3201_2e

Safety Standardsof theNuclear Safety Standards Commission (KTA)

KTA 3201.2 (06/96) (incl. rectification from BAnz 129, 13.07.00)

Components of the Reactor Coolant Pressure Boundaryof Light Water ReactorsPart 2: Design and Analysis

Komponenten des Primärkreises von Leichtwasserreaktoren;Teil 2: Auslegung, Konstruktion und Berechnung

Previous versions of this safety stan-dard were issued 10/80 and 3/84.

If there is any doubt regarding the information contained in this translation, the German wording shall apply.

Editor:

KTA-Geschaeftsstelle c/o Bundesamt fuer Strahlenschutz (BfS)Albert-Schweitzer-Strasse 18 • D-38226 Salzgitter • GermanyTelephone +49-5341/225-(0) 201 • Telefax +49-5341/225-225

KTA SAFETY STANDARD

June 1996Components of the Reactor Coolant Pressure Boundary of

Light Water Reactors;Part 2: Design and Analysis

KTA 3201.2

Previous versions of this safety standard (10/80 and 3/84) were made public in Bundesanzeiger No. 152a on Aug. 18, 1981 and No. 20a on Jan. 30, 1985

This KTA safety standard was prepared on behalf of Kerntechnischer Ausschuss (KTA) by the Fachverband Dampfkessel-, Behälter- undRohrleitungsbau e.V. (FDBR) and the Verband der Technischen Überwachungs-Vereine e.V. (VdTÜV)

CONTENTSFundamentals................................................................................... 5

1 Scope ...................................................................................... 5

2 General principles ................................................................ 6

3 Load case classes as well as design, service and testloadings and limits of components ................................... 6

3.1 General................................................................................... 63.2 Load case classes of the primary coolant circuit ............. 73.3 Loadings levels for components ........................................ 7

4 Effects on the components due to mechanical andthermal loadings, corrosion, erosion, and irradiation.... 8

4.1 General................................................................................... 84.2 Mechanical and thermal loadings ..................................... 94.3 Documentation of component loadings ........................... 94.4 Superposition of loadings and classification into

loading levels ........................................................................ 94.5 Corrosion and erosion ......................................................... 94.6 Irradiation.............................................................................. 9

5 Design .................................................................................. 105.1 General requirements ........................................................ 105.2 General requirements for components and their

welds .................................................................................... 115.3 Component-specific requirements .................................. 14

6 Dimensioning...................................................................... 186.1 General................................................................................. 186.2 Welds.................................................................................... 186.3 Claddings............................................................................. 186.4 Wall thickness allowances ................................................ 196.5 Wall thicknesses ................................................................. 19

7 General analysis of the mechanical behaviour .............. 197.1 General................................................................................. 197.2 Loadings .............................................................................. 227.3 Stress/strain loadings........................................................ 227.4 Resulting deformations ..................................................... 227.5 Determination, evaluation and limitation of mecha-

nical forces and moments ................................................. 227.6 Mechanical system analysis.............................................. 227.7 Stress analysis ..................................................................... 237.8 Fatigue analysis .................................................................. 277.9 Brittle fracture analysis...................................................... 297.10 Strain analysis ..................................................................... 317.11 Structural analysis.............................................................. 317.12 Stress, strain and fatigue analyses for flanged joints.... 317.13 Avoidance of thermal stress ratcheting .......................... 32

8 Component-specific analysis of the mechanicalbehaviour............................................................................. 45

8.1 General................................................................................. 458.2 Vessels.................................................................................. 458.3 Valve bodies........................................................................ 53

8.4 Piping systems.................................................................... 648.5 Component support structures ....................................... 78

9 Type and extent of verification of strength andpertinent documents to be submitted............................. 79

Annexes

A Dimensioning ..................................................................... 80A 1 General ................................................................................ 80

A 2 Dimensioning of parts of the pressure retainingwall....................................................................................... 81

A 2.1 General ................................................................................ 81A 2.2 Cylindrical shells ............................................................... 81A 2.3 Spherical shells................................................................... 84A 2.4 Conical shells...................................................................... 85A 2.5 Dished heads (domend ends) .......................................... 87A 2.6 Flat plates ............................................................................ 91A 2.7 Reinforcement of openings .............................................. 92A 2.8 Bolted joints ........................................................................ 98A 2.9 Flanges............................................................................... 105A 2.10 Gaskets .............................................................................. 113

A 3 Valves ................................................................................ 118A 3.1 Valve bodies ..................................................................... 118A 3.2 Valve body closures ........................................................ 124A 3.3 Bolts for valves ................................................................. 127A 3.4 Self-sealing cover plates.................................................. 127A 3.5 Valve flanges .................................................................... 128

A 4 Piping systems.................................................................. 128A 4.1 General .............................................................................. 128A 4.2 Cylindrical shells under internal pressure .................. 128A 4.3 Bends and curved pipes under internal pressure....... 128A 4.4 Bends and curved pipes under external pressure ...... 129A 4.5 Reducers ............................................................................ 129A 4.6 Butt welding tees ............................................................. 134A 4.7 Reinforcement of openings in pipe run........................ 136

B Calculation methods ....................................................... 139B 1 Freebody method............................................................. 139B 2 Finite differences method (FDM) .................................. 143B 3 Finite element method (FEM) ........................................ 149

C Brittle fracture analysis procedures .............................. 155C 1 Drawing-up of the modified Porse diagram with

example ............................................................................. 155C 2 Calculation method to determine the KI values ........ 156C 2.1 General .............................................................................. 156C 2.2 Prerequisites ..................................................................... 156C 2.3 Calculation ........................................................................ 156C 2.4 Alternative methods........................................................ 156

D Regulations and Literature referred to in thisSafety Standard ................................................................ 160

PLEASE NOTE: Only the original German version of this safety standard represents the joint resolution of the50-member Nuclear Safety Standards Commission (Kerntechnischer Ausschuss, KTA). The German version wasmade public in Bundesanzeiger No. 216a on November 19, 1996. Copies may be ordered through the Carl Hey-manns Verlag KG, Luxemburger Str. 449, D-50939 Koeln (Telefax +49-221-94373-603).All questions regarding this English translation should please be directed to:

KTA-Geschaeftsstelle c/o BfS, Albert-Schweitzer-Strasse 18, D-38226 Salzgitter, Germany

Comments by the editor:

Taking into account the meaning and usage of auxiliary verbs in the German language, in this translation thefollowing agreements are effective:

shall indicates a mandatory requirement,

shall basically is used in the case of mandatory requirements to which specific exceptions (and onlythose!) are permitted. It is a requirement of the KTA that these exceptions - other thanthose in the case of shall normally - are specified in the text of the safety standard,

shall normally indicates a requirement to which exceptions are allowed. However, the exceptions used,shall be substantiated during the licensing procedure,

should indicates a recommendation or an example of good practice,

may indicates an acceptable or permissible method within the scope of this safety standard.

KTA 3201.2

Fundamentals

(1) The safety standards of the Nuclear Safety StandardsCommission (KTA) have the task of specifying those safetyrelated requirements which shall be met with regard toprecautions to be taken in accordance with the state of sci-ence and technology against the damage arising from theconstruction and operation of the facility (Sec. 7 para. 2subpara. 3 Atomic Energy Act), in order to attain the pro-tection goals specified in the Atomic Energy Act and theRadiological Protection Ordinance (StrlSchV) and which arefurther detailed in "Safety Criteria for Nuclear Power Plants"and in "Guidelines for the Assessment of the Design of PWRNuclear Power Plants against Incidents 1) pursuant toSec. 28 para. 3 of the Radiological Protection Ordinance(StrlSchV) - Incident Guidelines".

(2) Criterion 1.1, "Principles of Safety Precautions", of theSafety Criteria requires, among other things, a comprehen-sive quality assurance for fabrication, erection and opera-tion, and Criterion 2.1, "Quality Assurance", requires,among other things, the application, preparation and obser-vation of design rules, material specifications, constructionrules, testing and inspection as well as operating instruc-tions and the documentation of quality assurance. Criterion4.1 "Reactor Coolant Pressure Boundary" principally re-quires, among other things, the exclusion of dangerousleakage, rapidly extending cracks and brittle fractures withrespect to the state-of-the-art. Safety Standard KTA 3201.2 isintended to specify detailed measures which shall be takento meet these requirements within the scope of its applica-tion. For this purpose, a large number of standards fromconventional engineering, in particular DIN standards, arealso used; these are specified in each particular case. For thecomponents of the reactor coolant pressure boundary therequirements of the aforementioned safety criteria are fur-ther concretized with the following safety standards

KTA 3201.1 Materials and Product Forms

KTA 3201.3 Manufacture

KTA 3201.4 Inservice Inspections and Operational Moni-toring

as well as

KTA 3203 Monitoring Radiation Embrittlement of theMaterial of the Reactor Pressure Vessel ofLight Water Reactors.

(3) KTA 3201.2 specifies the detailed requirements to be metby

a) the classification into code classes, load case classes andlevel loadings

b) the design and analysis of components

c) the calculation procedures and design principles forobtaining and maintaining the required quality of thecomponents

d) the documents for the certificates and demonstrations tobe submitted.

(4) Requirements not serving the purpose of safe inclusionof the primary coolant are not dealt with in this safety stan-dard.

1 Scope

(1) This safety standard applies to the design and analysisof the components of the reactor coolant pressure boundaryof light water reactors made of metallic materials, which areoperated up to design temperatures of 673 K (400° C).

(2) The primary coolant circuit as reactor coolant pressureboundary of pressurized water reactors comprises the fol-lowing components, without internals:

a) reactor pressure vessel

b) primary side of the steam generator; the steam generatorcalandria including the feedwater inlet and main steamoutlet nozzles up to the pipe connecting welds, howeverexcluding the smaller stubs and nipples, shall also fallunder the scope of this safety standard

c) pressurizer

d) reactor coolant pump casing

e) interconnecting pipework between the aforementionedcomponents and any valve body installed on this pipe-work

f) pipework downstream of the aforementioned compo-nents including the installed valve bodies up to and in-cluding the first isolating valve

g) pressure walls of the control element drive mechanismsand the in-core instrumentation.

(3) The primary coolant circuit as reactor coolant pressureboundary of boiling water reactors comprises the followingcomponents, without internals:

a) reactor pressure vessel

b) pipework belonging to the same pressure space as thepressure containment including the installed valve bod-ies up to and including the first isolating valve; pipe-work penetrating the containment shell and belonging tothe same pressure space as the reactor pressure vessel upto and including the first isolating valve located outsidethe containment shell

c) pressure walls of the control element drive mechanismsand the in-core instrumentation.

(4) This safety standard also applies to the die-out lengthsof component support structures with integral connections.

Note:

For the limitation of the d ie-out lengths o f component supportstructures with integral connection clause 8.5 shall apply.

Regarding component support structures with non-integralconnections for components o f the reactor coolant pressureboundary KTA 3205.1 shall apply.

(5) This safety standard shall also apply to the design ofpipes and valves with diameters not exceeding DN 50where loadings occur which require a fatigue analysis.

Note:

Simplified procedures are given in cl. 8.4.1 (6).

Requirements for instrument lines are laid down in KTA 3507.

KTA 3201.2

2 General principles

(1) For the design and analysis the principles laid down inthis section shall be adhered to. According to Section 3"Load case classes of the primary circuit and design, serviceand test loadings and limits of components" the load casesshall be classified for each specific plant and system due totheir different safety-criteria and the related loading levelsshall be laid down for each specific component. Dependingon this the loadings occurring shall be evaluated and belimited in which case the influence of the fluid (corrosionand erosion) shall be properly taken into account (seeclause 4.5).

(2) The design shall be made in accordance with the rules ofSection 5 "Design". The use of other designs than thosespecified in Section 5 and Annex A shall be subject to spe-cific verifications.

(3) The mechanical strength shall be verified in two steps:

a) as dimensioning in accordance with Section 6

b) as analysis of the mechanical behaviour according toSection 7 or 8 or in combination of sections 7 and 8.

(4) Within dimensioning the effective sections (wall thick-nesses) shall be determined to ensure that internal pressure,external pressure and external forces of all loading levels arewithstood to meet the limit values fixed for the primarystresses.

(5) With respect to the safety criteria to be satisfied by thecomponent the stability, structural integrity and functionalcapability shall be verified as explained hereinafter.

a) Stability of the component

aa) Stability means the safety against inadmissiblechanges in position and location of installation (e.g.overturning, fall, inadmissible displacement).

ab) Stability is mainly proved by a verification ofstrength of the support, in which case the connectionof the support to the component and the anchorage(support, component) shall be taken into account.

b) Structural integrity of the component

ba) Structural integrity means that the pressure loadedwalls withstand all specified pressure and other me-chanical loads within the scope of the specified num-ber of occurrences and the service life to an admissi-ble extent.

bb) Structural integrity is proved by a verification ofstrength of the pressurized wall.

When verifying the structural integrity, the stabilityof the component shall also be taken into account.

c) Functional capability of the component

ca) Functional capability means the capability of thecomponent beyond the stability and integrity re-quirements to fulfil the specified task at the respec-tive event. This safety standard only considers therequirements for pressure-retaining walls for safe-guarding the functional capability of the component.The required distortion limits for pressure-retainingwalls are also specified for this purpose.

cb) Regarding functional capability distinction is madewhether it is to be ensured during or after the eventor during and after the event in which case distinc-tion is also made between active and passive func-tional capability.

cc) Active functional capability ensures that the specifiedmechanical movements (relative movements betweenparts) can be made (consideration of the possibility ofclosing clearances, generating or altering frictionalforces).

cd) Passive functional capability means that distortionsand displacement limits are not exceeded.

ce) Active components are components for which me-chanical movements are specified to satisfy safety re-quirements, e.g. pumps, valves. All other compo-nents are passive components, e.g. vessels, pipingsystems.

These verifications shall be made in accordance with Section7 "General analysis of the mechanical behaviour" or alterna-tively to Section 8 "Component-specific analysis of the me-chanical behaviour". Regarding the functional capability thecomponent-specific requirements shall be met.

(6) There is no limitation to the geometry and type of load-ing with regard to the applicability of Section 7. If Section 8is applied, the requirements of this section shall be consid-ered.

(7) The calculations required for performing the analysis ofthe mechanical behaviour according to Sections 7 and 8 shallbe made using the applicable methods of structural mechan-ics.

(8) The service limits given in clauses 7.7, 7.8, 7.9 and Sec-tion 8 generally apply to loadings that have been deter-mined on the basis of linear-elastic material laws.

(9) Where the numerical calculation procedures of Annex Bare applied, the requirements of this Annex shall be met.

(10) The stress analysis may be omitted if it has been dem-onstrated by means of dimensioning according to Section 6or in another way that the stresses are allowable.

(11) Verifications by means of experiments are permitted tosubstitute or supplement the analysis of components laiddown by this safety standard.

3 Load case classes as well as design, service and testloadings and limits of components

3.1 General

(1) Conditions and changes of state of the system resultfrom the events occurring in the total plant and are identi-fied as load cases in connection with the loadings on thecomponent. With respect to their importance for the totalplant and adherence to the protective goals the load cases ofthe primary circuit are classified in system-specific docu-ments into the load case classes as per clause 3.2.

KTA 3201.2

(2) To each of these load cases a loading level according toclause 3.3 is assigned with respect to the specific component.These loading levels refer to allowable loadings.

(3) Where loadings of considerable extent arise due to otherload cases (e.g. transport, assembly and repair cases) theyshall be verified by means of strength calculation. The al-lowable service limits shall be determined for each individ-ual case.

3.2 Load case classes of the primary coolant circuit

3.2.1 General

The load cases of the primary coolant circuit shall be as-signed to one of the following load case classes:

3.2.2 Design load cases (AF)

Design load cases are considered to be load cases whichcover the normal operational load cases (NB) according toclause 3.2.3.1 as far as they cause maximum primary stressesin the components or parts.

3.2.3 Specified operation

3.2.3.1 Normal operational load cases (NB)

Normal operational load cases are operating conditions orchanges in operating conditions intended for the plant withthe systems being in a functionally fit condition. They espe-cially comprise start-up of the reactor, full-load operation,part-load operation, and shutdown of the reactor includingthe transients occurring during these load variations.

3.2.3.2 Anomalous operational load cases (AB)

Anomalous operational load cases refer to deviations fromthe normal operating load cases which are caused by func-tional disturbance or control error of the component or adja-cent components. There are no objections to continue theoperation after such load cases.

3.2.3.3 Test load cases (PF)

These load cases comprise the first pressure test (componentand system pressure test) as well as periodic pressure andleakage tests.

3.2.4 Incidents

3.2.4.1 General

Incidents are deviations from specified operation in theevent of which the operation of the plant cannot be contin-ued for safety reasons and for which the plant is designed.

3.2.4.2 Emergencies (NF)

Emergencies are incidents having very little probability ofoccurrence.

3.2.4.3 Accidents (SF)

Accidents are incidents having an extremely little probabil-ity of occurrence, or are postulated load cases.

3.3 Loadings levels for components

3.3.1 General

According to clauses 3.3.2 and 3.3.3 distinction shall bemade between the various loading levels of the componentsregarding the continuation of operation and measures to betaken, with the loading levels being specific to each compo-nent. The loading limits pertinent to the loading levels arelaid down in Section 7 and 8 and shall be determined suchthat the integrity of the components is ensured at any load-ing level for the specific load cases.

3.3.2 Design loading (Level 0)

3.3.2.1 General

Level 0 covers such loadings which are due to the effect ofdesign pressure and additional design mechanical loads sothat the maximum primary stresses resulting from the loadcases under Level A according to clause 3.3.3.2, includingthe pertinent stability cases in the components and theirparts are covered. The load case data comprise the designpressure (see clause 3.3.2.2), the design temperature (seeclause 3.3.2.3) and additional design loads (see clause3.3.2.4).

3.3.2.2 Design pressure

(1) The design pressure to be specified for a component orpart shall be not less than the maximum difference in pres-sure between the pressure-loaded surfaces according toLevel A (see clause 3.3.3.2).

(2) For parts where the pressure on the inside is independ-ent from the pressure on the outside, the largest value of thevalues indicated hereinafter shall be taken as the designpressure:

a) maximum difference between internal and atmosphericpressure

b) maximum difference between external and atmosphericpressure to take the stability behaviour into account

c) maximum difference between internal and external pres-sure to take the stability behaviour into account.

(3) For parts where the pressure on the inside depends onthe pressure on the outside, the design pressure shall be themaximum pressure difference.

(4) Hydrostatic pressures shall be taken into account if theyexceed 5 % of the design pressure.

(5) It is assumed that safety valves and other safety devicesare designed and set such that the pressure of the primarycoolant circuit, in the case of operation as specified, exceedsthe design pressure only for a short period of time in whichcase the Level B service limits (see clause 3.3.3.3) are satis-fied.

KTA 3201.2

3.3.2.3 Design temperature

(1) The design temperature is used to determine the designstrength values and shall normally not be less than the high-est temperature according to Level A to be expected in thewall at the point under consideration.(2) The design temperature may be taken equal to the re-spective temperature of the primary coolant; lower designtemperatures shall be verified. Where heating due to in-duced heat (e.g. due to gamma radiation) is to be expected,the effect of such heating shall be considered in establishingthe design temperature.

3.3.2.4 Additional design mechanical loads

Additional design mechanical loads shall be selected to be atleast so high that, when combined with the design pressure,they cover the simultaneously acting unfavourable primarystresses of Level A service limits.

3.3.3 Service limits

3.3.3.1 General

The loadings for the various service limits shall be deter-mined and limited within the analysis of the mechanicalbehaviour in which case the respective actual loadings andtemperatures may be used.

3.3.3.2 Level A service limits

(1) The loadings resulting from normal operational loadcases (NB) shall be assigned to Level A.

(2) It shall be verified in accordance with clause 7.7.3 thatthe stress intensities and equivalent stress ranges are permit-ted.

3.3.3.3 Level B service limits

(1) For load cases assigned to Level B it shall be verified inaccordance with clause 7.7.3 that the stress intensities andequivalent stress ranges are permitted.

(2) Primary stresses need only be verified if the Level 0design loadings are exceeded.

3.3.3.4 Level C service limits

(1) Only primary stresses shall be considered within thestress analysis for the load cases assigned to Level C servicelimits. If the total number of stress cycles of all postulatedevents exceeds 25, the stress cycles exceeding the number of25 shall be taken into account in the fatigue analysis accord-ing to clause 7.8.

(2) These sets of Level C service limits permit large defor-mations in areas of structural discontinuity. Such deforma-tions may necessitate inspection of the respective compo-nent.

(3) 120 % of the allowable external pressure according toLevel 0 are permitted as external pressure without addi-tional proof of stability.

3.3.3.5 Level D service limits

Only primary stresses shall be considered for the load casesassigned to Level D service limits where it is accepted thatgross general deformations may occur which may necessi-tate repair or replacement of the respective component.

3.3.3.6 Level P service limits

(1) Only primary stresses shall be considered for the loadcases assigned to Level P service limits. If the number ofpressure tests does not exceed 10 they shall not be consid-ered in the fatigue analysis. If the number of pressure testsexceeds 10 the pressure tests exceeding the number of 10shall be considered in the fatigue analysis.

(2) The first pressure test of a component not installed in thesystem shall be conducted with 1.3 times the design pres-sure for rolled and forged steels, and with 1.5 times thedesign pressure for cast steel in which cases these pressuresshall be designated test pressure p'. The test temperatureshall be established according to brittle fracture criteria.

Note:

The determination of the test pressures and temperatures is laiddown in clause 3.5 of KTA 3201.4.

4 Effects on the components due to mechanical andthermal loadings, corrosion, erosion, and irradiation

4.1 General

(1) All relevant effects on the components due to mechani-cal and thermal loadings, corrosion, erosion, and irradiationshall be taken into account in the design and calculationwith exact or conservative values for each specific compo-nent.

(2) Mechanical and thermal loadings are the effects on thecomponent resulting from the load cases as defined in Sec-tion 3. These effects lead to loadings in the component forwhich the component has to be designed. Mechanical andthermal loadings may have direct effect on the componentsand parts and cause the respective loadings. They may alsohave indirect effect, as for example temperature transients inthe coolant which cause temperature differentials in thecomponent and then lead to restraints to thermal expansion.

(3) Corrosion and erosion may lead to local or large-areawall thinning. In connection with stresses corrosion mayalso lead to cracking.

(4) The effects of neutron irradiation will lead, in the corearea, to an embrittlement of the material and the generationof heat sources by γ-radiation. Heat sources caused by theabsorption of γ-radiation are a special type of thermal load-ing.

KTA 3201.2

4.2 Mechanical and thermal loadings

(1) Mechanical and thermal loadings comprise forces andmoments, imposed deformations and temperature differen-tials as far as they cause loadings in the components.

(2) The stresses and strains thus caused shall be determinedand evaluated within the analysis of the mechanical beha-viour in accordance with Section 7 or 8.

(3) Mechanical and thermal loadings are the following:

a) Loadings caused by the fluid, e.g. by its pressure, tem-perature, pressure transients, temperature transients,fluid forces, vibrations

b) Loadings caused by the component itself, e.g. deadweight, cold-spring, deviations from specified shape dueto manufacture

c) Loadings imposed by adjacent components, caused e.g.by pipe forces applied due to restraint to thermal ex-pansion or pump oscillations

d) Ambient loadings transferred by component supportstructures and imposed e.g. by anchor displacement, vi-brations due to earthquake

Note:

Special requirements for seismic design are contained inKTA 2201.4.

e) Loadings due to heat sources caused by γ-radiation (inthe core area of the reactor pressure vessel).

4.3 Documentation of component loadings

(1) The mechanical and thermal loadings including theirfrequency of occurrence, which have been established orfixed in due consideration of the load cases of the primarycoolant circuit, shall be recorded and documented for eachspecific component.

(2) Where a loading cannot be established by indicating oneunit only, it shall be verified by inclusion of its time history.

4.4 Superposition of loadings and classification into load-ing levels

Table 4-1 gives an example of the combination of componentloadings and their classification into loading levels.Plant-specific details shall be laid down in the respectiveplant specifications.

4.5 Corrosion and erosion

Special measures shall be taken to withstand corrosion (e.g.intergranular stress corrosion cracking on austenitic compo-nents under boiling water reactor conditions andstrain-induced corrosion cracking in the case of uncladcomponents in oxygen-containing high-temperature water)and erosion by selecting suitable materials, dimensioning,design or stress-reducing fabrication measures (cladding ordeposition welding of the base material, avoidance of nar-row gaps).

Note:

Special requirements for avoid ing and detecting corrosion arelaid down in KTA 3201.4.

4.6 Irradiation

The embrittlement of the material caused by neutron irra-diation shall be considered when assessing the material'sbrittle fracture behaviour.

Loadings 1)

Static loadings Transient loadings Vibration and dynamicloadings

Serviceloadinglevels

Designpres-sure

Designtempe-ratu-re 2)

Pres-sure

Tempe-rature 2)

Deadweightandotherloads

Mecha-nicalloads,reactionforces

Re-strainttother-malexpan-sion

Transient loads(pressure, tem-perature, me-chanical loads),dynamic loa-ding

Anoma-lous loa-dings(staticanddyna-mic)

Test loa-dings(staticand dy-namic)

Designbasisearth-quake

Effectsfromtheinside

Othereffectsfromtheoutside

Level 0 X X X

Level A X X X X X X

Level B X X X X X X

Level P X X X X

X X X X

X X X X X

X X X X X

Level D X X X X X

X X X X X

1) In each load case the type of loadings imposed shall be checked.

2) To determine the stress intensity value.

Table 4-1: Example for the superposition of component loadings and their classification into service loading levels

Level C

KTA 3201.2

5 Design

5.1 General requirements

5.1.1 Principles

(1) The design of the components shall

a) meet the functional requirements

b) not lead to an increase of loadings/stresses

c) meet the specific requirements of the materials

d) meet fabrication and inspection and testing requirements

e) be amenable to maintenance.

(2) The aforementioned general requirements are correlatedand shall be harmonized with respect to the compo-nent-specific requirements.

5.1.2 Design meeting functional requirements and notleading to an increase of loadings/stresses

Components shall be designed and constructed such as tomeet the specific functional requirements. The followingprinciples are based hereupon:

a) favourable conditions for component service loadingstaking the loadings imposed by the system into account(e.g. actuating, closing and fluid forces)

b) favourable distribution of stresses, especially in areas ofstructural discontinuity (nozzles, wall thickness transi-tions, points of support)

c) avoidance of abrupt changes at wall thickness transi-tions, especially in the case of components subject totransient temperature loadings (see clause 5.2.6)

d) avoidance of welds in areas of high local stresses

e) pipe laying at a specified slope.

5.1.3 Design meeting the specific requirements for materials

(1) The following criteria shall be satisfied regarding theselection of materials and the product form:

a) strength

b) ductility

c) physical properties (e.g. coefficient of thermal expansion,modulus of elasticity)

d) corrosion resistance

e) amenability to repair

f) construction (minimization of fabrication defects)

g) capability of being inspected and tested.

(2) The materials specified by KTA 3201.1 shall be used. Forspecial loadings, such as erosion, corrosion or increasedwear, "materials for special use" may be permitted.

(3) The materials shall be used in a product form suitablefor the loadings occurring (e.g. plates, forgings, castings,seamless tubes)

(4) The use of dissimilar materials in one component shallbe limited to the extent required.

5.1.4 Design meeting fabrication requirements

5.1.4.1 Design meeting manufacture and workmanshiprequirements

The following principles apply to design meeting manufac-ture and workmanship requirements:

a) Product forms and materials shall be selected to ensurefavourable conditions for processing and non-destruc-tive testing.

b) The number of welds shall be minimized accordingly.Welds shall be located such as to consider accessibilityduring welding (taking preheating into account) andminimization of weld residual stresses.

c) The structure shall be so designed that repairs, if any,can be done as simply as possible.

Note:

See also KTA 3201.3 regarding the fabrication requirements.

5.1.4.2 Design meeting testing and inspection requirements

(1) The shaping of the parts as well as the configuration andlocation of the welds shall permit the performance ofnon-destructive tests with sufficient defect interpretation onproduct forms, welds and installed components in accor-dance with KTA 3201.1, KTA 3201.3 and KTA 3201.4.

(2) The following principles apply to design meeting testand inspection requirements

a) Attachment welds on pressure-retaining walls shallbasically be full-penetration welds so that non-destruc-tive testing of the welded joint is possible. Clause 5.2.2.2(4) defines the permissibility of fillet welds.

b) Basically, all accessible welded joints on pressure partsshall be machined flush, and attachment welds on pres-sure retaining walls shall have a notch-free contour. Thesurface finish of welded joints shall meet the require-ments of clause 13.1.3 of KTA 3201.3.

c) Single-side welds are permitted if they can be subjectedto the non-destructive testing procedures prescribed byKTA 3201.3.

d) Forgings shall be so designed and constructed that thenon-destructive tests specified by KTA 3201.1, e.g. ultra-sonic and surface crack detection tests, can be performedon the finished part or forged blank upon the heattreatment specified for the material.

e) Cast steel bodies shall be so designed that non-destruc-tive testing (e.g. radiography, surface crack detection) isprincipally possible also on the inner surface.

Note:

See also KTA 3201.1 and KTA 3201.3.

5.1.5 Design amenable to maintenance

(1) When designing pressure-retaining walls of componentscare shall be taken to ensure that they are easily accessibleand in-service inspections can be adequately performed.

KTA 3201.2

(2) The following principles shall be observed:

a) Adequate accessibility for maintenance (especially ex-amination, visual inspection, repair or replacement) shallbe ensured. The geometries in the areas to benon-destructively tested shall be simple.

b) Adequate accessibility for repairs, if any, shall be en-sured taking the radiation protection requirements intoaccount.

c) Activity-retaining components shall be so designed thatdeposits are avoided as far as possible and decontami-nation can be performed.

d) Welds in the controlled area shall be located and de-signed in accordance with the Radiation Protection Or-dinance so that setting-up and inspection times for peri-odic inspections are as short as possible.

5.2 General requirements for components and their welds

5.2.1 General

Besides the requirements laid down hereinafter additionalgeometric conditions shall be taken into account when ap-plying special calculation procedures, if any.

5.2.2 Welds

5.2.2.1 Butt welds

Butt weld shall be full-penetration welds. Cruciform joints,weld crossings and built-up weld deposits shall normally beavoided. If the thickness of two parts to be joined by buttwelding differs, the thicker part shall be trimmed to a taperextending at least three times the offset between the abut-ting surfaces; the length of the taper, however, shall notexceed 150 mm. Figure 5.2-1 shows single-sided weld con-figurations.

