Guy Lagae

Elastic plastic buckling of internally pressurized torispherical vessel heads

Abstract Comparisons of test and theory are presented for the nonaxisymmetric bifurcation buckling of ten aluminium vessel heads fabricated and tested by Patel and Gill at the University of Manchester in 1976. In the test specimens, the sphere radius was equal to the cylinder diameter and only the torus radius was varied. All specimens were of constant internal cylinder diameter to nominal thickness ratio of 531.5. Meridional variation of thickness was accounted for in the analysis, which was carried out with the BOSOR5 computer program. The analysis includes both material and geometrical nonlinear prebuckling behavior. The results indicate that incipient nonsymmetric buckling can be predicted with reasonable accuracy by means of an eigenvalue formulation.

Stringer Stiffened Cylinders on Local Supports – The Plastic Buckling Behavior

The buckling behavior of locally supported cylinders is a topic that is still the subject of many investigations. Adequate design rules have yet to be incorporated into the codes. In this contribution, the plastic buckling behavior of a stiffened cylinder on local supports is studied. Our research consists of two principal components, i.e. experiments on scale models and numerical simulations. Here the numerical simulations are discussed. Firstly the effect of the yield stress is investigated. In order to find a design rule, a large parametrical study has to be performed. In this contribution, the characteristics and the results of this study are described. The simulations show that for a radius to thickness ratio of the cylinder equal to 250, the optimal stiffener dimensions correspond with a plastic buckling phenomenon and a failure stress that is larger than the yield stress. For larger values of the ratio, the elastic instability of the stiffeners precedes the plastic buckling and this shows that the stiffener configuration is not suitable for these values of the radius to thickness ratio.

Glass Structures and Plasticity: Contradiction or Future?

Under normal serviceability temperatures, glass behaves like a linear elastic material, which will break suddenly when tensile stresses exceed a critical value. This does not necessarily mean that fracture occurs without any visual warnings. Especially when appropriate tempered glass is used, glass beams show a considerable deformation capacity. Still, there is no plasticity involved since all deformations are linear. The main safety concept is to create an overall structural “plasticity” for the glass beam as a whole, rather than for the individual material. This is usually done by building laminates: individual glass leafs alternated with soft transparent interlayers are composed as one coherent structural element. Currently, polyvinyl butyral is the most used interlayer material. Experiments with other transparent interlay materials have been carried out at different research institutes, in order to introduce more plasticity in the structural behaviour of glass beams. Not all attempts are as successful, but some results are promising. It is the authors’ opinion that the ability to create an overall structural plasticity will strongly influence the breakthrough of load bearing glass constructions. In the available literature however, the authors lack an overall picture of the current state of the art. For this reason, an attempt is made to present the actual research and different aspects of “plasticity in glass constructions” in this paper.

Elastic and Elastic-Plastic Buckling of Liquid-Filled Conical Shells

SUMMARY The best way of interpreting experimental and numerical results regarding buckling of liquid-filled conical shells is discussed. The stabilizing effect of the normal pressure exerted by the fluid is emphasized. Design equations developed previously for buckling in the elastic range are recalled. A test set-up designed to investigate buckling in the elastic-plastic range is described. It required the use of mercury as the loading medium. The test results are discussed. Results obtained numerically and the experimental results match reasonably well. The test results substantiate a design equation for buckling in the elastic-plastic range which was put forward as a conjecture several years ago.

Design of cold-formed steel purlins attached to roof sheeting based on Eurocode 3: Effect of gravity load

In the design of cold-formed steel purlins based on Eurocode 3, the lateral bending moment in the free flange of the purlin, when in tension, is assumed to be zero due to flange curling and second order effects. To investigate the validity of this design assumption, non-linear analytical and finite element models for analyzing how the gravity load affects the maximum mid-span stresses in cold-formed steel purlins attached to the roof sheeting are presented in this paper. The second-order effect of tensile stresses induced by the gravity load in the free flange of purlins is investigated by emphasizing on Z and C sections. The results obtained from the two models are compared with Eurocode 3, and they are included in this article. It is observed that for shorter purlin span lengths the design assumption underestimates the maximum mid-span stresses.

