Showing papers in "Thin-walled Structures in 2008"

Concepts for morphing airfoil sections using bi-stable laminated composite structures

Abstract: The present paper investigates the potential of using bi-stable laminated composite structures for morphing an airfoil section. The objective of the paper is to identify geometries and lay-ups of candidate configurations that offer multiple stable shapes for the airfoil section. Carbon-fiber laminated composites with non-symmetric laminate configurations are used for morphing the airfoil section. Thermal curing is used to induce residual stresses into the structure in order to achieve bi-stability. Three concepts that focus on morphing a flap-like structure and the camber and chord of an airfoil section are proposed. Several geometries and laminate configurations are investigated using finite element nonlinear static analysis. The magnitude of loads required to actuate the airfoil section between the stable shapes is evaluated. The impact of manufacturability on producing viable morphing mechanisms within the airfoil section is also discussed.

Robust design of composite cylindrical shells under axial compression — Simulation and validation

Abstract: Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.

An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory

Abstract: Analytical investigation of the free vibration behavior of thin circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material based on the classical plate theory (CPT) is presented in this paper. The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from three-dimensional finite element analyses.

Optimization of the foam-filled aluminum tubes for crush box application

Abstract: Axial impact crush tests on empty and foam-filled square aluminum tubes have been performed. Furthermore, in order to find more details about the crush processes, finite element simulations of the experiments have been done. In terms of finding more efficient and lighter crush absorber and achieving maximum energy absorption, multidesign optimization (MDO) technique has been applied for optimizing the square rectangular tubes. Based on practical requirements the optimum tube geometry, which absorbs maximum energy and has a minimum weight, has been determined. Results of previous work indicated that using high density honeycomb for filling the tubes will results more energy absorption but the weight efficiency has been lost [Zarei HR, Kroger M. Optimum honeycomb filled crash absorber design. Mater Des 2007;29:193–204]. Therefore, a comprehensive study has been performed in order to find out the crush behavior of tube filled with foam with different densities. The MDO procedure has been implemented to find an optimum filled tube that absorbed the same energy as an optimum empty tube can absorb.

Strength and ductility of stiffened thin-walled hollow steel structural stub columns filled with concrete

Abstract: It is generally expected that inner-welded longitudinal stiffeners can be used to improve the structural performance of thin-walled hollow steel structural stub columns filled with concrete. Thirty-six specimens, including 30 stiffened stub columns and six unstiffened ones, were tested to investigate the improvement of ductile behaviour of such stiffened composite stub columns with various methods. The involved methods include increasing stiffener height, increasing stiffener number on each tube face, using saw-shaped stiffeners, welding binding or anchor bars on stiffeners, and adding steel fibres to concrete. It has been found that adding steel fibres to concrete is the most effective method in enhancing the ductility capacity, while the construction cost and difficulty will not be increased significantly.

Experimental behaviour of high performance concrete-filled steel tubular columns

Abstract: In recent years, the utilization of high performance concrete has been the interests of the structural engineers and researchers. As a high performance concrete, self-consolidating concrete (SCC) is a highly flowable concrete that can fill formwork without any mechanical vibration. SCC's unique property gives it significant economic, constructability and engineering advantages. The aim of this paper is thus an attempt to study the possibility of using thin-walled hollow structural steel (HSS) columns filled with very high strength SCC. Tests on 28 HSS columns filled with very high strength SCC were conducted, where the main parameters varied are: (1) section types, circular and square; (2) slenderness ratio, from 12 to 120; and (3) load eccentricity ratio, from 0 to 0.6. Comparisons are made with predicted column strengths using the existing codes such as AISC, EC4 and DBJ13-51-2003.

Prediction of residual stresses and strains in cold-formed steel members

Abstract: The objective of this paper is to provide an unambiguous mechanics-based prediction method for determination of initial residual stresses and effective plastic strains in cold-formed steel members. The method is founded on basic physical assumptions regarding plastic deformations and common industry practice in manufacturing. Sheet steel coiling and cross-section roll-forming are the manufacturing processes considered. The structural mechanics employed in the method are defined for each manufacturing stage and the end result is a series of closed-form algebraic equations for the prediction of residual stresses and strains. Prediction validity is evaluated with measured residual strains from existing experiments, and good agreement is shown. The primary motivation for the development of this method is to define the initial state of a cold-formed steel member for use in a subsequent nonlinear finite element analysis. The work also has impact on our present understanding of cold-work of forming effects in cold-formed steel members.