Note:

KTA 3201.3 lays down the requirements where single-sidedwelds are permitted.

1

2

3b3a

machined

Upon welding andsubsequent machining

Prior to welding

60°

2

7°- 8°

r=8

2

Figure 5.2-1: Examples of single-side butt welds

5.2.2.2 Attachment welds

(1) Attachment welds on pressure-retaining walls shallbasically be welded with a length not less than 50 mm. Ex-ceptions to this rule (e.g. pads for piping) shall be agreedupon with the authorized inspector.

(2) Corner joints and welding-over of butt joints are notpermitted. To avoid such welding-over, unwelded areasshall be left at the junction of brackets and support lugs,excluding parts with a wall thickness s less than 16 mm.

(3) Double-bevel butt welds and single-bevel butt weldswith backing run according to Figure 5.2-2 are permittedwithout restriction. Single-bevel butt joints without backingrun are permitted by agreement with the authorized inspec-tor in the case of restricted accessibility if the welds are ofthe full-penetration type and can be subjected to non-de-structive testing.

2

3

1

α

≥≥

α

≤

1)

1)

1

s

s

1

1s

s

s

s

30° to 60° 5mm

r

R

R

s

Perform with tangential transition

s

( also applies to fillet welds )Weld configuration and design of transitions

s

Attachment welds ( as-welded )

R

r

0.5

s

r s

Figure 5.2-2: Examples of single-bevel and double-bevelbutt welds for attachment welds

(4) Fillet welds shall be welded over the full circumferenceand are permitted in the following cases:

a) on nozzles for measuring, drain and vent pipes withnominal diameters smaller than DN 50 installed aspenetration pipe. In this case the pipe is not consideredto contribute to the reinforcement.

b) where full-penetration welds lead to a clearly more fa-vourable design than it would be the case if fillet weldswere used.

KTA 3201.2

c) as seal welds (see Figure 5.2-3).

d) as attachment welds on austenitic weld claddings (seeFigure 5.2-4).

Figure 5.2-3: Examples of welds primarily having sealingfunction

Figure 5.2-4: Examples for attachments welded to austeni-tic weld claddings

5.2.2.3 Nozzle welds

(1) The allowable configurations of nozzles, welded jointsand transitions are shown in Figure 5.2-5.

(2) Welded set-in nozzles shall be back welded where pos-sible on account of dimensions. Single-side welds are per-mitted if the root has been dressed. Where in exceptionalcases dressing of the root is not possible it shall be ensuredthat the weld can be tested.

2

22

2

2

r

r

Radius may be omitted ifdressing is not possibledue to geometric reasons.

Bore

rr

r

Figure 5.2-5: Configuration of welds on nozzles

5.2.3 Diameter and wall-thickness transitions

(1) In the case of diameter transitions care shall be taken toensure that the stresses are favourably distributed andnon-destructive examinations can be performed. Specificradii and cylindrical or tapered transitions shall be pro-vided.

(2) Wall thickness transitions shall be so designed that thestresses are favourably distributed. Abrupt transitions shallbe avoided. The wall thickness transitions shall be such thatthe welds can be properly and completely subjected tonon-destructive testing.

5.2.4 Flanges and gaskets

(1) Flanges shall only be of the forged, rolled without seam,or cast type.

(2) Reactor pressure vessel flanges and comparable designsshall be so designed as to favour the distribution of stressesand to meet the functional requirements (e.g. leak tightnesseven under transient loadings).

(3) For other flanges (nominal diameter smaller thanDN 300) the following shall be satisfied:

a) the face shall be designed to meet the design require-ments for the gasket

KTA 3201.2

b) the transition radii r1 and r2 according to Figures 5.2-6and 5.2-7 shall be not less than 0.25 ⋅ sR, but at least6 mm.

c) in accordance with clause 5.2.5 at least 4 bolts shall beprovided.

Figure 5.2-6 Welding necks

Figure 5.2-7 Welding-neck flanges

5.2.4.2 Gaskets

Only combined seals and metal gaskets shall be used asgaskets. The possibility of chemical influences on the basematerial by the gasket material (chemical compatibility ofthe material combination) shall be taken into account. Otherinfluences on the gasket resistance (e.g. by ionizing radia-tion) shall also be considered.

5.2.5 Bolts and nuts

(1) Bolts and nuts complying with DIN standards shall beused as far as the design permits. Necked-down or re-duced-shank bolts are to be preferred. The effective threadlength shall be adapted to the combination of materials (e.g.bolts - body) (see clause A 2.8). Reduced-shank bolts to DIN2510-2 or necked-down bolts shall be used at design tem-peratures above 300° C and design pressures above 40 bar.

(2) Bolts and nuts for connection with austenitic parts shallbe made, if possible, of the same or similar material as theparts to be joined. Where materials with different coeffi-cients of thermal expansion are used, the effect of differen-tial thermal expansion shall be taken into account.

(3) Bolts with < 10 M or respective diameter at root ofthread are basically not permitted. In special cases (e.g. inthe case of bolts for valves) smaller bolts may be used, how-ever, their dimension shall not be less than M 6 or respectivediameter at root of thread.

(4) Such designs shall be preferred which ensure that boltedconnections inside the vessel or parts thereof cannot enterthe circuit in case of fracture.

(5) Bolts in reactor pressure vessel flange connections andcomparable bolted joints shall be designed such as to makein-service inspections possible.

5.2.6 Nozzles

(1) The geometric conditions (wall thickness ratios, weldradii, nozzle lengths) are contained in Table 5.2-1. The defi-nition of the units contained in Table 5.2-1 can be taken fromFigures 5.2-5 and 5.2-8.

Limitation of wall thickness ratios

Nozzle dimensions Wall thicknessratio

Remark

dAi < 50 mm sA/sH ≤ 2

dAi > 50 mm and

dAi/dHi ≤ 0.2

sA/sH ≤ 2

dAi/dHi > 0.2 sA/sH ≤ 1.3 For exceptions seeclause A 2.7

Weld configuration requirements

Nozzle type Conditions Remark

Set-through nozzle r2 ≥ 0.5 ⋅ sH

Set-on nozzle r2 ≥ 0.5 ⋅ sH

Set-through orset-on nozzle

r2 at least10 mm or 0.1 ⋅ sH

In exceptionalcases, e.g. to avoidwelding-over ofweld edges

Configuration requirements for transitionsTransitions shall be smooth and edges be rounded. Thetransition radius r shall be fixed depending on the design.

r2 see Figure 5.2-5 and Figure 5.2-8

sA wall thickness of branch (nozzle)

sH wall thickness of main shell

Table 5.2-1: Recommendations for wall thickness ratios,welds and nozzle transitions

(2) For nozzles with an inside diameter not less than120 mm and a nozzle wall thickness sA not less than 15 mmthe main shell shall normally be reinforced, taking a favour-able distribution of stresses into account. At a diameter ratioqA above 0.8 a stress analysis shall be performed addition-ally unless this area has been covered by adequatedimensioning procedures, e.g. according to equation(A 3.1-22). The diameter ratio qA is defined as the ratio ofthe mean diameter of branch piping to the mean diameter ofthe reinforced area of the run pipe.

(3) The wall thickness ratio of nozzle to shell shall be basi-cally selected to be not greater than 1.3 (see Table 5.2-1). Thiswall thickness ratio may be exceeded in the following cases:

KTA 3201.2

a) the additional wall thickness of the nozzle is not used toreinforce the nozzle opening, but is selected for designreasons (e.g. manhole nozzle)

b) the nozzle is fabricated with reduced reinforcement area(e.g. nozzles which are conical to improve test conditionsfor the connecting pipe)

c) A wall thickness ratio sA/sH with a maximum value of 2is permitted for dAi less than 50 mm. This also applies tobranches with dAi not less than 50 mm where the diame-ter ratio dAi/dHi does not exceed 0.2.

Ai

H

2

R A

Hi

d d

s

r

s

r

3. Set-in nozzle (forging)

sitions see Figure 5.2-5Configuration of welded tran-

2. Set-on nozzle

sNotations

1. Set-through nozzle

Figure 5.2-8: Examples of nozzle designs

(4) Where the nozzle diameter is great in relation to themain shell, the wall thickness ratio shall be reduced. In thecase of a branch with qA exceeding 0.8 the wall thicknessratio sA/sH shall not exceed 1.0.

(5) Nozzles shall be made from forged bars (limitation ofdiameter depending on analysis), seamless forged tubularproducts or seamless pipes.

(6) Vessel and piping nozzles subject to rapid, high tem-perature changes of the fluid (transient inlet and outlet flowconditions) usually are provided with thermal sleeves to bedesigned such that a thermal resistance between fluid andnozzle wall as well as the nozzle transition area to the vesselwall is provided to reduce thermal stresses in this area.Therefore it is necessary to connect the thermal sleeve out-side the nozzle area required for reinforcement of opening.

5.2.7 Dished and flat heads

The following types of heads shall preferably be used:

a) flanged flat heads

b) torispherical heads

c) semi-ellipsoidal heads

d) hemispherical heads.

s

sR

L 1.5

R

Design 1 Design 2> DN 150 ≤ DN 150

Forgings or combination Fabricated from forged barsof forged and rolled parts

Wall thicknesss in mm

Design Condition for Rin mm

Conditionfor L

s ≤ 40 1 R s= .{ ; }max .5 0 5 ⋅ acc. to

s ≤ 40 2 R s= .{ ; . }max 8 0 5 ⋅ KTA

s > 40 1 and 2 R ≥ 0.3 ⋅ s 3201.3

Figure 5.2-9: Allowable designs of welded flat heads

Figure 5.2-9 shows permissible types of welded flat heads(e.g. end caps). Design types 1 and 2 are permitted for forg-ings or parts fabricated by a combination of forging androlling. Type 2 may also be made of forged bars for diame-ters not exceeding DN 150. Plates are permitted for flangedflat covers only subject to pressure perpendicular to thesurface. For pressure tests blanks made from plate arepermitted.

5.3 Component-specific requirements

5.3.1 General

The requirements of Sections 5.1 to 5.2 regarding the designapply primarily to all types of components. In the following,component-specific design requirements are additionallygiven to be met by various structural elements of apparatusand vessels, pumps, valves, and piping systems.

KTA 3201.2

5.3.2 Pressure vessels

5.3.2.1 Shells, heads

Shells and heads shall normally be designed as coaxial shellsof revolution of constant thickness and curvature, if practi-cable, in the meridian plane by using the design shapesgiven in KTA 3201.1.

5.3.2.2 Nozzles

(1) For the design of nozzles on vessels the requirements ofclause 5.2.6 apply .

(2) The portion of the nozzle calculated as reinforcement ofopening shall be considered to be part of the pressure-retai-ning wall of the vessel. The portion belonging to the vesselmay be extended to the first nozzle attachment weld or, inthe case of flanged attachments, to the interface between theflanges.

5.3.2.3 Inspection openings

(1) Inspection openings shall be provided to meet the re-quirements of the Pressure Vessel Order and AD-MerkblattA5.

(2) Nozzles for inspection openings shall meet the designrequirements of clause 5.2.6. Covers and sealings (e.g. man-hole) shall be so designed that multiple opening for inspec-tion and repair purposes is possible without affecting thetightness; weld lip seals shall be avoided.

(3) Vessels filled with radioactive fluids shall be providedwith access openings with DN 600, if required by AD-Merk-blatt A5.

5.3.2.4 Tubesheets

(1) Figure 5.3-1 shows examples of typical designs of tube-sheets with hubs for connection to cylindrical sections.These examples apply to ferritic and austenitic materials.

(2) The weld joining the cylindrical section and the tube-sheet shall be back-welded, be ground flush on the inside,i.e. it shall, basically, never be welded as final weld. Excep-tions to this rule are permitted in the case of small dimen-sions where access from the inside is not possible.

(3) Other designs than those shown in Figure 5.3.1 arepermitted if is has been proved that the stresses are allow-able and the geometric conditions for performingnon-destructive testing are given.

(4) The transition radii and angles shall satisfy the followingconditions:

0 ≤ α1 ≤ 10 degree

0 ≤ α2 ≤ 10 degree

r1, r2 ≥ 0,25 ⋅ s1

r3, r4 ≥ 0,25 ⋅ s2

α

α2

2

1

2

1

1

1

3

2 2

3

4

r

r

s

r

r

s

sr

s

r

Figure 5.3-1: Examples of tubesheet designs

(5) The welded joints shall be arranged according to KTA3201.1 such that tests and inspections can be performed.

5.3.2.5 Covers and blanks

5.3.2.5.1 Permanent covers and blanks

(1) The design shapes of flat covers and blanks shown inFigure 5.3-2 are permitted. In addition, the head shapescovered by clause 5.2.7 may be used.

(2) The attachment welds shall be full-penetration welded.

1 2

3

≥≥=≥

=minmin

= =

s

r

ssr 0.2

r

r s

r s

h

0.2

h5 mm

sr 5 mm

Figure 5.3-2: Covers and blanks

5.3.2.5.2 Temporary covers and blanks

(1) Temporary covers and blanks are such elements whichare only needed for nuclear test conditions of the plant (e.g.for pressure tests).

KTA 3201.2

(2) The design shapes of flat covers and blanks shown inFigure 5.3-2 are permitted. In addition, the head shapescovered by clause 5.2.7 as well as other comparable shapesmay be used.

(3) Temporary covers and blanks need not be attached byfull-penetration welds.

5.3.2.6 Permitted types of combinations and transitions

5.3.2.6.1 General

(1) Regarding the loadings the transitions between the mainbodies are designed in the best possible way if the followingconditions are satisfied:

a) the rotational axes of the design elements coincide at theintersection

b) there are no abrupt or sharp-edge transitions at the shellmid-surfaces

c) the deformation behaviour or wall thicknesses of theindividual elements are matching at the intersection(minimization of secondary and peak stresses).

(2) From the above principles the following stipulations arederived to ensure favourable distribution of stresses regard-ing the design. In addition, further requirements of KTA3201.3, especially with regard to the possibility of tests andinspections shall be taken into account.

5.3.2.6.2 Combination of shell elements, head elements andtube plates

(1) The elements of vessel shell and heads may be con-nected without specific requirements as to the shape oftransition if the conditions shown in Figure 5.3-3 are satis-fied in consideration of the manufacturing tolerances. Therestrictions of Figure 5.3-3 do not apply to the connection offlat heads and tube plates.

(2) If one of the conditions for ϕ, e and �s according to Fig-ure 5.3-3 is not satisfied, tapers or transition radii or bothshall be provided.

ϕ

ϕ

1

1 2

2

1

2

<e= min (

0.125 ss

))

s< 1.25

max (= s30˚<

e

, s

s

, ss

s

ss

Figure 5.3-3: Limit values for the connection of shells ofrevolutions without transition joints

(3) The taper shall meet the following requirements:

a) The sum of inside and outside taper angle shall normallynot exceed 45°.

b) In case of a taper on one side only with an angle of morethan 30° the concave edges shall be rounded to satisfy r ≥s2/4 (see Figure 5.3-4).

(4) Regarding the transition between flat heads, e.g. bet-ween tubesheet and vessel shell, clause 5.3.2.4 shall be con-sidered.

α

≥

α

α

α <1

21

2

1

2

2 45˚+

s

s

r/4s

Figure 5.3-4: Configuration of wall thickness transitions

5.3.2.6.3 Heat exchanger tube-to-tubesheet joints

Heat exchanger tubes shall be attached to the tubesheetcladding by means of a seal weld which shall be designed towithstand the tube forces. In addition, the tubes shall beexpanded or rolled, or expanded and rolled into the tube-sheet.

5.3.2.6.4 Arrangement of nozzles

(1) If practicable, nozzles shall normally be so arranged thatthe following conditions are satisfied:

a) The nozzle axis shall be vertical or nearly vertical to theshell centreline, and the angle between nozzle axis andshell normal shall not deviate by more than 15°.

b) The nozzle is not located in an area where the stressesmay combine with other stress raisers.

(2) Deviation from these criteria is only permitted for func-tional or other important reasons.

(3) The nozzles shall basically be attached to the shell bymeans of full-penetration welds.

(4) Only nozzles as per clause 5.2.2. (4) a) may also be at-tached by non-full-penetration welds, shrinkage fit orscrewing-in. The nozzle may be welded exclusively to thecladding.

(5) In the case of shrinkage or screwed joints a seal weldshall additionally be provided.

KTA 3201.2

5.3.2.6.5 Attachment of covers and blanks

(1) Covers and blanks as per clause 5.3.2.5 shall be attachedby

a) welding (full-penetration welds)

b) bolting or

c) flanged joint.

(2) In the case of temporary covers and blanks evennon-full-penetration weld are permitted.

5.3.2.7 Attachment of parts not covered by this safetystandard

5.3.2.7.1 Load-transferring parts

(1) The parts shall be connected to meet the requirements ofthis standard, if specified (e.g. nozzle connection)

(2) The parts for which this standard does not contain de-sign specifications shall be designed as:

a) full-penetration welded joint

b) bolted joint where the efficiency must be considered

c) clamped joint (e.g. reactor pressure vessel internals)

d) positive connections where the possibility of plays mustbe considered in the case of alternating direction offorce application.

5.3.2.7.2 Non-load-transferring parts

These parts shall be connected in accordance with the re-quirements of this standard. Where this standard cannot beapplied accordingly, the parts shall be connected such thatinadmissible influences which may reduce the quality areexcluded.

5.3.3 Pump casings

Pump casings may be of the forged, cast or welded design.The design requirements of Sections 5.1 and 5.2 apply. Thefollowing shall be considered additionally :

a) The pump casing shall be so designed that the requiredfunctional capability is maintained in the event of pipeforces and moments as well as loadings from externalevents occurring in addition to the operational hydraulicand thermal loadings.

b) The design of the pump casing and the pertinent systemsshall permit adequate accessibility for maintenance, re-placement of wear parts and repair purposes.

5.3.4 Valve bodies

Valve bodies may be of the forged, cast or welded design.The design requirements of Sections 5.1 and 5.2 apply. Thefollowing shall be considered additionally:

a) The valve body shall be designed to be so stiff that therequired stability is maintained in the event of pipeforces and moments as well as loadings from external

events occurring in addition to the operational hydraulicloadings.

b) The design of the valve body and the pertinent systemsshall permit adequate accessibility for maintenance, re-placement of wear parts and repair purposes.

c) The design of the valve body shall especially providesmooth tapers at cross-sectional transitions.

5.3.5 Piping systems

(1) Pipes, bends and elbows shall normally be seamless.

(2) The radius of pipe bends and elbows shall be not lessthan 1.5 ⋅ DN. Exceptions are permitted in justified cases.

(3) Bends shall basically be provided with straight pipeends.

Note:See also KTA 3201.1, clause 17.1 (2).

5.3.6 Component support structures

5.3.6.1 General

(1) Component support structures may be designed assupporting structures with integral or non-integral areas.

(2) The integral area of a supporting structure comprises theparts rigidly attached to the component (e.g. welded, cast,machined from the solid) with support function.

(3) The non-integral area of a supporting structure com-prises parts detachably connected or not connected (e.g.bolted, studded, simply supported) having supportingfunctions as well as those parts with supporting functions ofa supporting structure rigidly attached to the componentoutside the area of influence (see Figure 8.5-1).

Note:Non-integral areas o f a supporting structure shall be classifiedas structural steel components and fall under the scope o f KTA3205.1, and in the case o f standard supports fabricated in series(with approval test) fall under the scope of KTA 3205.3.

(4) For welded integral support structures the same re-quirements as for the pressure-retaining wall apply. At-tachment welds on the pressure-retaining wall shall befull-penetration welded.

5.3.6.2 Vessels

(1) Allowable design types are shown in Figures 5.3-5 to5.3-7.

(2) In the case of elevated temperature components thediffering thermal expansions of components and supportstructures shall be taken into account.

(3) In the case of horizontal loadings (e.g. external events)lateral supports may be required in the case of vertical ves-sels to ensure stability. Depending on the design these sup-ports may also reduce vertical forces.

KTA 3201.2

Examples:

a) Skirt supports with or without support ring (see Figure5.3-5)

b) Forged ring in the cylindrical shell (see Figure 5.3-6)

c) Guide pins (e.g. also use of nozzles or manhole)

d) Brackets (see Figure 5.3-7).

1 32

s

s

1 R

hemispherical head

Rs

s

R

RR

The radii Rs shall be fixed according to Figure 5.2-2.

Figure 5.3-5: Example of component support structureswith integral attachment of vertical pressurevessels with skirt supports

R

R

R

R

The transitional radii shall be smooth to avoid stresses

Figure 5.3-6: Examples of component support structures ofvertical vessels with forged rings

3 41 2

s

s

s

s

s

s s

s

s s

R

R

R R

RRR

R R

RR

Spherical shell

R

For the design types 1 to 4 two webs each per support skirtare provided. The radius Rs shall be fixed according to Fig-ure 5.2-2. The radius R shall be selected with regard to afavourable distribution of stresses.

Figure 5.3-7: Examples of component support structureswith integral attachment of vertical pressurevessels to bracket supports

5.3.6.3 Pumps

For welded component support structures the same re-quirements as for pressure parts apply (full-penetrationwelds, test requirements).

5.3.6.4 Valves

For valve supports not less than DN 250, PN not less than40 bar and TB not less than 100 °C forged fittings shall beused.

6 Dimensioning

6.1 General

(1) Dimensioning shall be effected on the basis of the designloading level (Level 0) in accordance with clause 3.3.2 andtaking into account the loadings and service limits of theother loading levels according to Section 3.3 as far as theygovern dimensioning.

(2) Dimensioning shall be effected, inter alia, according toone of the following procedures:

a) in accordance with Annex A

b) verification of primary stresses

c) limit analysis

d) shakedown analysis

e) strain limiting load method.

(3) In the case of verification of primary stresses the pri-mary stress shall be limited using the primary stress intensi-ties laid down in clause 7.7.3.4.

(4) In addition, a proof of stability, if required, shall also beperformed (see clause 7.11).

(5) Where the dimensioning rules given in Annex A do notsuffice to cover the given geometries and loadings, dimen-sioning shall be performed to the state-of-the-art by othermeans, e.g. by using the methods specified under Annex Bor experimental methods.

6.2 Welds

As the welds have to meet the requirements of KTA 3201.1and 3201.3, they need not be considered separately in thedimensioning of the parts.

6.3 Claddings

(1) When determining the required wall thicknesses andcross-sections, claddings, if any, shall be considered not tobe contributing to the strength.

(2) The design against internal pressure shall take the inter-nal diameter of the unclad part into account.

(3) Deposition weldings on the base metal with equivalentmaterial are not considered claddings.

KTA 3201.2

6.4 Wall thickness allowances

(1) When determining the nominal wall thickness the fabri-cation tolerances shall be considered by a respective al-lowance c1 which is equal to the absolute value of the minustolerance of the wall thickness in accordance with the accep-tance specification.

(2) An allowance c2 shall take wall thickness reductions dueto chemical or mechanical wear into account. This appliesboth to the wall thickness reduction and the extension of theinternal diameter. The allowance c2 may be omitted if nowear is expected or a cladding is provided.

6.5 Wall thicknesses

(1) The nominal wall thickness sn shall satisfy the followingcondition in consideration of the allowances c1 and c2:

s s c cn ≥ + +0 1 2 (6.5-1)

where s0 is the calculated wall thickness according to Sec-tion 6.1.

(2) This shall be verified by a recalculation with the wallthickness s0n = sn - c1 - c2; see Figure 7.1-1.

(3) When determining the wall thickness by means of thenominal external diameter dan

d da an= (6.5-2)

shall be taken and when determining the wall thickness bymeans of the nominal internal diameter din shall be taken asfollows:

( )d d c ci in= + ⋅ +2 1 2 (6.5-3)

7 General analysis of the mechanical behaviour

7.1 General

7.1.1 Objectives

(1) It shall be demonstrated by means of the analysis of themechanical behaviour that the components are capable ofwithstanding all loadings in accordance with the loadinglevels in Section 3.3

(2) Within the analysis of the mechanical behaviour theloadings and, if required, the forces and moments as well asdeformations due to loadings of the component to be ana-lysed shall be determined by satisfying the boundary condi-tions and taking into account the mutual influence of adja-cent components and individual parts in accordance withSection 7.6 including Annex B. The determination may beeffected by way of calculation or experiments, or a combi-nation of calculation and experiments, and to the extentrequired to meet safety requirements.

(3) The loadings and deformations thus determined shall beexamined for acceptability in accordance with Sections 7.7 to7.13.

(4) Here, it shall be taken into account that the exactness ofthe determined forces and moments depends on the idealgeometric shape of the component or part, the exactness ofassuming loadings, boundary conditions and material prop-erties as well as the features and performance of the calcu-lation method selected.

(5) The analysis of the mechanical behaviour may alterna-tively be made by means of design formulae if, in the case ofsufficiently exact and complete consideration of the loadingconditions and geometric shape the objectives of verificationaccording to Section 7 are obtained. If applicable, the designformulae will suffice for dimensioning.

7.1.2 Welds

As the welds have to meet the requirements of KTA 3201.1and KTA 3201.3, their influence on the mechanical behav-iour need not be considered separately according to thefollowing clauses.

7.1.3 Claddings

(1) When determining the required wall thicknesses andsections, claddings, if any, shall not be considered to becontributing to the strength. Deposition welds made on thebase metal with equivalent materials are not considered tobe claddings.

(2) For the thermal analysis the cladding may be consid-ered. If the cladding thickness exceeds the wall thickness bymore than 10 %, the cladding shall be taken into accountwhen analysing the mechanical behaviour. The stress classi-fication and evaluation shall be made separately for the basematerial and the cladding.

(3) In the brittle fracture analysis to Section 7.9 the influenceof the cladding shall be considered properly.

7.1.4 Wall thickness used for analysing the mechanicalbehaviour

(1) For the analysis of the mechanical behaviour of a partthe average wall thickness to be effected (or effective aver-age wall thickness) shall be taken as sc by subtracting thewear allowance c2 according to Section 6.4:

s sc c

cc n= +−

−3 122

(7.1-1)

where sn is defined in equation 6.5-1, c3 is equal to the plustolerance, and c1 is equal to the absolute value of the minustolerance in accordance with Section 6.4; see also Fig-ure 7.1-1.

The design wall thickness sc according to equation (7.1-1)shall be fixed such that it lies in the centre of the tolerancefield minus the wear allowance c2.

(2) Where adequate reason is given, e.g. due to an asym-metrical tolerance field or in the case of forgings, anotherwall thickness may be taken as sc if it is not less than therequired wall thickness (s0 + c2).

KTA 3201.2

(3) Where the wall thickness tolerances c1 and c3 each arenot more than 2 % of the nominal wall thickness sn theyneed not be considered in the determination of sc.

n

0n

0

c

312

231 c

s

c c

+

cs

c

Width oftolerance field

sc

2

s

Figure 7.1-1: Wall thicknesses

7.1.5 Deviations from specified shape and dimensions

7.1.5.1 General

(1) The deviations from the dimensions and shapes givenhereinafter, on which design is based, need not be consid-ered separately up to the specific limit values.

(2) Where these values are exceeded a substantiation byway of calculation shall be made to the extent required andbe based on the actual dimensions.

(3) All values refer to the unpenetrated membrane area ofthe shell unless defined otherwise.

7.1.5.2 Cylindrical parts

7.1.5.2.1 Deviations from wall thickness

(1) Deviations of the effective wall thickness minus theallowance c2 from the design wall thickness sc need not beconsidered separately in the analysis of the mechanicalbehaviour if they are less than ± 5 % of sc.

(2) For piping systems a deviation of the effective wallthickness minus the allowance c2 from the design wallthickness sc shall only be considered if this deviation liesoutside the tolerance field in accordance with a componentspecification or comparable documents.

(3) For thin-walled (sc ≤ 5 mm) and multi-layer componentsthe wall thickness of which shall meet further requirementsin addition to the strength requirements (e.g. heat exchangertubes, expansion joint bellows), the values on which theanalysis of the mechanical behaviour are to be based shall befixed for each individual case. This also applies to wallthickness tolerances in areas with structural discontinuity(e.g. penetrated area of a tee).

7.1.5.2.2 Deviations from internal diameter

The deviation from the actual internal diameter in across-section - averaged across the circumference - shallnormally not exceed 1% of the value specified in the draw-ing. In addition, the requirements of clause 7.1.6 shall bemet.

7.1.5.2.3 Ovalities

(1) Internal pressure

Ovalities and flattenings in longitudinal direction shall notshow a deviation > 1 % from the internal diameter upto and including an internal diameter di = 1000 mm.Where the inside diameter exceeds 1000 mm, the value(di + 1000)/(2 · di) [%] shall not be exceeded.

In this case, the ovality shall be determined as follows:

a) Ovality

[ ]Ud d

d di i

i i= ⋅

−+

⋅2 100,max ,min

,max ,min% (7.1-2)

b) Flattenings

[ ]Uqdi

= ⋅ ⋅4 100 % (7.1-3)

where q is shown in Figure 7.1-2.

i a

q

dd

Figure 7.1-2 : Flattening q

(2) External pressure

The ovality U shall not exceed the limit value Umax derivedfrom equation (7.1-4) where ∆ shall be taken from Figure7.1-3.

U Udi

= = ⋅max %∆ 100 (7.1-4)

di = internal diameter

(3) For pipes the following ovalities are permitted:

for internal pressure: 2 %,for external pressure: 1 %.

KTA 3201.2

∆

∆∆

∆

∆

∆

∆

c

c

c

c

c

c

c

the limi-= 1.0tation of internal pressure is governing

=0.5s

=0.6s

=0.4s

s

s

s

=0.3

Above the curve

2101.0

30

530.5

s

25

0.050.30.20.1

40

600

8001000

=1.0=0.8

500400

80

6050

300

200

100

a

c

a

a

c

d/ s

/ d

ds = wall thickness

= buckling length= outside diameter

Figure 7.1-3: Factor ∆ for external pressure

7.1.5.3 Spherical shells

7.1.5.3.1 Deviations from wall thickness

The requirements of clause 7.1.5.2.1 apply.

7.1.5.3.2 Deviations from diameter


7.1.5.3.3 Ovalities

(1) Internal pressure

Ovalities and flattenings normally shall not show a devia-tion from the internal diameter which is greater than one ofthe following values:

(di + 1000)/2 · di) [%] and (di + 300)/(di) [%].

