Showing papers in "Thin-walled Structures in 1996"

Shear capacity of plate girders with trapezoidally corrugated webs

Abstract: In this paper, the shear capacity of plate girders with trapezoidally corrugated webs is numerically studied using a non-linear finite element method. Effects of large deflections are taken into account and a perfectly elastic-plastic material model obeying a von Mises yield criterion is assumed. The following geometric parameters that influence the shear capacity of such girders are investigated: (1) the overall dimension of the web panel; (2) the web thickness; (3) the corrugation depth of the web; (4) the corrugation angle; and (5) the width of the plane sub-panel of the web. More specifically, the influence of these parameters both on the ultimate shear capacity and on the remaining shear capacity in the post-buckling range, as well as on the buckling modes, are reported. Based on the numerical results, empirical formulae that were proposed earlier for the prediction of the shear capacity are examined and suggestions for an optimal design of such girders in shear are given.

Buckling of orthotropic plates with free and rotationally restrained unloaded edges

Abstract: Solutions and parametric studies are presented for the buckling of rectangular plates whose axes of material orthotropy coincide with the axes of the plate. The results presented apply to homogeneous orthotropic plates, stiffened orthotropic plates, and laminated composite material plates having flexural orthotropy (i.e. single ply and multiply unidirectional, and symmetric cross-ply composite plates). The plates considered are subjected to uniform uniaxial compression and simply supported on the loaded edges. The boundary conditions are different on the two unloaded edges; one edge being free and the other edge being elastically restrained against rotation. Parametric studies showing the effect of the orthotropic properties of the plate materials, the plate aspect ratio, the rotational restraint of the one unloaded edge and the buckle half-wavelength are discussed. Results in the form of nondimensional buckling curves are given in terms of orthotropy ratios and in terms of properties of common unidirectionally reinforced composite material. The use of the solution in conjunction with experimental data to predict the edge rotational restraint coefficient for thin-walled composite material beams is described.

Analysis of failure mechanisms observed in axial collapse of thin-walled circular fibreglass composite tubes

Abstract: Theoretical analysis of the failure mechanism of the stable mode of collapse of thin-walled fibreglass composite tubes under static axial compression, based on experimental observations and taking into account all possible energy absorbing mechanisms developed during the process, is reported. Crushing loads and the energy absorbed are theoretically predicted. The proposed theoretical model was experimentally verified for various composite materials and tube geometries and proved to be very efficient for theoretically predicting the energy absorbing capacity of the shell.

Ultimate strength of girders with trapezoidally corrugated webs under patch loading

Abstract: Ultimate strength of steel plate girders with trapezoidally corrugated webs under patch loading is studied using a non-linear finite element method. Effect of large deflection is taken into account and a von Mises material either without strain hardening (elastic-perfectly plastic), or with strainhardening obeying Ramberg-Osgood's equation, is assumed. The following factors that influence the ultimate strength are investigate (1) strainhardening models; (2) initial imperfections (local and global); (3) variation of yield stress and strain-hardening degree at the corrugation corners due to cold forming, ‘corner-effects’; (4) loading position; (S) load distribution length, and (6) variation of geometric parameters. Based upon the numerical results obtained, an empirical formula for the prediction of the ultimate strength is suggested.

Compressive strength of rectangular plates under biaxial load and lateral pressure

Abstract: Equations are derived to assess the strength of plates subjected to biaxial compressive loads, including the effect of initial distortions and residual stresses. These equations are then extended to the case of simultaneous lateral pressure loads. In calibrating the proposed methods and in assessing their model uncertainty published results of experiments and of numerical calculations have been used. The proposed methods were shown to be unbiased as regards plate slenderness and aspect ratio. The model uncertainty of each method was quantified and thus can be used to derive design formulations with the desired level of safety.

Energy absorption capability of fibreglass composite square frusta subjected to static and dynamic axial collapse

Abstract: The crashworthy behaviour of square frusta of fibreglass composite material subjected to axial compression at various strain rates is reported. The effect of specimen geometry and the loading rate on the energy absorbing capability was experimentally studied. The mechanics of the axial crumbling process from macroscopic and microscopic points of view were also investigated theoretically and experimentally. The collapse modes at macroscopic and microscopic scale during the failure process were observed and analysed. A theoretical analysis of the observed stable collapse mechanism of the components crushed under axial compression, for calculating crushing loads and energy absorbed during collapse, is proposed. A good agreement between theoretical and experimental results was obtained indicating the efficiency of the theoretical model in predicting the energy absorbing capacity of the collapsed shell.

