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The Design-by-Analysis Manual

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EUROPEAN COMMISSION XDT4T RESEARCH CENTRE

EPERC EUROPEAN PRESSURE EQUIPMENT RESEARCH COUNCIL CONSEJl EUROPEEN DE LA RECHERCHE EN EQUIPMENTS SOUS PRESSION I EUROPAISHER RAT FUR DRUCKGERATE FORSCHUNG

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EUR 19020 EN

The Desìgn-by-Analysis Manual

REFERENCE ONLY DATE °l-3 - ^eo 1 *** *

EUROPEAN COMMISSION •

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JOINT RESEARCH CENTRE

*** *** * *

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EPERC EUROPEAN PRESSURE EQUIPMENT RESEARCH COUNCIL CONSEIL EUROPEEN DE LA RECHERCHE EN EQUIPMENTS SOUS PRESSION EUROPAISHER RAT FÜR DRUCKGERATE FORSCHUNG

EUR 19020 EN

1999

EUNA19020ENC

Published by the EUROPEAN COMMISSION Directorate-General Joint Research Centre NI-1755 ZG Petten, The Netherlands

Neither the Authors, the European Commission nor any person acting on behalf of the Commission are responsible for the use which might be made of the information contained in this volume.

All rights reserved No part of the material protected by this copyright may be reporduced or utilized in any form or by any means, electronic or machanical, including photocopying, recording or by any information storage and retrieval systems, without permission from the copyright owner.

©European Commission, DG-JRC/IAM, Petten-The Netherlands, 1999 Printed in Italy

DBA Design by Analysis

Foreword

Foreword In August 1996 the European Commission's Directorate General for Industry launched a call for tender to perform a study on the application of Design by Analysis (DBA). This was one of a series of measures to promote the proposed Pressure Equipment Directive, and in particular the draft unified European standards intended to provide a preferential route for its application. The scope of requested study was to establish guidelines for applying DBA to typical pressure vessel structures under a variety of loading conditions, focusing on aspects that would accelerate its uptake in the European pressure equipment industry. In contrast to the traditional rules-based approaches, DBA requires detailed investigation of the behaviour of a pressure vessel under the foreseen loading regime, typically applying finite element modelling techniques. Up to now its use has been limited by both technical and economic factors. However with the rapid growth of computing power DBA methods have attracted increasing interest as a more flexible analysis tool for the optimisation of structures. To support this, the draft CEN unfired pressure vessel standard prEN 13445-3 specifically includes a design by analysis option. Furthermore, it incorporates a number of measures that favour the use of the so-called direct route to establish safe design limits, by-passing many of the difficulties associated with the stress categorisation method, on which many existing DBA codes are based. The overall contract was awarded to the Joint Research Centre's Institute for Advanced Materials, based at Petten in the Netherlands. The key technical activities were assigned to the following group of leading European institutes drawn from the European Pressure Equipment Research Council (EPERC), of which the JRC is operating agent: University of Strathclyde (UK) Vienna University of Technology (Austria) RWTÜV (Germany) WTCM (Belgium) CETIM (France) TKS (Sweden) Sant'Ambrogio Servizi Industriali (Italy) The project work plan was designed to systematically examine the key factors in applying DBA, and encompassed a state-of-the-art review, a survey of European pressure equipment industry attitudes, analysis of demonstration cases, dissemination actions and identifying areas for further development. However the focal point has been the evaluation of ten example cases covering a range of component geometries and loading conditions. These were analysed by the consortium members in accordance with the draft CEN standard procedure, and using a variety of different approaches and modelling techniques. The results have been critically appraised and recommendations drawn up regarding the application of the standard and the use of DBA methods. It was quickly realised that these results could provide a valuable reference to engineers wishing to apply the new standard and indeed to structural analysis engineers in general. Hence the decision to bring together a large part of the project material in the manual form you now have in front of you. Since the project is very much directed to supporting the wider use of DBA, this manual has been designed to meet a range of needs. For those less familiar with the analysis technique, the first three sections are intended to provide an easy-to-follow introduction to the principles and application of DBA. This is backed up with a simple illustrative analysis in section four. A comprehensive bibliography has also been provided in Annex 1 for reference purposes and for those of you keen to have more detailed information on specific topics.

DBA Design by Analysis

Foreword

IV

Sections five, six and seven are the core of the manual. The problem definition information for the ten example cases is set out in section five. Section six provides a tabularised summary the results of the analyses performed by the consortium for each of the checks prescribed by the draft CEN standard. In many cases these analyses have been performed according to different methods and the results are reported as fully as possible to underline the variability to be expected. Section seven contains detailed description of the analysis of each of the load cases, with FE meshes, contour plots and the critical assessment details. By presenting the example definitions, results tables and analysis details as separate sections, it is intended that a user can opt, for instance, to work on an example case independently and then compare his or her results to those obtained by the consortium. Alternatively its possible to follow the detailed demonstration examples in section seven directly. For a limited number of cases we have been able to provide complete input listings for the FE analysis; these are given in Annex 3. The final section brings together the recommendations for the application of DBA analysis and its use in conjunction with the draft CEN standard prEN 13445-3'. On behalf of the consortium, I hope that this manual will provide a useful reference tool and wish you every success in applying DBA. Nigel Taylor Design by Analysis Project Co-ordinator JRC Petten, 17th December 1999

The relevant sections of prEN 13445-3 are included in Annex 2 for reference purposes. Users should however bear in mind that this document is in the enquiry phase and may be modified as a result of the comments received from national representatives. For further information on it status or to obtain full copies of the standard you arc referred to the CEN website at www.cen.be.

DBA Design by Analysis

Acknowledgements

V

Acknowledgements First and foremost thanks are due to the European Commission's Directorate General for Enterprise (formerly DG-III Industry) who have funded the contract in which this work was performed. We very much hope that their faith in our Consortium has been rewarded. As Co-ordinator, I am loath to single out individuals within the Consortium for special thanks. However I think my colleagues will agree with me when I say that this manual would not have come into being without the dedicated effort and enthusiasm of Prof. Jim Boyle and Mr. Colin Lapsely at University of Strathclyde and Prof. Josef Zeman and Mr. Reinhard Preiss at Vienna University of Technology. That said, this has of course been a team effort, and all of the following have played their part: Jean-Francois Maurel, Gilbert Gras and Alain Handtschoewercker at CETIM in Senlis, Heinz-Dieter Gerlach, Klaus Rohler and M. Ludeke at RWTÜV in Essen, Joris Decock, Filip van de Velde and Daniel van Leeuwen at WTCM in Ghent, David Nash, Donald Mackenzie and Bobby Hamilton at University of Strathclyde, Sune Malm and Tommy Arnesson at TKS in Stockholm, Franz Rauscher and Dzemal Vazda from Vienna University of Technology and, last but not least, Fernando Lidonnici and Uberto Marzot at Sant'Ambrogio Servizi Industriali in Milan. The Vienna Group would like to acknowledge the usage of Ansys under the Vienna University of Technology license, and the support given by CAD-FEM GmbH. The Strathclyde Group would also like to acknowledge the usage of Ansys through an educational license agreement. We are also grateful to CEN for their permission to include the Clause 18, Annexes B and C of prEN 13445-3, which constitute an essential reference for the anlayses described. Finally here at the JRC I'd particularly like to acknowledge the contribution of Serge Crutzen in initiating this project and of Stuart McAllister, who, in addition to playing a key role in preparing the original proposal, was Project Co-ordinator for its first year.

DBA Design by Analysis

Contents

VII

Contents Section 1

Section 2

Section 3

Section 4

Section 5

Section 6

Introduction 1.1 Why Design by Analysis 1.2 Aim of the Manual 1.3 Section-by-section preview 1.4 Who should read this manual 1.5 References

1.1 1.2 1.3 1.4 1.5

Design by Analysis 2.1 The current stress categorisation route 2.2 The ASME inelastic route 2.3 Analysis methods for the ASME approach 2.4 Implementation problems of the ASME elastic route 2.5 Implementation problems of the ASME inelastic route 2.6 Design by Analysis in the European Standard 2.7 References

2.1 2.6 2.9 2.20 2.33 2.42 2.48

Procedures 3.1 General 3.2 The Two Routes 3.3 Direct Route using elasto-plastic calculations 3.4 Wind actions 3.5 Direct Route using Elastic Compensation 3.6 Stress Categorization Route 3.7 Check against Instability 3.8 Check against Fatigue

3.1 3.1 3.2 3.3 3.13 3.16 3.17 3.20

Illustrative Examples 4.1 Introduction 4.2 Problem Specification 4.3 Finite element model and boundary conditions 4.4 Determination of the maximum admissible pressure according to the Gross Plastic Deformation Check 4.5 Check against Progressive Deformation 4.6 Fatigue Check Specification of Examples 5.1 General 5.2 Terminology and definitions 5.3 Abbreviations and symbols 5.4 Specifications of examples 5.5 Specific materials properties Analysis Summary

4.1 4.1 4.1 4.2 4.4 4.8 5.1 5.2 5.3 5.4 5.20 6.1

DBA Design by Analysis

Section 7

Section 8

Analysis Details 7.1 General Example 1.1 Example 1.2 Example 1.3 Example 1.4 Example 2 Example 3.1 Example 3.2 Example 4 Example 5 Example 6

Contents

Thick unwelded flat end Thin unwelded flat end Welded-in flat end without nozzle Welded-in flat end with nozzle Storage Tank (cylinder-cone junction) Thin walled cylinder-cylinder intersection Thick walled cylinder-cylinder intersection Dished end with nozzle in Knuckle region Nozzle in spherical end with cold-media injection Jacketed vessel with jacket on cylindrical shell only and flat annular end plates

VIII

7.1 7.2 7.22 7.40 7.63 7.93 7.122 7.149 7.176 7.206 7.244

Recommendations 8.1 Overview 8.2 Methodology 8.3 Software requirements 8.4 Analyst requirements 8.5 Concluding remarks 8.6 References

8.1 8.1 8.6 8.7 8.10 8.10

Annex 1

Bibliography

Al .1

Annex 2

Draft CEN unfired pressure vessel standard prEN 13445-3,

Clauses 18, Annex Β and Annex C Clause 18 Annex Β AnnexC

Annex 3

Input listings

A2.1

A2.2 A2.58 A2.80 A3.1

SECTION

1

DBA Design by Analysis

Introduction

1. 1

1 Introduction 1.1 Background Pressure vessel design has been historically based on Design By Formula. Standard vessel configurations are sized using a series of simple formulae and charts. In addition to the Design by Formula route, many national codes and standards for pressure vessel and boiler design do provide for a Design By Analysis (DBA) route, where the admissibility of a design is checked, or proven, via a detailed investigation of the structure's behaviour under the external loads (or 'actions') to be considered. Nevertheless Design By Formula remains the dominant approach. In an increasingly technically sophisticated society, it may be asked why this should be the case? All these DBA routes in the major codes and standards in the pressure equipment field are based on the rules first proposed in the ASME Pressure Vessel and Boiler Code, which was formulated in the late 1950's before being released, originally for nuclear applications, in 1964. All these routes lead to the same well-known problems, especially the stress categorisation problem1'"61, and all are outof-step with the continuing development of computer hardware and software. Further, all are focused on pressure, and possibly, and to a limited extent, temperature, treating other actions in an inflexible manner, giving them marginal attention only. The DBA route in the proposal of CEN's unfired pressure vessel standard prEN 13445-3 tries to avoid these problems: 1. 2. 3. 4.

by addressing the failure modes directly by allowing for non-linear constitutive models by applying a multiple safety factor format for the incorporation of actions other than pressure by specifying mainly the principal technical goals of the standard together with some application rules as possible methods for the fulfilment of these goals.