The allowable values can be taken from Figure 7.1-4.

Ovalities shall be determined in accordance with clause7.1.5.2.3 (1).

i

500

[ mm ]

1000 250020001500

d

1

0

0

3

U [

% ]

4

2

Figure 7.1-4 : Ovalities

(2) External pressure

The criteria of clause 7.1.5.2.3 (2) may be used in which casehalf the outside diameter shall be taken for l.

7.1.5.4 Conical shells

Conical shells shall be treated like cylindrical parts. Ovalitiesshall be referred to circular cross-sections vertical to the axisof symmetry.For the length l according to clause 7.1.5.2.3 (2) the axiallength of the cone shall be taken.

7.1.5.5 Pipe bends and elbows

7.1.5.5.1 Deviations from diameter


7.1.5.5.2 Ovalities

(1) For ovalities in the bent area of the pipe bend afterbending the following applies:

[ ]Ud d

d= − ⋅max min %

0100 (7.1-5)

where

dmax = maximum outside diameter after bending orforming

dmin = minimum outside diameter after bending orforming

d0 = pipe outside diameter prior to bending.

(2) For internal pressure, U normally shall not exceed 5 %.

(3) For external pressure Figure 7.1-3 applies where forl/da a value of 10 shall be taken.

7.1.6 Misalignment of welds

7.1.6.1 General

The limitation of weld misalignments for the purposes offabrication and inspection/testing is laid down in KTA3201.3. For the calculation of misalignments the followingrequirements apply. Misalignments are geometric disconti-nuities to be considered in the analysis of the mechanicalbehaviour if the values laid down in the clauses followinghereinafter are exceeded. The rules of Section 8.4 are notcovered hereby.

7.1.6.2 Double-side welds

(1) Double-side welds need not be considered separately inthe analysis of the mechanical behaviour if the maximummisalignment of the inner edges does not exceed the valueslaid down in Table 7.1-1.

KTA 3201.2

Wall thickness Maximum misalignment of inner edges

sc in mm longitudinal welds circumferential welds

sc ≤ 12.5 sc/4 sc/4

12.5 < sc ≤ 19.0 3 mm sc/4

19.0 < sc ≤ 38.0 3 mm 4.5 mm

38.0 < sc ≤ 50.0 3 mm sc/8

50.0 < sc the smaller value ofsc/16 and 9 mm

the smaller value ofsc/8 and 16 mm

Table 7.1-1: Maximum misalignment

(2) Remaining edges must be ground over. The roughnessrequirements and transition angles depend on the require-ments for the test and inspections to be performed on theweld. Within the weld area the required wall thickness mustbe adhered to.

7.1.6.3 Single-side welds

(1) The following requirements apply to the case where theinside of the components is not accessible.

(2) In the case of concentric connections the maximummisalignment on the inside shall not exceed 0.1 · sc with amaximum of 1 mm over the entire circumference.

(3) A locally limited misalignment shall not exceed 2 mmunless other requirements (see clause 7.1.5) are impaired. Tomeet these requirements the parts to be welded shall bemachined, if required, in which case the wall thickness ob-tained shall not be less than the minimum wall thickness.

(4) Transitions at the weld in the base material should notexceed a slope of 3:1 unless higher requirements are fixedwith regard to the possibility of testing and inspection of theweld.

7.2 Loadings

Loadings are assumed to be all effects on the component orpart which cause stresses in this component or part. Theloadings result from load cases of the primary circuit inaccordance with Section 3 and are explained in Section 4.They will be determined within the mechanical and ther-modynamic system analyses.

7.3 Stress/strain loadings

(1) These are stresses or strains or a combination of stressesand strains and are evaluated as equivalent stress or equiva-lent strain. In the case of a linear-elastic relationship stressesand strains are proportional to each other. In the stress,fatigue or brittle fracture analysis according to Sections 7.7,7.8 and 7.9 respectively this proportional ratio even when inexcess of the yield strength or proof stress of the materialshall be the basis of analysis (fictitious stresses). In the caseof elastic-plastic analyses the effective stress-strain relation-ship shall be taken into account.

(2) The loadings are (primarily) static loadings, cyclic load-ings or dynamic loadings. Pulsating loads are considered tobe a specific case of cyclic loading.

(3) The (primarily) static loadings shall be limited withinthe stress analysis according to Section 7.7, and among cer-tain circumstances, within the brittle fracture analysis. Thelimitation of cyclic loadings shall additionally be madewithin the fatigue analysis according to Section 7.8.

7.4 Resulting deformations

(1) Resulting deformations can be determined by means ofthe integrals calculated for strain and are changes in geome-try of the component or the idealized structure due to load-ings.

(2) Resulting deformations can be described by displace-ments and values derived therefrom (e.g. twisting). Theyshall be limited if required such that the functional capabil-ity of the component and its adjacent components is notimpaired.

7.5 Determination, evaluation and limitation of mechani-cal forces and moments

(1) The mechanical forces and moments mentioned inclause 7.1.1 shall be determined by way of calculation ac-cording to the methods laid down in Annex B or by experi-ments or by a combination of calculation and experiments.

(2) In the case of comparable physical conditions, suitabilityof methods and adherence to the pertinent requirements theresults obtained from various methods can be considered tobe equivalent

(3) Section 8 contains alternative requirements whichcompletely or in part replace the requirements set forth inthis Section 7.5 within the applicability of Section 8.

(4) The forces and moments thus determined shall be as-sessed and be limited such that ductile fracture, fatiguefailure and brittle fracture as well as inadmissible deforma-tions and instability are avoided.

7.6 Mechanical system analysis

7.6.1 General

(1) The external loadings (e.g. forces, moments, displace-ments, temperature distributions) shall be used to determinethe influence coefficients (e.g. unit shear forces, unit mo-ments, and displacements) for the points under considera-tion in the system to be evaluated or at the adjoining edgesbetween component and adjacent component.

(2) External system-independent loadings which do notchange the behaviour of the system (e.g. radial temperaturedistribution and internal pressure, if applied) need only beconsidered when determining and evaluating the stresses.

KTA 3201.2

7.6.2 Modelling

7.6.2.1 General

The modelling of a system shall be made with respect to thetasks set forth and in dependence of the mathematical ap-proach according to Annex B, in which case the require-ments of clauses 7.6.2.2 to 7.6.2.5 shall be met.

7.6.2.2 System geometry

The system geometry shall comprise the components andparts which considerably influence the structure to beevaluated. The geometry of a piping system may be shownas a chain of bars by means of straight and curved barswhich corresponds to the pipe axis routing.

7.6.2.3 Flexibilities

(1) Piping components

Piping components shall normally be considered in theanalysis of the mechanical behaviour of the structure withthe flexibilities according to their geometry (average di-mensions including cladding).

Note:In the case of symmetrical tolerances these are nominal dimensions.

(2) Small components

Small components are parts of the piping system (e.g.valves, header drums, manifolds, branches, and specialparts). Where these components only have little influence onthe flexibility of the total structure, suitable flexibility factors(limit values) (e.g. valves: rigid; insulation: without influ-ence on the rigidity) shall be selected.

(3) Expansion joints

The working spring rates of expansion joints shall be takeninto account. The spring rates of expansion joints having noconsiderable influence on the system need not be taken intoaccount.

(4) Large components

The influence of large components (e.g. vessels) shall betaken into account by suitable modelling in consideration ofthe anchor function of the vessel.

(5) Component supports and buildings

The influence of component supports and the building shallbe considered to the extent required and shall be considered,if necessary, by equivalent models with equivalent stiff-nesses (fictitious elements).

7.6.2.4 Distribution of masses

(1) The masses in the system comprise the masses of eachcomponent or their parts, the fluid, the insulation, and otheradditional masses.

(2) A system with uniform distribution of masses may alsotreated like a system with discrete masses.

(3) The distribution of masses shall satisfy the requirementsregarding the distribution of unit shear forces and unit mo-ments and the type of vibrations.

(4) In the case of essential eccentricity the mass moments ofinertia for the rotational degrees of freedom shall also betaken into account.

7.6.2.5 Edge conditions

Forces and moments and displacements shall be taken intoaccount as edge conditions with respect to their effects forthe considered load case.

7.6.2.6 Subdivision of structures (uncoupling) into sectionsto avoid interaction of loadings

7.6.2.6.1 Static method

In static load cases structures may be subdivided into sec-tions if the edge conditions at the interface between any twosections are considered. If one of the following conditions ismet these edge conditions need not be determined and con-sidered:

a) The ratio of second moments of area is does not exceed0.01.

b) The ratio of these elements in a flexibility matrix whichgovern the considered deformations is sufficiently small.

7.6.2.6.2 Dynamic method

In the case of dynamic loadings, structures may be subdi-vided into sections if the interaction between the sections istaken into account or the vibration behaviour is not inad-missibly changed.

7.6.3 Calculation methods

(1) The calculation methods to be used depend on the se-lected mathematical approach according to Annex B as wellas on the loading to be evaluated (static or dynamic). Whenevaluating dynamic load cases the following methods maybe used:

a) equivalent statical load method

b) response spectrum method

c) time history method.

(2) The requirements of KTA 2201.4 shall be consideredspecifically for earthquake load cases.

7.7 Stress analysis

7.7.1 General

(1) By means of a stress analysis along with a classificationof stresses and limitation of stress intensities it shall beproved, in conjunction with the material properties, that noinadmissible distortions and especially only limited plasticdeformations occur.

KTA 3201.2

(2) The stress analysis for bolts shall be made in accordancewith Section 7.12.2.

7.7.2 Classification of stresses

7.7.2.1 General

(1) Stresses shall be classified in dependence of the cause ofstress and its effect on the mechanical behaviour of thestructure into primary stresses, secondary stresses and peakstresses and be limited in different ways with regard to theirclassification.

(2) Where in special cases the classification into the afore-mentioned stress categories is unclear the effect of plasticdeformation on the mechanical behaviour shall be determin-ing where an excess of the intended loading is assumed.

Note:

The definitions and terms used hereinafter are taken from thetheory o f p lane load-bearing structures (shells, p lates, d isks,etc.) and shall be applied accord ingly to other load-bearingstructures and components (bars, p ipes considered to be bars,beams, bolts, fittings, circular ring subject to twisting, etc.). Forthe stresses mentioned hereinafter d istinction is to be madebetween the various components of the stress tensor.

7.7.2.2 Primary stresses

(1) Primary stresses P are stresses which satisfy the laws ofequilibrium of external forces and moments (loads).

(2) Regarding the mechanical behaviour of a structure thebasic characteristic of this stress is that in case of (an inad-missibly high) increment of external loads the distortionsupon full plastification of the section considerably increasewithout being self-limiting.

(3) Regarding primary stresses distinction shall be madebetween membrane stresses (Pm, Pl) and bending stresses(Pb) with respect to their distribution across the cross-sectiongoverning the load-bearing behaviour. Here, membranestresses are defined as the average value of the respectivestress component distributed over the section governing theload-bearing behaviour, in the case of plane load-bearingstructures the average value of the stress component dis-tributed across the thickness. Bending stresses are defined asstresses that can be altered linearly across the consideredsection and proportionally to the distance from the neutralaxis, in the case of plane load-bearing structures as the por-tion of the stresses distributed across the thickness, that canbe altered linearly.

(4) Regarding the distribution of membrane stresses acrossthe wall distinction is to be made between general primarymembrane stresses (Pm) and local primary membranestresses (Pl) . Axisymmetric primary membrane stresses indiscontinuity regions are considered to be local, if the stressintensity does not exceed 1.1 times the allowable generalmembrane stress in a region remote from the discontinuityand with a length 1 0. ⋅ ⋅R sc in the meridional direction.

Two adjacent regions of local primary membrane stressintensities shall not be closer than 2 5. ⋅ ⋅R sc in the meri-

dional direction where R is the minimum midsurface radiusof curvature and sc the wall thickness according to clause7.1.4. Discrete regions of local primary membrane stressintensity resulting from concentrated loads (e.g. acting onbrackets) shall be spaced so that there is no overlapping ofthe areas in which the membrane stress intensity exceeds 1.1of the allowable general membrane stress.

For components for which the above conditions cannot besatisfied or which do not satisfy the above conditions, thelocal character of membrane stresses may also be verified bymeans of a limit analysis as per clause 7.7.4.

(5) While general primary membrane stresses are distributedsuch that no redistribution of stresses due to plastificationoccurs into adjacent regions, plastification in the case oflocal primary membrane stresses will lead to a redistribu-tion of stresses.

7.7.2.3 Secondary stresses

(1) Secondary stresses (Q) are stresses developed by con-straints due to geometric discontinuities and by the use ofmaterials of different elastic moduli under external loads,and by constraints due differential thermal expansions.Only stresses that are distributed linearly across thecross-section are considered to be secondary stresses.

(2) With respect to the mechanical behaviour of the struc-ture the basic characteristics of secondary stresses are thatthey lead to plastic deformation when equalizing differentlocal distortions in the case of excess of the yield strength.Secondary stresses are self-limiting.

(3) Stresses in piping systems developed due to constraintsin the system or generally due to fulfilment of kinematicboundary conditions are defined as Pe. Under unfavourableconditions regions with major distortions may develop inrelatively long systems, and the constraints thus occurringwill then act as external loads. In addition, it shall be dem-onstrated for these locations that yielding is limited locally.

7.7.2.4 Peak stresses

(1) Peak stress (F) is that increment of stress which is addi-tive to the respective primary and secondary stresses. Peakstresses do not cause any noticeable distortion and are onlyimportant to fatigue and brittle fracture in conjunction withprimary and secondary stresses.

(2) Peak stresses also comprise deviations from nominalstresses at hole edges within tubehole fields due to pressureand temperature in which case the nominal stresses shall bederived from equilibrium of forces considerations.

7.7.3 Superposition and evaluation of stresses

7.7.3.1 General

(1) As shown hereinafter, for each load case the stressesacting simultaneously in the same direction shall be added

KTA 3201.2

separately or for different stress categories (e.g. primary andsecondary stresses) be added jointly.

(2) Tables 7.7-1 to 7.7.3 give examples for the classificationand superposition of stresses.

(3) From these summed-up stresses the stress intensity forthe primary stresses and the equivalent stress range each forthe sum of primary and secondary stresses or the sum ofprimary stresses, secondary stresses and peak stresses shallbe derived.

(4) In clauses 7.7.3.2 and 7.7.3.3 the determination of stressintensities and equivalent stress ranges shall be based on thestress theory of von Mises or alternately on the theory ofTresca.

7.7.3.2 Stress intensities

(1) Having chosen a three-dimensional set of coordinatesthe algebraic sums of all normal and shear stresses actingsimultaneously and in consideration of the respective axisdirection shall be calculated for

a) the general primary membrane stresses or

b) the local primary membrane stresses or

c) the sum of primary bending stresses and either the gen-eral or local primary membrane stresses.

(2) Taking this algebraic sum the stress intensity accordingto von Mises shall be derived as follows

( ) ( )σ σ σ σ σ σ σ σ σ σ τ τ τV v Mises x y z x y x z y z xy xz yz, . = + + − ⋅ + ⋅ + ⋅ + ⋅ + +2 2 2 2 2 23

(7.7-1)

(3) When deriving the stress intensity in accordance withthe theory of Tresca, the principal stresses shall be deter-mined for each of the three cases (1) a) to c) taking the re-spective primary shear stresses into account unless the pri-mary shear stresses disappear or are negligibly small so thatthe effective normal stresses are the principal stresses. Ineach case the stress intensity then equals the difference be-tween the maximum and minimum principal stress.

σ σ σV Tresca, max min= − (7.7-2)

(4) For the three cases (1) a) to c) thus the stress intensity isobtained from Pm, Pl and Pm + Pb or Pl + Pb.

7.7.3.3 Equivalent stress ranges

(1) To avoid failure due to

a) progressive distortion (ratcheting)

b) fatigue

the pertinent equivalent stress ranges shall be determinedfrom the various stress categories and be limited in differentways.

(2) In case (1) a) the required stress tensors shall be formedtaking the simultaneously acting stresses from primary and

secondary stress categories, and in case (1) b) taking thesimultaneously acting stresses from all stress categories.

(3) From the number of service loadings to be consideredtwo service loadings shall be selected by using one fixedcoordinate system so that the stress intensity derived fromthe difference of the pertinent stress tensors becomes amaximum in accordance with the stress theory selected. Thismaximum value is the equivalent stress range.

(4) Where, upon application of Tresca`s maximum shearstress theory, the loading conditions to be considered showno change in the direction of principal stresses it will sufficeto form the maximum value of the differences of any twoprincipal stress differences of equal pairs of principal stressdirections. This maximum value then is the equivalent stressrange (according to the stress theory of Tresca).

7.7.3.4 Limitation of stress intensities and equivalent stressranges

(1) For each service loading level the stress intensities andequivalent stress ranges shall be limited in dependence ofthe mechanical behaviour of the material in accordance withTables 7.7-4 to 7.7-7. The limits fixed in Tables 7.7-4 to 7.7-6only apply to full rectangular sections, as they are based e.g.on the considered distribution of stresses in shell structures.For other sections the shape factors shall be fixed in depend-ence of the respective load behaviour.

(2) In the case of stress intensities derived from primarystresses and of equivalent stress ranges derived from pri-mary and secondary stresses the limitation shall be based onthe stress intensity factor Sm, strain limit or tensile strengthminimum values.

(3) The Smvalue is obtained on the basis of the temperatureT of the respective component and the room temperatureRT. For the service levels the respective temperature at thepoint under consideration versus time may be taken. For thedesign level 0, however, the design temperature shall beused.

(4) Taking these assignments into account, the Sm value isderived as follows:

a) for ferritic materials except for bolting materials

SR R R

mp T mT mRT=

min.

.;

.;

.0 2

1 5 2 7 3(7.7-3)

b) for ferritic and austenitic cast steel

ba) for ferritic cast steel

SR R R

mp T mT mRT=

min. ;.

;.0 2

2 3 6 4(7.7-4)

bb) for austenitic cast steel

SR R R

mp T mT mRT=

min.0 2

2 3 6 4.

;.

; (7.7-5)

For austenite with a Rp0.2RT/RmRT ratio not exceeding 0.5the value of Rp1.0T may be used in the calculation insteadof Rp0.2T if KTA 3201.1 specifies values for Rp1.0T.

KTA 3201.2

c) for austenitic materials except for bolting materials

ca) for the analyses according to Sections 7 and 8

SR R R R

mp RT p T mT mRT=

min. 0 2 0 2

1 5 1 1 2 7 3. .

.;

.;

.;

(7.7-6)

cb) for the dimensioning with design formulae accord-ing to Annex A

SR R R R R

mp RT p T mT mRT p T=

min. 0 2 0 2 0 2

1 5 1 1 2 7 3 1 5. . .

.;

.;

.; ,

.

(7.7-7)

For austenite with a Rp0.2RT/RmRT ratio ≤ 0,5 thevalue of Rp1.0T/1.5 may be used in the calculationinstead of Rp0.2T/1.5 if KTA 3201.1 specifies valuesfor Rp1.0T.

d) for bolts

SR

mp T= 0 2

3.

(7.7-8)

(5) The given stress intensity values also apply to Annex A.

(6) The minimum values for strain limit or tensile strengthshall be taken from KTA 3201.1 for the respective materialsspecified in that safety standard.

(7) The equivalent stress ranges derived from primary,secondary and peak stresses shall be limited by means offatigue analysis.

(8) The stress limitations for Pm, Pl, Pl + Pb (based on elasticanalysis) need not be satisfied if it can be proved by limitanalysis or experiments that the specified mechanical andthermal loadings are not less than the allowable lowerbound collapse load as per clause 7.7.4.

7.7.4 Limit analysis

7.7.4.1 General

(1) The limit values for the general primary membranestress, the local primary membrane stress as well as theprimary membrane plus bending stress need not be satisfiedat any point if it can be proved by means of limit analysisthat the specified loadings multiplied with the safety factorsgiven in 7.7.4.2 are below the respective lowerbound collapse load.

(2) The lower bound collapse load is that load which iscalculated with a fictitious yield stress σF as the lowerbound (lower bound theorem of limit analysis) by assumingan ideally elastic-plastic behaviour of the material in whichcase any system of stresses in the structure must satisfyequilibrium. Multi-axial stress conditions shall preferably becalculated by means of the von Mises theory.

(3) The effects of plastic strain concentrations which are e.g.caused by plastic hinges on the fatigue and ratcheting be-haviour as well as the possibility of instability of the struc-ture (buckling) shall be considered in the design.

(4) This procedure applies to plate and shell type compo-nents and shall not apply to threaded fasteners.

7.7.4.2 Allowable loadings

(1) Loading Level A

For this loading level σF = 1.5 ⋅ Sm is used as yield stressvalue for calculating the lower bound collapse load.

The use of the Sm value may lead, in the case of non-linearelastic materials, to small permanent strains during the firstload cycles. If these strains are not acceptable the value ofthe stress intensity factor shall be reduced by using thestrain limiting factors as per Table 7.7-8.

The specified load shall not exceed 67% of the lower boundcollapse load.

Permanent strain % Factors

0.20 1.00 *)0.10 0.900.09 0.890.08 0.880.07 0.860.06 0.830.05 0.800.04 0.770.03 0.730.02 0.690.01 0.63

*) For non-linear elastic materials the Sm value may exceed 67%of the proof stress Rp0.2T and attain 90% of this value at tem-peratures above 50 °C which leads to a permanent strain ofapprox. 0.1%. If this strain is not acceptable the Sm value maybe reduced by using the factors of this table.

Table 7.7-8: Factors for limiting strains for non-linearelastic materials

(2) Loading Level B


The use of 1.1 times the Sm value may lead, in the case ofnon-linear elastic materials, to small permanent strainsduring the first load cycles. If these strains are not accept-able the value of the stress intensity factor shall be reducedby using the strain limiting factors as per Table 7.7-8.


(3) Loading Level C



KTA 3201.2

(4) Loading Level D

For this loading level the smaller value of 2.3 ⋅ Sm or0,7 RmT⋅ is used as yield stress value σF for calculating the

lower bound collapse load.


(5) Test Level P



7.8 Fatigue analysis

7.8.1 General

7.8.1.1 Objectives and methods to be used

(1) A fatigue analysis shall be made in dependence of thetype of component to avoid fatigue failure due to cyclicloading.

(2) The basis for fatigue evaluation are the design fatiguecurves (Figures 7.8-1 to 7.8-3) based on test carried out atambient air.

Note:Cf. Section 4, esp. clause 4.5.

7.8.1.2 Fatigue analysis methods to be used

(1) The following fatigue analysis methods are permitted:

a) Simplified fatigue evaluation in accordance with clause7.8.2

This evaluation is based on a limitation of pressure cycleranges, temperature differences and load stress cyclicranges with regard to magnitude and number of cycles.If these limits are adhered to, safety against fatigue fail-ure is obtained. This evaluation method is based on alinear-elastic stress strain relationship.

b) Elastic fatigue analysis in accordance with clause 7.8.3

This analysis method shall be used especially if thesafety against fatigue failure according to clause 7.8.2cannot be demonstrated. The elastic fatigue analysis isonly permitted if the equivalent stress range resultingfrom primary and secondary stresses does not exceed avalue of 3 · Sm for steels and 4 · Sm for cast steel.

c) Simplified elastic-plastic fatigue analysis in accordancewith clause 7.8.4.

This analysis method may be used for load cycles wherethe equivalent stress range resulting from all primaryand secondary stresses exceeds the limit value of 3 · Sm

for steel and 4 · Sm for cast steel, however, these limitvalues are adhered to by the equivalent stress range re-

sulting from primary and secondary stresses due to me-chanical loads. The influences of plastification are con-sidered by using the factor Ke according to clause 7.8.4.In lieu of this Ke value other values may be used in in-dividual cases, which have been proved by experimentsor calculation or have been taken from literature. Theirapplicability shall be verified.

Note:The literature referenced in [1] contains a proposal for the de-termination of Ke values.

In addition, it shall be demonstrated that no ratcheting(progressive distortion) occurs.

d) General elastic-plastic fatigue analysis

While the abovementioned methods are based on lin-ear-elastic material behaviour, a fatigue analysis basedon the elasto-plastic behaviour of the material may bemade in lieu of the abovementioned methods in whichcase it shall be demonstrated that no progressive distor-tion (ratcheting) occurs.

Note:Clause 7.13 contains specific requirements as to the avoidance o fprogressive deformations.

(2) For piping the component-specific fatigue analysis ofsection 8.4 shall preferably be used in lieu of the analysismethods of clauses 7.8.3 and 7.8.4.

(3) For valves the component-specific fatigue analysis ofclause 8.3.6 shall preferably be used.

(4) For the fatigue analysis of bolts section 7.12.2 applies.

7.8.2 Simplified evaluation of safety against fatiguefailure

The peak stresses need not be considered separately in thefatigue evaluation if for the service loadings of level A of thepart the following conditions of sub-clauses a) to f) are sat-isfied.

Note:Where load cases o f level B are to be analysed regarding theirfatigue behaviour, the same conditions as for level A apply.

a) Atmospheric to service pressure cycles

The specified number of times (including start-up andshutdown) that the pressure will be cycled from atmos-pheric pressure to service pressure and back to atmos-pheric pressure does not exceed the number of cycles onthe applicable fatigue curves (see Figures 7.8-1 and 7.8-2)corresponding to an Sa value of three times (for steels)and four times (for cast steels) to the Sm value for thematerial at service temperature.

b) Normal service pressure fluctuations

The specified range of pressure fluctuations during levelA Service does not exceed 1/3 times the design pressure,multiplied with the (Sa/Sm) ratio, where Sa is the valueobtained from the applicable design fatigue curve for thetotal specified number of significant pressure fluctua-

KTA 3201.2

tions and Sm is the allowable stress intensity for the ma-terial at service temperature. If the total specified num-ber of significant pressure fluctuations exceeds 106, theSa value may be used for n = 106. Significant pressurefluctuations are those for which the total excursion ex-ceeds the quantity of 1/3 times the design pressure,multiplied by the S/Sm ratio, where S is the value of Sa

obtained from the applicable design curve for 106 cycles.

c) Temperature difference - start-up and shutdown

The temperature difference, K (Kelvin) between any twoadjacent points of the component during level A servicedoes not exceed the value of Sa/(2 · E · α), where Sa is thevalue obtained from the applicable design fatigue curvefor the specified number of start-up-shutdown cycles, αis the value of the instantaneous coefficient of thermalexpansion at the mean value of the temperatures at thetwo points, and E is the modulus of elasticity at themean value of the temperatures at the two points.

For adjacent points the following applies:

ca) For surface temperature differences:

- For surface temperature differences on shellsforming surfaces of revolution in the meridional di-rection, adjacent points are defined as points thatare less than the distance 2 ⋅ ⋅R sc , where R is the

radius measured normal to the surface from theaxis of rotation to the midwall and sc is the thick-ness of the part at the point under consideration. Ifthe product R · sc varies, normally the averagevalue of the points shall be used.

- For surface temperature differences on surfaces ofrevolution in the circumferential direction and onflat parts (e.g. flanges and flat heads), adjacentpoints are defined as any two points on the samesurface.

cb) For through-thickness temperature

For through-thickness temperature differencesadjacent points are defined as any two points on aline normal to any surface.

d) Temperature difference for services other than start-upand shutdown

The temperature difference, K (Kelvin), between any twoadjacent points is smaller than the value of Sa/2 · E · α,where Sa is the value obtained from the applicable de-sign fatigue curve for the total number of significanttemperature fluctuations. A temperature differencefluctuation shall be considered to be significant if its totalalgebraic range exceeds the quantityS/(2 · E · α), where S is the value obtained from the ap-plicable design curve for 106 cycles.

e) Temperature differences for dissimilar materials

For components fabricated from materials of differingmoduli of elasticity or coefficients of thermal expansion,the total algebraic range of temperature fluctuation ex-perienced by the component during normal service doesnot exceed the magnitude Sa/[2 · (E1 · α1 - E2 · α2)].

Here Sa is the value obtained from the applicable designfatigue curve for the total specified number of significanttemperature fluctuations, E1 and E2 are the moduli ofelasticity, and α1 and α2 are the values of the instantane-ous coefficients of thermal expansion at the mean tem-perature value for the two materials. A temperaturefluctuation shall be considered to be significant if its totalalgebraic range exceeds the quantity S/[2 · (E1 · α1 - E2 ·α2)], where S is the value of Sa obtained from the appli-cable design fatigue curve for 106 cycles.

If the two materials used have different design fatiguecurves the smaller value of Sa shall be used when apply-ing this sub-clause.

f) Mechanical loads

The specified full range of mechanical loads, excludinginternal pressure, but including pipe reactions, does notresult in load stresses whose range exceeds the value ofSa obtained from the applicable design fatigue curve forthe total specified number of significant load fluctua-tions. If the total specified number of significant loadfluctuations exceeds 106 cycles, the Sa value may betaken for n = 106 . A load fluctuation shall be consideredto be significant if the total excursion of load stress ex-ceeds the value of Sa obtained from the design fatiguecurve for 106 cycles.

7.8.3 Elastic fatigue analysis

(1) Prerequisite to the application of the elastic fatigueanalysis is that the 3 · Sm criteria for steels and the 4 · Sm

criteria for cast steel are satisfied in accordance with clause7.7.3.4.

(2) As the stress cycles σV = 2 · σa = 2 · ET · εa in level A andB service assume different magnitudes they shall be subdi-vided in suitable types of stress cycles 2 · σai and their cumu-lative damage effect shall be evaluated as follows:

For each type of cycle σai = Sa the allowable number of cy-cles �ni shall be determined by means of Figure 7.8-1 or 7.8-2and be compared with the specified number of cycles ni ornumber of operation cycles ni verified by calculation.

The sum of these ratios ni/ �ni is the cumulative usage factorD for which the following applies within the design:

Dnn

nn

nn

k

k= + + ≤1

1

2

21 0

� �...

�. (7.8-1)

7.8.4 Simplified elastic plastic fatigue analysis

Within the simplified elastic-plastic analysis the 3 · Sm limitfor steels and 4 · Sm limit for cast steel with a stress cyclerange resulting from primary and secondary stresses may beexceeded if the requirements in a) to e) hereinafter are met.

