the eu approach to dba

1 Copyright © 2002 by ASME

Proceedings of the 2002 ASME PVP ConferenceAugust 4-8, Vancouver, British Columbia, Canada

THE EUROPEAN APPROACH TO DESIGN BY ANALYSIS

Josef. L. ZemanInstitute for Pressure Vessel & Plant Technology

Vienna University of TechnologyGusshausstr. 30/329, A-1040, Vienna, Austria

Email: [email protected]

ABSTRACTThis paper discusses the background of a new approach to

check the admissibility of pressure vessels via the Direct Route(DR) to Design by Analysis (DBA), and the various designchecks required, in general and in detail. Emphasis is on thevarious tools and procedures used in applications, and ontypical applications.

INTRODUCTIONWithin the European Union, the coming into force of

common national laws in the pressure equipment field, basedon the so-called Pressure Equipment Directive (PED) [1],paralleled by a serious need for corresponding complementaryHarmonised Standards – i. e. standards which provide forpresumption of conformity with the so-called Essential SafetyRequirements (ESR) of the PED –, created a unique chanceand challenge:

The chance for a new approach to Design by Analysis(DBA), using all the knowledge in engineering mechanics –theoretical as well as practical –, all the experience withnumerical methods and the commercially available hard- andsoftware used in the simulation of the behaviour of structuresunder various actions.

Work started in 1992, the first sketch of a draft datesOctober 1992, the draft went through (informal) enquiriesrepeatedly. The final public enquiry in 1999 was supported byan EU-research project, which resulted in proposals forchanges and in a handbook [2], with numerous examples, inputlistings, etc. The revised version of the draft standard [3] willbe subject to the Formal Vote from March 21 to April 21, 2002.

GENERALThe draft standard is restricted to sufficiently ductile

materials – A5 ≥ 14%, KCV ≥ 27 J.

The most advanced approach in the draft standard, the so-called Direct Route to Design by Analysis (DBA-DR), dealtwith in a normative annex, Annex B, is intended

- as an alternative to the "usual" Design by Formulae(DBF) route,

- as a complement to the DBF-route for:- cases not covered by DBF,- cases involving superposition of actions, e. g. wind,

snow, earthquake,- cases where DBA is required, e. g. by authorities in

potential major hazard, or environmentally sensitivesituations,

- exceptional cases where manufacturing tolerances areexceeded.

This route, DBA-DR, deals with various failure modesdirectly, in so-called Design Checks (DC).

These design checks are named after the main failuremode they deal with. Some design checks deal also with otherfailure modes, other than the main, name-giving one.

Design checks are formulated in the form of so-calledPrinciples, of design goals, allowing for different procedures toassess the fulfillment of the principles' goals. Some of theseprocedures are specified, as so-called Application Rules –generally recognized rules which follow the Principle andsatisfy its requirements. It is permissible to use alternativedesign rules, different from the Application Rules given,provided that it is shown that the alternative rule accords withthe corresponding Principle and is at least equivalent withregard to resistance, serviceability and durability.

To allow for flexibility, for easier future adaptations, apartial safety factor format is used in this Direct Route toDBA:

- Characteristic values of actions shall be multiplied bypartial safety factors of actions to obtain the so-calleddesign values of actions,


- (Relevant) characteristic values of material parameters,used in the design models, shall be divided bycorresponding partial safety factors (of resistances, ofmaterial parameters) to obtain their design values.

Partial safety factors of actions depend on the considereddesign check and the actions, and also whether an action actsfavourably or non-favourably.

Partial safety factors of resistances depend on theconsidered design check and the material.

The partial safety factors are calibrated with regard toresults for simple geometries with the formulae and thenominal design stresses in the main body of the standard, theDBF-route; and they are calibrated with regard to the Europeancivil engineering standards, thus adapted to standards ofenvironmental actions – wind, snow, earthquake.