In the new proposal of a European Standard, two documents are included concerning design by analysis: • •

Document prEN 13445-3, Annex B, Direct Route for Design by Analysis Document prEN 13445-3, Annex C, Stress Categorisation Route for Design by Analysis

For various reasons SG-DC of the Working Group (WGC) of the CEN Technical Committee TC54 decided to use in the new European Standard an approach similar to the one used in Eurocodes (for steel structures), using the notions of principles and application rules as well as the notion of partial safety factors. One reason is that the DBA-approach is flexible and simplifies the incorporation of constructional requirements (wind, snow, earthquake, etc.), if required, in a consistent manner. Another reason is, that there has been considerable criticism of the ASME stress classification (or categorisation) method, which is used in principle in almost all countries: One solution to the annoying problem of stress classification is to apply limit analysis, as proposed in the rules for DBA. Limit analysis does not require categorisation into primary and secondary stresses and it gives a unique result (which stress categorisation in general does not). The calculations can be made using existing software, but no doubt special software could be readily

DBA Design by Analysis

Introduction

developed if there were sufficient demand. Nevertheless, part of the usual stress categorisation approach is included in the Standard, as an application rule. The DBA route is included in the new European Standard • • • • •

as a complement to Design by Formula (DBF) for cases not covered there as a complement for cases requiring superposition of environmental actions - wind, snow, earthquake, etc. as a complement for fitness-for-purpose cases where (quality related) manufacturing tolerances are exceeded as a complement for cases where local authorities require detailed investigations, e. g. in major hazard situations, for environmental protection reasons as an alternative to the Design by Formula route.

For the time being, this route is restricted to sufficiently ductile steels and steel castings with calculation temperatures below the creep range. The main concepts are dealt with here in detail, because • • • • •

it is a real alternative to DBF, as stated above, with many advantages many concepts are new in pressure equipment design it may be used as a yard-stick for DBF solutions, to show possible improvements some concepts have already influenced the DBF-section, their discussion will shed light onto some DBF-details it may lead to an improved design philosophy by indicating more clearly the critical failure modes, especially of importance for in-service inspections.

1.2 Aims From the point of view of an analyst or designer, the rules in the new European Standard are quite general, and in fact as mentioned above this is intentional. In broad terms, in the context of the Direct Route either an admissibility check, or a check on maximum allowable load, has to prepared on the basis on either detailed elastic-plastic finite element analysis or some method of estimating plastic failure loads for gross and progressive plastic deformation. In principle this seems straightforward, but in practice can be difficult. The aim of this study has been to provide guidelines on the application of elastic-plastic analysis (in its broadest sense) to the Standard and in doing so to highlight possible problem areas and suggest methods of resolving these. This has been achieved using a new collection of ten benchmark problems. These example problems have been chosen to be typical of cases where design by formula cannot be used. A substantial part of this document provides detailed, step-by-step, studies of each of the example problems. This study has been undertaken by experts either in the research and development of design by analysis itself or in its practical use. This expertise is apparent in the review of the current state-ofthe-art of pressure vessel design by analysis in Section 2, which highlights unexpected, but now well-known, problem areas, and in the detailed description of the analysis procedures and their application to the Standard in Sections 3 and 7. The solutions reported in Section 7 were carried out independently, although unusual results were re-checked.

DBA Design by Analysis

Introduction

1 .3

It is intended that this document should be read in conjunction with the Standard, and can be looked on as a supplement. Particular emphasis is placed on the expected readership, and the expertise and knowledge required of them. While the Standard itself is fairly simple and transparent, the writers have also been aware that the current state-of-the-art in finite element analysis technology, and the expected continuing increase in sophistication, renders elastic-plastic analysis ever more routine. However the issue here is whether or not the analyst/ designer understands the underlying mechanics. Many users of elastic-plastic finite element analysis are unaware of the assumptions and approximations of the Classical Theory of Plasticity, which are embodied in most finite element software. They generally do not recognise the implications of the neglect of the Bauschinger effect and hysteresis, the assumptions concerning yield in compression in general, or that the basic mathematical models of initial and subsequent yield are approximations which are valid in some situations but not in others. At a more basic level, very few analysts are even aware of the fundamental assumptions of the engineering yield stress itself, for example it is measured from a tensile test and arbitrarily used as a reference to develop multiaxial yield criteria. Further, plasticity in metals is a shear mechanism, yet we use yield measured in tension rather than torsion and the measured value can be difficult to identify and is usually subjective. An overview of the contents of this study is given in the next sub-section, followed by some additional comments on the expected readership and recommendations of how the document should be used. 1.3 Overview This document is divided into nine Sections, including this Introduction: Section 2 provides an overview of the current state of design by analysis, as typified by the ASME Pressure Vessel and Boiler Code. The ASME Code offers two routes to design by analysis, the socalled elastic route and an inelastic route which requires the calculation of limit and shakedown loads - these are briefly summarised, together with definitions of basic terminology. Following this a short discussion of the most common method of analysis, using finite element techniques, is provided. This is not intended as an introduction to the finite element method applied to pressure vessels, rather several issues related to choice of element type are raised since they have implications for code interpretation - specifically the two main problem areas of the elastic route: linearisation and categorisation. These problem areas are then discussed in some detail, to give the reader an insight into the nature of major difficulties in application of what seems a fairly simple and straightforward set of design by analysis rules. Following this discussion, application problems with the inelastic route are then examined, in particular the difficulty of extracting meaningful plastic design loads from elastic-plastic finite element analysis. This Section then concludes with an introduction to the novel features of the new European standard in relation to design by analysis. In Section 3 a description of the various procedures used in this document to satisfy the analysis requirements is given. Some detail is provided on using the results of elastic-plastic analysis in the Direct Route for the checks on both gross plastic deformation and progressive deformation. In the case of the latter, problems with estimating shakedown loads when shell elements are used, or when there are stress singularities are discussed in some detail. The use of deviatoric maps to assist the shakedown analysis is also described. As an alternative to elastic-plastic analysis a new technique for directly estimating limit and shakedown loads from elastic finite element analysis alone is also used. This technique - the elastic compensation method - is briefly described in the context of the requirements of the Standard. Also, the treatment of shell elements is discussed. This Section also

DBA Design by Analysis

Introduction

1.4

reviews various other issues related to the practical use of the Standard - in particular wind action, the stress categorisation route and checks against fatigue and instability. In Section 4 a simple example - a circular plate - is used to describe and discuss each step in the application of the Standard before proceeding to the main examples examined in this document. Sections 5, 6 and 7 contain the main body of this study - the detailed application of the European Standard to ten benchmark problems. Section 5 gives a specification of each example, followed by a summary of the results of the analysis and application of the Standard in Section 6. Section 7 provides the detailed results for each benchmark problem using the analysis procedures described in Section 3. Finally, in Section 8, recommendations and concluding remarks are given. This covers comments on the appropriateness and difficulties with the methodology, software requirements, expertise and knowledge expected by the analyst and various warnings. For example, it is apparent that the fatigue rules - which are used for both design by formula and design by analysis - need special care. Appended to the report are various Annexes, specifically a bibliography, analysis input files (where appropriate) and excerpts of the Standard. 1.4 How to read this document This document is not aimed at the complete novice, but two broad types of reader are envisaged. It is presumed that anyone starting to read this has a basic familiarity with the concepts of plasticity theory and the behaviour of structures under plastic strain. In addition, familiarity with the practice of elastic finite element analysis for pressurised components, preferably with basic experience of elastic-plastic analysis is suggested. Also it is recommended that the reader should read the European Standard in some detail beforehand, if necessary. It is then envisioned that the reader will either already be broadly familiar with pressure vessel design by analysis and elastic-plastic finite element analysis and is comfortable with the Standard (whom we will call the Expert), or has read the Standard and has some basic experience of elastic design by analysis (whom we will call the Novice). In the case of the Expert, it is anticipated that this reader will begin with Section 5, the specification of the examples, followed by Section 6, the analysis summary and then initially carry out his own analysis and code check. It is possible that some reference will have to be made to Section 3 on procedures if substantial variation from the results reported here are obtained, or if details on application of the Standard need to be clarified. In the case of the Novice, it is expected that more or less the whole document will be carefully read, from Section 2 through to 7 before carrying out his own analyses. (Of course only a few of the benchmarks may be read in detail so that the Novice may test his understanding of the basic principles and procedures on the remainder). Finally it is also expected that engineering managers may wish to review Section 8, which deals with recommendations - in particular the discussion of assumed expertise on the part of the analyst/designer.

DBA Design by Analysis

Introduction

1 .5

1.5 Literature [I] J. L. Hechmer & G. L. Hollinger, "Considerations in the calculations of the primary plus secondary stress intensity range for Code stress classification," "Codes & Standards and Applications for Design and Analysis of Pressure Vessel and Piping Components" Ed. R. Seshardi, ASME PVP Vol. 136,1988. [2] A. Kalnins & D. P. Updike, "Role of plastic limit and elastic plastic analyses in design", ASME PVP-Vol. 210-2 Codes and Standards and Applications for Design and Analysis of Pressure Vessel & Piping Components, Ed. R. Seshardi & J. T. Boyle, 1991. [3] A. Kalnins & D. P. Updike, "Primary stress limits ion the basis of plasticity", ASME PVP-Vol. 230, Stress Classification, Robust Methods and Elevated Temperature Design, Ed. R. Seshardi & D. L. Marriott, 1992. [4] A. Kalnins, D. P. Updike & J. L. Hechmer, "On Primary Stress in Reducers", ASME PVP-Vol. 210-2, pp. 117-124 [5] D. Mackenzie & J. T. Boyle, "Stress Classification: A Way Forward", IMechE Presentation 5.5.92 [6] T.P. Pastor & J.L. Hechmer: "ASME task group report on primary stress" Proc. ASME PVP Conf, 1994, Minneapolis, 277, 67-78.