KTA 3201.2

a) The equivalent stress range resulting from primary andsecondary membrane and bending stresses withoutthermal bending stresses across the wall shall be notgreater than 3 · Sm for steel and 4 · Sm for cast steel.

b) The value of half the equivalent stress range Sa to becompared with the design fatigue curve acc. to Figure7.8-1 or 7.8-2 shall be multiplied with the factor Ke whereKe is to be determined for steel as follows:

Ke = 1.0 for Sn ≤ 3 · Sm (7.8-2)

( )( )K

nn m

SSen

m= +

−⋅ −

⋅⋅

−

1 0

11 3

1. for

3 · Sm < Sn < m · 3 · Sm (7.8-3)

Ke = 1/n for Sn ≥ m · 3 · Sm (7.8-4)

Sn = Range of primary plus secondary stress intensity

In the foregoing equations the 3 · Sm value shall be sub-stituted by 4 · Sm for cast steel.

The material parameters m and n shall be taken fromTable 7.8-1.

c) The limitation of thermal stress ratcheting shall be dem-onstrated (cf. e.g. clause 8.4.3.4.1 b).

d) The limitation of the cumulative usage factor due tofatigue shall be in acc. with clause 7.8.3.

e) The temperature for the material used shall not exceedthe value of Tmax in Table 7.8-1.

Type of material m n Tmax (°C)

Low-alloy carbon steel 2.0 0.2 370

Martensitic stainless steel 2.0 0.2 370

Carbon steel 3.0 0.2 370

Austenitic stainless steel 1.7 0.3 425

Nickel based alloy 1.7 0.3 425

Table 7.8-1: Material parameter

For local thermal stresses the elastic equations may be usedin the fatigue analysis. The Poisson`s ratio ν shall be deter-mined as follows:

ν = − ⋅

0 5 0 2

0 2. .

.R

Sp T

a, but not less than 0.3

(7.8-5)where:

T = 0.25 ·�

T + 0.75 · �T (7.8-6)

with

�T maximum temperature at the considered load cycle�

T minimum temperature at the considered load cycle

7.9 Brittle fracture analysis

7.9.1 General

(1) The safety against brittle fracture shall be verified. Thestress intensities referred to in clause 7.7 allow, for levels Aand B, for the sums of primary plus secondary stresses in-cremental collapse as per clause 7.8.3 and under certainconditions limited cyclic plastic deformations (e.g. as perclause 7.8.4).

(2) In addition it is possible that in levels C and D limitedplastic deformation results from primary stresses. Therefore,it must be ensured that both at new condition and duringthe whole service life of the component the required de-formability is assured.

(3) According to this it shall be proved that in zones possi-bly subject to irradiation, especially in the case of great wallthicknesses and high-strength materials initiation of brittlefracture can be excluded in the heat affected zones of welds.

(4) Safeguarding against brittle fracture shall be ensuredduring the initial pressure test and the in-service inspectionsby means of suitable pressure test conditions. To this endthe test temperature shall be at least 33 K above RTNDT onthe basis of the Pellini concept, where RTNDT is the highesttemperature of T1 to T3:

T1 = TNDT (7.9-1)

T2 = TAV (68 J) - 33 K (7.9-2)

T3 = TAV (0.9 mm) - 33 K (7.9-3)

where

TNDT temperature equal to or higher thanthe NDT (nil ductility transition) tem-perature in which case the NDT tem-perature is the highest temperature atwhich the specimen fails indrop-weight testing

°C

TAV (68 J) Temperature at which an impact en-ergy of at least 68 J (lower bound) isdetermined on ISO-V-notch specimensby means of impact testing

°C

TAV (0.9 mm) Temperature at which a lateral exten-sion of at least 0.9 mm is determinedon ISO-V-notch specimen by means ofimpact testing

°C

Note:These values are to be determined according to KTA 3201.1.

In individual cases lower temperatures are acceptable ifcomparable safety is ensured by specific verification.

(5) The in-service pressure test shall normally be conductedso that a verification of safety comparable to that of theinitial pressure test is obtained.

(6) The procedures mentioned in clause 7.9.2 or 7.9.3 shallnormally be used to verify the safety against brittle fracturewhere it shall be taken into account that the nil-ductilitytransition temperature is increased during operation onaccount of neutron irradiation. The influence of irradiation

KTA 3201.2

(on ferritic steels) shall be taken into account if at the end ofdesign lifetime, the neutron fluency is greater than

1 · 1017 cm-2 (referred to neutron energies above 1 MeV). Insuch cases the safety against brittle fracture shall be verifiedalso for all loading conditions of the irradiated parts. For theother areas a verification shall be made for such conditionsas are not covered by the initial pressure test.

7.9.2 NDT temperature concept

(1) In the NDT temperature concept according to Pel-lini/Porse it can be assumed that unstable cracks at tem-peratures above crack-arrest temperature are arrested.

(2) This NDT temperature concept shall be applied to thecylindrical section of the reactor pressure vessel core areabecause at this area the highest primary membrane stressesare applied and the influence of neutron irradiation must beconsidered.

(3) The NDT temperature concept according to Pel-lini/Porse leads to a brittle fracture diagram that containsstress intensities depending on minimum temperatures inthe form of the modified Porse diagram in which case thestresses occurring in the part shall lie outside these stressintensities under all service conditions. This can be shownby means of a start-up/shutdown diagram.

Note:Annex C 1 contains a guidance to establish a modified Porsediagram as well as an example with an insertedstart-up/shutdown diagram.

7.9.3 Fracture mechanics concept

7.9.3.1 General conditions

(1) By means of the total stress determined normal to thecrack plane the stress intensity factors KI (t, T) are estab-lished for any time. Unstable crack extension, e.g. brittlefracture, does not occur if this curve does not reach thecurve of static fracture toughness KIc (T) or if the crack tip incourse of the considered actual transient has been subjectedto thermal loading beforehand (warm prestress). If the stressintensity KI (t, T) is less than the crack arrest toughnessKIa (T) a global or local unstable crack is arrested.

(2) The fracture toughness of the material shall have beendetermined in dependence of the temperature. For the ma-terials 20 MnMoNi 5 5 and 22 NiMoCr 3 7 the fracturetoughness curve to Figure 7.9.1 shall be used. Where valuesmeasured on the component and verified to a sufficientextent are available they shall be taken. The influence ofirradiation shall be considered by increasing the referencetemperature RTNDT by ∆T41 (see definition of transitiontemperature shift in KTA 3203).

The KIc- and KIR values shall only be determined by ap-proximation for the non-irradiated and the irradiated con-dition by means of the following equations:

( )[ ]K T RT TIc NDT= + ⋅ ⋅ − + −1153 97 51 0 036 55 5 41. . .exp ∆

(7.9-4)

( )[ ]K K T RT TIR Ia NDT= = + ⋅ ⋅ − + −930 42 5 0 026 88 9 41. . .exp ∆

(7.9-5)

with

KIc static fracture toughness N/mm3/2

T temperature °C

RTNDT reference nil-ductility transitiontemperature for the non-irradiatedcondition

°C

∆T41 temperature shift at an impactenergy of 41 J for the irradiatedcondition

K

KIR reference fracture toughness N/mm3/2

KIa crack arrest toughness N/mm3/2

Note:Section C 2 contains the design procedure for determining theKI values.

7.9.3.2 Levels A and B

(1) For the cylindrical section of the reactor pressure vesselthe respective stress intensities shall be determined from thesum of the determined primary and secondary stresses byassuming a surface defect the plane of which is vertical tothe highest stress (depth: 0.25 x wall thickness; length: 1.5 xwall thickness; the assumption of smaller defects is accept-able if justified). In this case the stress intensities derivedfrom the primary stresses shall be multiplied with a safetyfactor of 2. This sum must be less than the reference fracturetoughness (KIR)

of the material; see examples in Figure 7.9-2.

(2) For the other areas of the reactor pressure vessel thestress intensities derived from the primary stresses need notbe multiplied with a factor of 2, the assumption of smallerdefects with a depth of less than 0.25 x the wall thicknessand a length of less than 1.5 the wall thickness is acceptableif this can be justified.

7.9.3.3 Levels C and D

For Levels C and D the brittle fracture resistance for thecylindrical section in the core area of the reactor pressurevessel shall be verified by means of fracture mechanics. Thestress intensity factor KI (t, T) is the sum of stress intensityfactors caused by internal pressure, temperature gradientetc. It shall be proved that a defect with half the magnitudeon which the calculation is based can be detected positively.For transients which upon attainment of the load pathmaximum show a stress intensity being strictly monotoneversus time, crack initiation can be excluded for the crackpostulated by the calculation if the crack tip has been sub-jected beforehand to thermal loading (warm prestress) in thecourse of the actually considered transient. At a stress in-tensity increasing versus time the KIc value may be exceeded(e.g. in case of an increased portion of secondary stresses,thermal shock to Figure 7.9-3), however, it must be provedthat for cracks which may have become unstable (ai from the

KTA 3201.2

condition KI > KIc) crack arrest will occur in the wall (aa notgreater than 0.75 · s; aa from the condition KI smaller thanKIa; at the RTNDT concept KIa is identical to KIR). Figure 7.9-3shows the example of thermal shock effect on possible de-fects.

7.9.3.4 In-service inspections

(1) If defects detected by in-service inspections are checkedfor permissibility, the critical defect size shall normally bedetermined at these locations as follows:

a) for the part to be inspected the inspection areas shall bedetermined on the basis of the mechanical behaviouranalysis in consideration of the basic measurements andformer inspections

b) the initial defect size shall be determined for each in-spection area by means of linear-elastic fracture mechan-ics which shall be based on the following boundaryconditions:

Type of defect

Where the geometry permits, a surface defect of theshape a/2c = 1/6 is considered. In other cases (e.g. noz-zles) the defect shape shall be selected according to thegeometric conditions. Inadmissible indications shall beconsidered to be cracks independently of their origin.

Defect location

Normal to the maximum stress (principal stress)

Fracture toughness

Fracture toughness is based on the KIc value of the ma-terial used corresponding to the (static) material condi-tion of the respective part for the governing load case.

For the materials mentioned in clause 7.9.3.1 the staticfracture toughness (KIc) as per Figure 7.9-1, determinedon the basis of the RTNDT temperature or according toequation (7.9.1), applies.

c) Requirements for defect detection

The governing load case is that case leading to the small-est critical defect size.

(2) The maximum allowable defect shall be determinedwith KI,allow = KIc/1.5 where KI shall be determined for thestresses acting in dependence of the crack depth in consid-eration of the detected crack for the considered period oftime and for KIc at the end of this period.

(3) This defect must be positively detected by means of theintended test procedure.

7.10 Strain analysis

A strain analysis shall only be made if specified strain limitsare to be adhered to for functional reasons.

7.11 Structural analysis

Where under the effect of pressure loading a sudden defor-mation without considerable increase in load may be ex-pected, a structural analysis shall be performed.

7.12 Stress, strain and fatigue analyses for flanged joints

7.12.1 General

(1) The loading conditions of flanged joints shall be deter-mined for the governing load cases. The verification bycalculation of the strength and deformation conditions maybe made by approximation in accordance with the simpli-fied procedure of clause A 2.9.5. The exact verification shallbe made according to this section in consideration of theelastic behaviour of the structure. Dimensioning may bemade in accordance with Sections 2.8 and 2.9.

(2) The following shall be included, where required, in thestructure:

a) identical flange pairs, non-identical flange pairs or theflange with flat or dished cover

b) bolts

c) the gasket and

d) the connected shell.

(3) The following load cases shall be examined:

a) the bolting-up condition(s)

b) the conditions of specified operation

c) upset conditions (incidents), if any.

(4) The loadings on the flanged joint in the load cases ofspecified operation and incidents, if any, shall be calculatedin connection with the respective bolting-up condition e.g.taking consistent bolt elongation into account (definition seeunder clause A 2.9.5.1 (2) ).

(5) For the flanges, the covers, if any, belonging to theflanged joint and the connected shell a stress analysis andlimitation as per Section 7.7 and a fatigue analysis as perSection 7.8 shall be performed. For bolts a stress and fatigueanalysis as per clause 7.12.2 is required.

(6) The assessment of the gasket loading condition shall bemade taking the gasket factors of Section A 2.10 or the veri-fied data of the gasket manufacturer into account. The re-sidual gasket load shall be controlled according to the re-spective requirements in due consideration of the seatingconditions (correlation of gasket seating load, gasket com-pression load for operating condition and internal pressure).

KTA 3201.2

7.12.2 Stress and fatigue analysis for bolts

(1) When evaluating stress limits for bolts the followingstresses are referred to: average tensile stresses, bendingstresses, torsional stresses, and peak stresses.

(2) A specific fatigue analysis shall be made if the bolts arenot covered by the simplified evaluation of safety againstfatigue failure of the component in acc. with clause 7.8.2. Inthis fatigue analysis the material properties and geometricboundary conditions of threaded members shall be consid-ered e.g. when determining the load cycles resulting frompressure fluctuations and temperature differences.

(3) The allowable stress limits for bolts are contained inTable 7.7-7 using the Sm value as per clause 7.7.3.4.

(4) The fatigue behaviour shall be evaluated on the basis ofthe range of maximum stress intensity in due considerationof the elasticity of threaded members, in which case therange of normal stress intensity shall be multiplied with afatigue strength reduction factor of not exceeding 4. Theusage factor shall be accumulated and be limited in acc.with equation (7.8.-1).

Fatigue strength reduction factors smaller than 4 shall beverified.

(5) For bolts with a specified tensile strength RmRT not ex-ceeding 690 N/mm2 the design fatigue curves acc. to Fi-gures 7.8-1 and 7.8-2 apply, and for high-strength bolts withspecified tensile strength RmRT above 690 N/mm2 the de-sign fatigue curve for temperatures up to and including 370°C of Figure 7.8-3 applies. These bolts shall be designed asnecked-down bolt in accordance with A 2.8.3. The upper fa-tigue curve of Figure 7.8-3 may be used if without consid-eration of the notch effect the average tensile strength doesnot exceed the value 2 ⋅ Sm and the total tensile plus bendingstrength does not exceed the value of 2.7 ⋅ Sm.

7.13 Avoidance of thermal stress ratcheting

7.13.1 General

(1) Where the equivalent stress intensity range derived fromprimary stresses P and secondary stresses Q exceeds thevalue of 3 · Sm for steels and 4 · Sm for cast steels (see clause7.8.1), it shall be proved my means of the following stipula-tions that the distortions developing as a result of stressratchet remain within acceptable limits.

(2) When evaluating the limitation of progressive distor-tions under cyclic loading the same load cases and combi-nation of these load cases as verified by means of fatigueanalysis shall be considered.

(3) The evaluation of limitation of thermal stress ratchetingmay be a simplified evaluation (clause 7.13.2) using ap-proximation formulae; more exact evaluations require veri-fication of strains by elasto-plastic analysis (clause 7.13.3) orby means of measurements (clause 7.13.4).

7.13.2 Simplified evaluation by approximation formulae

7.13.2.1 Range of application

(1) The simplified evaluation may be used for:

a) axisymmetric structures under axisymmetric loadingconditions, which are located sufficiently away from lo-cal structural discontinuities, or

b) general structures where thermal peak stresses are neg-ligible (i.e. linear thermal stress distribution through thewall).

(2) The evaluations are based on the results of elasticanalysis and a stress classification in accordance with clause7.7.3; here the following stress parameters referred to theelevated temperature proof stress Rp0.2T are used:

X = (Pl + Pb/K)max/Rp0.2T (7.13-1)

Y = (QR)max/Rp0.2T (7.13-2)

where T = 0.25 · �

T + 0.75 · �T (7.13-3)

(referred to the respective load cycle considered) with

(Pl + Pb/K)max maximum value of primary stress in-tensity where the portion of bendingstress Pb has been adjusted with the fac-tor K

(QR)max maximum secondary stress intensity

�T maximum temperature

�

T minimum temperature

K factor, e.g. K = 1.5 for rectangularcross-sections.

(3) Where the conditions of clause 7.13.2.1 (1) a) are satis-fied, the stress relationships are simplified as follows:

X = maximum general membrane stress due to inter-nal pressure, divided by Rp0.2T, and

Y = maximum allowable range of thermal stress,divided by Rp0.2T.

(4) The use of the yield strength instead of the proportionalelastic limit allows a small amount of growth during eachcycle until strain hardening raises the proportional elasticlimit to the yield strength.

(5) This evaluation procedure can be applied as long as theload cycle number to be assessed does not exceed the value

n n S Ra p T= ( = ).� 2 0 2⋅ (7.13-4)

KTA 3201.2

7.13.2.2 Evaluation by limitation of stresses

(1) If the evaluation requirements are met thermal stressratcheting can definitely be excluded.

(2) When calculating the allowable secondary stress inten-sity the secondary stress parameter Y may be multipliedwith the higher value of Rp0.2T or 1.5 ⋅ Sm.

(3) At given primary stress parameter X the following sec-ondary stress parameter is permitted for the stress intensityrange:

Case 1: Linear variation of temperature or linear variationof secondary stress through the wall:

for 0.0 < X ≤ 0.5, Y = 1/X (7.13-5)

for 0.5 < X < 1.0, Y = 4 (1-X) (7.13-6)

Case 2: Parabolic constantly increasing or constantly de-creasing variation of temperature through the wall:

for 0.615 ≤ X ≤ 1.0, Y= 5.2 (1-X) (7.13-7)

for X < 0.615, Y (X=0.5) = 2.70

Y (X=0.4) = 3.55

Y (X=0.3) = 4.65

Case 3: Any component geometry and any loading:

for X ≤ 1.0, Y= 3.25 (1-X) + 1.33 (1-X)3 + 1.38 (1-X)5

(7.13-8)

Guide values: Y (X=1.0) = 0.00

Y (X=0.0) = 5.96

7.13.2.3 Evaluation by limitation of strains

(1) This evaluation shall only be used for conditions as perclause 7.13.2.1 (1) a).

(2) When determining the strains, the following conditionsidentified by the index i are considered:

Index 1 the lower bound at extreme value formation of therange of thermal stresses or secondary stresses (lowtemperature) and with

Index 2 the upper bound at extreme value formation of therange of thermal stresses or secondary stresses(high temperature).

(3) Where the stress parameters

X1, Y1 are determined by using the elevated temperatureproof stress Rp0.2T1 at temperature T1 averaged

across the wall for condition 1

X2, Y2 are determined by using the elevated temperatureproof stress Rp0.2T2 at temperature T2 averaged

across the wall for condition 2,

distinction shall be made between the following cases whendetermining the auxiliary values of Zi (i=1,2):

a) for Yi ⋅ (1-Xi) > 1, Zi = Xi ⋅ Yi (7.13-9)

b) for Yi ⋅ (1-Xi) ≤ 1 and Xi + Yi >1,

Zi = Yi + ( )1 2 1− ⋅ − ⋅X Yi i (7.13-10)

c) for Xi + Yi ≤ 1, Zi = Xi (7.13-11)

(4) From this the plastic strain increment ∆ε for each cyclecan be derived in dependence of the auxiliary value Zi andin consideration of the ratio of the proof stress valuesρ = R Rp T p T0.2 2 0.2 1/

Z1 ≤ ρ: ∆ε = 0 (7.13-12)

ρ < Z1 ≤ 1:( ) ( )

∆ε =⋅ − + ⋅ −R Z R Z

Ep T p T

T

0 2 1 1 0 2 2 2

2

1 1. .

(7.13-13)

Z1 > 1:( ) ( )

∆ε =⋅ −

+⋅ −R Z

E

R Z

Ep T

T

p T

T

0 2 1 1

1

0 2 2 2

2

1 1. .

(7.13-14)

where in the calculation of ∆ε negative individual strainportions which may occur at conditions 1 or 2 shall not berejected.

(5) The sum of plastic strain increments ∆ε to the end ofservice life shall not exceed the value 2 %.

7.13.3 General evaluation by elastic-plastic analysis

(1) For the determination of plastic strains at cyclic loadingan elasto-plastic analysis may be made. The material modelused in this analysis shall be suited to realistically determinethe cyclic strains.

KTA 3201.2

(2) Where in the case of strain hardening materials the de-crease of the strain increment from cycle to cycle is to betaken for the determination of the total strain, the load his-togram shall comprise several cycles. From the strain historydetermined from the respective load histogram the maxi-mum accumulated strain may be calculated by conservativeextrapolation.

(3) At the end of service life, the locally accumulated prin-cipal plastic tensile strain shall not exceed, at any point ofany cross section, the following maximum value: 5.0% in thebase metal, 2.5% in welded joints.

7.13.4 Specific evaluation by measurement

(1) the cyclic accumulated strain may also be determined bymeans of measurements.

(2) Regarding an extrapolation for accumulated total plasticstrain as well as the limits of allowable strain clause 7.13.3applies.

Vessel Part Location Origin of Stress Type of stress Classification

Cylindrical orspherical shell

Shell plate remotefrom discontinuities

Internal pressure General membrane

Gradient through plate thickness

Pm

Q

Axial thermal gradi-ent

Membrane

Bending

Q

Q

Junction with heador flange

Internal pressure Membrane 3)

Bending

Pl

Q 1)

Any shell orhead

Any section acrossentire vessel

External load ormoment, or internalpressure 2)

General membrane averaged across fullsection. (Stress component perpendicular tocross section)

Pm

External load ormoment 2)

Bending across full section. (Stress compo-nent perpendicular to cross section)

Pm

Near nozzle orother opening

External load ormoment, or internalpressure 2)

Local membrane 3)

Bending

Peak (fillet or corner)

Pl

Q

F

Any location Temperature differ-ence between shelland head

Membrane

Bending

Q

Q

Dished head orconical head

Crown Internal pressure Membrane

Bending

Pm

Pb

Knuckle or junc-tion to shell

Internal pressure Membrane

Bending

Pl 4)

Q

Flat head Centre region Internal pressure Membrane

Bending

Pm

Pb

Junction to shell Internal pressure Membrane

Bending

Pl

Q

Table 7.7-1: Classification of stress intensity in vessels for some typical cases

KTA 3201.2

Vessel Part Location Origin of Stress Type of stress Classification

Perforated head Typical ligament ina uniform pattern

Pressure Membrane(averaged through cross section)

Bending(averaged through width of ligament, butgradient through plate)

Peak

Pm

Pb

F

Isolated or atypicalligament

Pressure Membrane (as above)

Bending (as above)

Peak

Q

F

F

Nozzle Cross section per-pendicular to noz-zle axis

Internal pressure orexternal load ormoment 2)

General membrane, averaged across fullcross section (Stress component perpendicu-lar to section)

Pm

External load ormoment 2)

Bending across nozzle section Pm

nozzle wall Internal pressure General membrane

Local membrane

Bending

Peak

Pm

P1

Q

F

Differential expan-sion

Membrane

Bending

Peak

Q

Q

F

Cladding Any Differential expan-sion

Membrane

Bending

F

F

Any Any Radial temperaturedistribution 5)

Equivalent linear stress 6)

Non-linear stress distribution

Q

F

Any Any Any Stress concentration by notch effect F

1) If the bending moment at the edge is required to maintain the bending stress in the middle of the head or plate within acceptable limits,the edge bending is classified as Pb.

2) To include all pipe end forces resulting from dead weight, vibrations and restraint to thermal expansion as well as inertial forces.3) Outside the area containing the discontinuity the membrane stress in meridional and circumferential direction of the shell shall not

exceed 1.1 ⋅ Sm and the length of this area shall not exceed 1.0 ⋅ R sc⋅ .

4) Consideration shall be given to the possibility of wrinkling and excessive deformation in thin-walled vessels (large diameter-to-thicknessratio)

5) Consider possibility of failure due to thermal stress ratcheting.

6) The equivalent linear stress is defined as the linear stress distribution which has the same net bending moment as the actual stress distri-bution.

Table 7.7-1: Classification of stress intensity in vessels for some typical cases (continued)

KTA 3201.2

Piping compo-nent Location Origin of stress Type of stress Classification

Internal pressure Average membrane stress Pm

Sustained mechani-cal loads incl. deadweight and inertialforces

Bending across section (stress componentperpendicular to cross section)

Pb

Internal pressure Membrane (through wall thickness)

Bending (through wall thickness)

Pl

Q

Sustained mechani-cal loads incl. deadweight and inertialforces

Membrane (through wall thickness)

Bending (through wall thickness)

Pl

Q

Restraint to thermalexpansion

Membrane

Bending

Pe

Pe


Membrane

Bending

Q

Q

Any Any Peak F

Branch connec-tions and tees

In crotch region Internal pressure,sustained mechanicalloads incl. deadweight and inertialforces as well as re-straint to thermalexpansion

Membrane

Bending

Pl

Q


Membrane

Bending

Q

Q

Any Peak F

Bolts and flanges Remote from dis-continuities

Internal pressure,gasket compression,bolt loads

Average membrane Pm

Wall thicknesstransitions

Internal pressure,gasket compression,bolt loads

Membrane

Bending

Pl

Q

Axial or radial ther-mal gradient

Membrane

Bending

Q

Q

Restraint to thermalexpansion

Membrane

Bending

Pe

Pe

Any Peak F

Any Any Radial thermal gra-dient 1)

Bending through wall

Peak

F

F

1) Consider possibility of failure due to thermal stress ratcheting.

Table 7.7-2: Classification of stress intensity in piping for some typical cases

Straight pipe ortube, reducers,intersections andbranch connec-tions, except incrotch regions

Location remotefrom discontinui-ties

Location with dis-continuities (wallthickness transiti-ons, connection ofdifferent pipingcomponents)

KTA 3201.2

Type of componentsupport structures

Location Origin of stress Type of stress Classification

Any shell Force or moment to bewithstood

General membrane, averaged across full section(stress component perpendicular to cross section)

Pm

Force or moment to bewithstood

Bending across full section(stress component perpendicular to cross section)

Pb

Near discontinuity 1)

or openingForce or moment to bewithstood

MembraneBending

Pm

Q 2)

Any Restraint 3) MembraneBending

Pe

Pe

Any plate or disk Any Force or moment to bewithstood

MembraneBending

Pm

Pb

Near discontinuity 1)

or openingForce or moment to bewithstood

MembraneBending

Pm

Q 2)

Any Restraint 3) MembraneBending

Pe

Pe

1) Discontinuities mean essential changes in geometry such as wall thickness changes and transitions between different types of shells. Local stress concentra-tions, e.g. on edges and boreholes are no discontinuities.

2) Calculation not required.3) These are stresses resulting from restraints of free end displacements or different displacements of component support structures or anchors, including stress

intensifications occurring at structural discontinuities, but excluding restraint due to thermal expansion of piping systems. The forces and moments from re-strained thermal expansions of piping systems are considered to be "forces or moments to be withstood" by the component support structure.

Table 7.7-3: Classification of stress intensity of integral areas of component support structures for some typical cases

Loading levels Designloading

Service limits

Stress category (Level 0) Level A Level B Level P 2) Level C 4) Level D

Primary Pm Sm 1.1 ⋅ Sm 0.9 ⋅ Rp0.2PT Rp0.2T 3) 0.7 ⋅ RmT

stresses Pl 1.5 ⋅ Sm 1.65 ⋅ Sm 1.35 ⋅ Rp0.2PT 1.5 ⋅ Rp0.2T 3) RmT

Pm + Pbor

Pl + Pb

1.5 ⋅ Sm 1.65 ⋅ Sm 1.35 ⋅ Rp0.2PT 1.5 ⋅ Rp0.2T 3) RmT

Primary plus Pe 3 ⋅ Sm 1) 3 ⋅ Sm

1) 5)

secondary stresses Pm + Pb + Pe + Qor

Pl + Pb + Pe + Q 3 ⋅ Sm

1) 3 ⋅ Sm 1) 5)

Primary plus secondarystresses plus peak stresses

Pm + Pb + Pe + Q + For

Pl + Pb + Pe + Q + F

D ≤ 1.0;

2 ⋅ Sa

D ≤ 1.0;

2 ⋅ Sa 6)

The material strength values shown shall be taken as minimum values.

When using the component-specific analysis of the mechanical behaviour in accordance with Section 8 the values indicated in this section shall apply.

1) If the 3 ⋅ Sm limit is exceeded an elastic-plastic analysis shall be made taking the number of cycles into account (see clause 7.8.1). Where the respective condi-tions are given, this analysis may be a simplified elastic-plastic analysis according to clause 7.8.4.

2) If the allowable number of cycles of 10 is exceeded, the cycles exceeding 10 shall be incorporated in the fatigue analysis according to Levels A and B.

3) However, not more than 90 % of Level D.


5) Verification is not required for those cases where the loadings from load cases "emergency" and "damage" have been assigned to this level for reasons offunctional capability or other reasons.

6) A fatigue evaluation is not required for those cases where the loading from load cases "emergency" and "damage" have been assigned to this level and theseload cases belong to the group with 25 load cycles for which no fatigue analysis is required.

Table 7.7-4: Allowable values for stress intensities and equivalent stress ranges derived from stress categories when per-forming a linear-elastic analysis of the mechanical behaviour, using ferritic steels except for cast steel

Any section throughthe entire componentsupport structure

KTA 3201.2


Service limits


Primary Pm Sm 1.1 ⋅ Sm 0.9 ⋅ Rp0.2PT 1.2 ⋅ Sm 0.7 ⋅ RmT

stresses Pl 1.5 ⋅ Sm 1.65 ⋅ Sm 1.35 ⋅ Rp0.2PT 1.8 ⋅ Sm RmT

Pm + Pbor

Pl + Pb

1.5 ⋅ Sm 1.65 ⋅ Sm 1.35 ⋅ Rp0.2PT 1.8 ⋅ Sm RmT


1) 4) secondary stresses Pm + Pb + Pe + Q

orPl + Pb + Pe + Q

3 ⋅ Sm 1) 3 ⋅ Sm

1) 4)




D ≤ 1.0;

2 ⋅ Sa

D ≤ 1.0;

2 ⋅ Sa 5)








Table 7.7-5: Allowable values for stress intensities and equivalent stress ranges derived from stress categories when per-forming a linear-elastic analysis of the mechanical behaviour, using austenitic steels


Service limits


Primary Pm Sm 1.1 ⋅ Sm 0.75 ⋅ Rp0.2PT Rp0.2T 3) 0.7 ⋅ RmT

stresses Pl 1.5 ⋅ Sm 1.65 ⋅ Sm 1.15 ⋅ Rp0.2PT 1.5 ⋅ Rp0.2T 3) RmT

Pm + Pb

orPl + Pb

1.5 ⋅ Sm 1.65 ⋅ Sm 1.15 ⋅ Rp0.2PT 1.5 ⋅ Rp0.2T 3) RmT


1) 5)

secondary stresses Pm + Pb + Pe + Qor

Pl + Pb + Pe + Q 4 ⋅ Sm

1) 4 ⋅ Sm 1) 5)




D ≤ 1.0;

2 ⋅ Sa

D ≤ 1.0;

2 ⋅ Sa 6)





3) However, not more than 90 % of Level D.




