maximum difference between analytical calculation results and finite element simulation results being about 7%. • Finite element modelling of the behaviour of local buckling of the compression skin of beetle elytron plate. • Analytical derivation of local buckling load of the compression skin of beetle elytron plate. • Regression equation based on the compression skin of honeycomb sandwich structure. [ABSTRACT FROM AUTHOR]

The elastic buckling load of an axially compressed piecewise member was derived under various ideal boundary conditions based on the differential element method; then, the result was simplified for a symmetrical member. The theoretical results were found to be consistent with existing formulas for the elastic buckling load of uniform members. Then, the elasto-plastic buckling of an axially compressed piecewise member composed of steel and elastic materials was investigated and found to be quite different from that of a pure steel member, and a theoretical analysis approach was developed. In elasto-plastic buckling analysis, the load-bearing capacity of the steel section in the ultimate state is determined considering initial imperfections and steel hardening. Furthermore, the symmetric method for obtaining the load-bearing capacity of this member was obtained based on the ultimate state of the critical section, which is simple and reparative for design. The theoretical results of the elasto-plastic buckling analysis were consistent with experimental results, therein obtaining an average error of 4%. [ABSTRACT FROM AUTHOR]

Interacted buckling behaviors and ultimate strength of thin-walled aluminum alloy columns with irregular-shaped cross section were studied using a verified Finite Element Model (FEM). Six interacted buckling failure modes were studied, which were: (1) the interaction of Local bucking and sectional Yielding (LY); (2) the interaction of Local and Global buckling (LG); (3) the interaction of Distortional buckling and sectional Yielding (DY); (4) the interaction of Distortional and Global buckling (DG); (5) the interaction of Local bucking, Distortional bucking and sectional Yielding (LDY or DLY); and (6) the interaction of Local, Distortional and Global buckling (LDG). The load-axial displacement curve, the deflection-axial displacement curve, the development of the axial stress at different positions in the section at mid-span, the out-of-plane displacement at failure along the column length and the axial stress distribution at failure across the section at mid-span were presented. The local buckling and distortional buckling were detected by the turning points on the load-axial displacement curves. The out-of-plane displacement along the column length at failure was used to illustrate the failure mode of the column. Ultimate strengths and failure modes of 174 columns failed by interacted buckling failure modes were investigated by both FEM and current design approaches. For the ultimate strength of the columns under DY failure mode, the results predicted by North American specification for the design of cold-formed steel structural members of American Iron and Steel Institute (AISI) were higher than FEM simulation results. The ultimate strength predicted by American Aluminum Design Manual (AA), Direct Strength Method (DSM), European Code (EN1999) and Chinese Design Specification for Aluminum Alloy Structures (GB50429) were lower than FEM simulation results, no matter what kind of failure modes the column encountered. Mean values of P AA / P FEA , P EC9 / P FEA and P GB / P FEA were 0.81, 0.79 and 0.74. DSM could precisely predict the Global buckling (G), LG and DY failure modes. However, for the columns failed by LY, DG, LDY and LDG, they were LG, G, DY and LG when predicted by DSM, respectively. The applicability of DSM to thin-walled aluminum alloy columns with irregular-shaped cross section should be investigated further. [ABSTRACT FROM AUTHOR]

In this work, parametric finite element models are used to generate new design charts that provide the local buckling coefficient (k s l) of integrally web-stiffened panels (ISPs) subjected to uniaxial compressive loads, including the fillet radius effect. The numerical results from linear buckling analyses of hundreds of different panel geometries are presented in terms of four non-dimensional parameters: t w / t s , b w / b s , t s / b s and R / b w f , whereby the latter represents the effect of the fillet radius on k s l. An extensive survey based on ISPs geometries used in different types of aircraft wings was conducted to define the ranges of these four ratios. Within each range, discrete values of the four ratios were chosen and randomly combined to enable the construction of the finite element models used to obtain the new k s l curves. The proposed finite element modeling was validated by comparing the results with numerical and experimental results from the literature, showing a good agreement. Compared to non-filleted ISPs results, it is shown that the local buckling stresses of filleted ISPs may be significantly increased, allowing designers to optimize different ISPs geometries. • Local buckling coefficients of integrally stiffened panels with filleted junctions are presented in tabular form. • Results are presented in non-dimensional quantities, allowing the use for different panel geometries. • Results can be easily implemented in numerical programs to provide local buckling stresses for different geometries. • Finite element results were compared with other numerical and experimental results showing a good agreement. • Geometries considered in this work are based on wing upper panels found in commercial aircraft of large and medium sizes. [ABSTRACT FROM AUTHOR]

There are two aims in the present paper. The first one is to see and understand the detailed buckling process, especially the interactions between material nonlinearity and geometric nonlinearity on the post-buckling stage, of stiffened panels subjected to in-plane compressive load. The second one is to validate the similarity criteria of designing different sizes of stiffened panels which have the same buckling modes and proportional ultimate strength. These similar relationships make it possible to predict the buckling behavior and ultimate strength of a full-size structure by testing its scale-down model. To these ends, three different sizes of stiffened panels with the same flexural rigidity ratio, plate slenderness and column slenderness, were designed, manufactured and tested. In order to trace and analysis the detailed buckling process, three-dimensional digital image correlation (3D-DIC) method was employed. So, the integrated evolution process of global deformation and strain distribution fields of the stiffened panels were obtained. These data also provide accurate data to verify the numerical or theoretical method in predicting the bulking, especially post-buckling process and ultimate strength of stiffened panel. Results show that the three stiffened panels have reasonable similarity relationships of the buckling failure process. Finally, finite element models with measured initial imperfections were established to reappear the experimental process. The numerical results agree well with the experimental data. • Experiments of stiffened panels subjected to in-plane compressive load were performed. • The detailed buckling process of the stiffened panels were obtained by employed the 3D-DIC method. • Similarity relationships of buckling behavior and ultimate strength of the different stiffened panels were derived and analyzed. • Numerical simulations faithfully reproduced the detailed buckling process of the stiffened plates. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation on the local buckling behaviour of high strength steel (HSS) and hybrid I-sections under axial compression, which has not been comprehensively discussed in previous literature. Three sectional steel combinations, featuring different web strength grades (Q690, Q460, and Q355) and using HSS Q690 flange plates, were studied. Through the validated numerical method, parametric studies on the effect of web strength grade, boundary condition and plate slenderness were carried out. The design specifications in European, Australian, and American codes were evaluated using the results of 243 numerical models and collated test data. In addition, the continuous strength method (CSM), direct strength method (DSM), and Kato's method, which can account for element interaction were extended to design for the local buckling behaviour of HSS and hybrid I-sections subjected to axial compression. Assessment results showed that ANSI/AISC 360-16 provides more accurate results than Eurocode 3 and AS 4100. Statistical and reliability results demonstrated the satisfactory reliability level of the proposed design expressions for CSM, DSM, and Kato's design methods. This paper provides insight into the local buckling behaviour and mechanism behind plate interaction of hybrid I-sections. • Three web strength grades-Q690, Q460 and Q355 are considered for welded I-sections with Q690 flange. • A parametric study of 243 numerical models for welded I-sections under axial compression is carried out. • Critical plate element governs the local buckling behaviour of welded I-sections in compression. • Normalised ultimate loads of welded I-sections are marginally affected by the web strength grade. • Newly developed design methods, including the direct strength method, the continuous strength method, and the method by Kato are extended. [ABSTRACT FROM AUTHOR]