Quasi-static axial and lateral crushing of radial corrugated composite tubes

Abstract: This paper presents the effect of corrugation geometry on the crushing behavior, energy absorption, failure mechanism, and failure mode of woven roving glass fibre/epoxy laminated composite tube. Experimental investigations were carried out on three geometrical different types of composite tubes subjected to axial and lateral compressive loadings. On the addition to a radial corrugated composite tube, cylindrical composite tube, and corrugated surrounded by cylindrical tube were fabricated and tested under the same condition in order to know the effect of corrugation geometry. The results showed that the loading carrying capability is significantly influenced by corrugation geometry in axial crushing. However, no affect of corrugation geometry was observed for lateral crushing. Load–displacement curve was plotted for all conducted tests, thus clear comparison between different specimen's geometry was achieved. It is also found that radial corrugation could significantly applicable as a stable and effective energy absorber.

Experiments on cold-formed steel columns with holes

Abstract: The objective of this paper is to observe and quantify the relationship between elastic buckling and the tested response of cold-formed steel columns with holes. Compression tests were conducted on 24 short and intermediate length cold-formed steel columns with and without slotted web holes. For each specimen, a shell finite element eigenbuckling analysis was also conducted such that the influence of the boundary conditions and the hole on local, distortional, and global elastic buckling response could also be captured. Slotted web holes may modify the local and distortional elastic buckling half-wavelengths, and may also change the critical elastic buckling loads. Experimentally, slotted web holes are shown to have a minimal influence on the tested ultimate strength in the specimens considered, although post-peak ductility is decreased in some cases. Tangible connections are observed between elastic buckling and load–displacement response during the tests, including mode switching between local and distortional buckling. The columns are tested with friction-bearing boundary conditions where the columns ends are milled flat and parallel, and bear directly on steel platens. These boundary conditions, which greatly speed specimen preparation, are determined to be viable for evaluating the tested response of short and intermediate length columns, although the post-peak response of intermediate length specimens must be considered with care.

Axi-symmetrical deflection and buckling of circular porous-cellular plate

Abstract: The main goal of this paper is a solution of the problem of buckling and deflection. A circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure) is considered. Mechanical properties of the isotropic porous material vary across the thickness of the plate. Middle plane of the plate is its symmetry plane. A field of displacements (geometric model of nonlinear hypothesis) is described. The principle of stationarity of the total potential energy allowed to get a system of differential equations that govern the plate stability. A critical load and a deflection are determined. The results obtained for porous plates are compared to homogeneous circular plates.

Thermal and mechanical instability of functionally graded truncated conical shells

Abstract: Thermal and mechanical instability of truncated conical shells made of functionally graded material (FGM) is studied in this paper. It is assumed that the shell is a mixture of metal and ceramic that its properties changes as a function of the shell thickness. The governing equations are based on the first-order shell theory and the Sanders nonlinear kinematics equations. The results are obtained for a number of thermal and mechanical loads and are validated with the known data in the literature.

Crashworthiness design of multi-corner thin-walled columns

Abstract: This paper presents a crashworthiness design of regular multi-corner thin-walled columns with different types of cross-sections and different profiles, including straight octagonal columns and curved hexagonal columns. In this paper, the straight octagonal section columns are first optimized, which mainly take axial crash loads during crashes. Next, the curved hexagonal section columns are optimized following the same approach, which are subject to bending moment when impact occurs. During the design optimizations, specific energy absorption (SEA) is set as the design objective, side length of the cross-sections and wall thickness are selected as design variables, and maximum crushing force (Pm) is set as the design constraint. Both the objective and constraint are formulated using the response surface method (RSM) based on sets of finite element (FE) results obtained from FE analyses (FEA). After obtaining the optimal designs, parametric studies are performed to investigate the influences of the design variables on the crash performance of such multi-corner thin-walled columns.