Buckling of Stringer Stiffened Cylinders on Local Supports

Summary Cylinders on discrete supports are prone to local instability. This failure phenomenon can be avoided by reinforcing the cylindrical wall by means of stringer stiffeners in combination with ring stiffeners. The goal of our research is to find design rules for this kind of shell structures. For this purpose, a numerical model was developed. In this contribution, the numerical model is validated by verifying the correspondence with the results of experiments on scale models. Two experiments are here discussed. The corresponding failure patterns are examples of the two possible patterns that were found in all the experiments. For the numerical simulations of these experiments, the measured geometrical imperfections and the real stress-strain relationship of the steel were incorporated into the numerical model. The results of the simulations show that the correspondence between experiments and simulations is sufficient.

ON THE IMPERFECTIONS OF CYLINDRICAL SHELLS ON LOCAL SUPPORTS

Times Cited: 0 1st International Conference on Computational Methods (ICCM04) Dec 15-17, 2004 Singapore, SINGAPORE Natl Univ Singapore, Dept Mech Engn

Design Curve to Use for Lateral Torsional Buckling of Tapered Cantilever Beams

Beams with tapered webs are used to adapt the bending resistance of a beam to the moment distribution. In this study, tapered cantilevers are loaded at their free end with a point load at the upper flange. A large number of beams with different tapers, lengths and cross section classes are simulated with the finite element code Abaqus. Welding stresses and geometrical imperfections are included in the model and the use of geometrical and material nonlinearities result in a realistic behaviour up to failure. The results are presented in a buckling diagram and confronted with existing buckling curves of Eurocode 3. The results indicate that the “General method for lateral torsional buckling of frames” can safely be used as a design rule. Introduction For large span frames, the weight of the beams is often the dominating load. Weight can be saved by adapting every cross section to the internal forces. Adapting the cross section in a continuous way can only be achieved when beams are welded from strips with a varying width, resulting in so called tapered beams. Practical realisations indicate that the additional fabrication cost can be compensated by the achieved weight reduction. The I-beams studied here have a linearly varying height and two equal flanges. The use of tapered beams results in slender constructions that are more susceptible to instability phenomena such as lateral torsional buckling (LTB). Unfortunately, there are no general and simple design rules as for prismatic beams yet available for tapered beams. The draft version of Eurocode 3 [1] describes in section 6.3.3. a method that may be used for the verification of frames with non uniform cross sections. In this contribution, the results of finite element simulations are used to verify the applicability of this method for the case of tapered cantilever beams which are loaded with a concentrated force which is applied at the upper flange of the tip section.

Stresses in and buckling of unstiffened cylinders subjected to local axial loads

Abstract Local force introduction in cylinders has received relatively little attention in the past and the designer often finds himself lost by the lack of design regulations or experimental evidence. This research activity, starting at the Ghent University, examines this stability problem and its purpose is to develop simple recommendations in order to assist designers in the steel industry. A short overview of the available literature on this particular topic is brought into the present contribution, together with our preliminary experimental observations and theoretical analyses with respect to unstiffened cylindrical shells subjected to local forces.

Residual Stresses in TIG-Welded I-Beams. Experimental Test-Setup and Validation of Numerical Model

The presence of residual stresses is a determining factor in the buckling behaviour of steel beams. It is therefore necessary to know the magnitude and the distribution of residual stresses in welded beams. Experimental measurements of these residual stresses are expensive, timeconsuming and they give no insight in the evolution of the stresses during the welding process. For these reasons it is interesting to have a numerical model which allows a prediction of the residual stresses due to welding and which allows a study of the parameters that have an influence on the residual stresses (e.g. yield stress, heat-input, thermal expansion coefficient, …). Such a numerical model can result in a proposal for a welding process that leads to less detrimental residual stress distributions in welded I-beams. However, the results of the numerical model must always be checked with reality. This contribution contains the experimental verification of the finite element model for both single plates and I-beams with rather small dimensions. First, an overview of generally accepted influencing factors on the residual stresses is given. After this introduction, a setup which allows control of the parameters for making reproducible weld seams is presented. This setup is usable for both plates and I-beams. Next it is described how the residual stresses in a plate and a beam were measured. Finally the results obtained from different configurations in the experiments are compared with the results from the FE-model. It is shown that the FE-model gives reliable predictions for the residual stresses.