J. Michael Rotter

Shell structures: the new European standard and current research needs

Abstract Shell structures are widely used in a great variety of applications from space rockets to domestic food and drink containers. Civil engineers are principally concerned with steel shell structures such as silos, tanks, pipelines, chimneys, towers and masts, though other examples may be found in offshore structures and stadium roofs. This paper describes the treatment of terrestrial shell structures in Eurocode 3: Steel structures. It outlines the principles which are guiding the development of the standard, the range of applications covered, and some details of the current proposals. The axially compressed cylindrical shell is then chosen as an example illustrating the range of real problems which need to be addressed, and the paucity of current data on many aspects of these problems. This example is also used to outline the complexity involved even in this one area, recent progress and current needs.

Imperfections and buckling in cylindrical shells with consistent residual stresses

Metal silo walls are often constructed from isotropic plates, and the controlling design condition is buckling under axial compression. It has long been recognised that this buckling strength is highly sensitive to imperfections in the cylindrical shell, but most attention has been paid to geometric imperfections and imperfect boundary conditions. Imperfections in the form of residual stresses have only rarely been investigated, and the challenges facing a rigorous treatment of them have often not been faced. This paper adopts a rigorous treatment technique to investigate residual stresses and their effect on the axial compression buckling strength under elastic conditions. It achieves this by considering consistent stress and displacement fields arising from local geometrical incompatibilities, and adopting their consequent geometric imperfections. The calculations of the strength of imperfect shells with residual stresses are compared with corresponding calculations for the same imperfections but with the residual stresses ‘annealed’ out of the analysis. The results show that consistent residual stresses generally appear to strengthen a thin shell relative to the corresponding strength with only geometric imperfections present.

Study of buckling in steel silos under eccentric discharge flows of stored solids

The most serious loading condition for slender thin-walled metal silos has long been recognized to be the condition of discharge, with eccentric discharge causing more catastrophic failures than any other. Two key reasons for this high failure rate are the difficulties in characterizing the pressure distribution caused by eccentric solids flow, and in understanding the associated unsymmetrical stresses in the silo wall. Few studies have addressed either the linear elastic behavior of such a silo or its buckling failure under eccentric discharge. In this study, the eccentric discharge pressures are characterized using the new rules of the European Standard EN 1991-4 on Silos and Tanks. This novel description of unsymmetrical pressures permits a study of the structural behavior leading to buckling during eccentric discharge, including the critical effects of change of geometry and imperfection sensitivity, to be undertaken using geometrically and materially nonlinear computational analyses. The mechanics of...

Buckling of Thin Cylindrical Shells Under Locally Elevated Compressive Stresses

Thin cylindrical shells used in engineering applications are often susceptible to failure by elastic buckling. Most experimental and theoretical research on shell buckling relates only to simple and relatively uniform stress states, but many practical load cases involve stresses that vary significantly throughout the structure. The buckling strength of an imperfect shell under relatively uniform compressive stresses is often much lower than that under locally high stresses, so the lack of information and the need for conservatism have led standards and guides to indicate that the designer should use the buckling stress for a uniform stress state even when the peak stress is rather local. However, this concept leads to the use of much thicker walls than is necessary to resist buckling, so many knowledgeable designers use very simple ideas to produce safe but unverified designs. Unfortunately very few scientific studies of shell buckling under locally elevated compressive stresses have ever been undertaken. The most critical case is that of the cylinder in which locally high axial compressive stresses develop extending over an area that may be comparable with the characteristic size of a buckle. This paper explores the buckling strength of an elastic cylinder in which a locally high axial membrane stress state is produced far from the boundaries (which can elevate the buckling strength further) and adjacent to a serious geometric imperfection. Care is taken to ensure that the stress state is as simple as possible, with local bending and the effects of internal pressurization eliminated. The study includes explorations of different geometries, different localizations of the loading, and different imperfection amplitudes. The results show an interesting distinction between narrower and wider zones of elevated stresses. The study is a necessary precursor to the development of a complete design rule for shell buckling strength under conditions of locally varying axial compressive stress.

Development of proposed European design rules for buckling of axially compressed cylinders

Thin axially compressed cylinders are used in a wide range of civil engineering shell structures: towers, chimneys, tanks and silos. Design standards throughout in the world differ considerably in their strength predictions, and all are based on empirical lower bounds to laboratory test results. The chief reason for the scatter in strength assessments is the sensitivity to geometric imperfections, which naturally vary from one laboratory to another and according to the method of fabrication. This paper sets out some of the development behind the new proposed rules for the European standard on Strength and Stability of Shells. These rules cover cylinder buckling under axial compression alone, and the strength of internally pressurised cylinders. The design strengths are related to recent calculated buckling strengths, and an attempt is made to indicate the appropriate relationship between design assumed imperfections and tolerances during construction.