‘Hybrid’ light steel panel and modular systems

Abstract: Modern methods of construction (MMC) are defined as those which are highly pre-fabricated and which achieve tangible benefits to the client in terms of speed of construction, higher quality and more efficient and adaptable space use. There are many examples of MMC in light steel framing and modular construction, which are targeted on the residential and mixed-use building sectors. Modular units can be designed with partially or fully open sides so that two or more modules can be placed side by side to create larger spaces. An alternative ‘hybrid’ approach is to combine 3D-modules for the highly serviced and higher value parts, such as kitchens and bathrooms, and to use long span 2D-panels for the floors and walls in the more open plan areas. The long span floor cassettes typically span up to 6 m between separating walls or the sides of the modules. The floor cassettes occupy the same depth as the floor and ceiling of the module and achieve a target depth of 450–500 mm. The paper reviews the design and construction of a ‘hybrid’ demonstration building addresses the background development work and testing of the modules and floor cassettes.

A parametric study on ultimate strength of single shear bolted connections with curling

Abstract: Recommended procedures of finite element modeling for predicting the structural behaviors of single shear bolted connections in cold-formed austenitic stainless steel are presented in this paper. It was shown that predictions by FE analysis method were in a good correspondence with test results for ultimate behaviors such as failure mode, ultimate strength and out-of-plane curling. A parametric study on four-bolted connections with extended variables; plate thickness, end distance and edge distance is performed in order to consider the influence of curling on ultimate strength for practical design and ultimate strengths obtained from FE analysis results are also compared with those calculated by current design standards and recently modified equations by Kuwamura. It is found that Kuwamura's equations, which are specified by SSBA design manual are more valid for predicting ultimate strength of bolted connection without curling compared to other design specifications, while for specimens curled in FE analysis, Kuwamura's equations overestimated the ultimate strength due to strength reduction caused by curling and current other design standards showed a tendency to underestimate the ultimate strength of block shear fracture regardless of curling occurrence. Consequently, revised design formula for considering the effect of curling on bolted connection is proposed in this paper using correlations between strength reduction ratio and plate thickness. Furthermore, the validation of proposed design equations in predicting the ultimate strength is verified through comparisons with existing test results and additional FE analysis results.

Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory

Abstract: An improved higher order zigzag theory is presented and it is applied to study the buckling of laminated sandwich plates The present theory satisfies the conditions of transverse shear stress continuity at all the layer interfaces including transverse shear stress free conditions at the top and bottom surfaces of the plate The variation of in-plane displacements through thickness direction is assumed to be cubic for both the face sheets and the core, while transverse displacement is assumed to vary quadratically within the core but it remains constant over the face sheets The core is modeled as a three-dimensional elastic continuum An efficient C 0 finite element is proposed for the implementation of the improved plate theory The accuracy and range of applicability of the present formulation are established by comparing the present results with 3D elasticity solutions and other results available in literature

Elastic buckling of elliptical tubes

Abstract: Hot-rolled and cold-formed structural steel tubular members of elliptical cross-section have recently been introduced into the construction sector. However, there is currently limited knowledge of their structural behaviour and stability, and comprehensive design guidance is not yet available. This paper examines the elastic buckling response of elliptical hollow sections in compression, which has been shown to be intermediate between that of circular hollow sections and flat plates. The transition between these two boundaries is dependant upon both the aspect ratio and relative thickness of the section. Based on the results of numerical and analytical studies, formulae to accurately predict the elastic buckling stress of elliptical tubes have been proposed, and shortcomings of existing expressions have been highlighted. Length effects have also been investigated. The findings have been employed to derive slenderness parameters in a system of cross-section classification for elliptical hollow sections, and form the basis for the development of effective section properties for slender elliptical tubes.