There is one important exception:For materials with a ratio of the specified yield strength, or

proof strength, at calculation temperature and the specifiedultimate strength at ambient temperature above 0.625, theDirect Route to DBA allows for thinner walls – the safetyfactor of 2.4 against the ultimate strength at ambienttemperature, used in the determination of nominal designstresses in the DBF route, is replaced by a less stringentrequirement.

DESIGN CHECKS, GENERALDesign Checks are investigations of a component's safety

under the influence of actions with respect to specified limitstates.

Design checks shall be performed for various Load Cases– actions, or combination of coincident actions, classified intonormal operating load cases, special load cases and exceptionalload cases. Actions shall be specified by their characteristicvalues which are representative of the variation of the actionthat can occur under reasonably foreseeable conditions.

For the determination of the effects of (design) actionsspecific (physical) models – the Design Models – shall be used,and these depend on the design check considered.

Design Models are specified in detail in the next chapter.In the design models first-order-theory, i. e. geometrically

linear kinematic relations and equilibrium conditions for theundeformed structure, shall be used, except for the twofollowing cases.

- Instability design checks shall be based on non-lineargeometric relations – equilibrium conditions for thedeformed structure and non-linear kinematic relations;second-order theory – linear kinematic relations andequilibrium conditions for the deformed structure – maybe used, if it can be shown to be accurate enough

- In checks on structures and for actions wheredeformation decreases the action carrying capacity, i. e.where deformation has an unfavourable (weakening)effect, geometrically non-linear effects shall be takeninto account in gross plastic deformation and fatiguechecks. Examples are nozzles in cylindrical shells undertransverse moment, nozzles in cylindrical shells under

axial compressive forces, bends under closing moments,cylindrical shells with out-of-roundness, or withpeaking, under external pressure.

In the draft standard five design checks are specified:- Gross Plastic Deformation Design Check (GPD-DC)- Progressive Plastic Deformation Design Check (PD-

DC)- Instability Design Check (I-DC)- Fatigue Design Check (F-DC)- Static Equilibrium Design Check (SE-DC). All of these shall be considered. Some of these design

checks may not be relevant, and in some cases it may benecessary to investigate additional failure modes, like leakagesto the environment.

In general, each design check comprises various loadcases.

The design checks shall be carried out for the following(classes) of load cases, where relevant:

- Normal Operating Load Cases, where normalconditions apply

- Special Load Cases, where conditions for testing,construction, erection or repair apply

- Exceptional Load Cases, (voluntary) load cases whereonly general requirements are given, details left to thediscretion of the parties concerned

For each design check all relevant load cases shall beconsidered.

Of the five design checks prescribed as a minimum in thedraft standard, the two most interesting ones are discussed inthe following: GPD-DC and PD-DC.

The third prescribed one – the I-DC – incorporates nounusual, no new ideas, but specifies several useful applicationrules. Additional hints are given in [2].

The third prescribed one – the F-DC – refers to the "usual"fatigue calculation specified in the main body of the draftstandard. Of course, results of linear-elastic calculationsobtained in the course of design checks can be used, as inputvalues.

The fifth prescribed one – the SE-DC – encompasses theusual checks against overturning and rigid body displacement.

GROSS PLASTIC DEFORMATION DESIGN CHECKS The geometry of the Design Models used in these checks

shall agree with the actual design in all non-local details.Nominal values shall be used for individual dimensions withthe exception of thicknesses, for which analysis thicknessesshall be used, i. e. effective thicknesses available to resistactions in corroded condition – nominal thickness minusallowance for material tolerances, allowance for possiblethinning during manufacture, and corrosion allowance.

In case of sub-models or part-models, the models shouldencompass all the necessary parts of the structure to includepossible elastic follow-up effects.