SECTION

2

DBA Design by Analysis

Design by Analysis

2. Design by Analysis The aim of this section is to summarise issues related to the current use of design by analysis in order to put the new European rules in context. The concept of design by analysis was first formulated in the US ASME Pressure Vessel and Boiler Code in the early 1960's; with almost forty years of use various critical problem areas have arisen, most of which have been addressed in the new European rules. These problem areas are discussed in the following since they highlight implicit difficulties with an apparently simple and straightforward set of design rules. In the following the approach devised by ASME is briefly summarised, followed by a description of the usual methods by which the rules are implemented and a discussion of the problem areas which arise. After this the differences in implementation of design by analysis rules in the European Standard are described. 2.1 Design by analysis: the current Stress Categarisation route The design by analysis procedure is intended to guard against eight possible pressure vessel failure modes by performing a detailed stress analysis of the vessel. The failure modes considered are: 1. Excessive elastic deformation including elastic instability. 2. Excessive plastic deformation. 3. Brittle fracture. 4. Stress rupture/creep deformation (inelastic). 5. Plastic instability - incremental collapse. 6. High strain - low cycle fatigue. 7. Stress corrosion. 8. Corrosion fatigue. Most of the design by analysis guidelines given in the codes relates to design based on elastic analysis - this is the so-called elastic route. Essentially it was recognised when the rules were being developed that only elastic stress analysis was feasible. In the 1960s, most designers were restricted to linear elastic stress analysis, and in the case of pressure vessel design most analysis was defined in terms of elastic shell discontinuity theory (also known as the influence function method). The nature of elastic shell analysis impinges significantly upon the way the above failure modes are treated in the Code. Thus, rules were developed to help the designer guard against the various failure mechanisms using elastic analysis alone. These guidelines guard against three specific failure modes - gross plastic deformation, incremental plastic collapse (ratchetting) and fatigue. These failure modes are precluded by failure criteria based on limit theory, shakedown theory and fatigue theory respectively. It is essential to appreciate at the beginning, the excessive plastic deformation and incremental plastic collapse cannot be dealt with simply in an clastic analysis, as the failure mechanism is inelastic. In addition, the type of loading causing the stress can significantly affect the level of permissible stress. Ideally, these inelastic failure modes should be assessed by an appropriate analysis which adequately models the mechanism of failure. In this approach the designer is required to classify the calculated stress into primary, secondary and peak categories and apply specified allowable stress limits. The magnitude of the allowable values assigned to the various stress categories reflect the nature of their associated failure mechanisms, therefore it is essential that the categorisation procedure is performed correctly.

DBA Design by Analysis

Design by Analysis

2.2

Stress categorisation (sometimes, classification) is probably the most difficult aspect of the design by analysis procedure and, paradoxically, the problem has become more difficult as stress analysis techniques have improved. When the design by analysis procedure was introduced, the dominant analysis technique in pressure vessel design was thin shell discontinuity analysis or the influence function method. This is reflected in the definitions of stress categories given in the Codes, which are based on the assumption of shell theory stress distributions; membrane and bending stress. It is therefore difficult to equate the calculated stresses and the code categories unless the design is based on shell analysis. The various stress categories are described first in the following: 2.1.1 Stress Categories The object of the elastic analysis is to ensure that the vessel has adequate margins of safety against three failure modes: gross plastic deformation, ratchetting and fatigue. This is done by defining three classes or categories of stress, which have different significance when the failure modes are considered. These three stress categories are assigned different maximum allowable stress values in the code: the designer is required to decompose the elastic stress field into these three categories and apply the appropriate stress limits. The total elastic stress which occurs in the vessel shell is considered to be composed of three different types of stress primary, secondary and peak. In addition, primary stress has three specific sub-categories. The ASME stress categories and the symbols used to denote them in the code are given below; (1) Primary Stress General Primary Membrane Stress, Pm Local Primary Membrane Stress, PL Primary Bending Stress, Pb (2) Secondary Stress, Q (3) Peak Stress, F and depend on location, origin and type. Before we can give a proper definition of these stresses, we must first give some terminology: Gross Structural Discontinuity: A gross structural discontinuity is a source of stress or strain intensification that affects a relatively large portion of a structure and has a significant effect on the overall stress or strain pattern or on the structure as a whole. Examples of gross structural discontinuities are: * end to shell junctions, * junctions between shells of different diameters or thickness, * nozzles. Local Structural Discontinuity: A local structural discontinuity is a source of strain intensification that affects a relatively small volume of material and does not have a significant effect on the overall stress or strain pattern or on the structure as a whole. Examples of local structural discontinuities are:

DBA Design by Analysis

* * *

Design by Analysis

2.3

small fillet radii, small attachments, partial penetration welds.

Normal Stress: The normal stress is the component of stress normal to the plane of reference; this is also referred to as direct stress. Usually the distribution of normal stress is not uniform through the thickness of a part, so this stress is considered to be made up in turn of two components one of which is uniformly distributed and equal to the average value of stress across the thickness of the section under consideration, and the other of which varies with the location across the thickness. Shear Stress: The shear stress is the component of stress acting in the plane of reference. Membrane Stress: The membrane stress is the component of stress that is uniformly distributed and equal to the average value of stress across the thickness of the section under consideration. Bending Stress: The bending stress is the component of stress that varies linearly across the thickness of section under consideration. With this terminology a? background, we now can define primary, secondary and peak stresses properly. Primary Stresses: A primary stress is a stress produced by mechanical loading only and is so distributed in the structure that no redistribution of load occurs as a result of yielding. It ¡s a normal stress or a shear stress developed by the imposed loading, that is necessary to satisfy the simple laws of equilibrium of external and internal forces and moments. The basic characteristic of this stress is that it is not self-limiting. Primary stresses that considerably exceed the yield strength will result in failure, or at least in gross distortion. A thermal stress is not classified as a primary stress. Primary stresses are divided into 'general' and 'local' categories. The local primary stress is defined hereafter. Typical examples of general primary stress are: * The average stress in a cylindrical or spherical shell due to internal pressure or to distributed live loads, * The bending stress of a flat cover without supporting moment at the periphery due to internal pressure. Primary Local Membrane Stress: Cases arise in which a membrane stress produced by pressure or other mechanical loading and associated with a primary together with a discontinuity effect produces excessive distortion in the transfer of load to other portions of the structure. Conservatism requires that such a stress be classified as a primary local membrane stress even though it has some characteristics of a secondary stress. A stressed region may be considered as local if the distance over which the stress intensity exceeds 110% of the allowable general primary membrane stress does not extend in the meridional direction more than 0.5 times (according to BS5500 - I time according to ASME and CODAP) the square root of R times e and if it is not

DBA Design by Analysis

Design by Analysis

2.4

closer in the meridional direction than 2.5 times the square root o f R times e to another region where the limits of general primary membrane stress are exceeded. R and e are respectively the radius and thickness of the component. An example of a primary local stress is the membrane stress in a shell produced by external load and moment at a permanent support or at a nozzle connection. Secondary Stresses: Secondary stresses are stresses developed by constraints due to geometric discontinuities, by the use of materials of different elastic moduli under external loads, or by constraints due to differential thermal expansion. The basic characteristic of secondary stress is that it is self-limiting. Local yielding and minor distortions can satisfy the conditions that cause the stress to occur and failure from one application of the stress is not to be expected. Examples of secondary stresses are the bending stresses at dished end to shell junctions, general thermal stresses. Peak stresses: Peak stress is that increment of stress which is additive to the primary-plussecondary stresses by reason of local discontinuities or local thermal stress including the effects (if any) of stress concentration. The basic characteristic of peak stresses is that they do not cause any noticeable distortion and are only important to fatigue and brittle fracture in conjunction with primary and secondary stresses. A typical example is the stress at the weld toe. 2.1.2 Stress intensity Pressure vessels are subject to multiaxial stress states, such that yield is not governed by the individual components of stress but by some combination of all stress components. Most Design by Formula rules make use of the Tresca criterion but in the DBA approach a more accurate representation of multiaxial yield is required. The theories most commonly used to relate multiaxial stress to uniaxial yield data are the Mises criterion and the Tresca criterion. ASME chose the Tresca criterion for use in the design rules since it is a little more conservative than Mises and sometimes easier to apply. For simplicity we will consider a general three-dimensional stress field described by its principal stress components, which we will denote σ„ σ2 ando,, and define the principal shear stresses: ^,=^2-σ3)

τ2=-(σ,-σ,)

τ, = - ( σ , - σ 2 )

According to the Tresca criterion yielding occurs when τ = max(T,,T2,T3) = — ar where σγ is the uniaxial yield stress obtained from tensile tests.

DBA Design by Analysis

Design by Analysis

2.5

In order to avoid the unfamiliar (and unnecessary) operation of dividing both calculated and yield stress by two, a new term called "equivalent intensity of combined stress" or simply Stress Intensity was defined: Stress differences, S12, S23 and S31 are equated to twice the principal shear stress given above, such that: 5 Ι 2 = ( σ , - σ 2 ) = τ3

5 2 , = ( σ 2 - σ , ) = τ,

5 31 = ( σ 3 - σ , ) = τ 2

The Stress Intensity, S is then defined as the maximum absolute value of the stress differences, that is S = max (\S12l \S23l \S31D, so that the Tresca criterion reduces to:

S=Oy Once an analysis has been performed, the Stress Intensity for each stress category is evaluated and used in the design stress limits. 2.1.3 Stress limits The primary stress limits are provided to prevent excessive plastic deformation and provide a factor of safety on the ductile burst pressure (ductile rupture) or plastic instability (collapse). The primaryplus-secondary stress limits are provided to prevent progressive plastic deformation leading to collapse, and to validate the application of elastic analysis when performing the fatigue analysis. The allowable stresses in the Codes are expressed in terms of design stress Sm. The tabulated values of Sm given in the Code are based on consideration of both the yield stress and ultimate tensile strength of the material. Sm is notionally two-thirds of the "design" yield strength σγ. Code allowable stresses for primary and secondary stress combinations are shown in the following table in terms of both S„, and σ γ .