Global buckling analysis of plane and space thin-walled frames in the context of GBT

Abstract: This paper reports research work concerning the use of Generalised Beam Theory (GBT) to analyse the global buckling behaviour of plane and space thin-walled frames. Following a brief overview of the main concepts and procedures involved in the performance of a GBT buckling analysis, one presents in detail the formulation and numerical implementation of a GBT-based beam finite element that includes only the first four (rigid-body) deformation modes — namely, one describes (i) the kinematical models developed to simulate the warping transmission at frame joints connecting two or more non-aligned U- and I-section members, (ii) the procedures adopted to handle the effects stemming from the non-coincidence of the member centroidal and shear centre axes (cross-sections without double symmetry), and (iii) the definition of joint elements, which involves providing a relation between the connected member GBT degrees of freedom and the joint generalised displacements. Finally, one presents and discusses numerical results that make it possible to illustrate the application and show the capabilities of the above GBT-based finite-element formulation and implementation. For validation purposes, the GBT-based results (critical buckling loads and mode shapes) are also compared with values yielded by shell (mostly) and beam finite element analyses carried out in the code ANSYS.

Ultimate strength of perforated steel plates under combined biaxial compression and edge shear loads

Abstract: The present paper is a sequel to the author's papers [Paik JK, Ultimate strength of perforated steel plates under edge shear loading. Thin-Walled Structures 2007; 45: 301–6, Paik JK Ultimate strength of perforated steel plates under axial compressive loading along short edges. Ships Offshore Struct, 2007; 2(3): (in press)]. In contrast to the previous papers with the focus on edge shear or uniaxial compressive loads, the aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under combined biaxial compression and edge shear loads, which is a typical action pattern of steel plates arising from cargo weight and water pressure together with hull girder motions in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges, keeping them straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the plate dimension (thickness). Based on the FEA results obtained, closed-form empirical formulae of the ultimate strength interaction relationships of perforated plates between combined loads, which can be useful for first-cut estimations of the ultimate strength in reliability analyses or code calibrations, are derived.

Numerical and experimental investigations on buckling of steel cylindrical shells with elliptical cutout subject to axial compression

Abstract: The effect of cutouts on load-bearing capacity and buckling behavior of cylindrical shells is an essential consideration in their design. In this paper, simulation and analysis of thin steel cylindrical shells of various lengths and diameters with elliptical cutouts have been studied using the finite element method and the effect of cutout position and the length-to-diameter (L/D) and diameter-to-thickness (D/t) ratios on the buckling and post-buckling behavior of cylindrical shells has been investigated. For several specimens, buckling test was performed using an INSTRON 8802 servo hydraulic machine and the results of experimental tests were compared to numerical results. A very good correlation was observed between numerical simulation and experimental results. Finally, based on the experimental and numerical results, formulas are presented for finding the buckling load of these structures.

Analysis of circumferentially arc welded thin-walled cylinders to investigate the residual stress fields

Abstract: The control of weld-induced imperfections like welding deformations and residual stresses is of critical importance in circumferentially welded thin-walled cylinders due to their wide utilization in high tech engineering applications in aerospace and aeronautical structures, pressure vessels and nuclear engineering fields. The paper presents a computational procedure for the analysis of temperature distributions and the subsequent residual stress fields during the course of arc welding of thin-walled cylinders of low carbon steel. Parametric studies based on numerical simulations are conducted to investigate the effects of critical welding process parameter on weld-induced residual stresses. Temperature-dependent thermo-mechanical behavior for low carbon steel, filler metal deposition along with double ellipsoidal heat source model is incorporated. The accuracy of the developed finite element simulation strategy is validated for transient temperature distributions and residual stress fields through full-scale shop floor welding experiments with proper instrumentation for data measurement. The aim is to present data to confirm the validity of in-process circumferential welding technology for thin-walled cylinders so that the in service failures of these structures due to process specific inherent stresses may be minimized.

