Martin Pircher

THE SHAPE OF CIRCUMFERENTIAL WELD-INDUCED IMPERFECTIONS IN THIN-WALLED STEEL SILOS AND TANKS

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.

The influence of circumferential weld-induced imperfections on the buckling of silos and tanks

Abstract The load carrying behaviour of cylindrical thin-walled shell structures under axial load is strongly dependent on imperfections invariably caused by various manufacturing processes. Axisymmetric imperfections have been known to result in particularly severe reductions in strength. Imperfections in the vicinity of circumferential welds in steel silos and tanks fall into this category and therefore deserve special attention. A detailed bifurcation and post-buckling finite element analysis was performed on imperfect cylindrical shells. Special care was taken to model the weld-induced circumferential imperfection. The geometry was calibrated against data gained from measuring such imperfections on existing silos and residual stresses were taken into account. Interaction between neighbouring weld imperfections and the role of the strake height in this interaction was investigated. Weld-induced residual stresses were found to have a small strengthening influence on the buckling load. Interaction between neighbouring imperfections was found to reduce the buckling strength of the structures. A post-buckling analysis was undertaken and an explanation of the load-carrying behaviour of the structure after initial bifurcation was given.

The influence of the fabrication process on the buckling of thin-walled steel box sections

Steel box sections are usually fabricated from flat plates which are welded at the corners. The welding process can introduce residual stresses and geometric imperfections into the sections which can influence their strength. For some thin-walled sections, large periodic geometric imperfections have been observed in manufactured sections. Subsequent investigations have indicated that the imperfections are in fact buckling deformations i.e. the box section has buckled due to welding residual stresses prior to any application of external load. The welding procedure and the behaviour of the box sections under load has been modelled using a finite element analysis that accounts for both geometric and material non-linearities. Tests have been carried out on box sections with a range of width to thickness ratios for the plate elements. Modelling has been shown to give good correlation with the test results. The conditions for buckling to take place as a result of the welding process have been established. A design method has been proposed.

THE UNIT LOAD METHOD - SOME RECENT APPLICATIONS

The unit load method has been developed to achieve a pre-defined target configuration of section forces in cable-stayed bridges by optimizing the tensioning of the stay-cables. The method has been further developed into a versatile design tool that allows the definition of a target distribution of section forces or deflections in any structure. This paper briefly describes the method and provides three application examples where this method has been used: a cable stayed bridge, a concrete arch and the application of the method to the automated simulation of the incremental launching process of bridges.

Measured imperfections in six thin-walled steel tubes

Abstract The structural behaviour of thin-walled members is often extremely imperfection sensitive. For many types of such members only little information of the exact nature of the present imperfections is available. A method of measuring imperfections of circular cylindrical members has been developed and was used to measure six thin-walled tubes. The method is simple to implement in a laboratory environment yet very accurate. Numerical methods to process the measurements into three-dimensional imperfection maps and an algorithm to distinguish between significant imperfection patterns from measurement “noise” have been derived. Results of the measurement of these six tubes are presented in this paper. Conclusions about the nature of the imperfections are drawn and imperfection amplitudes for the six tubes are given.

Towards a Holistic Approach to Bridge Design

The design of bridges is typically split into two, quite distinctly different stages: the design of the overall structure on the one hand; and the detailed design of the individual components on the other hand. Typically the overall design takes place on generalised and simplified models of the bridge structure. Section forces and displacements gained from such models are then used as boundary conditions for the much more detailed models used in the second stage. An integrated process whereby requirements for both design stages are incorporated into one model has in the past been made difficult or impossible by the lack of computing resources. This situation is about to change. Generally available computers will soon be powerful enough to allow such a holistic approach. This paper outlines the strategies employed in a current research project which provides the scientific background for such an integrated design approach. The outcomes of this research project are to be directly incorporated into a state-of-the-art bridge design software package. First results of this research project are documented and future developments are explained in this paper

Stresses in Elastically Supported Cylindrical Shells under Wind Load and Foundation Settlement

Thin-walled shell structures of a circular cylindrical shape are widely used in structural engineering to serve in applications such as silos, tanks or chimneys. The design of such structures poses some considerable challenges to structural engineers as the load carrying behaviour of cylindrical shells is quite complex, especially for non-axisymetric load cases. Very often a comprehensive analysis causes considerable expenses and the vast amounts of results which are typically generated make it hard to understand the underlying load-carrying principles of the structure. The introduction of an engineering method to handle two typical non-axisymetric load cases on circular cylindrical thin-walled shell structures is the goal of this paper. The proposed method offers a quick way to generate critical section forces and displacements. The load cases discussed herein are wind-loading and foundation-settlement. Ground support for many cylindrical steel structures is often realised by anchoring the lower shell boundary to a concrete foundation. This is accomplished by steel bolts that can be looked at as spring elements providing elastic support for the shell structure. The influence of this type of support on the section forces and displacements under wind loading can be modelled by combining the two abovementioned load cases via an interaction diagram also given in this paper.

The measurement of imperfections in cylindrical thin-walled members

Abstract The structural behaviour of thin-walled circular cylindrical members has been shown to be imperfection sensitive. However, only little information of the exact nature of imperfections in such members is available. In this paper a method of measuring imperfections in circular cylindrical members is described, the method is simple to implement in a laboratory environment while providing accurate measurements. Numerical methods to process the measurements into three-dimensional imperfection maps are also presented along with an algorithm to distinguish between significant imperfection patterns and measurement ‘noise’. Results from a recent research project where this method has been used illustrate the derivations in this paper.

CASE STUDY OF A MEDIUM-LENGTH SILO UNDER WIND LOADING

The paper presents a case study for a thin-walled cylindrical shell structure under wind loading. The geometric parameters of the cylinder were chosen so that a particular buckling pattern occurred. This pattern is characterized by horizontal ripple-like buckles in the upper half of the side of the cylinder facing the wind. The considerable axial compressions that occurred were recorded for a finite element model and compared to the critical axial buckling stress for constant axial loading. Two critical factors were identified: the ovalization at the critical cross section and the disproportional increase of axial compression due to geometrically nonlinear effects. Further reductions of the expected buckling resistance were suspected to be caused by interaction with tangential compression in the area and additional displacements.

ELASTIC BUCKLING OF THIN-WALLED CYLINDERS UNDER WIND LOADING: AN EXPERIMENTAL STUDY

Thin-walled cylindrical structures have been found to display three distinctly different stability failure modes under wind loading, depending on their geometric and material properties. In low cylinders the radial compression at the meridian facing the wind causes a buckling mode similar to that for cylinders under constant radial compression, while very long cylinders display a failure mode characterized by buckling in the lower third of the structure at the side which faces away from the wind. The failure of medium height cylinders is characterized by a number of horizontal, ripple-like buckles in an area around the upper half of the meridian which faces the wind. In an ongoing experimental study, a series of small-scale specimens with a wide range of geometric parameters is being tested in a wind tunnel. To the knowledge of the authors, this is the first time that the particular buckling mode for medium height cylinders has been documented in an experiment. The present paper gives a summary of the results gained from this study so far and compares them qualitatively to those of a previous numerical study.