Stability of thin-walled pultruded structural members by the finite element method

Abstract: A finite element having seven degrees of freedom at each node is developed to study the stability problem of thin-walled fibre-reinforced plastic (FRP) structural members. The influence of the in plane shear strain on the stability of the members is taken into account. The shape functions for the rotation and unit length rotation induced by warping are derived. The static and geometric stiffness matrices of a general beam element are established on the basis of the developed shape functions. The bifurcation buckling problem of thin-walled pultruded open-sections subjected to various loading and boundary conditions is examined through a number of examples. It is shown that the influence of the shear strain on the buckling capacity of the FRP structural members is significant and must be taken into account in the design of such members.

Lateral distortional buckling of monosymmetric I-beams under distributed vertical load

Abstract: An energy method is developed for analyzing the lateral buckling behaviour of beams subjected to distributed vertical load, with full allowance for distortion of the web. The paper presents a simple method which uses nonlinear elastic theory to obtain the external work due to buckling, and which obtains a new formulation of total potential energy for a monosymmetric I-beam. The method is validated by comparison with the classical energy methods when distortion of the web is suppressed (rigid web case). For both uniform distributed load and end moments the solution matches the critical lateral load obtained from the classical energy equations. For the case when the web is flexible, a 5th order polynomial shape function is used to describe the web buckling shape. The accuracy of the method is verified by results obtained from ABA QUS. The paper shows that for short beams the classical method seriously overestimates the critical load.

The shear behaviour of press-joining in cold-formed steel structures

Abstract: This paper describes a relatively new joining technique for cold formed steel structures called press joining. Press joining is a technique whereby a joint is created from the sheets to be connected, requiring no additional fixing items. A series of shear test results are given. The effect of UTS, steel thickness and angle of inclination of the join on both strength and deformation characteristics of the press join are discussed. A theoretical expression based on the results is developed linking all of the influencing factors to the shear strength of the join.

Creep buckling of thin-walled polymeric pipe linings subject to external groundwater pressure

Abstract: Repair of deteriorated sewer pipes is now often undertaken by installing a tight fitting thin-walled polymeric lining inside the cracked/deformed host pipe. It is demonstrated that structural design of these systems is most appropriately focused on proving a suitable factor of safety against long term creep buckling of the lining subject to external groundwater pressure within the confines of the host pipe. A programme of research identifying the appropriate performance criteria is then described. Firstly a suitable means of defining the required long term constitutive behaviour is considered. Secondly a series of laboratory tests which enable system behaviour to be defined is described. Finally a finite element model is developed, capable of predicting the required time dependent, highly nonlinear, long term system behaviour, and which therefore provides a suitable basis for the development of appropriate design guidelines.

Towards the understanding of material property influence on automotive crash structures

Abstract: Developing general crashworthiness guidelines for the design engineer is a complex task. This study begins to show that large parameter studies using actual vehicle models may prove fruitful in this endeavor. For the midrail component and the vehicle side structure studied, an initial generalized guideline developed is as follows: • • for a specific stress, a 10% change in thickness results in a 14% change in energy absorption • • for a specific thickness, a 10% change in stress results in a 7% change in energy absorption. These results are relative to baseline models, and are limited to the practical range of thickness and stress of actual vehicle components. Although the analyst must strive for precise solutions, the benefit of generalizing behavior for the design engineer must also be recognized.

Stability of cold formed purlins braced by steel sheeting

Abstract: The concept of equivalence of the behaviour of compressed lower (free) flange and a single compressed member on elastic foundation has been developed in the CTICM (France, 1979) and after later investigations and experiments, introduced in the EUROCODE 3, Part 1.3. Nevertheless, all the design cases have not yet been solved. This is, for instance, the case of the uplift load when anti-sag bars are used, for the resolution of which only a roughly approximate calculation can be used after choosing among the already existing formulae given for other similar applications. In this way, even if the first aim of the calculation, i.e. the safety, is attained, the second one, the economical aspect, is generally not achieved. The purpose of the present study is to give a generally operative approach to the solution of all the practical cases that, in addition, would correspond better with the actual structural design. The missing solutions may thus be found and the existing ones may be appreciably improved.