Lateral buckling of thin-walled beam-column elements under combined axial and bending loads

Abstract: Based on a non-linear stability model, analytical solutions are derived for simply supported beam-column elements with bi-symmetric I sections under combined bending and axial forces. An unique compact closed-form is used for some representative load cases needed in design. It includes first-order bending distribution, load height level, pre-buckling deflection effects and presence of axial loads. The proposed solutions are validated by recourse to non-linear FEM software where shell elements are used in mesh process. The agreement of the proposed solutions with bifurcations observed on non-linear equilibrium paths is good. It is proved that classical linear stability solutions underestimate the real resistance of such element in lateral buckling stability especially for I section with large flanges. Numerical study of incidence of axial forces on lateral buckling resistance of redundant beams is carried out. When axial displacements of a beam are prevented important tension axial forces are generated in the beam. This results in important reduction of displacements and for some sections, the beam behaviour becomes non-linear without any bifurcation.

A beam model for the flexural–torsional buckling of thin-walled members with some applications

Abstract: A beam model aimed at describing the flexural–torsional buckling of thin-walled members with non-symmetric cross-sections is presented. Two beam axes are introduced, and strain is defined with respect to both. The shearing strain between the cross-section and one of the two axes is assumed to vanish; the warping is supposed to be linear in the twist. Non-linear hyperelastic constitutive relations are introduced; by means of standard localization and static perturbation techniques, the field equations describing the flexural–torsional buckling are obtained. One benchmark example is given and some numerical values of the critical load for various warping constraints at the beam ends are provided.

Bending collapse of thin-walled circular tubes and computational application

Abstract: This paper focuses on describing the bending collapse behavior of thin-walled circular tubes In this paper, global energy equilibrium theory is applied to derive the relationship between the applied moment and the bending angle of circular tubes A general bending collapse mode of circular tubes is referenced for the derivation, and it is assumed that during bending crush, all impact energy is absorbed and distributed along the hinge lines After obtaining the relationship, it is compared to a published theory of tubular structure's bending resistance, which was obtained from analytical and experimental studies The derived bending resistance is then applied to generate simplified circular tube models, which have different cross-sections and are made of different materials Crashworthiness analyses are performed on these simplified models as well as detailed tube models, and the crash results are compared to verify the efficiency of the generated simplified model and the accuracy of the derived tube's bending resistance All the problems involved in this paper are solved by means of LS-DYNA

Thermal buckling load optimization of laminated composite plates

Abstract: In this study, the applicability of the Modified Feasible Direction (MFD) method on the thermal buckling optimization of laminated plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used in the mathematical formulation. For this purpose, a program based on FORTRAN is used for the optimization of laminated plates. Finally, the effect of aspect ratio, antisymmetric lay-up, boundary condition, material anisotropy, ratio of coefficients of thermal expansion, and hybrid laminates on the results is investigated and the results are compared.

GBT-based buckling analysis of thin-walled members with non-standard support conditions

Abstract: This paper reports on the use of a recently developed Generalised Beam Theory (GBT) formulation, and corresponding finite element implementation, to analyse the local and global buckling behaviour of thin-walled members with arbitrary loading and support conditions — this formulation takes into account longitudinal normal stress gradients and the ensuing pre-buckling shear stresses. After presenting an overview of the main concepts and procedures involved in the performance of a GBT-based (beam finite element) member buckling analysis, one addresses in detail the incorporation of non-standard support conditions, such as (i) full or partial localised displacement or rotation restraints, (ii) rigid or elastic intermediate supports or (iii) end supports corresponding to angle connections. In order to illustrate the application and capabilities of the proposed GBT-based approach, one presents and discusses numerical results concerning cold-formed steel (i) lipped channel beams and (ii) lipped I-section beams and columns with various “non-standard” support conditions — while the beams are acted by uniformly distributed or mid-span point loads, applied at the shear centre axis, the columns are subjected to uniform compression. In particular, it is possible to assess the influence of the different support conditions on the beam and column buckling behaviour (critical buckling loads and mode shapes). For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code A nsys .