Table 7.7-6: Allowable values for stress intensities and equivalent stress ranges derived from stress categories when per-forming a linear-elastic analysis of the mechanical behaviour, using cast steel

KTA 3201.2


Service limits

Stress category (Level 0) Levels A and B Level P 2) Level C 3) Level D

Average tensile stress (due to internal pressure) Sm 0.7 ⋅ RmT

Average tensile stress (due to internal pressure,required gasket load reaction and additionalloads)

2 ⋅ Sm 0.7 ⋅ RmT

Average tensile stress 4) (due to internal pressure,bolt pretensioning, temperature influence andadditional loads)

2 ⋅ Sm 2 ⋅ Sm 2 ⋅ Sm

Average tensile stress 1) 4) (due to internal pres-sure, bolt pretensioning, temperature influenceand additional loads)

3 ⋅ Sm 3 ⋅ Sm 3 ⋅ Sm

Total stress 4) (including peak stresses) D ≤ 1.0;

2 ⋅ Sa

The material strength value shown shall be taken as minimum value.1) In the case of torsion: stress intensity2) If the allowable number of cycles of 10 is exceeded, the cycles exceeding 10 shall be incorporated in the fatigue analysis according to Levels A and B.3) If the allowable number of cycles of 25 is exceeded, the cycles exceeding 25 shall be incorporated in the fatigue analysis according to Levels A and B.4) To be determined by strain analysis (e.g. correlation of gasket seating load, gasket compression load for operating condition and internal pressure)

Table 7.7-7: Allowable bolt stresses

Allowable half stress intensity range Sa 1) 2)

Figure at allowable number of load cycles �n

1⋅101 2⋅101 5⋅101 1⋅102 2⋅102 5⋅102 1⋅103 2⋅103 5⋅103 1⋅104 1.2⋅104 * 2⋅104 5⋅104 1⋅105 2⋅105 5⋅105 1⋅106

7.8-1: curvetensile strength790 - 900 N/mm2

2900 2210 1590 1210 931 689 538 427 338 303 296 248 200 179 165 152 138

7.8-1: curvetensile strength≤ 550 N/mm2

4000 2830 1900 1410 1070 724 572 441 331 262 214 159 138 114 93.1 86.2

7.8-2 4480 3240 2190 1650 1280 938 752 614 483 407 352 293 259 228 197 179

7.8-3: curve max.nominal stress 3)

≤ 2.7 ⋅ Sm

7930 5240 3100 2210 1550 986 689 490 310 234 186 152 131 117 103 93,1

7.8-3: curve max.nominal stress 3)

= 3.0 ⋅ Sm

7930 5240 3100 2070 1415 842 560 380 230 155 105 73 58 49 42 36.5

1) The values of Sa shown here are based on the respective elastic moduli of Figures 7.8-1, 7.8-2 and 7.8-3.2) Straight interpolation between tabular values is permitted based upon a double-logarithmic representation: (straight lines between the data points on the

log-log plot). Where for a given value of Sa = S the pertinent number of load cycles �n is to be determined, this shall be done by means of the adjacent datapoints Sj < S < Si and nj > n > ni as follows:

( )� / � � / �log /log

n n n ni j i

SiS

SiSj=

Example: Given: Steel with tensile strength ≤ 550 N/mm2, Sa = 370 N/mm2

from which follows: Si = 441 N/mm2, Sj = 331 N/mm2, �ni = 2 ⋅ 103, �nj = 5 ⋅ 103

( )� / / log /logn 2000 5000 2000441370

441331=

�n = 35003) Nominal stress = tensile stress + bending stress

* This data point is included to provide accurate representation of the curve.

Table 7.8-2: Table of values for the design fatigue curves of Figures 7.8-1, 7.8-2 and 7.8-3

KTA 3201.2

Des

ign

fatig

ue c

urve

for

ferr

itic

stee

lsF

igur

e 7.

8-1:

==≤

2 23

78

9

6 345

1093

102

5 4687

10

1.5

1.5

1.5

2

1.5

1.5

1.5

1.5

1.5

1.5

98

10

45

4 35

76

78

68

109

55

104

39

43

23

27

47

65

82

106

34

9 103

2

10

47

65

2

78

9

6 345

87

69

25

105

1098

64

32

22

25

2

22

T

T

i

i

and

nth

e re

latio

nshi

p be

twee

nar

e gi

ven

in T

able

7.8

-2.

a

Rem

ark:

The

exac

t val

ues

to b

e us

ed fo

rS

RN

/mm

550

mE

2.07

790

to 9

00N

/mm

Allowable half stress intensity rangeS

Allo

wab

le n

umbe

r of c

ycle

s n

Rm

a[N/mm ]

Whe

re th

e ca

lcul

ated

stre

ss in

tens

ity

mod

ulus

E

may

be

subj

ect t

o st

raig

ht in

terp

olat

ion.

rang

e is

bas

ed o

n st

rain

s w

ith a

n el

astic

with

the

ratio

E/E

.

E th

e ca

lcul

ated

stre

ssin

tens

ity ra

nge

shal

l be

mul

tiplie

d

Valu

es fo

r ten

sile

stre

ngth

s be

twee

nN

/mm

N/m

m10 79

0N

/mm

550

and

KTA 3201.2

Des

ign

fatig

ue c

urve

for

aust

eniti

c st

eels

Fig

ure

7.8-

2:

=

23 3 2489 7

56

1093

102

5 4687

10

1.5

1.5

1.5

2

1.5

1.5

1.5

1.5

1.5

1.5

98

10

45

4 35

76

9

32

44

76

56

54

7109

88

56

74

102

33

1092

89 10

35

63

47

106

89

6 587

4

10

2

3 2

29

810

52

43

57

6

25

2

T

i

i

T

10

Allowable half stress intensity range

N/m

m

Whe

re th

e ca

lcul

ated

stre

ss in

tens

ityra

nge

is b

ased

on

stra

ins

with

an

elas

tic

nAl

low

able

num

ber o

f loa

d cy

cles

a[N/mm ]

1.79

S

E mod

ulus

E

Rem

ark:

and

are

give

n in

Tab

le 7

.8-2

.aS

n

inte

nsity

rang

e sh

all b

e m

ultip

lied

E th

e ca

lcul

ated

stre

ss

the

rela

tions

hip

betw

een

The

exac

t val

ues

to b

e us

ed fo

r

with

the

ratio

E/E

.

KTA 3201.2

Des

ign

fatig

ue c

urve

s fo

r hi

gh s

tren

gth

stee

l bol

ting

for

tem

pera

ture

s 37

0 ˚C

Fig

ure

7.8-

3:≤

≤

=

4 3 289

10

567

2

98

310

7

4 36 5

4

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.52

98

510

7

4 36 5

42

9 105

63

43

45

27

85

66

58

72

104

39 10

78

1093

26

74

510

7

89

4 356

23

2

10

78

56

102

9 106

89

43

2

25

2

T

i

T

i

inte

nsity

rang

e sh

all b

e m

ultip

lied

w

ith th

e ra

tio E

/E

.

and

are

give

n in

Tab

le 7

.8-2

.

E th

e ca

lcul

ated

stre

ss

N/m

m2.

07E

10

mod

ulus

E

Whe

re th

e ca

lcul

ated

stre

ss in

tens

ityra

nge

is b

ased

on

stra

ins

with

an

elas

tic

stre

ss

Max

. nom

inal

2.7

mS

Allowable half stress intensity range

Allo

wab

le n

umbe

r of c

ycle

s n

[N/mm ] Sa

m

Rem

ark:

The

exac

t val

ues

to b

e us

ed fo

ra

nS

the

rela

tions

hip

betw

een

3.0

S=

Max

. nom

inal

st

ress

KTA 3201.2

IcIR

a

nd K

F

ract

ure

toug

hnes

s K

a

s a

func

tion

of te

mpe

ratu

reF

igur

e 7.

9-1:

Ia

Ic

IR

IRIc

Ic

IR

IR

ND

T

3/2Ic

ND

T

100

150

[ N / mm ]

KK

=

( T -

0 ˚C

)R

T[ K

]

0 -100

RT

Fracture toughness K , K

Fo

r the

mat

eria

ls 2

0 M

nMoN

i 5 5

and

22

NiM

oCr 3

7 a

ll m

easu

red

K

val

ues

are

abov

e th

e sh

own

K

lim

it cu

rve

and

6000

5000

-50

500

1000

al

l mea

sure

d K

an

d K

v

alue

s ar

e ab

ove

the

show

n K

l

imit

curv

e so

that

thes

e re

fere

nce

curv

es m

ay a

lso

be u

sed.

2000

4000

3000

KTA 3201.2

∆

′

′

Im It

It

I

IR

ImI

IR3/

2

I

IR

41

Stationaryoperation

T

=

+=

[ N /

mm

]

+

2

KKK

K K K

200150100 350300250

[ ˚C ]Temperature

0

50- 40 0

1000

(before irradiation) KK operationStationary

(after irradiation)

4000

3000

2000

Stre

ss in

tens

ity fa

ctor

K ,

refe

renc

e fra

ctur

e to

ughn

ess

K6000

5000

Figure 7.9-2: Fracture mechanic analysis: specified operation (Example)

∗)

∗

I

Ic

3/2

Ia

s

2a

crackinitiation

p = 2a / 2

p = a / 2

[N/m

m]

a

For internal defects:

For edge defects:

crack arrest

0.2 0.4

Str

ess

inte

nsity

fact

or

Crack depth / wall thickness ( p )

0 0.6

K K

K

0.8 1.0

Figure 7.9-3: Fracture mechanic analysis: Incidents (Example of thermal shock)

KTA 3201.2

8 Component-specific analysis of the mechanicalbehaviour

8.1 General

(1) The following component-specific analyses and verifica-tions of strength are usually applied calculation methods.Other suitable methods may also be used.

(2) The component-specific analyses of the mechanical be-haviour are intended to evaluate loadings and replace, fullyor in part, the verification by the general analysis of themechanical behaviour in acc. with Section 7 on the conditionthat the respective design and loading limit requirementsare met as well as the pertinent specified stress limits areadhered to.

(3) Where effective loading cannot fully be determined byone of the following component-specific analyses, thestresses resulting from partial loadings may be evaluatedseparately and be determined accordingly by superposition.

(4) As welds have to meet the requirements of KTA 3201.1and KTA 3201.3 the effects of the welds on the allowablestresses in Section 8 need not be considered separately.

8.2 Vessels

8.2.1 Radial nozzles subject to internal pressure andexternal nozzle loadings due to connected piping

8.2.1.1 General

(1) Nozzles in pressure-retaining cylindrical or sphericalshells including the attachment-to-shell juncture shall beable to withstand all loadings applied simultaneously, suchas internal pressure and external nozzle loadings.

(2) Depending on the respective service limits, code classand stress category the allowable stress intensities shall betaken from Tables 7.7-4 and 7.7-5.

(3) The requirements regarding the design according tosection 5.2 shall be met.

(4) The methods indicated in clause 8.2.1.3 do not considerthe effects of mutual influence by adjacent openings which,however, are to be taken into account if the distancebetween adjacent openings is less than 2 ⋅ ⋅d sHm H .

8.2.1.2 Nozzles mainly subject to internal pressure

Nozzles that are mainly subject to internal pressure, such asmanhole, blanked-off and other nozzles not connected topiping shall be dimensioned in accordance with AnnexA 2.8 without limitation of nominal size. Analyses of themechanical behaviour are not required.

8.2.1.3 Nozzles subject to internal pressure and externalnozzle loadings

(1) The opening reinforcement shall first be dimensionedfor internal pressure in acc. with Annex A 2.8 to includereserves for external nozzle loadings.

To verify the acceptability of external nozzle loads a sup-plementary stress evaluation shall be made to cover stressesdue to internal pressure and external nozzle loadings.

(2) To determine the stresses due to internal pressure themethods described in clauses 8.2.2.1 to 8.2.2.3 are permitted.

(3) External loads may be considered separately using themethod described in clause 8.2.2.4.

(4) The calculation methods described in clauses 8.2.2.1 to8.2.2.3 do not cover stresses in the nozzle wall outside thenozzle-to-shell transition. For nozzles with a wall thicknessratio sA/sR ≤ 1,5 according to Figure 8.2-1 or 8.2-2 the stressin the nozzle wall shall therefore be evaluated separately.

Hm

Am

H

A

R

Sect

ion

B-B Section A-A

Location A

s

Location C

d

d

S

s

z

y

x

Figure 8.2-1: Nozzle in cylindrical shell

8.2.2 Method of analysis for radial nozzles

8.2.2.1 Stress index method for total maximum stresses dueto internal pressure

(1) This method deals only with maximum stresses, at cer-tain general locations, due to internal pressure. Stress indi-ces are defined as the respective numerical ratio of the nor-mal stress component under consideration or the stressintensity to the mean circumferential stress (membranehoop stress σmu) in the unpenetrated shell.

imu

= σσ

(8.2-1)

The stress intensity values and ranges determined by usingstress indices shall be limited in accordance with Section 7.

KTA 3201.2

(2) The nomenclature for the stress components are shownin Figure 8.2-3 and are defined as follows:

σa = stress component in axial direction (in the plane of thesection under consideration and parallel to the bound-ary of the section)

σt = stress component in circumferential direction (normalto the plane of the section)

σr = stress component in radial direction (normal to theboundary of the section)

and additionally:

S = stress intensity at the point under consideration

di = inside radius or radius of dishing of head

sc = wall thickness at unpenetrated area in accordance withclause 7.1.4.

H

Hm

R

Am

A

S

s

d

d

s

Figure 8.2-2: Nozzle in spherical shell

σ

σσ

σ

σ

σ

t

aa

t

r

r

Figure 8.2-3: Direction of stress components

(3) The stress indices of Table 8.2-1 only apply to the maxi-mum stresses within the nozzle area under internal pressure

and shall only be used if the conditions set forth in a)through i) exist.

a) Design as per Figure 8.2-4

b) The nozzle axis shall be normal to the vessel wall; oth-erwise dAi/dHi shall be less than 0.15.

c) in the case of several nozzles in a main body, the arcdistance measured between the centre lines of adjacentnozzles along the inside surface shall not be less than1.5 · (dAi1 + dAi2) for adjacent nozzles in heads or forshells in meridional direction, and not be less than(dAi1 + dAi2) for adjacent nozzles along the circumfer-ence of the shell. When the two nozzles are neither inline in a circumferential arc nor in meridional direction,their centre line distance shall be such that

( ) ( )l lu m2 32 2+ is not less than 0.5 · (dAi1 + dAi2), where

lu is the component of the centre line distance in the cir-cumferential direction and lm is the component of thecentre line distance in the meridional direction.

d) The following dimensional ratios for spherical and cy-lindrical shells are met:

dHi/sH ≤ 100

dAi/dHi ≤ 0.5

d d sAi Hi H/ .⋅ ≤ 0 8

e) In the case of cylindrical shells, the total nozzle rein-forcement area on the transverse axis of the connections,including any reinforcement outside of the reinforce-ment limits (effective length) shall not exceed two timesthe reinforcement required for the longitudinal axis un-less a tapered transition section is incorporated into thereinforcement and the shell.

f) In the case of spherical shells and formed heads, at least40% of the total nozzle reinforcement area shall be lo-cated beyond the outside surface of the calculated vesselwall thickness.

g) 0.1 ⋅ sH < r1 < 1.0 ⋅ sH.

h) the outside corner radius r2 is large enough to provide asmooth transition between the nozzles and the shell. Inspecial cases the following applies:

r2 ≥ max. { }0.5 s , 0.5 s , 0.5 sH A R⋅ ⋅ ⋅

if for cylindrical shells dAi > 1.5 ⋅ sH,

for spherical shells dAi > 3 ⋅ sH,

and for ellipsoidal heads a/b = 2, dAi > 1.5 ⋅ sH

i) ( ){r d sAi A3 0 2≥ ⋅ + ⋅max. .002 , α

( )} 2 3⋅ −sin α s sA R

The radii r2 and r3 refer to the actual wall thicknesses.

If required, the effects due to external loadings or thermalstresses are to be considered. In such cases, the total stress ata given point may be determined by superposition.

(4) If the axis of a nozzle makes an angle with the normal tothe vessel within the limits given in 8.2.1 (3), the stress indi-ces for tangential stress on the inside shall be multipliedwith the following values:

KTA 3201.2

1 + 2 · sin2ϕ for hillside branches in cylinders or spheres(non-radial connection)

1 + (tan ϕ)4/3 for lateral branches in cylinders (lateralconnections)

where ϕ is the angle formed between branch axis and nor-mal to the vessel.

5 6

3

1 2

4

ααα ≤ α ≤

R

A

A

RR

A

R

A

1

2

1Ai

2

3

3

Hi

2

Ai

Ai

Hi

Hi

HH

iH

HH

2

Ai

Hi

H

1

Hi

2

2

3

1

Ai

11

AiHs

s

s

s

d

r

d

s

45˚

d

30˚

ddd

d

r

r

ss

d

s

s

r

d

sd

s

r

r

r

r

r

s

d s

r

dr

r

sr

rr

Figure 8.2-4: Acceptable nozzle details when using thestress index method

Nozzles in spherical shells and formed heads

Stress Inside Outside

σt 2.0 2.0

σa - 0.2 2.0

σr - 4 · sc/di 0

S 2.2 2.0

Nozzles in cylindrical shells

Longitudinal plane Lateral plane

Inside Outside Inside Outside

σt 3.1 1.2 1.0 2.1

σa - 0.2 1.0 - 0.2 2.6

σr - 2 · sc/di 0 - 2 · sc/di 0

S 3.3 1.2 1.2 2.6

Table 8.2-1: Stress indices for nozzles (Stress index method)

8.2.2.2 Alternative stress index method for total maximumstresses due to internal pressure

In lieu of the stress index method as per clause 8.2.2.1 thisalternative stress index method may be used if dimension-ing is made in accordance with clause A 2.7.3 and the fol-lowing geometric conditions are satisfied:

a) Design as per Figure 8.2-5

3

1 2

Bild 8.2-5:Anwendung der alternativen SpannungsindexmethodZulässige Ausführungsformen für Stutzen bei

α α

α

A

R R

R

1

Hi

Ai

HH

i

2

5

Ai

Ai

H

Hi

4

3 3

11

H

2

s

r

d

d

s

r

r

d

d

r

r

d

r

r

s

s

s

s

s

r

d

r

Figure 8.2-5: Acceptable nozzle details when using thealternative stress index method

b) The nozzle is circular in cross section and its axis is nor-mal to the shell surface.

c) In the case of spherical shells and formed heads, at least40% of the total nozzle reinforcement area shall be lo-cated beyond the outside surface area of the calculatedshell wall thickness.

d) The spacing between the edge of the opening and thenearest edge of any other opening is normally not lessthan the smaller of

1.25 ⋅ (dAi1 + dAi2) or 1.8 ⋅ d sH H⋅ ,

but in any case not less than dAi1 + dAi2.

e) The following dimensional limitations are met:

Nozzle in cylin-drical shell

Nozzle in sphericalshell or head

dHi/sH 10 to 200 10 to 100

dAi/dHi ≤ 0.33 ≤ 0.5

dAi/ d sHi H⋅ ≤ 0.8 ≤ 0.8

f) Regarding the corner radii the following requirementsshall be met:

0.1 ⋅ sH ≤ r1 ≤ 0.5 ⋅ sH

r d sAi R2 ≥ ⋅ or r2 = sH/2;

the greater value shall be used

Stress

KTA 3201.2

r d sAi R3 90≥ ° ⋅ ⋅α / or r3 ≥ (α/90°) ⋅ sR;


( )r d sAi R4 1 90≥ − ° ⋅ ⋅α / or

r4 ≥ (1 - α/90°) ⋅ (sH/2);


r5 ≥ (α/90°) ⋅ sH

where the angle α is in degrees.

(2) This method deals only with maximum stresses, at cer-tain general locations of individual nozzles, due to internalpressure. The acceptability of the total stresses determinedby this method shall be proved in accordance with Section 7.

(3) Stress indices are defined as the respective numericalratio of the normal stress component under consideration orthe stress intensity to the stress intensity derived from themembrane stresses in the unpenetrated shell.

iV

= σσ

(8.2-2)

σV = p · (di + sc)/4 · sc for spherical shells or formedheads (8.2-3)

and

σV = p · (di + sc)/2 · sc for cylindrical shells (8.2-4)

Nozzles in spherical shells and formed heads

Stress Inside Outside

σt 2.0 - dAi/dHi 2.0 - dAi/dHi

σa - 0.2 2.0 - dAi/dHi

σr - 4 · sc/(dHi + sc) 0

S

the greater value of 2.2 - dAi/dHi

or2.0 + [4 · sc/(dHi + sc)]-

dAi/dHi

2.0- dAi/dHi

Nozzles in cylindrical shells

Longitudinal plane Lateral plane

Inside Outside Inside Outside

σt 3.1 1.2 1.0 2.1

σa - 0.2 1.0 - 0.2 2.6

σr

- 2 · sc/

(dHi + sc)

0 - 2 · sc/

(dHi + sc)

0

S 3.3 1.2 1.2 2.6

Table 8.2-2: Stress indices for nozzles (Alternative stressindex method)

(4) The nomenclature for the stress components are shownin Figure 8.2-3 and are defined as follows:

σa = stress component in axial direction (in the plane of thesection under consideration and parallel to the bound-ary of the section)

σt = stress component in circumferential direction (normalto the plane of the section)


and additionally:

S = stress intensity at the point under consideration

p = working pressure

sc = wall thickness in unreinforced area according to clause7.1.4.

(5) The stress indices shall be taken from Table 8.2-2.

8.2.2.3 Stress index method for primary and secondarystresses due to internal pressure

Note:This method is based on a parameter study assuming ideallyelastic material behaviour. With this method the stress compo-nents o f membrane as well as membrane plus bending stressescan be determined using stress indices. These stress indices referto planes normal to the vessel wall which govern the combina-tion o f stresses resulting from mechanical loads and internalpressure.This method is suited to determine stresses for superpositionwith stresses resulting from external load ings. It does not resultin peak stresses and therefore no total stress intensity is ob-tained.

To determine primary or primary plus secondary stresses inthe shell e.g. for cylindrical and spherical shells, the follow-ing stress index method may be used:

a) Radial nozzles in cylindrical shells

The following dimensional ratios shall be adhered to:

Diameter-to-wall thickness ratio 30 ≤ dHm/sH ≤ 200

Wall thickness ratio 0.75 ≤ sA/sH ≤ 1.3

Diameter ratio dAm/dHm ≤ 0.6

To cover stresses in the transitional area ofshell-to-nozzle juncture the stresses at the locations Aand C shall be determined and limited in accordancewith Figure 8.2-1.

The stresses due to internal pressure are determined asfollows:

σ α= ⋅⋅

⋅ds

pHm

H2(8.2-5)

The stress indices α shall be taken from the figures laiddown in Table 8.2.-3 depending on the referred nozzlediameter d d sAm Hm H/ ⋅ and the wall thickness ratio

sA/sH.

Location Stress category Figure

A PL 8.2-6

C PL 8.2-7

A Inside PL + Q 8.2-8

C Outside PL + Q 8.2-9

A Inside PL + Q 8.2-10

C Outside PL + Q 8.2-11

Table 8.2-3: Assignment of stress indices α forcylindrical shells

Stress

KTA 3201.2

b) Radial nozzles in spherical shellsThe following dimensional ratios shall be adhered to:Diameter-to-wall thickness ratio 50 ≤ dHm/sH ≤ 400

Wall thickness ratio 0.77 ≤ sA/sH ≤ 1.3

The stresses due to internal pressure are determined asfollows:

σ α= ⋅⋅

⋅ds

pHm

H4(8.2-6)

The stress indices α shall be taken from the figures laiddown in Table 8.2-4 depending on the referred nozzlediameter d d sAm Hm H/ ⋅ and the wall thickness ratio

sA/sH.

Stress category Figure

PL 8.2-12

PL + Q 8.2-13

Table 8.2-4: Assignment of stress indices α forspherical shells

8.2.2.4 Design method for openings subject to externalforces and moments

Suitable methods for determining stresses may be takenfrom

a) WRC Bulletin 297 [2]

and, if required, from

b) WRC Bulletin 107 [3] and

c) BS 5500: 1985, Appendix G [4]

in which case the respective geometric limits for the designmethods and the general requirements according to clause5.2.6 have to be considered. The acceptability of the totalstresses determined by any of theses methods shall beproved.

Figure 8.2-6: Stress index α for nozzle in cylindrical shell subject to internal pressure


KTA 3201.2



KTA 3201.2

Figure 8.2-12: Stress index α for nozzle in spherical shellsubject to internal pressure for PL

Figure 8.2-13: Stress index α for nozzle in spherical shellsubject to internal pressure for PL + Q

KTA 3201.2

8.3 Valve bodies

8.3.1 Design values and units relating to Section 8.3

Nota-tion

Design value Unit

daA nominal outside diameter of valve inSection A-A, excluding allowances

mm

daR nominal outside diameter of con-nected piping, excluding allowances

mm

diA nominal inside diameter of valve inSection A-A, excluding tolerances

mm

diG valve body inside diameter as perFigure 8.3-5

mm

diR nominal inside diameter as per Figure8.3-1

mm

e effective length mm

eA effective length in branch mm

eH effective length in main shell mm

h height according to Figure 8.3-3 mm

m, n material parameters according to Ta-ble 7.8-1

p design pressure for design loadinglevel 0 or the respective internal pres-sure for loading levels A and B

N/mm2

pB internal pressure at the respectiveload case

N/mm2

∆pfi full range of pressure fluctuationsfrom normal operating to the consid-ered condition

N/mm2

pf(max) maximum range of pressure fluctua-tions ∆pfi

N/mm2

r mean radius in Section A-A accordingto Figures 8.4-3 and 8.3-5

mm

r2, r4 fillet radius according to Figure 8.3-2 mm

r3 radius according to Figure 8.3-3 mm

ri inside radius according to Figure 8.3-5 mm

rt fillet radius according to Figure 8.3-7 mm

sA wall thickness of branch mm

sAn wall thickness according to Figure8.3-7

mm

sG wall thickness of valve body mm

sH wall thickness of body (run) mm

sHn wall thickness according to Figure8.3-7

mm

sn wall thickness of valve (acc. to cl.7.1.4) in Section A-A according toFigures 8.3-4 and 8.3-5

mm

sne wall thickness according to Figure8.3-5

mm

sR wall thickness of connected pipingaccording to Figure 8.3-4

mm

A cross-sectional area of valve in SectionA-A acc. to Figures 8.3-4 and 8.3-5

mm2

Ap pressure loaded area mm2

Aσ effective cross-sectional area mm2

Nota-tion

Design value Unit

Ca stress index for oblique valves acc. toequation (8.3-14)

Cb stress index for bending stress acc. toequation (8.3-11)

Cp stress index

C2 stress index for secondary thermalstresses due to structural discontinu-ity in acc. with Figure 8.3-9

C3 stress index for secondary stresses atlocations of structural discontinuitydue to changes in fluid temperaturein acc. with Figure 8.3-8

C4 factor acc. to Figure 8.3-10

C5 stress index for thermal fatigue stresscomponent acc. to Figure 8.3-11

C6 stress index for thermal stresses N⋅mm4

D usage factor De1 diameter of the largest circle that can

be drawn entirely within the wall atthe crotch region, as shown in Figure8.3-7

mm

De2 diameter of the largest circle that canbe drawn in an area of the crotch oneither side of a line bisecting thecrotch

mm

D0 outside diameter of valve in SectionA-A acc. to Figures 8.3-4 and 8.3-5

mm

E modulus of elasticity at design tem-perature

N/mm2

Fax axial force N

′Fax axial force obtained from connectedpiping

N

Mb bending moment Nmm

′Mb bending moment obtained from con-nected piping

Nmm

MR resulting moment Nmm

Mt torsional moment Nmm

′Mt torsional moment obtained from con-nected piping

Nmm

Ni allowable number of cycles

Nri specified number of cycles

Pb primary bending stress according toTable 7.7-5

N/mm2

Peb secondary stress from pipe reactions N/mm2

Peb max secondary stress from pipe loadingswith full utilization of the allowablestress

N/mm2

Plp local membrane stress due to internalpressure acc. to equation (8.3-5)

N/mm2

Pm general primary membrane stress acc.to Table 7.7-5

N/mm2

Q resulting transverse force N

KTA 3201.2

Nota-tion

Design value Unit

Q´ transverse force from connectedpiping

N

Qp sum of primary plus secondarystresses resulting from internal pres-sure acc. to equation (8.3-13)

N/mm2

QT1 thermal stress component fromthrough-wall temperature gradientassociated with a fluid temperaturechange rate ≤ 55 °C / hr

N/mm2

QT3 thermal secondary stress resultingfrom structural discontinuity accord-ing to equation (8.3-15)

N/mm2

RmT minimum tensile stress of connectedpiping at elevated temperature

N/mm2

Rp0.2T 0.2% elevated temperature proofstress of connected piping

N/mm2

Sa one-half the value of cyclic stressrange

N/mm2

Si peak stress N/mm2

Sm design stress intensity according toclause 7.7.3.4

N/mm2

Sn sum of primary plus secondary stressintensities for one load cycle

N/mm2

Sn(max) maximum range of primary plus sec-ondary stresses according to equation(8.3-30)

N/mm2

Sp1 fatigue stress intensity at inside sur-face (crotch region) of body

N/mm2

Sp2 fatigue stress intensity at outside sur-face (crotch region) of body

N/mm2

SR stress intensity Sm for material ofconnected piping at design tempera-ture acc. to clause 7.7.3.4 (see Table8.3-1)

N/mm2

T design temperature K

TDe1 temperature acc. to Figure 8.3-6 K

Tsn temperature acc. to Figure 8.3-6 K

∆T´ maximum magnitude of the differ-ence in wall temperatures for walls ofthicknesses (De1, sn) resulting from55° K/hr fluid temperature changerate acc. to Figure 8.3-12

K

∆Tf fluid temperature change K

∆Tfi fluid temperature change in Section i K

∆Tf(max) maximum change in fluid tempera-ture

K

∆∆∆∆∆∆

TTTTTT

f1

f2

f3

1

2

3

change in fluid temperature(range of temperature cycles)

K

Nota-tion

Design value Unit

WA axial section modulus at valve bodynominal dimension referring to Sec-tion A-A in Figures 8.3-4 and 8.3-5acc. to equation (8.3-8)

mm3

WR axial section modulus of connectedpiping referring to the nominal di-mension acc. to equation (8.3-7)

mm3

Wt valve body section torsional modulusin Section A-A acc. to Figure 8.3-4 and8.3-5 (Wt = 2 ⋅ WA for circularcross-section with constant wallthickness)

mm3

α linear coefficient of thermal expansionat design temperature

1/degree

α1 acute angle between flow passagecentre lines and bonnet (spindle,cone) acc. to Figure 8.3-4

degree

σb stress resulting from bending mo-ments

N/mm2

σL stress from loadings in direction ofpipe axis

N/mm2

σV stress intensity N/mm2

τa max stress resulting from transverse forces N/mm2

τt stress resulting from torsional mo-ment

N/mm2

8.3.2 General

(1) For valves meeting all the requirements of this clause,the most highly stressed portions of the body under internalpressure is at the neck to flow passage junction and is char-acterized by circumferential tension normal to the plane ofcentre lines, with the maximum value at the inside surface.The rules of clause 8.3.3 are intended to control the generalprimary membrane stress in the crotch region,

(2) In the crotch region, the maximum primary membranestress is to be determined by the pressure area method inaccordance with the rules of clause 8.3.3. The procedure isillustrated in Figure 8.3-1.

