1
DBA
Design by Analysis
Introduction
Page
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 problem[1-6], 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
2
DBA
Design by Analysis
Introduction
Page
1.2
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
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
3
DBA
Design by Analysis
Introduction
Page
1.3
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.
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
4
DBA
Design by Analysis
Introduction
Page
1.4
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
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
5
DBA
Design by Analysis
Introduction
Page
1.5
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.
1.5 Literature
[1] 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.