General primary membrane, Pm

ALLOWABLE STRESS

STRESS INTENSITY

kSm

2/3 k a,

Local primary membrane, PL

1.5 k Sm

kOv

Primary membrane plus bending

1.5 k Sm

k a,

3 Sm

2 (Ty

(Pm + P„) or (P L + Pb) Primary plus secondary (Pm +

PB

+ Q) or (P L + P„ + Q)

DBA Design by Analysis

Design by Analysis

2.6

In addition to these allowables, when fatigue is considered relevant the total sum of (Pi+Pt+Q+F) should be less than an allowable fatigue stress intensity range, Sa. The value of the k factor depends on the load combinations experienced by the vessel. For load combinations including design pressure, the dead load of the vessel, the contents of the vessel, the imposed load of the mechanical equipment and external attachment loads the k factor has a value of 1. When earthquake, wind load or wave load are added to the above, a k value of 1.2 is used. Special limits are also stipulated for hydraulic testing. Under design load conditions k = 1 and the maximum value of the primary stress combinations is yield the yield stress of the material. Primary stress is yield limited to ensure gross plastic deformation does not occur. The primary plus secondary stress combinations have a much higher allowable stress: twice the yield stress of the material. Primary plus secondary stress is limited to ensure shakedown of the vessel. Because of the different allowable values for primary and primary plus secondary stress, it is essential that the calculated elastic stress is correctly decomposed into the various categories. This is one of the most difficult problems encountered in DBA and has potentially critical effect on the final design. If primary stresses are classified as secondary the design may be unsafe, whilst if secondary stresses are classified as primary the design will be over-conservative. The code provides explicit classification guidance for certain typical vessel geometries and load through Table 4.120.1 Classification of stresses for some typical cases. In situations other than these cases the designer must rely on the basic code definitions of primary, secondary and peak stress and his own judgement to properly classify the elastic stress. In fact some of the stress classifications recommended in Table 4.120.1 have been in doubt for some time, and must be used with care. 2.2 Design by Analysis: the ASME inelastic route The ASME VIII Division 2 rules for inelastic analysis are given in Appendix 4-136 Applications of Plastic Analysis. These rules "provide guidance in the application of plastic analysis and some relaxation of the basic stress limits which are allowed if plastic analysis is used." The rules for inelastic analysis considered here pertain to calculation of permissible loads for gross plastic deformation only. Rules are given in the Code for shakedown analysis but in practice shakedown analysis is difficult and it is simpler to apply the 3S„, limit to an elastic analysis. Two types of analysis may be used to calculate allowable loads for gross plastic deformation: limit analysis and plastic analysis. Limit analysis is used to calculate the limit load of a vessel. By definition, the analysis is based on small deformation theory and an elastic-perfectly plastic (or rigid-perfectly plastic) material model. Plastic analysis is used to determine the plastic collapse load of a vessel. The analysis is based on a model of the actual material stress-strain relationship and may assume small or large deformation theory as required. Material models can vary in complexity (or degree of approximation) from simple bilinear kinematic hardening models to more complex curves defining the actual stress-strain curve in a piecewise continuous manner. Including strain hardening in the analysis may give a higher plastic collapse load than the limit load but in the design by analysis procedure the allowable load is dependent on the criterion ofplastic

DBA Design by Analysis

Design by Analysis

2.7

collapse used. Including large deformation effects in the analysis may increase or decrease the calculated allowable load depending on the geometry of the vessel. Some structural configurations exhibit geometrical strengthening when non-linear geometry is considered whilst others exhibit geometric weakening. The expression 'plastic collapse load' is to some extent a misnomer, as a real vessel may not physically collapse at this load level, hence the 'plastic collapse load' is often referred to simply as the 'plastic load'. 2.2.1 Limit analysis ASME VIII Division 2 Appendix 4-136.3 Limit Analysis states: "The limits on general membrane stress intensity ...local membrane stress intensity ... and primary membrane plus primary bending stress intensity ... need not be satisfied at a specific location if it can be shown by limit analysis that the specified loadings do not exceed two-thirds of the lower bound collapse load. The yield strength to be used in these calculations is 1.55m." 2 Thus allowable load/"„is Ρ = — P, 3

where Pu„, is the limit load of the vessel.

Clearly, if the limit load can be calculated this procedure is much simpler to apply than the elastic analysis stress categorisation procedure. However, there are two additional requirements that must be satisfied when applying this approach. Firstly, the effects of plastic strain concentrations in localised areas of the structure such as points where plastic hinges form must be assessed in light of possible fatigue, ratchetting and buckling failure. Secondly, the design must satisfy the minimum wall thickness requirements given in the design by rule section of the Code. In effect, the design by rule formulae for wall thickness have priority over design by analysis calculations. 2.2.2 Plastic analysis ASME VIII Division 2 Appendix 4-136.5 Plastic Analysis states: "The limits of general membrane stress intensity ...local membrane stress intensity ... and primary membrane plus primary bending stress intensity ... need not be satisfied at a specific location if it can be shown by limit analysis that the specified loadings do not exceed two-thirds of the plastic analysis collapse load determined by application of 6-153, Criterion of Collapse Load (Appendix 6) [Mandatory Experimental Stress Analysis], to a load deflection or load strain relationship obtained by plastic analysis." 2 Thus allowable load Pais Ρ = —P., , where Pp is the plastic load of the vessel. ° 3 Calculating plastic loads is more problematic than calculating limit loads as no rigorous definition of what constitutes a plastic load is given. Instead, the twice elastic slope criterion as used in experimental analysis is prescribed.

DBA Design by Analysis

Design by Analysis

2.8

2.3 Analysis methods for the ASME approach Design by analysis procedures do not specify particular implementation tools: it has been left to the analysts to choose the technique they feel most appropriate. Shell discontinuity analysis was the primary tool in the early days of design by analysis, where stresses could easily be categorised in terms of shell-type membrane and bending stress. By now analysis techniques have developed significantly and although shell discontinuity analysis is still used very often in structural analysis, it is replaced more and more by computer based numerical methods. The most widely used technique in contemporary pressure vessel design is the finite element method, a powerful technique allowing the detailed modelling of complex vessels. Shell discontinuity analysis and the finite element method are discussed in relation to pressure vessel design by analysis in the following sections. 2.3.1 Shell discontinuity analysis Shell discontinuity analysis was the primary means of stress analysis in the early days of design by analysis procedures. Although largely replaced by finite element analysis, shell discontinuity analysis remains a useful tool for simple geometries, and indeed many engineering software companies still supply programs for discontinuity analysis. iv

1

■ F orces

A-H

Λ

*QC

Hemisphere I

Cone F lat end Figure 2.1.: Shell discontinuity forces and moments.

Shell discontinuity analysis is primarily used to evaluate shell membrane and bending stresses for axisymmetric vessels under internal pressure. It makes use of the fact that typical vessel configurations are composed of regular parts - spheres, cylinders, cones and flat ends in particular. For pressure loading, simple regular shapes exhibit mainly membrane stress. However, at junctions local bending (and additional membrane) stresses are generated. These stresses are called discontinuity stresses for obvious reasons. Shell discontinuity analysis allows these junction

DBA Design by Analysis

Design by Analysis

2.9

stresses, and their effect in the vessel, to be readily calculated using a simple engineering force method. This force method uses analytical solutions for the local bending and shear stress close to junctions which allow so-called edge forces and moments to be related to edge displacements and rotations, Figure 2.1. These edge relations are evaluated for each part of the vessel and then assembled at junctions. Continuity of displacement and rotation between parts then allows the edge forces and moments at the junction to be derived and finally the stresses in the various parts can be calculated.

2.3.2 Finite Elements for Pressure Vessel Analysis In creating a model, element selection and mesh definition are crucial aspects of finite element analysis. The type of element used in a finite element analysis for pressure vessel design can greatly influence the design procedure, so a brief overview is given here. Most commercial programs include large finite element libraries, however, in pressure vessel design the most common element types are 3-D solid, axisymmetric and shell elements. 2.3.2.1 3-D Solid Elements Solid (or continuum) elements are based on the mathematical theory of elasticity, which describes the behaviour of a deformable component under load assuming small deformation and strain. The most general theory is three dimensional, but under specific circumstances certain two dimensional reductions are possible. 3-D solid elements are used to model real three-dimensional structures such as the part model of a nozzle-vessel intersection shown in Figure 2.2.

Figure 2.2: 3-D solid model of a nozzle-vessel intersection.

DBA Design by Analysis

Design by Analysis

2.10

Elastic 3­D solid elements are based on 3­D elasticity theory. A general system of forces acting on a three dimensional elastic body sets up internal forces within the body, which vary with position throughout the body. The state of stress at a point in the body is fully defined by six components: Direct stresses: σχ, Oy, σζ Shear stresses: Tsy, Xyz, τα as illustrated in Figure 2.3. Three degrees of freedom are defined at each node of a 3­D solid element: orthogonal displacements ux, Uy and uz. Displacement throughout the domain of the element is defined in terms of these nodal displacements by the interpolation functions used in the element formulation. Most commercial finite element packages offer solid elements based on two different orders of interpolation: Figure 2.3: Stresses acting on a differential cube of 3-D elastic continua.

8 node linear element: Figure 2.4. Each element has 24 (8 node χ 3) associated degrees of freedom.

-xf)ax,R-dx>· 2

*-ik-*> h

The hoop stress is evaluated in a similar manner to the above; however in this case the meridional curvature, ρ must be taken into account: The membrane component of the hoop stress is given by

DBA Design by Analysis

2.26

Design by Analysis

f, \\σβ(ρ + χ3)\φάχ3 A t (σβ) = o = 2 = \σ„·1+*3

'"

A>

pe-Αφ

e{

θ

{

\ \dx3

ρ)

3

where the area Ae of a small segment extending over die angle Αφ in meridional direction is given by Ae=p1e ΊΑφ. In this linearisation the bending stress component of hoop stress on the classification line vanishes at x3 = xh, where xh is the x}- co-ordinate of the resultant of a constant stress distribution σθ and of the centroid of the considered area, where xh is given by

12 ?p Thus the bending stress component is given by Μ

β(χί~χι,)

(Pel

h

where e

M„

\\fa

-χ„)-σθ{ρ

+ χ3)Αφ dx3 ,

and I h= pe-A(p\

i 2

" ,

which leads to

«

v

3

e

\

12

Λ

η

- xi *

\ { ^ - ^ β γ + Χί\-άχ}.

DBA Design by Analysis

Design by Analysis

2.27

(Local) radial stress on the classification line is treated in a special way: in most situations the radial stress will equal the applied pressure at the internal surface and be free (zero) at the outer surface. Therefore, membrane stress may be evaluated,

{σ"Χ

=

ίΛ σ *, Λ 3

but it is questionable whether a bending stress should be evaluated. Either this should be taken as zero

or as the simple difference between actual and averaged value

K , ) „= oXi-(oXt)m which may not be linear. Similarly, an average membrane shear stress can be determined along the classification line KA)

=

1 D

\22 106

fc = F e i f N > 2 I O ' ' withFe = (25/e,)°,,2=

fe= 1

fe=

fa =

18­11­1­3 Mean stress correction factor fj IfAø„ruc Rpo,2/t·

J

eq, r

­

Ασ,„

KR,,

po,2/t· ­

9

Δσ

Λ 2" ' " R ρ0.2Λ·

. MPa

and σθ

For Ν > 2 1 0 6 cycles See figure 18­14

ForN= MPa

MPa (class or

principal stresses m = 3 Cx= C„ =

m=5 d= C„ =

m=5 C=

[stressesl ACTstmc -

MPa (structural equivalent stress range.determined by extrapolation) [orAc stru ci= MPaandAc slnic/ /= MPa]

|l8.8 Plasticity correction factor kJ Thermal loading

mechanical loading

IfAa smic > 2 Rpo,2/t·

lfAo smic >2R Dl Δσ k = 1 + A, e ' 2R p0,2/t*

with A0 =

0,7

1 0,5 +

0,5 for 800 MPa < Rra < 1000 MPa 0,4 for Rm < 500 MPa 0,4 +

MTI

500

3000

k„= Δσ =lt„Ao slnic = .