(3) The Pm value calculated in accordance with clause 8.3.3will normally be the highest value of body general primarymembrane stress for all normal valve types with typical wallproportioning, whereas in regions other than the crotchunusual body configurations shall be reviewed for possiblehigher stress regions. Suspected regions are to be checked bythe pressure area method applied to the particular localbody contours.

(4) The use of the methods of component-specific stressanalysis described in clauses 8.3.4 and 8.3.5 necessitates thatthe requirements set forth in clause 8.3.3 regarding theevaluation of primary membrane stress due to internal pres-sure are satisfied.

(5) The stress analysis of valve bodies usually is performedin accordance with the methods of clause 8.3.4. Loadings

KTA 3201.2

resulting from connected pipe are to be generally considered(i.e. by using the maximum possible bending moment of theconnected piping).

(6) Clause 8.3.5 may be applied alternately or if the condi-tions of clause 8.3.4 have not been satisfied.

8.3.3 Primary membrane stress due to internal pressure

(1) From an accurately drawn layout of the valve body,depicting the finished section of the crotch region in themutual plane of the bonnet and flow passage centre lines,determine the fluid (load-bearing) area Ap and the effectivecross-sectional (metal) area Aσ. Ap and Aσ are to be basedon the internal surface of the body after complete loss ofmetal assigned to corrosion allowance.

(2) Calculate the crotch general membrane stress intensityas follows:

( )P A A p Sm p m= + ⋅ ≤/ .σ 0 5 (8.3-1)

The allowable value of this stress intensity Sm shall be de-termined as per clause 7.7.3.4.

(3) The distances eH and eA which provide bounds on thefluid and metal areas are determined as follows; see Figure8.3-1:

{ }eH = ⋅max. ; 0.5 d - s siR A H (8.3-2)

( )e r s d sA A iR A= ⋅ + ⋅ ⋅ +0 5 0 3542. . (8.3-3)

In establishing appropriate values for the above parameters,some judgement may be required if the valve body is irregu-lar as it is for globe valves and others with nonsymmetricshapes. In such cases, the internal boundaries of Ap shall bethe lines that trace the greatest widths of internal wettedsurfaces perpendicular to the plane of the stem and pipeends (see Figure 8.3-1, sketches b, d and e).

(4) If the calculated boundaries for Ap and Aσ, as defined byeA and eH, fall beyond the valve body (Figure 8.3-1, sketchb), the body surface becomes the proper boundary for es-tablishing Ap and Aσ. No credit is to be taken for any area ofconnected piping which may be included within the limitsof eA and eH. If the flange is included with Aσ, the area ofone bolt hole is to be subtracted for determining the netvalue of Aσ.

(5) Web or fin-like extensions of the valve body are to becredited to Aσ only to an effective length from the wallequal to the average thickness of the credited portion. Theremaining web area is to be added to Ap (Figure 8.3-1,sketch b). In addition, the web area credited to Aσ shallsatisfy the following condition: A line perpendicular to theplane of the stem and pipe ends from any points in Aσ doesnot break out of the wetted surface but passes through acontinuum of metal until it breaks through the outer surfaceof the body.

Figure 8.3-1: Pressure area method

KTA 3201.2

(6) In the case of normal valve body configurations, it isexpected that the portions defined by Aσ in the illustrationsof Figure 8.3-1 will be most highly stressed. However, in thecase of highly irregular valve bodies, it is recommended thatall sections of the crotch be checked to ensure that the larg-est value of Pm has been established considering both openand fully closed conditions.

8.3.4 General stress analysis

(1) This method shall only be applied if the following geo-metric conditions are satisfied:

a) radius r2 ≥ 0.3 ⋅ sn

b) Radius rh3 0 1

max. 0.05 sn≥

⋅⋅

.

c) Radius r4 < r2 is permitted

d) The edges must be chamfered or trimmed.

The radii r2 and r4 are shown in Figure 8.3-2 for the varioustypes of fillet radii. r3 and h are explained in Figure 8.3-3. sn

is the nominal wall thickness according to clause 7.1.4 andFigures 8.4-3 and 8.3-5.

4

2

2

22

24

r

r

r

r

r

r

r

Figure 8.3-2: Fillets and corners

33 3

3

r h rr

r

Figure 8.3-3: Acceptable ring grooves

(2) It shall be checked by means of equation (8.3-4) whetherthe range of allowable primary membrane plus bendingstresses in loading levels 0, A and B is not exceeded.

Plp + Peb ≤ 1.5 ⋅ Sm (8.3-4)

P Cslp p

n= +

⋅

r p Ci

a0 5. (8.3-5)

with

Cp = 1.5

Ca acc. to equation (8.3-14)

Peb acc. to equation (8.3-6).

(3) For the purpose of verifying the stress portions resultingfrom unit shear forces and unit moments of the connectedpiping, bending stresses in the governing sections acc. toFigure 8.3-4 and 8.3-5 shall be evaluated as essential stresscomponents.

(4) The bending stresses are determined from:

PC W S

Webb R R

A=

⋅ ⋅(8.3-6)

with

( )W

d d

dRaR iR

aR=

⋅ −

⋅

π 4 4

32(8.3-7)

( )W

d d

dAaA iA

aA=

⋅ −

⋅

π 4 4

32(8.3-8)

where the following condition must be satisfied:

WA ≥ WR (8.3-9)

(4) For valve bodies with conical hub acc. to Figure 8.3-5 theSection A-A shall be taken in consideration of the die-outlength e. Here, the following applies:

e = 0.5 ⋅ r si ne⋅ (8.3-10)

with ri and sne according to Figure 8.3-5.

(5) The stress index value Cb is determined as follows:

Cb = max. ; 0.335r

s 1.0

n⋅

23

(8.3-11)

with r and sn according to Figure 8.3-7.

(6) The SR value in equation (8.3-6) refers to the material ofthe connected piping. The values of Table 8.3-1 shall betaken.

KTA 3201.2

Composite materials Pipe Valve Pipe Valve

Ferrite Ferritic steel forging Austenite Austenitic steel forging

Ferrite Ferritic cast steel Austenite Ferritic steel forging

Ferrite Austenitic steel forging Austenite Austenitic cast steel

Ferrite Austenitic cast steel Austenite Ferritic cast steel

Loading level SR SR

0 Rp0.2T 1.35 ⋅ Rp0.2T

A Rp0.2T 1.35 ⋅ Rp0.2T

B Rp0.2T 1.35 ⋅ Rp0.2T

C 1.2 ⋅ Rp0.2T 1.62 ⋅ Rp0.2T

D min.1.6 R R

p0.2T

mT

⋅

min.2.16 R R

p0.2T

mT

⋅

Rp0.2T , RmT = design strength values of connected piping at design temperature

Table 8.3-1: List of limit values for SR to be used in the analysis (equation 8.3-6) of the connected piping for compositematerials of piping and valve

(7) No greater loadings on the valve shall be consideredthan are allowed by the stress intensity level in the pipingsystem. Provided that the same pipe materials, same diame-ters and section moduli of the valve are considered by thedesign and the valve itself does not constitute an anchor, thevalve body side with the smallest section modulus of theconnected piping shall govern the maximum loading of thevalve. Otherwise, both sides of the valve body shall be as-sessed to determine the maximum possible loading.

(8) For equation (8.3-6) the allowable stresses in the variousloading levels acc. to Table 8.3-2 shall be adhered to.

When using Table 8.3-2, the following design requirementsapply:

a) diA ≤ diG (see Figure 8.3-5)

b) sn ≤ sG

c) No angle valve is used.

The stress intensity Sm shall be determined as per clause7.7.3.4.

Loading level Allowable value for Peb

0 1.5 ⋅ Sm

A 1.5 ⋅ Sm

B 1.5 ⋅ Sm

C 1.8 ⋅ Sm

D 2.4 ⋅ Sm

Table 8.3-2: Allowable stress in the body resulting frompipe loadings

ca b

e

α

i

i

i

ii

1

n

R

n

n

n

R nA

A

2 r

2

2

rr

r

2

2

A

A

AA

A

AA A

rs

s

s

s

s

s

s

Figure 8.3-4: Critical sections of valve bodies

in ne

iGG ds

e

s

A

ArS

2

Figure 8.3-5: Critical section at conical valve bodies

KTA 3201.2

(9) For the calculation of the sum of primary and secondarystresses in Levels A and B the following applies:

Sn = QP + Peb + 2 QT3 (8.3-12)

Q Csp p

n= +

⋅

r p Ci

a0 5. (8.3-13)

with

CP = 3.0 (stress intensity)

Ca = +0 20 8

1.

.sin α

(8.3-14)

α1 angle between flow passage centre lines in valve bodyand bonnet (spindle, cone) acc. to Figure 8.3-4

Peb shall be inserted acc. to equation (8.3-6)

ri and sn shall be taken from Figures 8.3-4 and 8.3-5

QT3 is determined as follows:

QT3 = E ⋅ α ⋅ C3 ⋅ ∆T´ (8.3-15)

nT

De1 sTDe1 ns

∆T´ = (TDe1 - Tsn)

Figure 8.3-6: Determination of ∆T´

De1 and De2 shall be determined by means of a detail sketchwith reference to the original drawing at a suitable scale.

(10) For the loading Levels C and D the following applies:

Sn = Plp + Peb (8.3-16)

Plp is determined from equation (8.3-5) ; for p the respectiveinternal pressure of Level C or D shall be used.

(11) In the individual loading levels the stress intensityvalues acc. to Table 8.3-3 shall not be exceeded in equations(8.3-12) and (8.3-16). The stress intensity Sm shall be deter-mined according to clause 7.7.3.4.

Loading level Allowable Sn value

Forged steel Cast steel

A 3 ⋅ Sm 4 ⋅ Sm

B 3 ⋅ Sm 4 ⋅ Sm

C 2.25 ⋅ Sm 3 ⋅ Sm

D 3 ⋅ Sm 4 ⋅ Sm

Table 8.3-3: Allowable stress intensity values for Sn

(12) The verification for loading levels C and D shall only bemade if the respective requirement has been fixed in thecomponent-specific documents.

(13) Valve and piping system may be classified into differ-ent loading levels for specific load cases (see compo-nent-specific document). In such a case the SR value forequation (8.3-6) shall be taken with respect to the loadinglevel of the system (see Table 8.3-1).

(14) The verification with the equations given here is onlypermitted if for all load cases the allowable stress intensitylevel is not exceeded in the connected piping.

(15) Where pipe rupture is assumed and no anchor is pro-vided between valve and location of rupture, the calculationshall be made with the effective pipe unit shear forces andunit moments if valve integrity or functional capability isrequired by the component-specific document.

8.3.5 Detailed stress analysis with unit shear forces andunit moments obtained from the calculated con-nected piping

(1) The verification according to this clause is only requiredif, in the general stress analysis to clause 8.3.4, the allowablestress limit is exceeded or the required condition cannot besatisfied in any case. In such a case, the geometric conditionsin accordance with clause 8.3.4 (1) shall also be satisfied.Load cases and superposition of loads shall be taken fromthe component-specific documents.

(2) From the calculation of the connected piping the follow-ing forces and moments are obtained which act on the twopoints of attachment of the valve for the various load cases:

a) axial forces ′Fax

b) transverse forces Q´

c) bending moments ′Mb

d) torsional moments ′Mt

In accordance with the superposition rule Fax, Q, Mb and Mt

shall be determined for each loading level and the stresscomponents shall be calculated from the unit shear forcesand unit moments from the connected piping as follows:

Stress resulting from loadings in the direction of pipe axis:

σLB

n

axD ps

FA

=⋅

⋅+0

4(8.3-17)

Stress resulting from transverse forces:

τa maxQ

A= ⋅2

(8.3-18)

Stress resulting from bending moments:

σbb

Ab

MW

C= ⋅ (8.3-19)

KTA 3201.2

Stress resulting from torsional moment:

τtt

t

MW

= (8.3-20)

When determining A, WA and Wt it shall be taken into ac-count that the wall thickness at the valve body inside is to bereduced by the wear allowance.

(3) These individual stresses are simplified to form a stressintensity on the assumption that the maximum stresses alloccur simultaneously:

( ) ( )σ σ σ τ τV L b t= + + +2 23 a max (8.3-21)

(4) For equation (8.3-21) the stress intensity limit values forPm + Pb according to Tables 7.7-4 to 7.7-6 shall be adhered toin the various loading levels. The stress intensity Sm shall bedetermined in accordance with clause 7.7.3.4.

(5) The primary and secondary stresses shall be determinedin accordance with clause 8.3.4. Here the stress intensity σV

determined according to equation (8.3-21) shall be taken forPeb in equations (8.3-12) and (8.3-16). For Sn the allowablestress intensity values according to Table 8.3-3 then apply.

(6) Where at the time of calculation the valve design hasalready been made and the unit shear forces and unit mo-ments obtained from the calculation of the connected pipingare not yet available they may be fixed as follows:

a) From equations (8.3-12) or (8.3-16) for Sn a value Peb max

is obtained for each individual loading level if the allow-able stress is fully utilized.

b) Where this value (Peb max) exceeds the allowable stressintensity for equation (8.3-21), Peb max shall be reduced toobtain this value.

c) Taking:

( )σ σ τ τL b a max t= = ⋅ +2 (8.3-22)

and

τ τ σa max t

b= =4

(8.3-23)

and

σV ≤ Peb max (8.3-24)

the following is obtained:

σ σb Leb maxp

= =5

(8.3-25)

d) With these values the stress intensity σV according toequation (8.3-21) shall be determined, and the reliabilityof this value shall be checked.

e) Where the allowable stress intensity value is adhered to,Fax, Q, Mb and Mt can be determined directly from thevalues in subclause c). Otherwise, the individual stressesin subclause c) shall be reduced uniformly until the al-lowable stress intensity value is no more exceeded.

These unit shear forces and unit moments then shall not beexceeded within the calculation of the connected piping orvaried only such that they do not lead to a higher loading ofthe valves. In addition, it shall be taken into accountwhether, with respect to the classification of the valve ac-cording to the component-specific documents, a classifica-tion into another loading level and thus a reclassification ofthe unit shear forces and unit moments may be required toperform a verification of the functional capability by way ofcalculation.

8.3.6 Fatigue analysis

8.3.6.1 General

A fatigue analysis shall be made for all valves with thespecified number of load cycles - to be at least 1000 - .

Note:The fatigue analysis methods described hereinafter are so con-servative that stress intensifications for valve bodies with mul-tip le external contours are covered by the examination of thecritical section according to Figure 8.3-7.

8.3.6.2 General fatigue evaluation

General fatigue evaluation shall be made for loading LevelsA and B in accordance with the methods described hereinaf-ter and shall replace the fatigue analysis according to clause8.3.6.3 or Section 7.8 if the resulting number of load cycles isgreater than the specified number of cycles, however, isgreater than 2000, and the conditions of clause 8.3.6.3 (3) a)to d) are satisfied.

The maximum total stresses Sp1 on the body inside and Sp2

on the body outside can be determined by assuming a fluidtemperature change rate not exceeding 55 K/hr as follows:

S QP

Q Qp peb

T T1 3 123 2

1 3= ⋅ + + + ⋅. (8.3-26)

S Q P Qp p eb T2 30 4 2= ⋅ + + ⋅. (8.3-27)

with

( )Q CT1 62= ⋅ De1 (8.3-28)

in N/mm4

1.3 ⋅ QT1 stress component from non-linear temperaturedistribution

C6 stress index for thermal stresses

4.06 ⋅ 10-3 N/mm4 for austenitic steel

1.07 ⋅ 10-3 N/mm4 for ferritic steel.

With the larger value of Sp1 and Sp2 taken as Sa the allow-able number of load cycles is obtained from the fatiguecurves according to Figures 7.8-1 and 7.8-2 where it shall betaken into account that the difference between the elasticmodulus from the curves and that of the valve materials atdesign temperature is to be considered. The Sa value shall bemultiplied with the ratio of E (curve)/E (valve) at designtemperature.

KTA 3201.2

a

b

Hn

e1

e2

Hn

An

Hn

t

e1

e2 e1

e2

Hn

2r

r

R

ss

2r

s

D

s

D D

2r

D

D

2r

D

s

De1 = diameter of the largest circle which can be drawnentirely within the wall at the crotch region

De2 = diameter of the largest circle which can be drawn inan area of the crotch on either side of a line bisectingthe crotch

For De1 < sn the following applies: De1 = sn

Figure 8.3-7: Model for determining secondary stresses invalve bodies (crotch region)

8.3.6.3 Detailed fatigue analysis

Note:The procedure outlined hereinafter can lead to non-conservativeresults at temperature change rates exceeding 10 K/min.

(1) To perform a detailed fatigue analysis the pressurechanges ∆pfi and temperature changes ∆Tfi with the perti-nent number Nri shall be determined for all specified loadcycles resulting from operational loadings.

(2) If both heating or cooling effects are expected at fluidtemperature change rates exceeding 55 K/hr, the tempera-ture range associated with the pertinent number of cyclesper load case each shall be determined assuming e.g. thefollowing variations:

Example:

20 variations ∆T1 = 250 K heating

10 variations ∆T2 = 150 K cooling

100 variations ∆T3 = 100 K cooling

Lump the ranges of variation so as to produce the greatesttemperature differences possible:

10 cycles Tf1 = 150 K + 250 K = 400 K

10 cycles Tf2 = 250 K + 100 K = 350 K

90 cycles Tf3 = 100 K

(3) Pressure fluctuations not excluded by the condition insubclause a) hereinafter are to be included in the calculationof the peak stresses. The full range of pressure fluctuationsfrom normal operating condition to the condition underconsideration shall be represented by ∆pfi.

During the fatigue analysis the following load variations orload cycles need not be considered:

a) pressure variations less than 1/3 of the design pressurefor ferritic materials

pressure variations less than 1/2 of the design pressurefor austenitic materials

b) temperature variations less than 17 K

c) accident or maloperation cycles expected to occur lessthan five times (total) during the expected valve life

d) start-up and shutdown cycles with temperature changerates not exceeding 55 K/hr at a number of load cycles nnot exceeding 2000.

(4) For the greatest pressure fluctuations max ∆pfi =∆pf(max) and temperature changes max ∆Tfi = ∆Tf(max) thefollowing equation must be satisfied:

Qp

E C Cp ⋅ + ⋅ ⋅ ⋅ ⋅≤ ⋅≤ ⋅

pT

3 S for forging steel4 S for cast steel

f(max)f (max)

m

mα 2 4 ∆

(8.3-29)

where p shall be taken from clause 8.3.4 and Qp from equa-tion (8.3-13).

The factors C2 and C4 shall be taken from Figures 8.3-9 and8.3-10, respectively. The stress intensity value Sm shall bedetermined according to clause 7.7.3.4.

KTA 3201.2

(5) Sn(max) shall be determined as follows:

S Qp

pE C C Tn p

ff(max)

(max)(max)= ⋅ + ⋅ ⋅ ⋅ ⋅

∆∆α 3 4 (8.3-30)

Stress index C3 shall be taken from Figure 8.3-8.

Equation (8.3-30) for Sn(max) can be calculated separately foreach load cycle. Here ∆pfi and ∆Tfi are then inserted.

n

n

n

n

n

r / s

r / s

=16

=100

=8

=2

/ s

/ sr

/ sr

r =4

ne2

3

65 70.4

8

/ s

1 2 43

1.8

1.6

2.0

C

D

0.8

0.6

1.0

1.4

1.2

Figure 8.3-8: Stress index for secondary stresses resultingfrom structural discontinuity due to fluidtemperature changes

n

n

n

n

n

r / s =16

/ sr =100

=2

/ s

/ sr

r

r =8

=4

/ s

e2 n

2

2 3

/ s

1 7 864 5

0.9

0.8

1.0

C

D

0.4

0.3

0.5

0.7

0.6

Figure 8.3-9: Stress index C2 for secondary thermal stressesresulting from structural discontinuity

e14

n

0.2

8

0.1

0.6

0.7

0.8

0.3

0.4

0.5

73 421

/ sC

6

D

50

Figure 8.3-10: Maximum magnitude C4 of the difference inaverage wall temperatures for wall thick-nesses De1 and sn, resulting from a stepchange in fluid temperature ∆Tf

(6) The peak stresses Si shall be calculated as follows:

( )S Qp

pE C C Ci p

f i= ⋅ ⋅ + ⋅ ⋅ ⋅ + ⋅43 3 4 5

∆∆α Tfi (8.3-31)

C5 shall be taken from Figure 8.3-11.

(7) The half-value of the cyclic stress range Sa for determin-ing the allowable number of cycles Ni shall be calculated asfollows:

a) for Sn(max) ≤ 3 ⋅ Sm

SS

ai=

2(8.3-32)

b) for 3 ⋅ Sm < Sn(max) ≤ 3 ⋅ m ⋅ Sm

( )Sn

n mSS

Sa

n

m

i= +−

−⋅

⋅−

⋅11

1 31

2(8.3-33)

Here, the value of Sn(max) or the value Sn determinedseparately for each load cycle may be used in lieu of Sn.Where in individual load cycles Sn does not exceed3 ⋅ Sm, the method of subclause a) shall be applied. Thematerial parameters m and n shall be taken from Table7.8-1.

c) for Sn(max) > 3 ⋅ m ⋅ Sm

Sn

Sa

i= ⋅12

(8.3-34)

For cast steel the value of 3 ⋅ Sm shall be substituted by4 ⋅ Sm in the conditions of subclauses a) to c).

KTA 3201.2

The allowable numbers of load cycles Ni shall be taken fromthe fatigue curves in Figures 7.8-1 and 7.8-2 where it shall betaken into account that the difference between the elasticmodulus from the curves and that of the valve material atallowable operating temperature (design temperature) areconsidered.

The Sa value shall be multiplied with the ratio E (curve)/E(valve) at allowable operating temperature (design tempera-ture).

(8) The fatigue usage (usage factor) D shall be determinedas follows:

D NN

ri

i= ≤∑ 1 0. (8.3-35)

where Ni is the allowable number of load cycles and Nri thespecified number of cycles according to the compo-nent-specific documents.

8.3.7 Other methods of stress and fatigue analysis

Where the allowable limit values are exceeded when apply-ing the clauses 8.3.4 to 8.3.6 the verification may also bemade in accordance with Section 7.7 and 7.8, if required.

0.1

5

0.2

0.4

0.3

6310

97 8

1.2

1.1

1.3

10

1.4

1.0

0.6

0.5

0.7

0.9

0.8

54 7632

0

210

8 4 52 3 6 99 7 8

e1

5

Ferrite

Austenite

in mmD

C

Figure 8.3-11: Stress index C5 for consideration of thermal fatigue stresses resulting from through-wall temperature gradi-ents caused by step change in fluid temperature

KTA 3201.2

∆′

′∆

n

e1n

e1

n

e1

e1

ne1

e1 e1

e1

nne1

n

ne1

n

n

e1

n

e1e1e1

nn

ne1e1

n

n

= 2

D

/ s=

6

D

/ s

/ s

= 3.

5/ s

/ s

= 4

D/ s

/ s

DDD

= 3

= 1.

5/ s

= 5

/ s

D

= 2.

5

= 3

D

DD

= 3.

5/ s

= 2

/ s

D

/ s

= 1.

5

D

/ s

= 2.

5

D

/ sD

= 4

2

/ s

2

2

2

/ sDD

= 6

= 5

n e1

n

n

9

5

7

6

8

10

60

50

40

70

10090

80

4

198 100

s

1073

2

3

654

30

/ K )( E = 42580 mm

T

/ K )== ( E = 16775 mm

Ds

- 13 E

=55 s

60 70 8050

20

30 40

[ K ]

FerriteAustenite

T

9020

[ mm ]

Figure 8.3-12: Maximum temperature difference in valve body (area De1/sn), associated with a fluid temperature changerate of 55 K/hr

KTA 3201.2

8.4 Piping systems

8.4.1 General

(1) Prerequisite to the application of the component-specificstress and fatigue analysis outlined hereinafter is the designof piping components as per clause 5.3.5 and the dimension-ing of the piping components in accordance with Annex A4. Their range of application extends to the tube-side effec-tive length ea of the reinforced or unreinforced nozzle. Thislimit is not relevant to the modelling of the system analysisaccording to clause 7.6.

(2) The analysis of the mechanical behaviour of the totalsystem shall be used to determine the directional compo-nents of forces and moments at various points of the system,which shall be used to evaluate the various piping elementsindependently of the total system. When determining thestresses the axial and radial temperature distributions aswell as the internal pressure shall also be considered inaddition to the forces and moments obtained from theanalysis of the mechanical behaviour.

(3) When applying the component-specific design methodin accordance with this clause, clause 7.7.2.3 shall also betaken into account with regard to the classification ofstresses from restrained thermal expansions.

(4) Where the design stress intensity or allowable usagefactor is exceeded or if stress indices for the consideredgeometry are not available, it is permitted to perform a de-tailed stress analysis in accordance with Section 7.7 or, ifrequired, a fatigue analysis in accordance with Section 7.8 inlieu of the procedure outline in this Section.

(5) The component-specific analysis of the mechanical be-haviour described hereinafter applies to piping systemswhere diameters are greater than DN 50.

(6) For piping systems with diameters not exceedingDN 50 the primary stress intensity according to equation(8.4-1) shall be determined in addition to the dimensioningas per Annex A, and the primary plus secondary stress in-tensity range shall also be determined and limited in accor-dance with equation (8.4-2). The verifications according toequations (8.4-1) and (8.4-2) can be omitted if the pipe layingprocedure ensures that the allowable stress intensities as perequations (8.4-1) and (8.4-2) can be adhered to. Where equa-tion (8.4-2) cannot be satisfied, a complete verification as perSection 8.4 is required.

Note:

The stress values σI to σVI , given in Section 8.4 as stress inten-sity or equivalent stress range do no exactly correspond to therespective definitions o f Section 7, but are conservative evalua-tions of the respective stress intensity or equivalent stress range.

8.4.2 Design condition (Level 0)

For the determination and limitation of the primary stressintensity the following condition applies:

σIa

c

aiI mB

d ps

Bd

IM S= ⋅

⋅⋅

+ ⋅⋅

⋅ ≤ ⋅1 22 21 5. (8.4-1)

where

σI primary stress intensity N/mm2

B1, B2 stress indices, see clause 8.4.7

Sm stress intensity value acc. to Section 7.7at design temperature

N/mm2

p design pressure N/mm2

da pipe outside diameter

where either da = dan orda = din + 2 sc + 2 c2

shall be taken (see Section 6.5)

mm

sc wall thickness without cladding acc. toclause 7.1.4 or measured wall thicknessminus corrosion allowance and clad-ding; regarding the cladding clause7.1.3, subclauses (1) and (2) shall betaken into account

mm

I moment of inertia mm4

MiI resulting moment due to design me-chanical loads. In the combination ofloads, all directional moment compo-nents in the same direction shall becombined before determining the resul-tant moment (moments resulting fromdifferent load cases that cannot occursimultaneously need not be used incalculating the resultant moment). Ifthe method of analysis of dynamicloads is such that only magnitudeswith relative algebraic signs are ob-tained, that combination of directionalmoment components shall be usedleading to the greatest resultant mo-ment.

Nmm

8.4.3 Level A and B

8.4.3.1 General

(1) For each load case, directional moment componentsshall be determined which always refer to a reference con-dition. The same applies to load cases under internal pres-sure and temperature differences.

(2) Where a verification of primary stresses accordingclause 3.3.3.3 is required for Level B, the primary stressintensity shall be determined according to equation (8.4-1)and be limited to the smaller value of 1.8 · Sm and 1.5 · Rp0,2T

in which case p is the operating pressure of the respectiveload case. If the maximum internal pressure exceeds 1.1times the design pressure, the primary stress intensity re-sulting from the circumferential stress due to internal pres-sure shall be limited as for Level B according to Tables 7.7-4to 7.7-6.

8.4.3.2 Determination and limitation of the primary plussecondary stress intensity range

The application of the equations given in this clause resultsin the equivalent stress intensity range where the stressesare caused by operational transients occurring due tochanges in mechanical or thermal loadings. Cold-spring, if

KTA 3201.2

any, need not be considered. The following condition shallnormally be satisfied, otherwise clause 8.4.3.4 shall apply:

σ

α α

IIa

c

aiII

rl r mr l ml m

Cd p

sC

dI

M

C E T T S

= ⋅⋅⋅

+ ⋅⋅

⋅ +

+ ⋅ ⋅ ⋅ − ⋅ ≤ ⋅

10

2

3

2 2

3∆ ∆(8.4-2)

where

σII primary plus secondary stress intensityrange

N/mm2

da, sc see clause 8.4.2

I moment of inertia mm4

C1, C2 stress indices, see clause 8.4.7

Sm stress intensity value according to Sec-tion 7.7 at the temperature:

T = 0.25 · �

T + 0.75 · �T

where�T maximum temperature at the con-

sidered load cycle�

T minimum temperature at the con-sidered load cycle

N/mm2

p0 range of operating pressure fluctuations N/mm2

Erl average modulus of elasticity of the twosides r and l of a gross structural dis-continuity or a material discontinuity atroom temperature

N/mm2

αr (αl) linear coefficient of thermal expansionon side r (l) of a gross structural dis-continuity or a material discontinuity atroom temperature

1/K

MiII resultant range of momentsIn the combination of moments fromload sets, all directional moment com-ponents in the same direction shall becombined before determining the resul-tant moment. Here that combination ofplant service conditions of Level A andB shall be selected resulting in thegreatest values of MiII. If a combinationincludes the effects of earthquake orother dynamic loads it shall be based onthat range of the two following rangesof moments which results in highervalues for MiII:

- the resultant range of moments due tothe combination of all loads of twoservice conditions of Level A and B,where one-half range of the earth-quake and other dynamic loads shallbe considered

- the resultant range of moments due toearthquake and other dynamic loadsalone.