The constitutive law used in the Design Model shall be- linear-elastic ideal-plastic with


- Tresca's yield condition (maximum shear stresscondition) and associated flow rule

- specified strength parameters (design yield strength)

Rd /RMRM γ= , e. g. like the ones given in Table

B.8.2 for normal operating load cases. Mises' yield condition (maximum distortion energy

condition) may be used, but then the design strength parameter

(design yield strength) shall be multiplied by 23 / . The Principle reads: For each load case, the design value of the action, or the

combination of actions, with specified partial safety factors foractions, e. g. like the ones in Table B.8.1 for normal operatingload cases, shall be carried by the design model with, forproportional increase of all considered actions and a stress-free initial state, a maximum absolute value of the principalstructural strains less than

- 5% in normal operating load cases, and- 7% in testing load cases;

in exceptional load cases this strain limitation requirementdoes not apply.

The structural strain is the strain in a stress/strain-concentration-free model of the structure, i. e. the straindetermined in an idealized model which takes into account the(real) geometry of the structure with the exception of localdetails which cause only local stress/strain concentrations,which affect the stress or strain distribution only through afraction of the thickness.

Some models, e. g. FEM models with shell or beamelements, may give structural strains directly. Otherwise,models with lesser strain concentrations than the real ones maybe used, or quadratic extrapolation into the critical point – thehot-spot – with pivot points in distances from the hot-spot of0.4, 0.9 and 1.4 times the thickness at the hot-spot, see [3],B.7.6, and [2].

This strain limitation reflects the failure mode LocalExcessive Strain, but, of course, renders limit analysis results(and theorems) non-usable, at least in general – the GPD-DC isnot a limit analysis check (in the strict sense).

Usage of structural strains eliminates problems withmodels with possible singularities, allows for simpler models,and gives a clearly defined break-up point for the simulation.

PROGRESSIVE PLASTIC DEFORMATION DESIGNCHECKS

For the geometry of the Design Models used in thesechecks the same specification as for those in the GPD-DesignChecks apply, i. e. the very same model geometry may be used.

The constitutive law used in the Design Model shall be- linear-elastic ideal-plastic with- Mises' yield condition (maximum distortion energy

condition) and associated flow rule- specified design material strength parameters (design

yield strengths), e. g. for steels other than austeniticones the design yield strength is given by the specifiedyield strength, or the 0.2% - proof strength, at a

temperature not less than mincmaxc t.t. 250750 + , where

maxct and minct are highest and lowest calculation

temperatures at the position under consideration duringthe whole action cycle

The partial safety factors – for actions and for materialparameters – are equal to unity.

The Principle reads: For all relevant load cases, on repeated application of

specified action cycles to the design models progressive plasticdeformation shall not occur.

Two important application rules are specified:- Shakedown (SD) rule:

The principle is fulfilled, if the equivalent stress/strain-concentration-free model shakes down to linear-elasticbehaviour under the action cycles considered.

- Technical Adaptation rule:The principle is fulfilled if it can be shown that themaximum absolute value of the principal structuralstrains is not exceeding 5% after the application of thenumber of cycles specified for the considered load case.If the number is not specified, then a reasonablenumber, but not less than 500, shall be assumed.

PROBLEMS In the Gross Plastic Deformation Design Check Tresca's

yield condition in the constitutive law of the Design Modelposes a serious problem for usual soft- and hardware:

Most of the commercially available software packages doprovide for evaluation of equivalent stresses for Tresca's yieldhypothesis, but do not provide for elasto-plastic calculationswith Tresca's yield condition.

The Ansys distributor CADFEM had a complementarysub-routine "General Multisurface Plasticity" adapted for us,giving us the opportunity to use the principle fully. But theroutine is, on presently used computers very slow, and itrequires great care to avoid stability problems.

On the other hand, numerous simulations have shown thatin most cases, especially in cases involving more complicatedstructures, the usage of Mises' yield condition with reduceddesign yield strength does render quite acceptable results, at afraction of CPU-time: Given the possibility (by the equilibriumconditions, in the interior and at the boundaries) the stressdistribution (in the model) will converge to an optimal one withregard to the yield condition used – the decrease of the designyield strength will be partially compensated by the gain due tothe less conservative Mises' yield condition.