MPa

Else Δσ = Aasmc=

p0,2/t*

for 500 MPa < R m < 800 MPa

Ao= k«= Δσ = ke ΔΟΗΠ»; =

0.4

Δσ

MPa

MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors. ke and kv are to be calculated with the above formulas where Aoeqi is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor k„ is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. ¡18-10-6-1 Thickness correction factor feJ en < 25 mm

25 mm < en < 150 mm

e„ > 150 mm

f „ = (25/e„)0·25 =

f =

few = 0,639

Welded material ­ Ferritic steel Fatigue calculation

DBA Design by Analysis

|l8­10­6­2 Temperature correction factor f(*| Fort* > 100 °C Elsef,.= l

f,.= 1,03 ­ 1.510"4 t* ­1.5­10"61*2 =

118­10­6­3 Overall correction factor fj tw

'ewM»

|l8­10­7 Allowable number of cycles N| ¥- =

MPa

N = =oif Δσ 5 io cycles then m = 3 and C (C x or C„) = .

If -(" < Δσ 5 io cycles and other 6

cycles with j ­ > Δσ 5 1 0 cycles then m = 5andC(C±orC„) =

If ^ σ < Δθ5 îo'cycies and all other cycles with γ σ < Δσ 5 ι 0 6 cycles then N = oo

err"

it) with C from Table 18­7 of prEN 13445­3,

in dependence ofthe (weld) class, given by prEN 13445­3, Tables 18.4and 18.5, respectively.

3.24

DBA Design by Analysis

Unwelded material - Ferritic steel Fatigue calculation

Rz = en = Ao D =

°C

'Mnax nij\

°c* -

lEmin

min

t* = 0,75 t m « + 0,25 t„,.n=.. .°C Rm= MPa Rpi,o/f=

MPa

3.25

μιτι (table 18-8) mm MPa (table 18-10 forN >2 lO'cycles)

Ν -

(for the first iteration)

Δθ|ί =

M P a (allowable stress range forN 2 R„i

IfAo cq .i>2R, pl.0/1*

1+0,4

0.7

Λσ„ 0,5 +

2 R ρΐ,θ/t*

0.4

Δσeq,l R

ACtotal = ke.AOeq.t =

.MPa

Else AOtotai - Aoe(

....MPa

pl,0/t*

ku= Δσ,ο,,ι = ku.Aoe,,t = ■ ... MPa El..., Λ/τ

. — \rr

-

\ΛΌ

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors. ke and kv are to be calculated with the above formulas where Δσ,^,ι is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor ku is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. Δσ,

mc

^ Ασ

total

Κ (for usage in 18-11-3) t

18-10-6-2 Temperature correction factor ft*

18-11-1-1 Surface finish correction factor fj

Fort»> 100 °C ft. = 1,043-4,3 ΙΟΛ*: Else f,. = 1

fs =

F s [0,lln(N)-0.465| ¡ f N < 2 | 0 6

f s = F s i f N > 2 106

DBA Design by A nalysis

Unwelded material ­ Ferritic steel Fatigue calculation

3.26

|l 8­11­1­2 Thickness correction factorfj en < 25 mm

25 mm < en < 150 mm

en > 150 mm

f. = F, [0,lln(N)­0,465] ifN 2 10*

fe= fe=

18­11­1­3 Mean stress correction factor fm| lfAa5lr : < 2 Rp|,0/t* and Ce, lax < Rpl.O/l·

lfAo sm , c >2R p ,.o

IfAo smic Rpio/i

If CTeq > 0 then CTeq. r = RP,M. If aeq

< 0 then a e q ,

r

J fin r= and σJ eq Ρ η = 0" e q , r"

F o r N > 2 10'cycles See figure 18­14

^

=

Δσ«ι, 2

Rpl.0/1»

MPa

For Ν < 210 6 cycles M = 0,00035 R m ­ 0 , L ·

¡f­R 0

< , < σ» 'eq

M(2

f,„

1 ­

Δσ , R . then

< cTeq < Rpi.o;,. pi IM then

2(l + MJ

+ M ) 2σ eq

l+M

Δσ 2(l + M)

0,5 f„,=

I + M/3 _ Μ í 2d eq l+ M

Δσ,«y

3[Δ(ΤΚ>

fm=l

|l 8­11­2­1 Overall correction factor fj

f .f .f .f f

=

If =

Δσ

s e m t*

eq, struc

K.„„­

u

|l8­U­3 Allowable number of cycles Ni

N:

i f N < 210'cycles

If

N = ooifAcr eq, struc

2 106cycles) Ν = 100 000 (for the first iteration)

Rpo.2/,· = 255 MPa

Ao R = 407.8 MPa (allowable stress range for N< 2.10ft cycles)

= 20°C

+ 0,25 t„,

[Stresses] Ao eqi , (total or notch equivalent stress range) = 344.5 MPa Ac5slmc (structural equivalent stress range) = 312.3 MPa (obtained by quadratic extrapolation) Λ 100 °C f,.= 1,03 - 1 , 5 10"41* -1,5 10"6t*2 Else ft. = 1

18-11-1-1 Surface finish correction factor fj k

= F_[0,lln(N>0,«5]

¡fN2.10 6 with F, = 1f, = 0.8539

= 0.7889

DBA Design by A nalysis

Unwelded material ­ Ferritic steel Fatigue calculation

4.10

18­11­1­2 Thickness correction factor fj en > 150 mm

25 m m < e n < 150 mm

en < 25 mm

fe = Fe(0'"",N)­0­4 2.10e

f.=

f,= l

fe=

18­11­1­3 Mean stress correction factor fj IfAa!ln,c2R p02 „.

IfAa slruc 0 then CTeq, r = Rpo.2'i· ■ 2 = 82.75 Δσ„, IfCTeq< 0 then CTeqr = —__­— ■ Rp0,2/l* and Ggq = CTeq r = 82.75 MPa

F o r N > 2 10" cycles See figure 18­14

F o r N < 2 10" cycles M = 0,00035 R m ­ 0,1 = . Δσ„

if­Rrf,.2;t· £ σ,e q

&a R 2(1+ M)

Λ — then 2(1+ M)

, r \­|0,5 M(2 + Μ) Ι 2 σ ε ς

l+M

(_ Δ σ κ

„. then

4

1 + Μ/3

Mίΐσ eq

l+M

31 Δσ„ fm=l

118-11-2-1 Overall correction factor fj

f .f .f .f fu= s e m t* =ο.7^— 8

κ

0

i2|\

...--"" ''i/

i. 20 02800

Figure 5.16

Figure 5.17

s

—20x110

DBA Design by Analysis

Specification of Examples

'. b a t c h ρ (inner

5.19

eye.e

snare) 11 b u r

\ 0 T

(inner

space) 160°C

\ 20° Γ.

0 ρ (outer

soz.ce,

4i5

_.

o T (oui t e r

spa

CP)

I60°C

10"C 0 a v e r age 2 c y c l e S

Figure 5.18

/

O Û ~C ^

y ­ ■'"

DBA Design by Analysis

Specification of Examples

5.5 Appendix: Physical properties of some materials P235GH β

oc

ß

•c

10"*/K

KrtK

-100

10,8

9,3

217

423

371

0

11,7

11,6

213

456

451

20 11,9

11.9

212

461

461

0,181

57,5

100 12,5

13.0

207

479

496 0,230

55,7

14,3

200 13,0

14.0

199

499

533

0.304

51,9

12,5

300

13.6

15,0

192

517

568 0,394

47,6

10,8

400

14,1

15,9

184

536

611 0,501

43,4

9,2

500

14,5

16.6

175

558

677

0,625

39.6

7,6

600

14,9

16,4

164

587

778

0,770

36.0

6.1

β

E

E

cï

­

LU

l u LU

CO C M IO

>

O "f

ι τ-

Ο

I ¿5 ¿s

CÛ Ç> un O en d

POST BOSOR 1.04

POSTBOSOR 1.04

1JB

•STRESSES"

•STRESSES*

COMP.­ST

GEN.DIR 1.00

­

.75

­

Is

SHELL 1 SHELL 1 "IMSJOE­ ."MEMBR"

\

.50

MN: MAX: I .20

I .40

I

I .60

I

BO

1.00

IZO

I 1.40

. 10

2.81 E+01 2.01 E+01

'S &?

/

•25

FUNC VALUES:

y

­

.25

/

OUTSIDE"

/ /

•JS)

FUNC. VALUES:

^ ^ ^

-.n

JOB N011E 9940­18 14.00.15

20

.40

MIN: MAX:

.60

BO

1.00

1 »

1.40

10

Z

­B.03E +01 I.32E+02

JOB N011E W08­IB 14.09.05

PI

3 > POSTBOSOR1.04

ia

io2

130

­

POSTBOSOR 1.04

.:

-β

CIRCUMF 1.00

•STRESSES* 150

­

1.10

­

LOO

­

TRESCA

­ SHELL 1

SHELL 1

.75 "INSIDE­

'INSIDE*

■OUTS­DE*

.50

■OUTSIDE· .90

2h .80

y

.00

■25

.70

/ /

-

^ ___^--^^

­.50

­.75

20

.40

60

80

FUNC. VALUES: MIN: MAX:

100

150

­

­

.60

^ 1.40

10

.50

FUNC. VALUES:

\

­8.03E. C 1 1.32E*02

JOB N011E 99­ 00­18 14.09.44

20

*·> *-< — 'SI v: c 'SI

'STRESSES*

.40

60

BO

1.00

\^/ 1.20

/ 1.40

MIN: MAX:

10

3.54E+01 1.32E+02

99­08­18 14.11 10

Π

ta

PC o

ΒΓ

POSTBOSOR 1.04

10

2

POST BOSOR 1.04

ζ ■STRESSES·

"STRESSES"

­

1.50

COMP.­ST

24.00

c

GEN.DIR

SHELL 2

b b

SHELL 2

­

1.00

22.00 'MEMBR'

"INSIDE" ■OUTSIDE·

*> -

20.00

IS *? tu a c

18.00

18.00

­

14.00

­

­.50

FUNC. VALU ES MIN: MAX:

12.00

..