Buckling of thin-walled conical shells under uniform external pressure

Abstract: Shells are for the most part the deep-seated structures in manufacturing submarines, missiles, tanks and their roofs, and fluid reservoirs; therefore it is a matter of concern to bring about some basic regulations associated with the existing codes. Above all, truncated conical shells (frusta) and shallow conical caps (SCC) subjected to external uniform pressure when discharging liquids or wind loads are discussed closely in this paper concerning and thrashing out their empirical nonlinear responses along with envisaging numerical methods in contrast. The buckling aptitude of shells is contingent upon two leading geometric ratios of “slant-length to radius” (L/R) and “radius to thickness” (R/t). In this paper, developing six frusta and four shallow cap specimens and their relevant FE models, use is made of laboratory modus operandi to enumerate buckling elastic and plastic responses and asymmetric imperfection sensitivity, whose adequacy has been reckoned through comparisons with arithmetical and numerical data correspondingly. These obtained upshots were aimed at validating and generalizing the data for unstiffened truncated cones and SCC in full scale.

Large deflection analysis of 3D membrane structures by a 4-node quadrilateral intrinsic element

Abstract: This paper presents a large deflection analysis of membrane structures, in which a 4-node quadrilateral membrane element is proposed. The element is developed based on an intrinsic model called vector form intrinsic finite element (VFIFE). The formulation includes a description of kinematics to dissect rigid body and deformation displacements, and a set of deformation coordinates for each time increment to describe deformation and internal nodal forces. A convected material frame and explicit time integration for the solution procedures are also adopted. The external loading is mainly a normal pressure to the membrane and the developments are made under the assumption of follower forces. Several numerical examples are presented to demonstrate the performance and applicability of the proposed element on the large deflection analysis of 3D membrane structures. It reveals that the proposed element could go through the patch tests and possesses stable, convergent and accurate results.

Analysis and optimization of smart hybrid composite plates subjected to low-velocity impact using the response surface methodology (RSM)

Abstract: Optimization of the volume fraction, the orientation and the through thickness location of the shape memory alloy (SMA) wires was used in order to minimize the maximum transverse deflection of the hybrid composite plate during the low-velocity impact phenomena. The prediction of optimal conditions of good geometrical properties of SMA wires in smart hybrid composites plays an important role in process planning. The present work deals with the study and development of a verified strict model for smart composite plate deflection, which embedded with the SMA wires, using response surface method (RSM). This method helped us to estimate deflection ratio as a mathematical function of the main process planning parameters. The experimentation was carried out with the first-order shear deformation theory, the Fourier series method and solving analytically the system of governing differential equations of the plate. The interaction between the impactor and the plate also modeled with a system having two-degrees-of-freedom, consisting of springs-masses. A nonlinear mathematical model, in terms of the volume fraction and layer sequence (the orientation and the through thickness location) of the SMA wires was delivered. The results indicated that the volume fraction is a more important factor affecting the optimization and the design process of the structures.

Recent developments in the design of cold-formed steel members and structures

Abstract: Cold-formed steel members and structures are extremely widespread in use at the present time. The design analysis of such structures is often complex, as their behaviour can be influenced by effects, which arise due to the slenderness of members, walls and cross-sections. Prime among these effects are the various types of buckling which can occur, and which may interact with each other to promote failure at loads substantially less than those, which would be obtained in the absence of these effects. The complications induced by such effects must be taken into account in design, if the potential benefits offered by the use of such members are to be realised, and in recent design specifications this has been realised. In this paper the main types of cold-formed steel members are described, the particular characteristics affecting their design are discussed, as are the ways in which design specifications deal with these characteristics.

Buckling of laminated plates with general boundary conditions under combined compression, tension, and shear-A semi-analytical solution

Abstract: A semi-analytical approach to the buckling analysis of generally supported laminated plates subjected to a general combination of inplane shear, compression, and tension loads is presented. Arbitrary out of plane and inplane boundary conditions at the edges of the plate are considered. The formulation is based on the variational principle of virtual work and the multi-term extended Kantorovich method. The semi-analytical method is used for the pre-buckling and buckling (stability) analyses of laminated rectangular plates with inplane restraints under arbitrary inplane loads. The accuracy and convergence are examined through a comparison with exact solutions (where available) and with finite element analyses. The applicability of the method is demonstrated through various numerical examples that focus on the buckling of rectangular composite plates with a variety of boundary conditions and various combinations of the inplane shear, compressive, and tensile loads.