Weight effects need not be consideredin equation (8.4-2) since they arenon-cyclic in character.

Nmm

∆Tmr

(∆Tml)range of average temperature on side r(l) of gross structural discontinuity ormaterial discontinuity (see clause8.3.4.6)

K

8.4.3.3 Determination of primary plus secondary pluspeak stress intensity range

The stress intensity range σIII resulting from primary plussecondary plus peak stresses shall be calculated accordingto equation (8.4-3) and is intended to determine the stressintensity range σVI according to equation (8.4-7)

( )

σ

να

α αν

α

III Ia

c

aiIII

rl

r mr l ml

K Cd p

sK C

dI

M

K E T K C E

T T E T

= ⋅ ⋅⋅⋅

+ ⋅ ⋅⋅

⋅ +

+⋅ −

⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅

⋅ ⋅ − ⋅ +−

⋅ ⋅ ⋅

10

2 2

3 1 3 3

2

2 2

12 1

11

∆

∆ ∆ ∆

(8.4-3)

where

σIII stress intensity range resultingfrom primary plus secondarystresses and peak stresses

N/mm2

( )

d , s , I, p ,E , ( ),

T

a c 0

rl r l

mr

α α∆ ∆Tml

see clause 8.4.3.2

MiIII = MiII see clause 8.4.3.2

C , C , CK , K , K

1 2 3

1 2 3

see clause 8.4.7

∆T1, ∆T2 see clause 8.4.3.6

α linear coefficient of thermal ex-pansion at room temperature

1/K

E modulus of elasticity at roomtemperature

N/mm2

ν Poisson's ratio (= 0.3)

8.4.3.4 Simplified elastic-plastic analysis

8.4.3.4.1 Conditions

Where the limitation of the stress intensity range given inequation (8.4-2) cannot be satisfied for one or several pairsof load sets, the alternative conditions of a), b) and c) here-inafter shall be satisfied:

a) Limit of secondary stress intensity range:

σIVa

iIV mCd

IM S= ⋅

⋅⋅ < ⋅2 2

3 (8.4-4)

where

σIV secondary stress intensity range N/mm2

C2, da, I see clause 8.4.3.2

MiIV greatest range of moments due toloadings resulting from restraint tothermal expansion and cyclic ther-mal anchor and intermediate anchormovement

Nmm

Sm see clause 8.4.3.2 N/mm2

KTA 3201.2

b) Limitation of thermal stress ratcheting

The temperature difference ∆T1 according to clause8.4.3.6 shall satisfy the following relation:

∆Ty R

EC

p T1

0 250 7

≤⋅

⋅ ⋅⋅.

. α(8.4-5)

Here, in dependence of

xp d

s Ra

c p T=

⋅⋅ ⋅2 0 2.

the following values for y apply:

x y

0.3 3.33

0.5 2.0

0.7 1.2

0.8 0.8

Intermediate values shall be subject tostraight interpolation.

wherep maximum pressure for the set of

operating conditions under consid-eration

N/mm2

C5 = 1.1 for ferritic steels, 1.3 for aus-tenitic steels

α, E as defined for equation (8.4-2)

Rp0.2T 0.2 % proof stress at average fluidtemperature of the transients underconsideration

N/mm2

c) Limitation of stress intensity range resulting from pri-mary plus secondary membrane and bending stresses:

The stress intensity range resulting from primary plussecondary membrane and bending stresses withoutstress components from moments due to restrainedthermal expansion in the system shall be limited accord-ing to equation (8.4-6).

σVa

c

aiV rlC

d ps

Cd

IM C E= ⋅

⋅⋅

+ ⋅⋅

⋅ + ⋅ ⋅10

2 42 2

⋅ ⋅ − ⋅ ≤ ⋅α αr mr l ml mT T S∆ ∆ 3 (8.4-6)

whereσV stress intensity range resulting

from primary plus secondarymembrane and bendingstresses

N/mm2

Sm see clause 8.4.3.2 N/mm2

C1, C2, C4 see clause 8.4.7

( )

d , s , I, p ,E , ( ),

T

a c 0

rl r l

mr

α α∆ ∆Tml

see clause 8.4.3.2

MiV Range of moments MiII withoutMiIV for the considered operat-ing conditions; if MiII wasformed as the range of mo-ments of the dynamic loads ofone operating condition, halfthe range of the dynamic loadportion of MiII shall be taken toform MiV

Nmm

8.4.3.4.2 Stress intensity range σVI

With the primary plus secondary plus peak stress intensityrange calculated according to equation (8.4-3) for all pairs ofload sets an increased stress intensity range σVI compared to σIII can be determined:

σ σVI e IIIK= ⋅ (8.4-7)

where

σVI equivalent stress intensity range N/mm2

Ke plastification factor

The magnitude of Ke depends on the value of the stressintensity range σII according to equation (8.4-2) and is ob-tained, e.g. by means of the following relationship:

a) σII ≤ 3 · Sm

Ke = 1

b) 3 · Sm < σII < 3 · m · Sm

( )( )K

nn m Se

II

m= +

−⋅ −

⋅⋅

−

1

11 3

1σ

c) σII ≥ 3 · m · Sm

Kne = 1

where the material parameters m and n can be used up tothe temperature T (see Table 7.8-1).

8.4.3.5 Fatigue analysis

8.4.3.5.1 Detailed determination of the cumulative usagefactor

The stress intensity ranges σIII (for Ke = 1) obtained from

equation (8.4-3) or the stress intensity ranges σVI (for Ke > 1)obtained from equation (8.4-7) shall be used for the deter-mination of the usage factor according to Section 7.8, whereSa equals σIII /2 or σVI/2 (Sa = one-half the stress intensity).For this purpose, the fatigue curves from Figures 7.8-1 and7.8-2 shall be used as basis.

8.4.3.5.2 Conservative determination of the usage factor

(1) Within the component-specific method for the determi-nation and evaluation of stresses the fatigue analysis may beperformed in accordance with the following procedure. Thismethod shall be used for a conservative evaluation of acomponent. Where upon application of this method theallowable usage factor D is not exceeded, no detailed fatigueanalysis need be performed.

(2) The stress intensity range 2 · Sa = σIII or σVI (see clause8.4.3.3 or 8.4.3.4) shall be determined by means of equation(8.4-3) if the stress intensity defined hereinafter is used forthe respective loadings:

KTA 3201.2

a) As stress intensity range for internal pressure the re-spective greatest pressure differences of the load casecombinations under consideration shall be taken.

b) As stress intensity range of the directional moment com-ponents MiIII the greatest range of resulting moments ofthe load case combinations under consideration shall betaken.

Here, MiIII shall be determined as follows:

M M M MiIII = + +12

22

32 (8.4-8)

M1,2,3 range of moments of directions 1, 2, 3 from theload case combinations under consideration

c) As stress intensity range of the stresses resulting fromtemperature differences (∆T1, ∆Tmr - ∆Tml, ∆T2) the dif-ference of the largest and smallest values (consideringthe relative algebraic signs) shall be taken for the loadcase combination under consideration in which case therespective simultaneously acting portions of the tem-perature differences may be considered. This also ap-plies to stresses resulting from the absolute value of thedifference of the products α αr mr l mlT T⋅ − ⋅∆ ∆ ,

d) As a conservative approach the number of all load cyclesshall be accumulated (cumulative damage) to define thenumber of load cycles to be used. The allowable numberof load cycles can be determined by means of Figure7.8-1 or 7.8-2.

(3) The cumulative usage factor D is found to be the ratio ofthe actual number of cycles to the allowable number of cy-cles thus determined. Where the usage factor is < 1, thislocation of the piping system need not be evaluated further.

8.4.3.6 Determination of the ranges of temperaturedifferences

(1) The determination of the ranges of temperature differ-ences ∆Tm , ∆T1 and ∆T2 shall be based on the actual tem-perature distribution through the wall thickness sc to thepoints of time under consideration.

(2) The range of temperature distribution ∆T(y) for locationy is found to read:

∆T(y) = Tk(y) - Tj(y) (8.4-9)

with

y radial position in the wall, measured positive outwardfrom the mid-thickness position

- sc/2 ≤ y ≤ sc/2

Tj(y) temperature, as a function of radial position y frommid-thickness to point of time where t = j

Tk(y) temperature, as a function of radial position y frommid-thickness to point of time where t = k

(3) The full temperature distribution range is composed ofthree parts as shown in Figure 8.4-1. Index a refers to theoutside and index i to the inside.

(4) For the determination of the pertinent stress ranges thefollowing relationships apply:

a) Average range ∆Tm as temperature difference betweenthe average temperatures Tmk and Tmj

( ) ( )[ ]∆Ts

T y T y dymc

k j

s

s

c

c

= −−∫1

2

2

/

/

( )= = −−∫1

2

2

sT y dy T T

cmk mj

s

s

c

c

∆/

/

(8.4-10)

with

Tmj, Tmk average value of temperature through wallthickness sc at point of time where t = j, k

∆Tm may be used to determine the range of moments Mi

resulting from restraint to thermal expansion in the sys-tem.

∆∆

∆

∆∆

∆∆

∆

m1

a

2a

c

i

cc

12i

(y)y

TT

T

T

+s / 2/ 2

inside (i) outside (a)

s

-s

/2T

TT

T/2

Figure 8.4-1: Decomposition of temperature distributionrange

The relationship (8.4-10) with the respective indices alsoapplies to the ranges of average wall temperatures onsides r, l of a structural discontinuity or material discon-tinuity.

∆Tmr = Tmrk - Tmrj; at point of time where t = j, k,

∆Tml = Tmlk - Tmlj; at point of time where t = j, k.

KTA 3201.2

These magnitudes may be inserted in equations (8.4-2)and (8.4-3). For cylindrical shapes Tmrk, Tmrj shall nor-mally be averaged over a length of (dir · sr)1/2 and Tmlk,Tmlj over a length (dil · sl)1/2.

where:

dir (dil) the inside diameter on side r (l) of astructural discontinuity or materialdiscontinuity

mm

sr (sl) the average wall thickness on a lengthof (dir · sr)1/2 or (dil · sl)1/2

mm

b) Range ∆T1 of the temperature difference between thetemperature on the outside surface and the temperatureon the inside surface, assuming moment generatingequivalent linear temperature distribution.

( ) ( )[ ]∆Ts

y T y T y dyc

k j

sc

sc

1 22

212= ⋅ ⋅ −

−∫

/

/

(8.4-11)

c) Range ∆T2 for that portion of the non-linear thermalgradient through the wall thickness

∆

∆ ∆ ∆∆

∆ ∆ ∆∆

T

T T TT

T T TT

a a m

i i m2

21

21

2

2

0

=

= − −

= − −

max. (8.4-12)

8.4.4 Level P

(1) The test conditions for Level P loadings shall be evalu-ated in correspondence with the requirements clause 3.3.3.6.

(2) The stresses shall be determined by means of equation(8.4-1) and limited to 1.35 · Rp0.2PT. Only if the load cyclesexceed the number of ten, the stresses shall be determinedby means of equation (8.4-3), and credit shall be taken of thepertinent load cycles as portion of the total accumulativedamage of the material in the fatigue analysis.

8.4.5 Levels C and D service limits

(1) For the component-specific stress analysis of pipingsystems the requirements of clauses 3.3.3.4 and 3.3.3.5 shallbe met.

(2) For Level C the primary stresses are calculated bymeans of equation (8.4-1), but are safeguarded with2.25 · Sm, and shall not exceed 1.8 · Rp0.2T. Here, for p the re-spective pressure shall be taken. Where the maximum inter-nal pressure exceeds 1.5 times the design pressure, the pri-mary intensity stress for Level C, which is due to the circum-ferential stress caused by the internal pressure p, shall belimited in accordance with Tables 7.7-4 to 7.7-6.

(3) For Level D the primary stresses are calculated bymeans of (8.4-1), but are safeguarded with the smaller valueof 3 · Sm and 2 ⋅ Rp0.2T. Here, for p the respective pressure

shall be taken. Where the maximum internal pressure ex-ceeds 2 times the design pressure, the primary stress inten-sity for Level D, which is due to the circumferential stresscaused by the internal pressure, shall be limited in accor-dance with Table 7.7-4 to 7.7-6.

8.4.6 Loading levels of special load cases

When performing strength calculations Section 3.2.1 shall beconsidered. The primary stresses according to equation(8.4-1) shall be limited such that the piping and componentsare not damaged.

8.4.7 Stress indices

8.4.7.1 General

(1) The applicable stress indices (B, C and K values) to beused in equations (8.4-1) to (8.4-4) and (8.4-6) of this sectionare indicated in Table 8.4-1.

(2) Table 8.4-1 contains stress indices for some commonlyused piping products and joints. Where specific data exist,lower stress indices than those given in Table 8.4-1 may beused.

(3) For piping products not covered by Table 8.4-1 or forwhich the given requirements are not met, stress indicesshall be established by experimental analysis or theoreticalanalysis.

(4) Stress indices may also be established by means of otherrules, guidelines and standards.

8.4.7.2 Definition of stress indices

(1) The general definition of a stress index for mechanicalload is

B, C, K = σσ

e (8.4-13)

where

σe ideally elastic stress, stress intensity, orstress intensity range due to load

N/mm2

σ nominal stress due to loading N/mm2

(2) The B values were derived from limit load calculations.For the C and K values σe is the maximum stress intensity orstress intensity range due to loading of the component. Thenominal stress σ is shown in equations (8.4-1) to (8.4-4) and(8.4-6), respectively.

(3) The general term for a stress index due to thermal load is

C, K = σα

e

E T⋅ ⋅ ∆(8.4-14)

where

σe highest stress intensity due to tempera-ture gradient or temperature range ∆T

N/mm2

E modulus of elasticity N/mm2

α linear coefficient of thermal expansion 1/K

KTA 3201.2

∆T temperature gradient or temperaturerange

K

8.4.7.3 Conditions for using stress indices

8.4.7.3.1 General

(1) The stress indices given herein and in Table 8.4-1 includ-ing the restrictions specified hereinafter shall be used withthe conditions of clauses 8.4.1 to 8.4.6.

(2) For the calculation of the numerical values of the stressindices and the stresses in accordance with equations (8.4-1)to (8.4-7) the nominal dimensions shall be used in whichcase between outside and inside diameter the relationship

di = da - 2 ⋅ sc (8.4-15)

with

sc pipe wall thickness according to clause8.4.2

mm

shall be taken into account.

(3) For pipe fittings such as reducers and tapered-walltransitions, the nominal dimensions of the large or smallend, whichever gives the larger value of da/sc, shall nor-mally be used.

(4) Loadings for which stress indices are given includeinternal pressure, bending and torsional moments, andtemperature differences. The indices are intended to besufficiently conservative to account also for the effects oftransverse shear forces normally encountered in flexiblepiping systems. If, however, thrust or shear forces accountfor a significant portion of the loading on a given pipingcomponent, the effect of these forces shall normally be in-cluded in the design analysis. The values of the forces andmoments shall normally be obtained from an analysis of thepiping system.

(5) The stress indices for welds are not applicable if theradial weld shrinkage exceeds 0.25 · sc.

(6) The stress indices given in Table 8.4-1 only apply to buttgirth welds between two items for which the wall thicknessis between 0.875 ⋅ sc and 1.1 ⋅ sc for an axial distance of

d sa c⋅ from the welding ends.

Internal pressure Moment loading Thermal loading

B1 C1 K1 B2 C2 K2 C3 K3 C4

Straight pipe, remote from welds or other discontinuities 1) 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5

Butt girth welds between straight pipes or pipe andbutt-welded item

a) flush 1)

b) as-welded 2)

0.5

0.5

1.0

1.0

1.1

1.2

1.0

1.0

1.0

1.0 2)

1.1

1.8

0.6

0.6

1.1

1.7

0.6

0.6

Cicumferential fillet weld on socket weld fitting, 1)

slip-on flange or socket weld flange 2) 0.75 1.8 3.0 1.5 2.1 2.0 2.0 3.0 1.0

Longitudinal butt welds in straight pipe 1)

(a) flush 2)

(b) as-welded sc > 5 mm

(c) as-welded sc ≤ 5 mm

0.5

0.5

0.5

1.0

1.1

1.4

1.1

1.2

2.5

1.0

1.0

1.0

1.0

1.2

1.2

1.1

1.3

1.3

1.0

1.0

1.0

1.1

1.2

1.2

0.5

0.5

0.5

Transitions 1)

(a) flush or no circumferential weld closer than (dRm/2 ⋅ sRc)1/2

(b) as-welded

0.5

0.5

3)

3)

1.2

1.2

1.0

1.0

3)

3)

1.1

1.8

3)

3)

1.1

1.7

1.0

1.0

Butt welding reducers to Fig. 8.4-4 1) 1.0 4) 4) 4) 1.0 4) 4) 1.0 1.0 0.5

Curved pipe or elbows 1) 0.5 5) 1.0 5) 5) 1.0 1.0 1.0 0.5

Branch connections to Annex A 2.7 1)

6) 0.5 7) 2.0 7) 7) 7) 1.8 1.7 1.0

Butt welding tees to Annex 4.6 1)

6) 0.5 1.5 4.0 8) 8) 8) 1.0 1.0 0.5

Stress indices shall only be used if the dimensioning requirements of Annex A have been met.In addition, B values can only be used if da/sc ≤ 50, C and K values only if da/sc ≤ 100.

1) see clause 8.4.7.3.1 5) see clause 8.4.7.3.52) see clause 8.4.7.3. 6) see clause 8.4.7.3.63) see clause 8.4.7.3.3 7) see clause 8.4.7.3.6.24) see clause 8.4.7.3.4 8) see clause 8.4.7.3.6.3

Table 8.4-1: Stress indices for use with equations (8.4-1) to (8.4-4) and (8.4-6)

Piping products and joints

KTA 3201.2

(7) For components with longitudinal butt welds, the K1, K2

and K3 indices shown shall be multiplied by 1.1 for flushwelds or by 1.3 for as-welded welds. At the intersection of alongitudinal butt weld in straight pipe with a girth buttweld or girth fillet weld, the C1, K1, C2, K2 and K3 indicesshall be taken as the product of the respective indices.

(8) In general and unless otherwise specified, it is not re-quired to take the product of stress indices for two pipingcomponents (e.g. a tee and a reducer, a tee and a girth buttweld) when welded together. The piping component andthe weld shall be qualified separately.

(9) For curved pipe or butt welding elbows welded togetheror joined by a piece of straight pipe less than one pipe di-ameter long, the stress indices shall be taken as the productof the indices for the elbow or curved pipe and the indicesfor the girth butt weld, except for stress indices B1 and C4

which are exempted.

(10) The stress indices given in Table 8.4-1 are applicable forcomponents and welds with out-of-roundness not greater

than 0.08 · sc where out-of-roundness is defined as �d - da a�

.

For straight pipe, curved pipe, longitudinal butt welds instraight pipe, girth butt welds, and wall thickness transi-tions not meeting this requirement, the stress indices shallbe modified as specified below:

a) If the cross-section is out-of-round but with no disconti-nuity in radius (e.g. an elliptical cross-section), an ac-ceptable value of K1 may be obtained by multiplying thetabulated values of K1 less the factor F1a:

Fd d

s sa

a a

c c1 3

1= + −+

⋅�

/ )

�

1.51 0.455 (d (p /E)a

(8.4-16)where

p maximum pressure at the con-sidered load cycle

N/mm2

�dalargest outside diameter ofcross-section

mm

�

dasmallest outside diameter ofcross-section

mm

E modulus of elasticity of thematerial at room temperature

N/mm2

b) If there are discontinuities in radius, e.g. a flat spot, and

if �d - da a�

is not greater than 0.08 · da, an acceptable

value of K1 may be obtained by multiplying the tabu-lated values of K1 with the factor F1b:

FM R

d pbp T

a1

0 212

= +⋅ ⋅

⋅

sc�

. (8.4-17)

where

M = 2 for ferritic steels and nonfer-rous metals except nickel basedalloys

M = 2.7 for austenitic steels and nickelbased alloys

Rp0.2T proof stress at design tempera-ture

N/mm2


8.4.7.3.2 Connecting welds

(1) The stress indices given in Table 8.4-1 are applicable forlongitudinal butt joints in straight pipe, girth butt weldsjoining items with identical nominal wall thicknesses andgirth fillet welds used to attach socket weld fittings, slip-onflanges, or socket welding flanges, except as modified here-inafter.

(2) Connecting welds are termed to be either flush welds oras-welded ones, if the requirements in a) or b) are met, re-spectively.

a) Welds are considered to be flush welds if they meet thefollowing requirements:

The total thickness (both inside and outside) of the rein-forcement shall not exceed 0.1 · sc. There shall be no con-

cavity on either the interior or exterior surfaces, and thefinished contour shall not have any slope greater than 7degree in which case the angle is measured between theweld tangent and the component surface (see Figure8.4-2).

α

αα

α

cs

Figure 8.4-2: Allowable weld contour

b) Welds are considered to be as-welded if they do notmeet the requirements for flush welds.

(3) For as-welded welds joining items with nominal wallthicknesses less than 6 mm, the C2 index shall be taken as:

C2 = 1.0 + 3 (δ/sc) (8.4-18)

but not greater than 2.1

where

δ allowable average misalignment ac-cording to Figure 8.4-3. A smaller valuethan 0.8 mm may be used for δ if asmaller value is specified for fabrica-tion. The measured misalignment mayalso be used. For flush welds δ = 0 maybe taken.

mm

8.4.7.3.3 Welded transitions

(1) The stress indices given in Table 8.4-1 are applicable tobutt girth welds between a pipe for which the wall thicknessis between 0.875 ⋅ sc and 1.1 ⋅ sc for an axial distance of

d sa c⋅ from the welding end and the transition to a cy-

lindrical component (pipe, attached nozzle, flange) with agreater thickness and a greater or an equal outside diameterand a smaller or an equal inside diameter.

KTA 3201.2

b)

a) Concentric centre lines

offset centre lines

δ

δ

≤

Ai

Rc

Rm

Ri

R

Rc

Pipe

If counterboringis not possible

max. mismatcharound the joint = 2 mm

at any one point

Pipe

Component

Component

s

d

s

d d d

smaller value of

max. mismatcharound the joint = 1 mm

or 6 mm

18.5˚

14˚

Figure 8.4-3: Butt weld alignment and mismatch tolerancesfor unequal inside diameter and outside di-ameter when fairing or back welding on theinside is not possible

(2) For transitions which on an axial distance of at least1.5 ⋅ sc from the welding end have a taper not exceeding 30°,and on an axial distance of at least 0.5 ⋅ sc have a taper notexceeding 45°, and on the inside on an axial distance of 2 ⋅ sc

from the welding end have a slope not greater than 1:3, thefollowing applies for indices C1, C2, C3:

C1 = 0.5 + 0.33 (da/sc)0.3 + 1.5 ⋅ (δ/sc) (8.4-19)but not greater than 1.8

C2 = 1.7 + 3.0 ⋅ (δ/sc) (8.4-20)but not greater than 2.1

C3 = 1.0 + 0.03 ⋅ (da/sc) (8.4-21)but not greater than 2.0.

(3) For transitions which on the outside, inside or on bothsides, on an axial distance of d sa c⋅ from the welding end,

have a slope not greater than 1:3, the following applies forindices C1, C2, C3:

C1 = 1.0 + 1.5 ⋅ (δ/sc) (8.4-22)but not greater than 1.8

C2 = �s /sc + 3 ⋅ (δ/sc) (8.4-23)but not greater than the smaller value

of [1.33 + 0.04 d sa / c + 3 (δ/sc)] and 2.1

C3 = 0.35 ( �s /sc) + 0.25 (8.4-24)but not greater than 2.0.

(4) For the transitions according to this Section δ shall beselected in accordance with Figure 8.4-3. For flush weldsand as-welded welds between components with wall thick-nesses sc greater than 6 mm δ = 0 may be taken.

(5) �s is the maximum wall thickness within the transitionalzone. If �s /sc does not exceed 1.1, the indices for circumfer-ential welds may be used.

8.4.7.3.4 Reducers

8.4.7.3.4.1 General

The stress indices given in Table 8.4-1 are applicable forconcentric reducers if the following restrictions are consid-ered (see Figure 8.4-4):

a) α does not exceed 60° (cone angle)

b) the wall thickness is not less than s01 throughout thebody of the reducer, except in and immediately adjacentto the cylindrical portion on the small end where thethickness shall not be less than s02. The wall thicknessess01 and s02 are the minimum wall thicknesses for thestraight pipe at the large end and small end, respec-tively.

α01

1

1

2

1

2

02

2

L

r

Ls

d s

r

dFigure 8.4-4: Concentric reducer

8.4.7.3.4.2 Primary stress indices

B1 = 0.5 for α ≤ 30°

B1 = 1 for 30° < α ≤ 60°

8.4.7.3.4.3 Primary plus secondary stress indices

(1) For reducers with r1 and r2 equal to or greater than0.1 · d1:

C1 = 1.0 + 0.0058 · α ⋅ d sn n/ (8.4-25)

C2 = 1.0 + 0.36 · α0.4 ⋅ (dn/sn)0.4 (d2/d1 - 0.5) (8.4-26)

(2) For reducers with r1 or r2 smaller than 0.1 · d1:

C1 = 1.0 + 0.00465 ⋅ α1.285 ⋅ (dn/sn)0.39 (8.4-27)

C2 = 1.0 + 0.0185 ⋅ α ⋅ d sn n/ (8.4-28)

KTA 3201.2

Here dn/sn is the larger value of d1/s1 and d2/s2 and α isthe cone angle according to Figure 8.4-4.

8.4.7.3.4.4 Peak stress indices

(1) The K1 and K2 indices given hereinafter shall normallybe used depending on the type of connecting weld, extent ofmismatch and thickness dimensions.

(2) For reducers connected to pipe with flush girth welds(see clause 8.4.7.3.2):

K1 = 1.1 - 0.1 · Lm/ d sm m⋅ (8.4-29)

but at least 1.0

K2 = K1

(3) For reducers connected to pipe with as-welded girthbutt welds (see clause 8.4.7.3.2), where s1 or s2 exceeds 5 mmand δ1/s1 or δ2/s2 does not exceed 0.1

K1 = 1.2 - 0.2 · Lm/ d sm m⋅ (8.4-30)

but at least 1.0

K2 = 1.8 - 0.8 · Lm/ d sm m⋅ (8.4-31)

but at least 1.0

(4) For reducers connected to pipe with as-welded girthbutt welds (see clause 8.4.7.3.2) where s1 or s2 does not ex-ceed 5 mm or δ1/s1 or δ2/s2 is greater than 0.1

K1 = 1.2 - 0.2 · Lm/ d · sm m (8.4-32)

but at least 1.0

K2 = 2.5 - 1.5 · Lm/ d · sm m (8.4-33)

but at least 1.0

Lm/ d sm m⋅ is the smaller value of

L1/ d s1 1⋅ or L2/ d s2 2⋅ .

δ1, δ2 is the offset at the large end or small end of the reducer(see clause 8.4.7.3.2 and Figure 8.4-3).

8.4.7.3.5 Butt welding elbows and curved pipes

The stress indices given in Table 8.4-1, except as added toand modified herein, are applicable to butt welding elbowsor curved pipe

a) Primary stress index

B2 = 1.3/h2/3 (8.4-34)

but at least 1.0

b) Primary plus secondary stress indices

( )( )CR r

R rm

m1

2

2=

⋅ −⋅ −

(8.4-35)

Ch

2 2 31 95= .

/ (8.4-36)

but at least 1.5

where

R = bending radius

rm = dm/2

dm = da - sc

hs R

dc

m= ⋅ ⋅4

2

8.4.7.3.6 Branch connections and butt welding tees

8.4.7.3.6.1 General

(1) When determining the stress intensities in accordancewith equations (8.4-1) to (8.4-4) and (8.4-6), the followingconditions shall be satisfied for branch connections.

(2) The moments are to be calculated at the intersection ofthe run and branch centre lines

For MA:

M M M MA A A A= + +12

22

32 = resulting moment on

branch (8.4-37)

For MH:

M M M MH H H H= + +12

22

32 = resulting moment on run

(8.4-38)

where M1H, M2H and M3H are calculated as follows:

Where the directional moment components of the run havethe same algebraic signs at intersections 1 and 2 as the mo-ment of the branch which are in the same direction, then therespective components shall be used to determine the resul-tant moment loading MH which then equals zero. Otherwisethe smaller of the absolute values at the intersections 1 and 2shall be used to determine MH.

z1

y1

x3

z3

y3

x2

z2

y2

x1

3

3

0 21

M

21

M

M

M

M

M

M

M

M

Figure 8.4-5: Designation of moments on branch connec-tion

KTA 3201.2

(3) For branches the Mi terms shall be replaced by the fol-lowing pairs of terms in equations (8.4-1), (8.4-2), (8.4-3),(8.4-4), and (8.4-6) :

a) In equation (8.4-1)

BMZ

BMZA

A

AH

H

H2 2⋅ + ⋅ (8.4-39)

b) In equation (8.4-2), (8.4-4) and (8.4-6)

CMZ

CMZA

A

AH

H

H2 2⋅ + ⋅ (8.4-40)

c) In equation (8.4-3)

C KMZ

C KMZA A

A

AH H

H

H2 2 2 2⋅ ⋅ + ⋅ ⋅ (8.4-41)

for which the following section moduli apply:

Z d sA Rm Rc= ⋅ ⋅π4

2

Z d sH Hm Hc= ⋅ ⋅π4

2

(4) For branches according to Annex A 2-7: dRm, sRc, dHm

and sHc are given in Figure 8.4-6.