0

1.12E+01 2.61 E+01

JOB

1 75

2.00

225

2JS0

2.75

3 .00

3.25

FUNC.VALUES:

­

•1.00

N011E

MM: MAX:

,

so

3.50 10 14.13.02

1.75

2­ 30

255

2.75

*LS0

9.00

3.25

' * 2 3.50 10

­153E+02 1.75E+02 NOI I L

JOB 14.13.40

3

8.00

POST BOSOH 1.04

POSTBOSOR 1.04

10

'


■o 3

2

10

r 2.75

■!■■■ ■ 1 3.00 355

^ ir. 3.50 10

MIN: MAX:

2.05E+00 1.7SE+02

JOB 1056 02

N011E

N O

POSTBOSOR 1.04

10

POST BOSOR 1.04

Ζ

70.00 "STRESSES" COMP­ST βε.00

c

•STRESSES" 8.00

GEN.DIR

SHELLS

SHELL 3 5.00

- r

mm 56.00

'INS1DF 4.00

­

3.00

­

S g •3 *? a c

2.00

50.00

1.00 45.00

OUTSIDE­

­

­

FU NC. VALUES: 40.00

MIN: MAX:

3Κ

3.80

4 00

4.20

4.40

4.Β0

10

3.72E+01 7.08E+01

FUNC. VALUES:

­1.00

MM: MAX:

­

JOB N011E 99­08­16

M 0

4 DO

3.80

450

4.40

4.80

10

­1.36E+01 8.B4E+01

JOB N011E 39­08­18 14.17.05

M 3 -α

80.00

POSTBOSOR 1.04

\

POSTBOSOR

80.00

70.00

SHELL 3

"STRESSES*

70.00

5β

SHELLS

η

SS

ο

~

^

"INSIDE" 80.00

60.00

50.00

40.00

40.00

»CO

'yi

■—

TRESCA

­INSIOE" "OUTSIDE"

'-· "— C 'Ji

_^^***"^

GIR C UMF

y^ ^

■ ■

■STRESSES*

^****"^ ^^~^^

"OUTSIDE"

30.00 FUNC. VALUES: MIN: MAX:

FUNC. VALUES:

1.9BE+01 8.1BE+01

MM: MAX: 20.00

3.60

3.80

4.00

450

4.40

4.80

102

»8­08­18 14.17.57

3.60

3.8

0

4.00

450

4,40

4.60

> 3

1.04

102

1.98E+01 S.18E+01

JOB N011E 9908­18 14 18 32

Ν NI

,„2

POSTBOSOR 1.04

POSTBOSOR 1.04

Mem. 122 MPa -STRESSES*

«).­. ί '

­

150

■STRESSES*

60.00

Ζ c

GEN.DIR

COMP-ST

b b

SHE1L4

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1.20

1.40

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8.B9E+01 157E40Z

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JOB NOUE β9-0β-1β 14,19.47

'2-

.80

FUNC. VALUES: MIN: MAX: .80

1.00

1.20

1.40

10

9.08E+00 6.S2E+01

JOB NOUE 9908­18 14.20.30

­­ι 3

,o

.o !

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POSTBOSOR 1.04

•a

POSTBOSOR 1.04 ■STRESSES­ •STRESSES ­ CIRCUMF

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TRESCA 150

­ SHELL 4

SHELL* 1.10 1.10

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.80

1.00

1.20

1.40

10

aeOE+01 159E* 02

JOB NOUE 99­08­18 1451.11

MIN: MAX

.70

.80

.80

1.X

150

1.40

10

6.66E+01 159E+ 02

JOB NOUE 99­08­1B 14.21.41

> 3

NJ 00

ta ™

DBA Design by Analysis

Analysis Summary Example 1.1 IV- Check

7.19 (A) Member:

Analysis Type: F - Check

A&AB ANSYS 5.4

FE -Software: Element Types:

4 - node, 2 - D axisymmetric solid PLANE42 Boundary Conditions:

Zero vertical displacement in the nodes at the undisturbed end of the shell. Symmetry boundary conditions in the nodes in the centre of the flat end.

Model and Mesh:

ΛΝ

Whole height of model: 751.2 mm Number of

Results: Fatigue life = infinity

DBA Design by Analysis

l)ata|

Analysis Details Example 1.1 / F ­ Check

7.20 (A)

t ma , = 2 0 ° C tm,„ = 20°C

Rz = 50 μιη (table 18­8) en = 101,6 mm

t* = 0,75 t m „ + 0,25 L™ = 20 °C Rm = 460 MPa Rpo2„. = 255MPa

Δσ 0 = 310.8 MPa (table 18­10 for Ν > 2­106 cycles) Ν = 2.106 (for the first iteration)

EStressesI Critical point: Point of maximum equivalent stress (Tresca) Δσ..4, (total or notch equivalent stress range) = 75.55 MPa for Δρ=15.3 MPa Δσ^ηκ (structural equivalent stress range obtained by quadratic extrapolation from the shell side into the critical point) = 116.28 MPa

o

eq

=37.78 MPa (mean notch equivalent stress)

O eqmax — 75.55 MPa (maximum notch equivalent stress)

Aoslruc = Δσ β ,,, if Aos,„c > Aoeq,,, A aslrm = 75.55 MPa [Theoretical elastic stress concentration factor kJ

[Effective stress concentration factorKefj 1,5* ­1)

K, =Aa c q ,,/Ao s l m c = 1.0

struc Δσ„

|l8.8 Plasticity correction factor j_j mechanical loading lfAo slruc >2R p o, 2 „.

Thermal loading IfAos„

Δσ '0

with An

struc pO,2/t* 0,5 for 800 MPa < Rm < 1000 MPa 0,4 for Rm < 500 MPa ~Rm ­500" 0,4 + for 500 MPa < R m < 800 MPa 3000 2R

k

> 2 Rpo,2/t·

= 0,5 +

0,7 _ 0,4

Δσeq,l {

p0,2/t*

Ao=

K= Aa,otai = ke.AceqJ=

MPa

Else Δσ,ο,,ι = Δσ,0., = 75.55 MPa

Aam¡¿ = ku.Aaeq,,= Else Δσ10„ι = Aoe,,,=

MPa MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors. Ke and k, are to be calculated with the above formulas where Δσ 0 ,, is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor k„ is applied to the thermal stress tensors. Then tensors are added and the new stress range is calculated. Δσ„!Κ,0=Δσ Κ = 75.55 MPa (for usage ¡η 18­11­3) total

t

| 18­10­6­2 Temperature correction factor f,. Fort*> I00°C f,. = 1,03 ­ 1,5 10"" t*­1,5 10"61*2 = Elsef,.= l

|l8­l 1­1­1 Surface finish correction factor fj fs = F,l0'"n(N,­°'465] if Ν 2.106, with Fs = 1­ 0,056 [In (Rz)]02.10 6 :f e = Fe ForN*;l.5f

-

-1Ό0

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1.00

1.20

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2.00

2.50 10

-1.62E+02 1.91E+02

JOB N012 99-08-20 1+.3S.45

//

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1.60

V

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1.40

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JOG N012 9 » 0 9-20 1+.3+.S2

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FUNC. VALUES: MIN: MAX:

637E.O' 2.47E+ 02

JOB N012 99­0Θ­20 14.38.51

Ν co 4^

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POSTBOSOR 1.04

7.0O

10

POSTBOSOR 1.04

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+.50 2.80

2.70

2.80

2.90

3.00

4.36E.O0 7 07E­00

Ι it.

a ^­ τ?

FUNC VALUES: MM: MAX:

JOB N012 S­"H»­20 14.37.56

10

s?

2.8

0

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zoo

3.00

V

­2.52E+01 3.38E+01

JOB N012 99­06­20 14 38.30

PI χ > io 1

POSTBOSOR 1 0 4

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■STRESSES" TRESCA SHELL 2

"INSIDE"

'OUTSIDE"

­OUTSIDE­

S ■ S B _ Ό i (linearised equivalent stress range) = 230.2 MPa (T e n =

135.8 MPa (mean notch equi\

^Theoretical elastic stress concentration factor KJ

Oeqmax = 271.6 MPa (maximum notch equivalent stress)

¡Effective stress concentration factorK^j 1,5« ­1)

Κ,=Δσ.„ 1 /Δσ ! , η10 = 1.1798

struc

|l8.8 Plasticity correction factor kJ mechanical loading lfAo e a ,>2R. p().2/l* ( Δσ eq, I k =1 + A 2R p0,2/t*

Thermal loading lfAa c2R p02 „. k

0,5 for 800 MPa < Rm < 1000 MPa with A0

0,4 for Rm < 500 MPa 0,4 +

R m ­ 500

­ ­ ­ 0 · 7 ­ 0,5 + Δσ eq, 1 l

for500MPa < R „ < SOOMPa

p0,2/t*

3000

Ao­.... ke = Δσ,ο,,] = ke.AOe,,^

k„ = Aolota] = ku.AaeqJ= . ...MPa MPa Else Δσ,οι,ι = Δσ„, =

MPa

Else Δσ10„ι = Δσ„,, = 271.66 MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors. Ke and kv are to be calculated with the above formulas where Aa eqJ is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor ku is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. Ασ„ 5 0 % 1 ς =Δσ

total

'Κ =228.7 MPa (for using in 18-11-3) t

18-10-6-2 Temperature correction factor f,. Fort*> 100 °C ft. = 1,03 - 1,5 W4 t* -1,5 10"6 t*2 = Elsef,.= l

[18-11-1-1 Surface finish correction factor fj f = F [0,!ln(N)-0,465]

with Fs = 1-0,056 [In (Rz)]0"4[ln(Rn1)] +0,289 [In (R2)]° Fs = 0.7735 f, = 0.8104

Analysis Details Example 1.2 / F-Check

DBA Design by Analysis

-2 Thickness correction factor fj en < 25 mm 25 mm 150 mm

_, [0,lln(N).0,465] re

f = 0 7217[0,""(N)'0,46S1

with F.= (25/e„)°,!2 = 0.9943 f. = 0.9953

f.= l

7.39(C)

f„ =

8-11-1-3 Mean stress correction factor f j If Δσ„„0 < 2 RP( and ocumax < Rpc

IfAo,„>2R 1 ) (

If Δσΐ1Γ« < 2 Rpo,2/,· and cftqlnax > Rpo,2/t·

If CTeq > 0 then c T e q r = Rpo,M. If CTCq < 0 then cr eqj r =

"

Δα», 2

2 ° " - Rp0,2/t*

and CTeq = c r e q r = 119.2 MPa

For Ν > 2-10 cycles See figure 18-14

For Ν < 2-10° cycles M = 0,00035 R m -0,1= 0,061 f-R„(

if — κ < a e qH < Rpo,2/,· then 2(1 + M)

2(1 + M ) M(2 + M ) ( 2 ø e q

0,5 = 0.9592

l + M Ι Δσ

m

_ l + M 3 ΜΓ2σ ε ς " l+M " 3 Δσ„ fm= 1

fm=.

18-11-2-1 Overall correction factor f, f .f .f ,f

f = s e m t« ^o.65l4 K.ff

118-11-3 Allowable number of cycles N| Ί2 4.6-10' Ασ

eq,struc

~1

0.63R

10

ifN 73

■OUTSIDE­

4.CO .00 3.50

­.50

3 00

­1.00 FUNC VALUES UN: MAX

-130 1so.