Free vibration and stability analysis of shells by the isoparametric spline finite strip method

Abstract: The isoparametric spline finite strip method has been applied to the free vibration and stability analysis of shells. The convergence of the method is reviewed critically. Additional numerical examples on shells of different geometry are also employed to demonstrate the efficiency, accuracy and versatility of the method.

Determination of effective breadth and effective width of stiffened plates by finite strip analyses

Abstract: A finite strip (FS) method is presented for the numerical investigation of two design parameters — effective breadth and effective width — of stiffened plates. For the effective breadth, stiffened plates under bending are studied. Due to the transverse bending loads there is shear transmission through the plate from the stiffener which leads to a non-uniform longitudinal stress distribution across the plate width. This phenomenon, termed as shear lag, can be represented by the ‘effective breadth concept’, and has been extensively studied by analytical methods. A linear FS method is presented which utilizes the advantages of decoupling of Fourier terms on the one hand and, on the other hand, allows the treatment of both webs and flanges using a plate model. A definitely different situation exists for estimating the effectiveness of the plate breadth (or width) of plates in the postbuckling range. The ‘concept of effect width’ is based on the fact that plates with supported longitudinal edges and/or stiffeners can accept additional load after buckling under longitudinal compression, and enables the designer to evaluate the postbuckling strength of plate structures simply by using the design parameter ‘effective width’. Several formulae (most of them empirically derived) exist for an approximative calculation of the load dependent value of the effective width. A nonlinear FS method is developed and applied to the investigation of the postcritical strength of locally buckled structures. An incremental successive iterative procedure is introduced for an effective numerical analysis.

An experimental verification of the generalized beam theory applied to interactive buckling problems

Abstract: Previous papers (Refs 1–4) have presented a method of analysis for any open unbranched thin walled section considering both rigid body movement and cross section distortion (including local buckling). Reference 1 described how the Generalized Beam Theory (GBT) can be used to calculate generalized section properties for all modes, including each of the four rigid body modes and the distortional modes. The additional section properties evolved from GBT were then used in Ref. 2 to consider second order elastic critical buckling problems. This paper compares the critical buckling predictions of GBT with the results obtained in two series of tests carried out on lipped and unlipped channels subject to a major axis bending moment. These predictions are then combined with the yield criteria of EC3 to allow a comparison with the analysis of these tests carried out by Lindner and Aschinger (Ref. 5). The paper concludes that the Generalized Theory is a powerful and effective analysis tool for the solution of interactive buckling problems where both local and overall buckling can occur.

Dynamic stiffness analysis of laminated composite plates

Abstract: An analysis is presented for the vibration and stability problem of composite laminated plates by using the dynamic stiffness matrix method. A dynamic stiffness matrix is formed by frequency dependent shape functions which are exact solutions of the governing differential equations. It eliminates spatial discretization error and is capable of predicting several natural modes by means of a small number of degrees of freedom. The natural frequencies and buckling loads of composite laminated plates are calculated numerically. The effects of the boundary conditions, the number of layers, the orthotropicity ratio, the side to thickness ratio, and the aspect ratio are studied. It is also illustrated that connected composite plate structures can be handled without difficulty by the present method.

Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints

Abstract: Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed inplane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behaviour with respect to fiber orientation changes significantly, in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behaviour has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally, determining the fiber orientations. The finite element method, coupled with an optimisation routine, is employed in analysing and optimising the laminates. Numerical results are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads.

Buckling of annular plates elastically restrained against rotation along edges

Abstract: The problem of elastic buckling of thin annular plates under in-plane radial loads along either free or simply supported with elastic rotational restraints at inner and outer edges has been analysed. A variant of the classical energy methods has been used to obtain a comprehensive set of new buckling results for several combinations of boundary conditions with partial rotational fixity. Results for the special case of simply supported full circular plates with elastic rotational restraint are also obtained by making the inner edge free and permitting the inner radius to become very small.

Flang curling in profiled steel decks

Abstract: The occurrence and magnitude of flange curling deflections in profiled cold-formed steel decking panels is investigated experimentally. The test panels examined were a roll-formed standing seam panel, and a brake-pressed trapezoidal panel. The test specimens were loaded in pure flexure and the load-response characteristics, and differential deflections of flanges relative to webs, were recorded for each specimen up to ultimate collapse. Estimates of flange curling deflections based on specifications contained within the Eurocode 3 (1993 draft) design standard are found to be comparable to experimentally determined deflections. A number of alternative curling models are developed and compared to the experimental curling behaviour. The effect of unrestrained longitudinal edges on curling deflections is determined and incorporated into the models.