In the Progressive Plastic Deformation Design Check theapplication of the principle itself does lead to problems: Thereis no generally valid theorem for progressive plasticdeformation available. Usage of the Technical AdaptationApplication Rule is cumbersome and time consuming.

For the Shakedown Application Rule two simple, buteffective, tools are available:

- Melan’s Shakedown Theorem, and the


- Deviatoric Map.Both are described in the following.

For Progressive Plastic Deformation not to occur, thestructure must shake down (to linear-elastic behavior) or purelyalternating plasticity must occur – action cycles which do notresult in shakedown may still show pure alternating plasticity,and non-occurance of progressive plastic deformation may stillbe possible.

The Technical Shakedown Theorem and the SymmetryConditions, given in the following, encompass specific plasticdeformation pattern only, together they proved to be veryeffective tools to extend the range of admissible cycles bythose including alternating plasticity. In the application of theTechnical Shakedown Theorem, the Ivanov-Function, or theIlyushin-functions, are easy-to-use, effective tools.

THE DEVIATORIC MAPThe Deviatoric Map is a map of the stress (tensor) in the

form of an isometric representation of the principal stressvector (in the principal stress space), see Fig. 1 and [4].

The Deviatoric Map is a very convenient tool to illustrate astructure's behavior (at specific points) with regard to (ideal)plasticity, especially useful in combination with Melan'sShakedown Theorem. The deviatoric map loses some of itsinformation value in cases where the principal stress directionschange during the considered action cycle, but is still ofillustrative value.

MELAN’S SHAKEDOWN THEOREMThis very easy-to-use, strong theorem, a necessary and

sufficient condition for shakedown, reads:A structure will shake down (to linear-elastic behavior)

under a given cyclic action if there exists a time-invariant self-

equilibrating stress field )P(*ijσ such that the sum of this

stress field and the stress field )t,P(Eijσ , determined with the

(unbounded) linear-elastic constitutive law for the cyclicaction, is compatible with the yield condition, i. e. thecorresponding equivalent stresses nowhere and at no timeexceed the yield strength.

So complicated the theorem reads, so easy it is to use inconnection with modern soft- and hardware [6 ÷ 9, 12] see alsoFig. 2.

Self-equilibrating stress fields, stress fields which satisfy(solely) the equilibrium conditions, in the interior of thestructure and at the boundaries, with the imposed forces, caneasily be deduced from results of the GPD-DC: The differenceof the stress fields calculated for the same action, including themagnitude, for two different constitutive laws is a self-equilibrating stress field.

Each multiple of a self-equilibrating stress field is again aself-equilibrating stress field, and each linear combination ofself-equilibrating stress fields is a self-equilibrating stress field.

Therefore, the difference of the stress field calculated for aspecific action with the elasto-plastic constitutive law and the

stress field for the same action but for the linear-elastic law is a(very convenient) self-equilibrating stress field.

THE TECHNICAL SHAKEDOWN THEOREMThis theorem [5], very similar to Melan's shakedown

theorem, deals with so-called generalized stresses – the "usual"stress resultants of shell, plate and beam theory, like normalforces, bending moments, etc. Therefore, it should be usedonly for (relatively) thin-walled structures: Principal radii ofcurvature much greater than the thickness, typically 10>t/r ,lengths much greater than the thickness or cross-sectionaldimensions, typically 10>t/l .

This theorem reads:If there exists a time-invariant generalised self-

equilibrating stress field )P(Q ref*i such that the sum of this

generalised stress field and the (cyclically varying) generalised

stress field )t,P(Q refEi determined with the (unbounded)

linear-elastic constitutive law for the given cyclic action iscompatible with the local technical limit condition, for allpoints refP of the reference surface of the structure and every

instant of time, progressive plastic deformation (of a specificdeformation type) cannot occur.