The New Framework for Shell Buckling Design and the European Shell Buckling Recommendations Fifth Edition

This paper outlines key aspects of the new European Standard on the Strength and Stability of Metal Shells EN 1993-1-6 with its extended commentary and expansion in the fifth edition of the European Recommendations on Shell Buckling. This European design standard is the first to be strongly oriented toward numerical analyses in design, with clear distinctions between different classes of both analysis and fabrication. It presents a different style of standard: Each limit state is defined in a separate chapter, but all shell geometries are treated and all analysis types are used within each chapter. The strength evaluation criteria differ according to the calculation that has been made. This new structure, with its new paradigm that permits generalization of the design procedure for all thin shells, geometries, load cases, boundary conditions, and qualities, represents a major step forward. It also offers the opportuniy for future research studies of shell structures to be undertaken within a coherent conceptual framework that is completely general. The EN 1993-1-6 standard goes a long way toward bridging the gap between the computational engineering mechanics and structural engineering design communities. Unfortunately, this European standard EN 1993-1-6 has a complex and extensive background that cannot be stated within the document so the European Recommendations on Shell Stability, now published in its fifth edition, gives an extensive commentary, many expanded rules, and many additional geometries and load cases that are not formally presented within the standard itself. The development of both EN 1993-1-6 and the recommendations has been the work of the Eurocode shell structures development committee CEN/TC250/SC3/PT4 and the European Convention for Constructional Steelwork committee (ECCS) TWG 8.4. It is presented here by the convener of these two committees. This paper explains the reasoning behind several particular choices that have been taken in developing the standard, occasionally running counter to traditional views. It also identifies several tricky issues that have not been addressed well in the shell buckling literature but that have arisen through the attempts to achieve completely general rules and which need imaginative answers to ensure a fully consistent treatment of all systems. It is hoped that this paper will assist researchers and designers to understand the rules and recommendations and will encourage researchers to undertake and present their work in a manner that permits its rapid adoption into the new standardized design procedures.

Ideal Location of Intermediate Ring Stiffeners on Discretely Supported Cylindrical Shells

Silos in the form of a cylindrical metal shell are commonly elevated to provide access to the space beneath, permitting the contained materials to be directly discharged. A few discrete column supports at evenly spaced intervals are commonly used. However, the structural design of discretely supported cylindrical shells presents a variety of challenges. The presence of discrete supports results in circumferential nonuniformity in the axial compressive stress as well as a progressive vertical decay above the support. Several approaches can be adopted in design depending on the severity of the nonuniformity of the stresses. Relevant research to date has focused mostly on the behavior of cylinders supported on brackets, local forces at the base, or stiff ring beams. The use of intermediate ring stiffeners to provide circumferential uniformity in the axial membrane stresses has long been recognized, but few studies have given a clear view of the practical requirements for such rings. In this paper, a combination of base and intermediate ring stiffeners is explored to develop a practical and cost-effective solution that leads to more uniformity in the axial membrane stresses above the intermediate ring stiffener. For the purposes of obtaining a simple analytical solution, the cylindrical shell is subjected to the fundamental harmonic of the column support and analyzed using membrane theory. It is shown that an ideal location exists for an intermediate ring stiffener such that the axial membrane stress above this ring is circumferentially completely uniform. The ideal location of this ring is determined analytically and is expressed in terms of the basic geometric variables. This ideal ring location is then independently verified using many linear finite-element analyses. A further study explores the effect of placing the intermediate ring stiffener below the ideal location. The results are presented in a manner that makes them suitable for direct adoption into traditional design specifications.

Ring Beam Stiffness Criterion for Column-Supported Metal Silos

Cylindrical metal silos are commonly elevated to provide access space beneath to directly discharge the contained materials into transportation systems. Evenly spaced column supports are commonly utilized. In larger silos, the discrete forces from supports are more evenly transferred and distributed into the cylindrical shell wall by using a ring beam. A fundamental assumption in the design of the silo shell is that the meridional compressive stresses are relatively uniformly distributed around the circumference. This assumption can easily be violated if the ring beam is flexible, so it is necessary to determine the ring stiffness needed to achieve a particular degree of uniformity of support. Current methods of assessing this stiffness rely on onerous finite-element analysis, which only provides information for the specific design being checked. In this paper, a criterion is developed to identify the required ring beam stiffness to achieve a particular degree of uniformity in the shell stresses. It is ba...

Structural Behavior of Thin-Walled Metal Silos Subject to Different Flow Channel Sizes under Eccentric Discharge Pressures

AbstractThe condition of eccentric discharge is known to be one of the most critical for the design of thin-walled cylindrical metal silos. Significant progress has been made in recent years in devising a relatively realistic set of representative pressures for this load case. However, the consequences these may have on the predicted structural behavior of a silo are not yet fully understood. This paper presents a detailed parametric study into the behavior of a custom-designed slender silo under a set of unsymmetrical pressures describing the action of an eccentric parallel-sided pipe flow channel of varying cross-sectional areas. The results are compared with the reference axisymmetric case of concentric discharge. It is found that the predicted behavior is very complex indeed, and that geometric nonlinearity is of much greater significance for cylindrical shells under unsymmetrical load patterns than under symmetrical patterns. Further, it is found that eigenmode-affine imperfections, which are very de...

Shell Buckling and Collapse Analysis for Structural Design

A very large literature exists on the static analysis of thin shell structures, covering elastic stress states, elastic buckling, plastic collapse and elasticplastic failures. Modern approaches to these problems usually involve the use of computer programs to perform a variety of different alternative types of calculation. However, the way in which different analyses should be used in the design process has received much less attention until recently. The new European Standard for the Strength and Stability of Shells sets out a philosophical framework that accommodates the results of both algebraic analysis and different levels of sophistication in computer analyses. This paper describes the philosophy on which the new standard is based, and outlines the way in which the various analyses should be used, when applied in design practice. It also identifies some of the remaining difficulties which pose challenges of definition and interpretation, and which need debate in the scientific community.