Behavior of low ductility steels in Cold-Formed Steel connections

Abstract: Accepted design approaches for the strength of a steel connection rely on adequate ductility of the connected parts. In cold formed steel connection design, adequate ductility is defined by the Specification for the Design of Cold-Formed Steel Members. To assess the influence of low ductility steels, i.e. steels not meeting the specification ductility requirements, single lap bolted connections were studied. The experimental study reflected key connection strength parameters: edge distance, sheet thickness, sheet width, bolt pattern, F u F y , and percentage elongation. Test results indicate that failure modes in low ductility steels are inconsistent with observed failure modes in adequate ductility steels. It has also been determined that specification connection strength equations will provide reasonable estimates of the connection load capacity for low ductility steels.

An effective four node degenerated shell element for geometrically nonlinear analysis

Abstract: The development of a new four node degenerated shell element is presented for the analysis of the shell structures undergoing large deformations. In the formulation of the new element, the assumed covariant transverse shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains which are separated from the covariant inplane strains by mid-surface interpolation, are applied to eliminate the membrane locking problem and also to improve the membrane bending performance. This element is free of serious shear and membrane locking problems and undesired spurious kinematic deformation modes. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting nonlinear equilibrium equations are solved by the Newton-Raphson method combined with load or arc-length control. The versatility and accuracy of this new degenerated shell element is demonstrated by solving several numerical examples.

Influence of joint detail on the flexural/torsional interaction of thin-walled structures

Abstract: For a structure formed from two thin-walled open members connected at 90°, torsion applied to one member can result in torsion as well as flexure in the second member, with the magnitude and direction of this torsion as well as flexure in the second member being determined by the type of joint used. Conventional structural analysis would normally assume the presence of only flexure in the second member. The results from a finite element study of structures formed from thin-walled channel sections connected by box, mitre and stiffened mitre joints is presented and an explanation for the behaviour of the different joint types is given. It is shown that for the box joint the warping deformation of the loaded member is the dominant factor in determining the magnitude and direction of the twisting of the second member, whilst this is determined for the stiffened mitre joint primarily by the St Venant rotation deformation of the loaded member. For the unstiffened joint it is shown that the warping and St Venant rotation deformation effects tend to cancel each other out.

Influence of local postbuckling behaviour on bending of thin-walled beams

Abstract: The influence of the local postbuckling behaviour on the bending of thinwalled beams is studied. The analysis of the postbuckling behaviour of a prismatic column-beam subject to compression and bending is employed in order to determine the overall flexural stiffness of a beam after local buckling. The asymptotic Koiter method is used in the second order approximation. The determination of post-buckling coefficients enables one to find the beam's flexural stiffness without the necessity of using hypotheses on effective widths of eccentrically compressed plates. It is shown that the post-buckling equilibrium branch in a bending moment-global curvature coordinate system for a perfectly elastic thin-walled beam is rectilinear (in the second order approximation of' the asymptotic method). Simple analytical relations are presented between the slope of the post-buckling equilibrium branch of global bending and post-buckling coefficients for local buckling mode. The results obtained are compared with data reported by other authors.

Fractal two-level finite element analysis of cracked Reissner's plate

Abstract: A cracked thick plate subjected to edge moment and transverse loading was customarily analysed either by a fine finite element mesh or by singular elements In this paper an alternative method is recommended in which conventional finite elements with infinitesimal mesh are used and the number of unknowns is reduced by interpolating the nodal displacements by means of the global interpolating function around the singular region The global interpolating function is derived by using eigenfunction technique based on Reissner's transverse shear plate theory The crack parameters such as stress intensity factor and moment intensity factor can be evaluated directly from the coefficients of the global interpolating function New elements need not to be generated and integration is avoided completely Accurate results with error less than 05% are achieved with little computational efforts Examples on edge cracked plate and central cracked plate subjected to both edge moment and transverse loading are considered

Dynamic response of large strain elasto-plastic plate and shell structures

Abstract: Large strain, elasto plastic response of plate and shell structures have been carried out. A nine-node degenerated shell element with assumed strain fields is modified to take into account the effect of large strain, large displacement as well as the change in shell thickness during the deformation process. An Updated Lagrangian approach is adopted in the formulation of the incremental form of the governing equations. A time marching scheme is carried out based on Newmark's time integration technique. The results from the present study as compared with existing experimental, analytical as well as other finite element solutions agree reasonably well. Convergence studies indicate that the proposed elements give results which converge rapidly to acceptable solutions.