224

22»

tM

2.30

222

234

2.36

uÌ

,»2

FUNC. VALUES:

200

­1.S8E+02 1.66E+02

MIN: MAX:

130 JOB

N0132 2,22

16.23.16

22

*

22t

2 26

uo

23t

JOB 234

2.36

2.38

1.39E+02 6.24E.02 N0132

10 16.24

χ •r.

m

5.00 .

­o_ -
2R p o, 2 ;,.

IfAo s l r u c >2R p 0 , 2 / t .

0,5+r

Δσ k

e

= I + A„ U

struc 2R

_ ,

p0,2/t*

0.7 0,4 Ασ p0,2/t*

0,5 for 800 MPa < Rm < 1000 MPa with Ao =

0,4 for Rm < 500 MPa 0,4 Η

Rm -500" 3000

for 500MPa < R m < 800 MPa

Ao=

Δσ = ky AOeqi = . .MPa Else Δσ = Aastmc ....MPa

K= Δσ = ke AOe,,] = MPa Else Δσ = Δσ„ Γ „ = 416.7 MPa

It both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors . Ke and kv are to be calculated with the above formulas where Δσ ες ι is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor k„ is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated.

8-10-6-1 Thickness correction factor feJ 25 mm 150 mm

few = ( 2 5 / e n ) 0 2 s = fTO=

few = 0,639

DBA Design by Analysis

Analysis Details Example 1.3/F-Check

7.60 (A)

|l8-10-6-2 Temperature correction factor ft.| Fort*> 100 °C Elsef,.= l

f,.= 1,03-1,5 10 V - 1 , 5 10 6 1 * 2 =

|l 8-10-6-3 Overall correction factor f J f«, = few-ff = 1

|l 8-10-7 Allowable number of cycles N| ί σ =416.7 MPa s then

M = 3andC(C 1 orC„) = 5-10"

m

N= ,

,„ =6910 cycles

If -Q < Δσ5 to cycles and other

If ,

cycles with f_* > Aa s to6 cycles

cycles with f

then M = 5andC(C L orC„) =

then

N= , c,„ =

N=°°

< AGs ,ο cycles and all other < Δσ 510 6 cycles

Note: All unwelded regions are less critical Note: In this example both approaches - the equivalent stress range approach and the principal stress range approach - have been used. The maximum principal stress is the tangential stress component and it is positive, the minimum one - pressure - is negative and small. Therefore, the difference in the results is small.

Analysis Details Example 1.3 / F­Check

DBA Design by Analysis

7.61(A)

l)ata| Critical point: Weld end to shell, inside; Equivalent stress range approach t„,„ = 20 °C Um = 20 °C t* = 0,75 Ux + 0,25 tm Rm = 410MPa ^pO.2/1*

en =21,5 mm Δσβ(5 m6Cycies) = 46 MPa (class 63) equivalent stresses or

= 20°C

■ 255 MPa

principal stresses

m = 3 C ­ 5­10"

m = 3 Ci =

m = 5 C = 1.08­10"

m = 5 C±=

C„=

¡Stresses! Adsiruc = 428.1 MPa (structural equivalent stress range.determined by extrapolation)

|l 8.8 Plasticity correction factor kJ

mechanical loading

Thermal loading

lfAo slruc >2R„ (

lfAa.. r „>2R 0 (

1 +A, p0,2/t*

0,5 +

0.7 0.4

0,5 for 800 MPa < Rm < 1000 MPa with A0 =

p0,2/l"

0,4 for Rm < 500 MPa 0,4 +

Ao= ke= Δ σ = k e AOeqJ =

Else Δσ = Δσ„

Rm­500 3000

for500MPa < R m < 800MPa

k„=

.MPa ■■ 428.1 MPa

Δσ =k„AOeq.i=

Else Δσ = Δσ„Γ„ =

MPa

MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors. K, and kv are to be calculated with the above formulas where Δσ 0 , ι is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor ku is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated.

18­10­6­1 Thickness correction factor fêJ en < 25 mm f.» = l

25 mm < en < 150 mm = (25/ few =

en > 150 mm fe„ = 0,639

Analysis Details Example 1.3 / F-Check

DBA Design by Analysis

7.62(Aj

118-10-6-2 Temperature correction factor f,.| Fort*> 100 °C Elsef,.= l

f,. = 1,03 — 1,5 10"" t* -1,5 10"V 2

|l 8-10-6-3 Overall correction factor f J f„ = fe„.f,· = 1

18-10-7 Allowable number of cycles N| f»

416.7 MPa

If f" >Δσ 5 to6 cdes then

If

M = 3andC(C 1 orC„) = 5.10'

cycles with fCT > Δσ5 io cycles then M = 5 and C (C ± or C„) = N=- c =

m

= 6373 cycles

POSTBOSOR 1.04

ñ 8.

260 "STRESSES"

­STRESSES* 2.40

■

220

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FUNC, VALUES:

\ .80

1.00

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MN: MAX

10

FUMO VALUES: 1.00

­ MIS: MAX:

7.17E+01 ? bZE­.C z

JOB N014 99W­19 12.50.58

20

.40

.60

.80

1.00

1.20

IO

2

7.­7Γ.01 3i8E*02

JOB N014 M­oe­1'i 12.57.38

Ν NI Ν

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POST BOSOR 1.04

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FUNC VALU ES:

FUNC. VALUES:

MW: MAX:

ΗΝ: MAX

6.43E·*» 3 81-.-fi·

JOB

­

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N014

1.80

1.80

2.00

220

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.40

MIN: MAX:

20

­1.17E+02 1.38E*02

10

­

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N014 1,40

13.07.05

η

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Q 1NSIDE­ OUTSIDE*

1.00

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140

120

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3 s Έ.3 TIME-, 1 SINT (AVO! PowerOraphice EFACET"-1 AVRE3=Nat DHX = , 1 6 3 2 3 1 SMN = 1 , 7 1 3 SMX - - 1 3 6 . 0 1 7

Figure 7.5.4-3

DBA Design by Analysis

Analysis Details Example 1.4 / F­Check

7. 83 (A)

Welded region / Principal stress range approach / Critical point: Node 3052 e„ = 13,7 mm t™„ = 20°C ΔσΠ(5 io6cycte) = 52 MPa (class 71) t* = 0,75 t m „ + 0,25 U , = 20 °C equivalent stress«? or principal stresses Rm = 410MPa m = 3 C; m = 3 C 1 = 7.16­10" Rpo 2i,- = 265/245 MPa Q, = Used: R,p0,2/t* ■ 245 MPa m = 5 C±= C„ = ■max "" *■·" *—

[Stresses! Critical point: Weld toe in nozzle (inside): Node 3052 Atomic = 225,6 M P a (structural equivalent stress range.determined by extrapolation) (obtained by quadratic extrapolation on inside of nozzle)

18.8 Plasticity correction factor kJ

thermal loadinu

mechanical loading

l f A a s m c > 2 R , p0,2/t*

If ACTstruc> 2 Rpo,2/t*

0,7

Ασ

0,5 + p0.2/t*

with A0 =

0.­1

Δσ . p0,2/t"

0,5 for 800 MPa < Rm < 1000 MPa 0,4 for R,„ < 500 MPa R m ­ 500 0,4 + for500MPa < R m < 800MPa 3000 k„=

A0=

Δσ =k„Ac slnic = . .MPa Ao = k e Ao smic = MPa Else Δσ = Aastn,c = ... MPa Else Δσ = Δσ„ Γ „= 225.6 MPa It' both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors . ke and kv are to be calculated with the above formulas where Aae_j is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor k^is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. ke =

18­10­6­1 Thickness correction factor f j en < 25 mm

25 m m < e „ < 150 mm

e„ > 150 mm

f„ = (25/00·25 = tew —

f™ = 0.639

Analysis Details Example 1.4 / F­Check

DBA Design by Analysis

7.84 (A)

118­10­6­2 Temperature correction factor ft«j Fort*> 100 °C Elsef,.= l

f,.= 1,03­1,5 10"* t* ­1,5 10"61*2 =

|l 8­10­6­3 Overall correction factor fj f =f •w

f.. = 1

íew­M*

'

118­10­7 Allowable number of cycles N| = 225.6 MPa

f.

If

f

­ >Δσ 5 ιο cycles then

m = 3 and C (C_ or C„) = 7,16­10'

if

< Δσ;5 10

cycles

and other

cycles with f° >Δσ 5 ., 0 cycles then m = 5andC(C1orC„) =

Ν

(tí

= 62380 cycles

c

m

N=­

=

If f° . is the full mechanical and thermal equivalent stress range. The factor k e is applied to the mechanical stress tensors and the factor ky is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. 18-10-6-1 Thickness correction factor few

en < 25 mm 'ew

—

t

25 mm < en < 150 mm few = (25/en)0-25 = few =

e n > 150 m m few = 0.639

Analysis Details Example 1.4/F-Check

DBA Design by Analysis

7.86 (A)

|l8-10-6-2 Temperature correction factor ft*| ft.= 1,03-1,5 10"V-1,5 10"61*2

Fort*> 100 °C Else ft-= 1

|l8-10-6-3 Overall correction factor fj fw = fcw.f,. = l

18-10-7 A Now a ble n um be r of cycles 1N| "ζ = 350.7 MPa If f" >Δσ 5 ιο cycles then m = 3 a n d C ( C 1 o r C „ ) = 7.16-10"

m

16600 cycles

If f

< Δσ 5 m cycles and other If 6

σ

(

< Δθ5 io cycles a n d all °th e r

Cycles with *" > Δσ 5 .| 0 cycles cycles with then m = 5andC(C1orC„) =

Ν

-(ίΓ

σ

{

< Ads m6 cycles then

DBA Design by Analysis

Analysis Details Example 1.4 / F­Check

7 . 8 7 (A)

| Data| Welded region / Principal stress range approach Critical point: Node 3038 W = 20 °C e„ = 13,7 mm t™, = 20 o C Δσ 0 ( 5 io6cycies) = 52 MPa (class 71) t* = 0,75 W + 0,25 tmir = 20 °C equivalent stressés or principal stresses R m =410MPa m = 3 C_ = 7.16­10 m = 3 c / Rpo,2/f = 265/245 MPa Q,= Used: R,p0,2/t* = 245 MPa

mÁ C =

m=5 d­

c„ = ptressesj Critical point: Weld toe in nozzle (outside): Node 3038 AOstmc = 318,0 M P a (structural equivalent stress range)

(maximum value used, since quadratic extrapolation on outside of nozzle gives larger value) |l8.8 Plasticity correction factor kJ

Thermal loading

mec 11anical loading

IfAo sm ,c>2 Rpo,2;t·

IfAas,r„c>2RD( Δσ 2R

0,5 +

0,7 0.4 Δσ

p0,2/t*

ρ0,2/Γ 0,5 for 800 MPa < Rm < 1000 MPa withA 0 =

0,4 for S^, < 500 MPa 0,4-

"Rm­500

for500MPa < R „ < 800 MPa

3000

k„= Δσ = ^ Δ σ 5 Μ 0 = Else Δσ = Δσί(Γι1

A0= ke=

Ao = keAasmic= ... .MPa ElseAo = AoslrUc = 318.0 MPa

.MPa ...MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors . kt. and kv are to be calculated with the above formulas where Δσος,ι is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor k„ is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. 18-10-6-1 Thickness correction factor fm en < 25 mm

25 mm < en < 150 mm f „ = (25/en)0·25 =

en > 150 mm = 0.639

Analysis Details Example 1.4/F­C heck

DBA Design by Analysis

7.88 (A)

|l 8­10­6­2 Temperature correction factor f,.| Fort* > 100 °C Elsef,.= l

f,.= 1,03­1,5 10"*t* ­1,5 10"61*2 = .