Since this theorem is valid only for a specific deformationpattern, with "synchronous" plastification, it is in general onlya necessary condition for the avoidance of progressive plasticdeformation (for non-PD), albeit a very useful one.

The local technical limit condition specifies thecombination of generalised stresses which correspond to fullplastification of a cross-section, or along a shell normal.

For local technical limit conditions, very goodapproximations exist in the form of the so-called Ilyushin-function, or the Ivanov-function, mostly used by us anddescribed in the following.

THE IVANOV APPROXIMATIONApproximations for the local technical limit condition for

thin shells made of an isotropic material with linear-elasticideal-plastic constitutive law and Mises' yield condition weregiven by Ilyushin, in the form of the Ilyushin-functions [10,11].

Another approximation, given by Ivanov [11], and used byus, is the following one:

Denoting the non-dimensional stress resultants of thetheory of thin shells, standardized by the equivalent fullplastification values, by

,)/tRM/(mm

)tRM/(nn

ii

ii

42⋅=

⋅=

where RM is the (design) yield strength, and using thequadratic forms


xyxyxyyxyyxxnm

xyyxyxm

xyyxyxn

nm/)nmnm(nmnmQ

mmmmmQ

nnnnnQ

32

3

3222

222

++−+=

+−+=

+−+=

Ivanov's approximation is given by

1480

422

22 =

+−

−+++mn

nmmnnmmmn Q.Q

QQQQ/Q/QQ

Especially in combination with shell or plate elementsthese approximations are very useful, short post-processormacros render illustrative plots [7, 12].

SYMMETRY CONDITIONSWith the exception of obscure cases, alternating plasticity

requires some kind of symmetry of the plastic deformationpattern. This fact can be used to formulate symmetryconditions for the check whether alternating plasticity ispossible for cyclic actions outside of the shakedown regime.

The two following ones are valid for the frequently metone-parametric action cycles of the form

.)t(,A)t(A ooji αααα ≤≤−+ ∑∑The first one reads:Alternating plasticity is possible if there exist two time-

invariant self-equilibrating stress fields )P(*ijσ and )P(**

ijσsuch that, for all points where plastification occurs, the sums

)(Eijo

)(Eij

**ij

*ij

10 σασσσ ++−

and)(E

ijo)(E

ij**

ij*ij

10 σασσσ −++

are compatible with the yield condition, and where )P()(Eij

0σ

and )P()(Eij

1σ are the stress fields corresponding to ∑ iA and

∑ jA , respectively, determined with the (unbounded) linear-

elastic constitutive law.The second one, the easier one, reads:Alternating plasticity is possible if there exists a time-

independent self-equilibrating stress field )P(*ijσ such that,

for all points where plastification occurs, the sum of this stress

field and the stress field )P()(Eij

0σ determined for ∑ iA with

the unbounded linear-elastic constitutive law, vanishes.Both conditions can nicely be visualized in the deviatoric

map.

CONCLUSIONThe discussed new approach has proven to be a major step

forward in design by analysis. The approach has been shown tobe sound, and its application gives the designer much insightinto the structure's behavior, into the safety margins againstindividual failure modes. Therefore, this approach can lead todesign improvements, but also to improved in-serviceinspection procedures.

There are already enough application "tools" available.

Computing time, which may, for the required elasto-plasticcalculation, still be a matter of concern, will, with the increaseof computing power, become negligible in the future.

ACKNOWLEDGMENTSLacking enough space to list them separately, my thanks

go to all of my colleagues in the Sub-Group Design Criteria ofCEN TC 54 WG C and in the DBA research consortium and toall those who helped, with questions and comments, to bringthe draft into its present form.

Usage of Ansys under a university licence, and thevaluable support by CADFEM AG , is acknowledged.