Analysis of the vibrations of inflatable dams under overflow conditions

Abstract: A two-dimensional analysis is applied to the vibrations of inflatable dams under overflow conditions. The cylindrical membrane dam is inextensible, air-inflated and anchored along two generators. The base width, curved perimeter and internal air pressure are given. The flow is incompressible, inviscid and irrotational, and the total head is specified. In the steady-state analysis, the equations of equilibrium of the dam from membrane theory are solved by a multiple shooting method, and the boundary element method is used to solve Laplace's equation defined on the overflow domain. An iterative scheme is adopted to obtain the shapes of the dam and the free surface of the fluid. Then the dynamic analysis is established by a finite difference form of the membrane's equations of motion, and the velocity potential problem is formulated by the boundary element method. The eigenvalues and eigenvectors obtained are employed to describe the small vibrations of the dam. The effects of the dam's density and damping coefficient on the stability and response of the dam are investigated.

Prediction of bending collapse behaviours of thin-walled open section beams

Abstract: Crushing behaviours of thin-walled open section beams are simulated using the simplified kinematic models. Systematic process of simulation is presented and applied to L-section and I-section beams. Basic processes can be conceptually divided into composition of mode shapes, location of deforming elements as a function of global process control parameter, calculation of plastic work done, estimation of mode parameters and calculation of crushing behaviours. A systematic numerical method is suggested to determine geometry and mode parameters according to the progress of collapse since it is generally very complicated to obtain closed form expressions for bending collapse problems. In the present method, mode parameters are determined by minimizing the plastic work done at very early stage of collapse, while it has been done conventionally by minimizing the mean crushing force. The results are in good agreement with those from finite element analyses and from the literature.

Vibration and elastic instability of thin-walled domes under uniform external pressure

Abstract: Two thin-walled varying meridional curvature axisymmetric shell elements are presented for the vibration and elastic instability of thin-walled hemi-ellipsoidal domes under uniform external pressure. The theoretical analysis is an extension of previous work carried out by the author, where for the two elements presented in the present report, a cubic and a quadratic variation was assumed for the meridional and the circumferential displacements along the meridian of these elements. In the previous study, only linear variations were assumed for the meridional and circumferential displacements along the meridian of these elements. Comparisons were made between experiment and theory for both buckling and vibration of hemi-ellipsoidal shell domes, which varied from very flat oblate vessels to very long prolate vessels. In general, agreement between experiment and theory was good for the hemi-spherical dome and the prolate vessels, but not very good for the fat oblate vessels. Additionally, the two new elements gave poorer results than the original simpler element for the cantilever mode of vibration, but better results for the lobar modes of vibration.

Buckling and postbuckling of stiffened elements with uncertainty

Abstract: The buckling and postbuckling behaviour of thin-walled stiffened elements under uniform compression with geometric and material uncertainties are examined. The uncertainties in the geometry can arise from tolerances in cold forming, and the ones in material properties result from the uncertain values of the maximum stress at buckling and from the scatter in the value of the modulus of elasticity. A convex model is used to model the uncertainties in both geometry and material properties. The results show that in the case of elastic buckling the reduction of the buckling load due to geometric uncertainties can be significant. In the case of postbuckling, the effective width in the presence of uncertainty is found to vary within the range of experimental results.

Crashworthiness of automotive steel midrails: Thickness and material sensitivity

Abstract: The automotive midrail is the main load carrying/energy absorbing component in a frontal vehicle crash. Three separate midrails, from three different manufacturers, each of a different size class of vehicle, and each with different crush modes, were found to exhibit the same sensitivity to variations in material thickness and stress-strain properties. From the results it was determined that a general design guideline for crashworthiness could be stated as: For every 10% change in thickness there is approximately a 14% change in energy absorption capability for a crushing midrail, while for every 10% change in material strength there is approximately a 7·3% change in energy absorption capability. The proposed design guideline can be used to help determine suitable modifications to make a structure more crashworthy and, additionally, to determine how manufacturing variations may affect the crashworthiness of a vehicle.