18­10­6­3 Overall correction factor fj fw = few.f,. = 1

[18­10­7 Allowable number of cycles N| fw" =318,0 MPa If f" >Δσ 5 ιο cycles then m = 3 and C (Ç. or C„) = 7.16Ί0 1

N = , \ m = 22270 cycles

t

If

a

f

2Rpo.2/,.

IfAOsmc>2Rpo,M· Δσ, _struc_ _ | 2 Κp0,2/t*

with A0 =

°·7

k - 0,5 +

0,5 for 800 MPa < Rm < 1000 MPa 0,4 for R„ < 500 M Pa Rm-500" 0,4 + 3000

Ao= ke= Δσ = ke Δσ51ηις = MPa Else Δσ = Δσ >ιπκ = 324.2 MPa

Γ

Δσ

struc

ρΟ,2Λ"

Δσ =kuAastnic= Else Δσ = Δσ5η110=

MPa MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made on each component of the stress tensors . ke and kv are to be calculated with the above formulas where Aa eq j is the full mechanical and thermal equivalent stress range. The factor ke is applied to the mechanical stress tensors and the factor ku is applied to the thermal stress tensors. Then both tensors are added and the new stress range is calculated. |l8-10-6-l Thickness correction factor f,J en < 25 mm f«- = l

25 mm < en < 150 mm ftv, = (25/e„f25 = f =

e„ ^ 150 mm few = 0.639

Analysis Details Example 1.4/F-Check

DBA Design by Analysis

7.92 (A)

¡18-10-6-2 Temperature correction factor ft.] f,.= 1,03-1,5 1 0 V - I , 5 10"Ί* 2 =

Fort* > 100 °C Elsef t .= l

|l8-10-6-3Overall correction factor fjj f„=fe„.f,.= l JI8-I0-7 Allowable number of cycles N| ¥■ = 324.2 MPa

If f > Ac5 10

cycles

then

m = 3 and C (C± or C„) = 7.16­10'

If f

Δθ 5 io' cycles then

If f" . Equivalent Stress for Wind Loading.

1 atr

V

, . ¿

s

2. Material properties: •

Shell (X6Cr Ni Ti 18­10): material strength parameter RM = 224MPa, modus of elasticity E = \93GPa, coefficient of linear thermal expansion a = 16.4 IO"6 il K.

•

ring (P235 GH): material strength parameter RM = 202MPa, modulus of elasticity E = 209 GPa, coefficient of linear thermal expansion a = 12.2 ■ 10­6 1 / K.

3. Admissiblity check against to GPD. Using the application rule in prEN­13445­3 Annex B.9.2.2 to check against GPD, the principle is fulfilled when for any load case the combination of the design actions do not exceed the design resistance. The analysis was carried out using the elastic compensation method conforming to the direct route rules for GPD in Annex B: linear elastic ¡deal ­ plastic material law, Tresca's yield condition and associated flow rule and first order theory. For shell elements it is not currently possible to calculate limit loads based directly on Tresca's condition from elastic compensation.

DBA Design by Analysis

Analysis Details Example 2 / GPD- & PD-Check

7.95 (S)

Models utilising shells have only one element through thickness. Instead of carrying out the analysis using a Tresca or Mises model directly, a generalised yield model is used which considers the element's thickness. In elastic compensation, the Ilyushin generalised yield model is used in the calculation of limit stress fields. Ilyushin's model is based Mises' condition, the limit load will require correction to meet the code rules on the use of the Tresca condition. The maximum ratio of Mises' equivalent stress to Tresca's equivalent stress for the same load is 2Λ/3. Therefore, applying a factor of V3/2 to the yield stress in the Mises analysis will always lead to a conservative result for the Tresca condition. Admissibility checks are required for the following three load cases: (1) Hydrostatic pressure at maximum medium level, dead weight, wind load. (2) Hydrostatic pressure at minimum medium level, draining pressure, dead weight and wind load. (3) Draining pressure, dead weight and wind load The full model is used in the check against GPD for the above three load cases. Materials defined for the analysis have proof strengths of 224 MPa and 202 MPa for the shell and ring respectively. From prEN-13445-3 Annex B, Table B.9-3, the partial safety factor yR on the resistance is 1.18 and 1.25 for the shell and ring respectively. The design material strength parameter used in the calculations are given by applying the partial safety factors and Mises' correction, i.e. the design material strength parameter for the shell is 164.4 MPa and for the ring it is 140 MPa. For the loading, according to prEN-13445-3 Table 5.B.9.2 the partial safety factors are Hydrostatic pressure (pressure with natural limit) Draining pressure (pressure without natural limit) Dead weight (action with unfavourable effect) Wind load (variable action) In the specification, the weight of the insulation is 220 N/m2 (weight per unit surface area) or 110 kg/m2. To apply this as a density to the model, the value has to be divided by the thickness of the shell. The resulting densities for the insulation are then added to those of the steel, 7930 kg/m3 for the shell and 7850 kg/m3 for the ring. A pressure equivalent to the weight of the roof is applied over the top edge of the shell. The partial safety factor for the dead weight is applied to the densities and roof weight for use in the model. The equivalent stress distribution for the dead weight only is shown in Figure 7.6.1-2.

γ ρ =1.0 γ ρ =1.2 γο=1·35

γο=ι.ο ANSYS 5 . 4 APR 2 7 1 9 9 9 14:28:50 NODAL S OL U T K 3TEP=1 SUB = 1 TIME=1 SEOy (AVG PoweiGraphics EFACET=1 AVRES=Mat DMX = . 9 4 8 6 9 SMN = . 2 3 9 1 2 5 SMX = 8 1 . 0 9 6 M

"5 S S S 5 I

Figure 7.6.1-2: Equivalent stress for dead weight

I

.239125 9.223 IB.207 27.191 36.175 45.159 54.144 63.126 72.112 81.096 .239125 9.223 18.207 27.191 54.144 63.128 72.112 81.096

DBA Design by Analysis

Analysis Details Example 2 / GPD- & PD-Check

7.96 (S)

Load case 1 For load case 1, hydrostatic pressure at maximum medium level of 19.68 m, dead weight and wind load corresponding to that defined in ANSYS 5 . 4 APR 27 1999 the specification are checked against 1 3 : 5 9 49 PLOT O. 17 GPD. In checking for admissibility of STEPthe applied loads using elastic com­ SUB TIKE= pensation a lower bound limit stress ILYIELD (NOAVG) field must have an Ilyushin function 688535 123E-04 329957 less than 1 where the Ilyushian function 123E-04 _ 073333 f(IL) is BOTTOM DHX

ƒ(/£) = £

=

SMN

=

3KX

=

rzrj

1D9994 14 6655 163315 219976 256636 329957

Where o e is the element stress and R Δσ 5 io6 cycles

cycles with

then

then

σ {

cycles5

and all other

Ν = 1984 cycles (each cycle is equal to 100 variations between hmax and hmm and 1 complete draining and filling)

DBA Design by Analysis

| Data|

Analysis Details Example 2 / F-Check

7.115(C)

Weld 5 / Equivalent stress range approach en = 6 mm Ασ0(5 loVies) = 59 MPa (class 80) equivalent stresses m = 3 C=l,02-10 12

t m „ =60 °C Un = 20 °C t* = 0,75 tmax + 0,25 U„= 50 °C Rm = 520MPa R pliM . = 224 MPa

m = 5 C = 3,56-1015

|Stresses| ACTstruc = 361,7 / 83,5 MPa (structural equivalent stress range, determined by extrapolation)

[l 8.8 Plasticity correction factor kj Thermal loading

mechanical loading

IfAa., m c >2R D ]

IfAosm,c>2Rpl,o„. k =1 + 0,4

Δσ

0,7

2 K

pi,O/t*

0,5-Ι­

Ο. 4

Ασ . pi, O/t"

k.= Λσ- k c Aa a .MPa Else Δσ = Δσ„Γ„, = 361,7 / 83,5 MPa

Δ σ = kyAOstruc

Else Δσ = Δσ»

.MPa ... MPa

If both mechanical and thermal loadings are to be considered, the correction has to be made in each component of the stress tensors . ke and kv are to be calculated with the above formulas where Δσ„ς,ι is the full mechanical and thermal equivalent stress range. The factor kc is applied to the mechanical stress tensors and the factor k„is applied to the thermal stress tensors. Then both tensors are added and the new stress ranee is calculated. 18-10-6-1 Thickness correction factor f j en < 25 mm

25 m m < e n < 150 mm

en > 150 mm

few=(25/e„)°-2s = few =

f™, = 0,639

Analysis Details Example 2 / F­Check

DBA Design by A nalysis

7.116(C)

|l 8­10­6­2 Temperature correction factor ft.| For t* > 100 °C Elsef,.= l

f,. = 1,043 ­ 4,3 10­41* = .

|l 8­10­6­3 Overall correction factor f J fw = few.f.. = 1

|18­10­7 Allowable number of cycles N| , ° = 361,7/83,5 MPa 'f C

> A

° 5 l0 "> Ν = 9718 cycles (each cycle is equal to 100 variations between hmax and hml„ and 1 complete draining and filling)

DBA Design by Analysis

Analysis Details Example 2 / I­Check

/ . I I / (A)

Stability check ofring at small end of cone: Load case: Self weight of vessel, vessel fully filled, wind: Maximum radial force resultant at inner ring surface: (diameter 4000 mm), determined from FE­analyses (Direct Route using elasto­plastic FE, corresponding linear­elastic calculation): qr= ­99 Nimm This value corresponds to the characteristic value of the actions. The partial safety factors for the actions are y0 = 1.35 for self weight Yp.hyiim = 1 ­0 f° r 'he hydrostatic pressure due to filling /__ = 1.0 for the wind action, seepages 7.104. Since the force (per unit length) due to the filling weight is much larger than the forces due to wind moment and self weight, see page 7.120, the characteristic value of the effective radial force given above is used also as design value, i. e. ya = 1.0 is used for all actions in the following. If a more accurate result is required, the contribution of self weight, given by nsw, could be multiplied by yG = 1.35. This results in a design value of the effective radial force of \n, + *■„ +yr -\n,J 1re.ä = -

ι

· 1re = 1.023