REFERENCES1. Directive 97/23/EC of the European Parliament and ofthe Council of 29 May 1997 on the approximation of the lawsof the Member States concerning pressure equipment 2. The Design-by-Analysis Manual. EuropeanCommission, DG-JRC/IAM, Petten – The Netherlands, 1999.Free internet-version: http://www.ped.eurodyn.com/ via thelinks JRC, DBA. For error corrections see:http://info.tuwien.ac.at/IAA, English, link DBA

3. European Standard. Final Draft. PrEN13445-3, March2002: Unfired Pressure Vessels – Part 3: Design. CENEuropean Committee for Standardization.

4. Zeman, J.L., Preiss, R. The deviatoric map – a simpletool in design by analysis. Int. J. Pres. Ves. & Piping 76(1999) 339-344.

5. König, J.A. Shakedown of elastic plastic structures.Elsevier Science Publ. Co. Inc., 1987, p. 63.

6. Preiss, R. On the shakedown analysis of nozzles usingelast-plastic FEA. Int. J. Pres. Ves. & Piping 76 (1999) 421-434.

7. Preiss, R. Design-by-analysis of a chemical reactor'shead under sustained and thermal loads. Int. J. Pres. Ves. &Piping 77 (2000) 277-288.

8. Preiss, R. CEN's DBA applied to axisymmetricalstructures – a storage tank as an example. ProceedingsICPVT-9, Sydney, Australia, 9-14 April 2000, Vol. 1, 405-417.

9. Rauscher, F. Design by Analysis (DBA) – the directroute applied to some nozzles. Proceedings ICPVT-9,Sydney, Australia, 9-14 April 2000, Vol. 1, 487-495.

10. Burgoyne, C.J., Brennan, M.G. Exact Ilyushin yieldsurface. Int. J. Solids & Structures 30 (1993) 1113-1131.


11. Robinson, M.A. Comparison of yield surface for thinshells. Int. J. Mech. Sci. 13 (1971) 345-354.

12. Preiss, R. Ratcheting and shakedown analysis ofpressure equipment using elasto-plastic Finite-Element-Analysis. Doctoral Thesis. Vienna University of Technology ,2000.


Table B.8-1: RM and γ R for normal operating load cases

Material RM γ R

Ferritic steelp0,2/teH or RR 1,25 for 80

m/20

p0,2/t,

R

R≤

1,5625 m/20

p0.2/t

R

R otherwise

Austenitic steel(30%≤A5<35%)

p1,0/tR 1,25

Austenitic steel( A5 ≥35%)

p1,0/tR

1,0 for 40m/t

1.0/t p,

R

R≤

m/t

p1.0/t52

R

R,for 0,4 <

t/m

t/.p

R

R 01 ≤ 0,5

1,25 for 50m/t

p1.0/t,

R

R>

Steel castingsp0,2/tR 19/12 for ≤

m/20

p0.2/t

R

R 19/24

m/20

p0,2/t2

R

Rotherwise

As reference temperature of the temperature dependent material strength parameters a temperature not less than the maximumcalculation temperature of the load case shall be used.

Table B.8-2: Partial safety factors for actions and normal operating load cases

Action Condition Partial safety factorPermanent For actions with an unfavourable effect 2,1G =γPermanent For actions with an favourable effect 8,0G =γVariable For unbounded variable actions 5,1Q =γVariable For bounded variable actions and limit values 0,1Q =γPressure For actions without a natural limit 2,1P =γPressure For actions with a natural limit, e.g. vacuum 0,1P =γ

The upper characteristic value of the pressure may be based on the maximum allowable pressure PS, i. e. the pressureaccumulation at a pressure relief device when the pressure relief device starts to discharge, the pressure increase over the maximumallowable pressure, need not be taken into account.


Figure 1: The Deviatoric Map

Figure 2: Melan's Shakedown Theorem

Figure 3: Deviatoric map, nozzle in knuckle region of dished end, AP

Figure 4: Strain vs "time", nozzle inknuckle region of dished end Figure 5: Deviatoric map, cylinder cone

intersection, PD

les(P,t

ss(P)

1

E P P L1

E P P L2

E P P L3

the eu approach to dba

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