8.4.7.3.6.2 Stress indices for branches complying with An-nex A 2.7

(1) Applicability of indices

The stress indices indicated are applicable for branch con-nections if the following conditions a) to h) are satisfied:

a) The branch-to-run radius ratio is

dAm/dHm ≤ 0.5

b) The run pipe radius-to-thickness ratio is limited as fol-lows:

dHm/sHc ≤ 50

c) The axis of the branch connection is normal to the runpipe surface.

d) The requirements for reinforcement of areas according toSection A 4.6 have been meet.

e) The inside corner radius r1 (see Figure 8.4-6) shall bebetween 0.1 and 0.5 · sHc.

f) The branch-to-run fillet radius r2 (see Figure 8.4-6) is notless than the larger of sAc/2 or (sAc + y)/2 (see Figure8.4-6 c) and sHc/2.

g) The branch-to-fillet radius r3 (see Figure 8.4-6) is not lessthan the larger of 0.002 · α · dAa or 2 ⋅ (sin α)3 times theoffset as shown in Figures 8.4-6 a and 8.4-6 b.

h) For several branch connections in a pipe, the arc distancemeasured between the centres of adjacent branchesalong the outside surface of the run pipe is not less than1.5 times the sum of the two adjacent branch inside radiiin the longitudinal direction, or is not less than the sumof the two adjacent branch radii along the circumferenceof the run pipe.

c d

ba

≥

αα ≤

α ≤

α =

α

Ac

Rc

Rc

Ac

RcAc

Ac

Ai

Rc

Rm

Rc Ac

Ac

Am

Ra

Ra

Am

Hc

Hm

Hc

1

Rm

Hm

Rm

Hc

Aa

Ai

Hm

Aa

Am

1

Ai

Offset

Aa

Ai

Hc

Ra

Hm

1

2

Hc

2

3

1

1

3

2

2

3

1

Rm

1

Am

Offset

1

Ai

Aa

s

s + 0,667

radius to the centre of

= s

.

d

0,5

90˚

d

d

2, then

d

sIf

d

d

s

can be taken as the

y/2

d

y

r

s

r

r

d

s

d

d

s

d

45˚

30˚

r

r

r

r

rr

r

r

d

d = s

s

d

s

d

s

d

d s

d

d

s

d

d

d

s

d

d

s

Nomenclature for Figure 8.4-6

Notation Design value Unit

dAa outside diameter of branch mm

dAi inside diameter of branch mm

dAm mean diameter of branch mm

dHm mean diameter of run pipe mm

dRa outside diameter of branch pipe mm

dRi inside diameter of branch pipe mm

dRm mean diameter of branch mm

sAc wall thickness of branch mm

sHc wall thickness of run pipe mm

sRc wall thickness of branch pipe mm

r1, r2,r3, y

(see Figure)

α angle between vertical and slope degree

Figure 8.4-6: Branch connection nomenclature

(2) Primary stress indices

B2A = 0.5 · C2A ≥ 1.0 (8.4-42)

B2H = 0.75 · C2H ≥ 1.0 (8.4-43)

KTA 3201.2

(3) Primary plus secondary stress indices

The C1, C2A and C2H indices can be determined using thefollowing relationships:

Cds

dd

ss

sr

Hm

Hc

Rm

Hm

Hc

Rc

Rc1

0 0 367 0 382

2

0

=

⋅

⋅

⋅

1.4

.182 . . .148

(8.4-44)

but at least 1.2.

If r2/sRc exceeds 12, use r2/sRc = 12 for computing C1.

Cd

sdd

ss

ddA

Hm

Hc

Rm

Hm

Rc

Hc

Rm

Aa2

2/3 1 2

2=

⋅

⋅

⋅

3

/

(8.4-45)

but at least 1.5.

Cd

sdd

ssH

Hm

Hc

Rm

Hm

Hc

Rc2

1 4

2=

⋅

⋅

1.15 /

(8.4-46)

but at least 1.5.

(4) Peak stress indices

The peak stress indices K2A and K2H for moment loadingsmay be taken as:

K2A = 1.0

K2H = 1.75

and K2H · C2H normally shall not be smaller than 2.65.

8.4.7.3.6.3 Stress indices for butt welding tees

(1) The stress indices given in Table 8.4-1 as well as theindices given hereinafter are applicable to butt welding teesif they meet the requirements of clause A 4.6.1 or A 4.6.2.

(2) To determine the stresses resulting from internal pres-sure and moments as well as the stress indices the diameters(dHa, dAa) and the equivalent wall thicknesses (sH

+ , sA+ ) of

the run and branch to be connected shall be used in compli-ance with clause A 4.6.1.5 or A 4.6.2.4.

(3) Primary stress indices

The primary stress indices B2A and B2H may be taken as:

Bd

sA

Ha

H2

2 3

0 42

= ⋅⋅

+.

/

(8.4-47)

but at least 1.0

Bd

sH

Ha

H2

2 3

0 52

= ⋅⋅

+.

/

(8.4-48)

but at least 1.0

(4) Primary plus secondary stress indices

The C2A and C2H indices for moment loadings shall be takenas follows

C 0.67d

2AHa= ⋅⋅

+2

2 3

sH

/

(8.4-49)

but at least 2.0

C2H = C2A (8.4-50)

(5) Peak stress indices

The peak stress indices K2A and K2H shall be taken as:

K2A = K2H = 1 (8.4-51)

8.4.8 Detailed stress analysis

8.4.8.1 General

(1) In lieu of the stress analysis according to clauses 8.4.2 to8.4.5 a detailed stress analysis in accordance with this clausemay be made.

(2) To determine a normal stress σ the following relationwith σN as nominal stress and i as stress index applies:

σ = i · σN

Accordingly the following applies to shear stresses:

τ = i · τN

(3) The following definitions apply to the nominal stressesin this clause:

for loading due to internal pressure p

σN (p) = p · di/ (2 · sc) (8.4-52)

for loading due to bending moment Mb

σN (Mb) = Mb/W (8.4-53)

for loading due to torsional moment Mt

τN (Mt) = Mt/ (2 · W) (8.4-54)

(4) For the stress components on the pipe section the follow-ing definitions apply in compliance with clause 8.2.2 andFigure 8.4-7:

σa = stress component in axial direction (in the plane ofthe section under consideration and parallel to theboundary of the section)

σt = stress component in circumferential direction (nor-mal to the plane of the section)


τat = τta = shear stress components in circumferential andaxial direction

(5) With these stress components the stress intensities forthe investigation points shall be determined by means of themaximum shear stress theory.

KTA 3201.2

8.4.8.2 Welding elbows and curved pipes

(1) The stress indices given in Tables 8.4-2 and 8.4-3 areapplicable to elbows and curved pipes provided that thepoints under investigation are sufficiently remote from girthor longitudinal welds or other local discontinuities. Other-wise, additional theoretical or experimental analyses arerequired.

(2) The nomenclature used for the stress indices can betaken from Figure 8.4-7 where the directional moment com-ponents are defined as follows:

Mx = torsional moment

My = bending moment for out-of-plane Ez displacement

Mz = bending moment for in-plane Ey displacement

ϕα

β

σ

ϕ

β

α

ϕ

σ

σ

c

r

a

a

c

c

2

1

m

i 2

a

x

z

y

z

x

1

i

a

t

E

2s-d=-

>=

d d

E

d

Direction

Direction d

r

x

d

y

z

M

M

M

y

z

Moment loads

=d

Out of round cross-section

s-d

z

y

s

Round cross-section

d

d

Figure 8.4-7: Pipe elbow nomenclature for detailed stressanalysis

(3) The stress indices of Table 8.4-2 for internal pressureloading have the following magnitudes

ir dr d

i

m1

00

= + ⋅ ⋅+ ⋅ ⋅

.25 sin

.5 sinϕϕ

(8.4-55)

i2 = 0.5 · di/dm (8.4-56)

( ) ( )i

d ds d s p Ec m c

31 2

31

1 02= − ⋅

+ ⋅ − ⋅ ⋅

.5

.5 / /cos

1 2να

(8.4-57)

is

dc

i4

2=

⋅(8.4-58)

Location SurfaceStress direc-

tionStress index

Round cross-sectionoutside i1 - 0.5 ⋅ i4

ϕ mid σt i1inside i1 + 0.5 ⋅ i4

outside i2Any mid σa i2

inside i2Out-of-round cross-section

outside i1 - i3 - 0.5 ⋅ i4mid σt i1

inside i1 + i3 + 0.5 ⋅ i4outside i2 - 0.3 ⋅ i3

mid σa i2inside i2 + 0.3 ⋅ i3

Round and out-of-round cross-sectionoutside 0

Any mid σr - 0.5 ⋅ i4inside - i4

Table 8.4-2: Stress indices for curved pipe or weldingelbows under internal pressure

(4) The stress indices of Table 8.4-3 for moment loading,with

λ ν= ⋅ ⋅ ⋅ −

4 12 2r s dc m/ (8.4-59)

( )ψ = ⋅ ⋅ ⋅ ⋅2 2p r E d sm c/ (8.4-60)

x125 6 24= + ⋅ + ⋅λ ψ (8.4-61)

x2217 600 480= + ⋅ + ⋅λ ψ (8.4-62)

x x x3 1 2 6 25= ⋅ − , (8.4-63)

( ) ( )x x x42

3 21 4 5= − ⋅ − ⋅ν , (8.4-64)

have the following magnitudes and only apply if λ ≥ 0.2.In the equation for ψ not more than the respective value ofthe internal pressure p shall be inserted.

The following applies to the bending moment My:

iamy = cosϕ + [(1.5·x2-18.75)·cos3ϕ + 11.25·cos5ϕ]/x4

(8.4-65)

itby =- λ ·(9·x2·sin2ϕ + 225·sin4ϕ)/x4 (8.4-66)

For the bending moment Mz the following applies:

iamz = sinϕ + [(1.5·x2 - 18.75)·sin3ϕ + 11.25·sin5ϕ]/x4

(8.4-67)

itbz = λ · (9·x2·cos2ϕ + 225·cos4ϕ)/x4 (8.4-68)

ϕ

KTA 3201.2

itmz = - 0.5 ⋅ (dm/r)·cosϕ · {cosϕ + [(0.5 ⋅ x2 - 6.25)

⋅ cos3ϕ + 2.25 ⋅ cos5ϕ]/x4} (8.4-69)

(5) Table 8.4-4 applies to the classification as per clause 7.7.2into stress categories of the stresses determined by the stressindices given here.

Location SurfaceStress direc-

tionStress index

for torsional moment Mx

outside 1Any mid τat 1

inside 1for bending moments My

outside itby

mid σt 0

inside - itby

outside iamy + ν ⋅ itby

mid σa iamy

inside iamy - ν ⋅ itby

for bending moments Mz

outside itmz + itbz

mid σr itmz

inside itmz - itbz

outside iamz + ν ⋅ itbz

mid σa iamz

inside iamz - ν ⋅ itbz

Table 8.4-3: Stress indices for curved pipe or weldingelbows under moment loading

Origin of stress Type of stress 1) Classification

Membrane stresses Pm

Bending stresses Q

Membrane and tor-sional stresses

Pl

Moments due toexternal loads

75 % of bendingstresses

Pb

25 % of bendingstresses

Q

Moments due torestrained thermalexpansion and freeend displacements

Membrane, bendingand torsional stresses

Q

1) Referred to through-wall stresses

Table 8.4-4: Classification of stresses for curved pipe orelbows in case of detailed stress analysis

8.4.8.3 Branches complying with Section A 2.7

For branches complying with Section A 2.7 the stresses dueto internal pressure may be determined according to clause8.2.2.1 and the stresses due to forces and moments accordingto clause 8.2.2.4 if the geometric conditions given in clause8.2.2.1 are satisfied.

8.4.9 Flexibility factors and stress intensification factors

8.4.9.1 General

(1) Compared to straight pipes individual piping compo-nents show an increased flexibility when subjected tobending on account of the ovalization of the pipecross-section causing an increase of stresses.

(2) Where the system analysis for the piping is made toconform to the theory of beams (straight beam with circularcross-section), this increased flexibility shall be taken intoaccount by k values not less than 1 for flexibility factors andC not less than 1 for stress intensification factors.

(3) Compared to the straight pipe, torsional moments aswell as normal and transverse forces do neither lead to anincreased flexibility nor to an increase of stresses.

8.4.9.2 Straight pipes

(1) For the determination of the deflection of straight pipesby bending and torsional moments as well as normal andtransverse forces the theory of a straight beam with annularcross-section applies.

(2) For the analysis of straight pipes all flexibility factorsshall be taken as k = 1 and the stress intensification factorsas C = 1.

8.4.9.3 Pipe elbows and curved pipes

(1) For the curved section of elbows and curved pipes thedeflections which according to the theory of beams resultfrom bending moments (My and Mz according to Figure8.4-8), shall be multiplied with the flexibility factors ky or kz

in which case the system analysis can either be made withaverage values or values for the point under investigation toobtain the flexibility factors.

α 0

x

z

y

M

M

M

Figure 8.4-8: Direction of moments

(2) For the determination of deformations due to torsionalmoments as well as normal and transverse forces the con-ventional theory of beams applies.

ϕ

ϕ

Internal pressure

KTA 3201.2

(3) The value given hereinafter for the mean flexibility fac-tor km = ky = kz not less than 1.0 applies if the followingconditions for pipe elbows and curved pipes are satisfied:

a) r/dm not less than 0.85

b) arc length not less than dm

c) there are no flanges or similar stiffeners within a dis-tance not exceeding dm/2 from either end of the curvedpipe section or from the ends of the elbows.

Otherwise, for such pipe elbows and curved pipe sectionskm = ky = kz = 1.0 shall be taken.

k khm p= ⋅ 1.65

; but at least 1 (8.4-70)

with k p d XE s

pm k

c

=+

⋅ ⋅⋅ ⋅

1

12

(8.4-71)

Xd

sr

dkm

c m= ⋅

⋅

⋅ ⋅

6

22

4 3 1 3/ /

(8.4-72)

hr s

dc

m=

⋅ ⋅42 (8.4-73)

(4) In the case of system analyses using mean flexibilityfactors the mean stress indices C2 shall be taken in accor-dance with clause 8.4.7.3.5.

(5) In the stress analysis using equations (8.4-1) to (8.4-6) thebending stress due to a resulting moment on account ofbending and torsional moments is determined to obtain themean stress index.

(6) The values given hereinafter for flexibility factors atcertain points under investigation kx ≠ ky ≠ kz apply to pipeelbows and curved pipe sections which at both ends areconnected to straight pipes showing the dimension of thecurved section and the distance of which to the next curvedsection is at least two times the outside diameter:

kx = 1.0 (8.4-74)

k khy p= ⋅ 1.25

; but at least 1 (8.4-75)

k kkhz p= ⋅ α ; but at least 1 (8.4-76)

with kp according to equation (8.4-71)

h according to equation (8.4-73)kα = 1.65 for α0 ≥ 180°

kα = 1.30 for α0 = 90°

kα = 1.10 for α0 = 45°

kα = h for α0 = 0°

The values for kz may be subject to linear interpolation be-tween 180° and 0°.

(7) In the case of system analyses using flexibility factors atcertain points under investigation the following stress indi-ces C2m related to certain points under investigation andmoments shall be used:

C2x = 1.0 (8.4-77)

C2y = 1.71/h0.53 but ≥ 1 (8.4-78)

C2z = 1.95/h2/3 for α0 ≥ 90° (8.4-79)

= 1.75/h0.58 for α0 = 45° (8.4-80)

= 1.0 for α0 = 0° (8.4-81)

The values for C2z may be subject to linear interpolationbetween 90° and 0° , however no value of α0 smaller than30° shall be used; C2z shall never be less than 1.

(8) In the case of system analyses using flexibility factors atcertain points under consideration, where the stress analysisis based on equations (8.4-1) to (8.4-6), the bending stressresulting from bending or torsional moments may be de-termined using the stress indices related to certain pointsunder consideration and moments. Here, the resulting val-ues shall be substituted as follows:

- instead of B2 ⋅ MiI now use

( ) ( ) ( )0 22

22

22.5 ⋅ ⋅ + ⋅ + ⋅C M C M C Mx x y y z z (8.4-82)

- instead of C2 ⋅ Mi(II-V) now use

( ) ( ) ( )C M C M C Mx x y y z z22

22

22⋅ + ⋅ + ⋅ (8.4-83)

8.4.9.4 Branches complying with Section A 2.7 withdAi/dHi ≤ 0.5

(1) The deflection behaviour of branch connections comply-ing with Section A 2.7 with dAi/dHi not exceeding 0.5 can bemodelled according to Figure 8.4-9 as follows:

a) Beam in direction of pipe run axis having pipe run di-mensions and extending to the intersection of the runpipe centre line with the branch pipe centre line.

b) Assumption of rigid juncture at intersection of pipe runand branch axes.

c) Assumption of rigid beam on a branch pipe length of 0.5 ⋅ dHa from the juncture (intersection of axes) to the runpipe surface.

d) Assumption of element with local flexibility at the junc-ture of branch pipe axis and run pipe surface.

(2) The flexibilities (unit of moment per radians) of theflexible element with regard to the branch pipe bendingmoments can be determined by approximation as follows:

a) for bending along axis x

CE I

k dxR

x Ra= ⋅

⋅ (8.4-84)

with

kds

ss

dd

ssx

Ha

Hc

Hc

n

Ra

Ha

Rc

Hc= ⋅

⋅ ⋅

⋅0 1

1 5 0 5

.. .

(8.4-85)

b) for bending along axis z

CE I

k dzR

z Ra=

⋅⋅

(8.4-86)

with

kds

ss

dd

ssz

Ha

Hc

Hc

n

Ra

Ha

Rc

Hc= ⋅ ⋅ ⋅

⋅0 2

0 5

..

(8.4-87)

KTA 3201.2

Regarding the notations Figure 8.4-6 applies with the addi-tional definitions

IR moment of inertia of the branch pipe

( )I d dR Ra Ri= ⋅ −π 4 4 64/ (8.4-88)

sn value for nozzle wall thickness, i.e.for designs a and b of Figure 8.4-6:

sn = sAc, if ( )L d s sAi A A1 0 5≥ ⋅ + ⋅.

sn = sRc, if ( )L d s sAi A A1 0 5< ⋅ + ⋅.

for design c of Figure 8.4-6:

sn = sRc + (2/3) ⋅ y, if α ≤ 30°

sn = sRc + 0.385 ⋅ L1, if α > 30°

For design d of Figure 8.4-6:

sn = sRc

(3) With regard to the deflection due to torsional, normaland transverse forces the flexible element shall be consi-dered to be rigid.

rigid length of beamelement with local flexibility

dimensionsbeam with pipe run

rigid juncture

y

z

x

dimensionsbeam with branch pipe

Figure 8.4-9: Modelling of branch connections in straightpipe

8.4.9.5 Branch connections with dAi/dHi > 0.5 and buttwelding tees

Branch connections with dAi/dHi greater than 0.5 and buttwelding tees shall also be modelled in accordance withclause 8.4.9.4 and Figure 8.4-9 where, however, the flexibleelement shall be omitted.

8.5 Component support structures

8.5.1 Integral areas of component support structures

8.5.1.1 General

This section applies to the calculation of the integral areas ofcomponent support structures which are intended to ac-commodate loadings. The integral areas of component sup-

port structures are attached to the pressure-retaining area bywelding, forging, casting or fabricated from the solid. There-fore, the portion of the support structure directly adjacent tothe component wall interacts with the component (area ofinfluence). For the design of component support structuresthe distribution of stresses and moments rather than internalpressure loading shall govern.

8.5.1.2 Limitation of integral area

(1) The limitation of the integral area of component supportstructures is shown in Figure 8.5-1. The distance l is calcu-lated as follows:

a) Shells (e.g. skirts, tubular nozzles)

l r sc= ⋅ ⋅0 5. (8.5-1)

where:

r mean radius of shell of support structure

sc thickness of support structure shell in accordancewith clause 7.1.4

b) bars or section

l r= ⋅0 5 22. / (8.5-2)

where

r radius of bar of-one-half the maximum cross-sectio-nal dimension of the section

c) other shapes

l r sc= ⋅ ⋅0.5 (8.5-3)

where

r on-half the maximum dimension of a flange, tee-sec-tion, plat or round section or one-half the maximumleg width of an angle section

sc flange thickness of sections or plate thickness accord-ing to clause 7.1.4

Building

limit of area

non-

inte

gral

inte

gral

Component support structure

: die-out length

of influenceof component

detachable

non-

inte

gral

non-detachable

Building

inte

gral

component

connectionconnection

component

Figure 8.5-1: Type of attachment of component supportstructures

(2) Where, however, a detachable connection is providedwithin a distance l, the limit between the integral andnon-integral area shall be set at this location.

KTA 3201.2

8.5.1.3 Design

(1) Integral areas of component support structures are to beconsidered part of the supporting component. All simulta-neously occurring loads shall be taken into account. Forcomponent support structures the following forces andmoments shall be determined:

a) normal force FN,

b) transverse force FQ,

c) torsional moment Mt,

d) bending moment Mb.

(2) The effects of external forces and moments on the com-ponent wall shall be considered in accordance with Section7.

(3) Accordingly, the stresses shall be evaluated in accor-dance with Section 7.

(4) In the case of pressure loading the stability behaviourshall be analysed.

8.5.2 Non-integral areas of component-support structures

Regarding component support structures with non-integralconnections for components of the reactor coolant pressureboundary KTA 3205.1 shall apply.

9 Type and extent of verification of strength and perti-nent documents to be submitted

(1) For the design approval to be made by the authorizedinspector in accordance with § 20 AtG (Atomic Energy Act)the following verifications of strength for the componentsand parts of the primary circuit shall be carried out and besubmitted in form of a report:

a) Dimensioning

b) Analysis of the mechanical behaviour

(2) The design, report and inspection shall be based on thepertinent sections of KTA safety standards 3201.1, 3201.2,3201.3, and 3201.4

(3) Each report on design and calculation shall normallycontain the following information at the extent required forreview of the strength verifications:

a) Explanation of design and calculation procedures, espe-cially of assumptions made

b) Indication of calculation procedures, theoretical basesand programmes used

c) Load data, combination of loads and their classification

d) Geometric data

e) Characteristic values (mechanical properties) of thematerials used

f) Input data

g) Results obtained including fatigue usage factors

h) Evaluation of results and comparison with allowablevalues

i) Conclusions drawn from the results obtained

j) References, bibliography and literature.

KTA 3201.2

Annex A

Dimensioning

A 1 General

(1) The design rules hereinafter apply to the dimensioningof components in accordance with Section 6 and their partssubject to design pressure and additional design mechanicalloads at design temperature. The general design values andunits are given in subclause (6). Further design values andunits are given separately in the individual sections.

(2) The stress intensity (Sm) to be used shall be determinedin dependence of the design temperature. Additional loads,e.g. external forces and moments, shall be separately takeninto account.

(3) The confirmatory calculation of parts with nominal wallthickness sn shall be made within this Annex with the wallthickness s0n = sn - c1 - c2 with sn ≥ s0 + c1 + c2. Regardingallowances Section 6.4 applies.

(4) The figures contained in this Annex do not include al-lowances.

(5) The requirements laid down in Annex A 2 for generalparts of the pressure retaining wall are also applicable, inconsideration of the respective requirement, to specific partsof valves complying with A 3 and piping complying with A4 unless other requirements have been fixed in these An-nexes.

(6) Design values and units


b width mm

d diameter mm

h height mm

c wall thickness allowance mm

l length mm


p´ test pressure N/mm2

r, R radii mm

s wall thickness mm

s0 calculated wall thickness accordingto Figure 7.1-1

mm


s0n nominal wall thickness minus al-lowances c1 and c2 according to Fig-ure 7.1-1

mm

sn nominal wall thickness according toFigure 7.1-1

mm

v efficiency

A area mm2

E modulus of elasticity N/mm2

F force N

I second moment of area mm4

M moment N⋅mm

S safety factor

ϕ angle degree

q flattening mm

W section modulus mm3

U ovality %

T temperature °C

ν Poisson's ratio= 0.3 for steel

σ stress N/mm2

σl longitudinal stress N/mm2

σr radial stress N/mm2

σu circumferential stress N/mm2

σV stress intensity N/mm2

Sm stress intensity N/mm2

τ shear stress N/mm2

Signs Meaning

Indicator at head � maximum value e.g. �p

Indicator at head � minimum value e.g. �p

Indicator at head mean value e.g. σ

Indicator at head � fluctuating, e.g. �σ

Indicator at head ´ belonging to pressure test, e.g. p´

Subscript numerical index, e.g. ni

1 N/mm2 = 10 bar = 10.2 at = 0.102 kp/mm2 = 106 Pa

KTA 3201.2

A 2 Dimensioning of parts of the pressure retaining wall

A 2.1 General

The equations given in Section A 2.2 to A 2.10 for dimen-sioning only apply to the determination of the required wallthickness of the individual parts under internal or externalpressure, however, without consideration of the elastic rela-tionship of the entire structure.

A 2.2 Cylindrical shells

A 2.2.1 Design values and units relating to Section A 2.2


da outside diameter of cylindrical shell mm

di inside diameter of cylindrical shell mm

dm mean diameter of cylindrical shell mm

fv safety factor against elastic instabil-ity

fk additional safety factor against grossplastic deformation

l unsupported length mmn number of lobes pzul. allowable pressure N/mm2

Z design value: Z = 0.5⋅ π ⋅ da/l

A 2.2.2 Cylindrical shells under internal pressure

A 2.2.2.1 Scope

The calculation method hereinafter applies to cylindricalshells under internal pressure, where the ratio da/di doesnot exceed 1.7. Diameter ratios da/di not exceeding 2 arepermitted if the wall thickness s0n does not exceed 80. Rein-forcements of openings in cylindrical shells under internalpressure shall be calculated in accordance with Section 2.7.

A 2.2.2.3 Calculation

(1) For the calculation of the required wall thickness of theshell the following applies

s0 =⋅

⋅ +d pS p

a

m2(A 2.2-1)

or

s0 =⋅

⋅ −d pS p

i

m2(A 2.2-2)

(2) For the recalculation at given wall thickness the follow-ing applies:

σVi

nmp

ds

S= ⋅⋅

+

≤

20 5

0. (A 2.2-3)

A 2.2.3 Cylindrical shells under external pressure

A 2.2.3.1 Scope

The calculation method hereinafter applies to cylindricalshells under external pressure where the ratio da/di doesnot exceed 1.7.

A 2.2.3.2 Safety factors

(1) The additional safety factor against gross plastic defor-mation shall be taken as fv = 1.2 irrespective of the materialused.

(2) The safety factor against elastic instability shall be takenas fk = 3.0 irrespective of the material used. Where a highertest pressure as 1.3 ⋅ p is required, fk shall be at least 2.2.


A 2.2.3.3.1 General

(1) It shall be verified by calculation according to the follow-ing clauses that there is sufficient safety against elastic in-stability and plastic deformation. The smallest calculatedvalue of pzul shall govern.

(2) The buckling length is the length of the shell. For vesselswith dished heads the buckling length begins at the junctureof cylindrical flange (skirt) to knuckle.

A 2.2.3.3.2 Calculation against elastic instability

(1) The calculation shall be made according to

( ) ( )[ ] ( )pEf n n Z

sdzul

k

n

a= ⋅

− ⋅ +⋅ +

⋅ −⋅

2

1 1

2

3 12 2 20

2/ ν

nn

n Z

sd

n

a

22

03

12 1

1− +

⋅ − −+

⋅

ν( / )2 (A 2.2-4)

where for Z = 0.5 ⋅ π ⋅ da/1 shall be taken; n is a full numberand shall satisfy the conditions n ≥ 2 and n > Z and shall beselected such that p becomes the smallest value. n means thenumber of lobes (circumferential waves) which may occurover the circumference in case of instability. The number oflobes shall be calculated by approximation as follows:

nd

l sa

n= ⋅

⋅1 63

3

20

4. (A 2.2-5)

(2) The required wall thickness s0n may be determined inaccordance with Figure A 2.2-1 for usual dimensions. Thisfigure applies to a Poisson's ratio of ν = 0.3. Where the Pois-son' s ratio extremely differs from 0.3, equation (A 2.2-4)shall be taken.

KTA 3201.2

0n

for

calc

ulat

ion

agai

nst e

last

ic in

stab

ility

Req

uire

d w

all t

hick

ness

sF

igur

e A

2.2

-1:

ν =

109 8

0.8

0.9

1

7 3 2

1.56 5 4

0.7

45

0.4

0.6

0.5

810

96

70.

150.

2

0.15

0.1

0.1

0.9

0.7

0.8

0.3

160

5070

8090

40

0.5

0.6

0.4

0.2

0.3

100

21.

53

3020

15

6

a

k

a

0n

d

s

5.0

3.0

4.0

d

fp

E

100

10

2.0

0.1

0.2 0

0.3

valid

for

0.3

1.0

1.5

0.8

0.4

0.6

KTA 3201.2

0n

Req

uire

d w

all t

hick

ness

s f

or c

alcu

latio

n ag

ains

t gro

ss p

last

ic d

efor

mat

ion

Fig

ure

A 2

.2-2

:

1 0.99

10

0.6

0.5

0.8

0.734

1.5278 56

0.06

0.08

0.9

0.05

0.2

0.1

0.04

0.4

0.5

0.6

0.3

0.8

0.7

0.03

0.15

94

35

76

810

0.4

1

0.3

0.2

21.

5

0n

a

mv

a

2

Sfp

10

s

d

100

4.6

4.4

4.2

d

5.0

4.8

4.0

1.0

0

valid

for U

=1.5

3.5

3.0

2.0

KTA 3201.2

A 2.2.3.3.3 Calculation against gross plastic deformation

(1) For dla ≤ 5 the following applies:

( )pSf

sd U d l d

s

zulm

v

n

a a a

n

= ⋅ ⋅ ⋅+

⋅ ⋅ − ⋅ ⋅⋅

2 1

11 5 1 0 2

100

0

0

. . / (A 2.2-6)

The required wall thickness s0n may be determined directlyin accordance with Figure A 2.2-2 for usual dimensions andwith U = 1.5 %.

(2) For dla > 5 the larger value of the pressure determined

by the two equations hereinafter shall govern the determi-nation of the allowable external pressure:

pS

fsd

pzulm

v

n

a=

⋅⋅ ≥

2 0 (A 2.2-7)

pS

fs

lpzul

m

v

n=⋅

⋅

≥3 0

2(A 2.2-8)

(3) Equation (A 2.2-8) primarily applies to small unsup-ported lengths. Equations (A 2.2-6) to (A 2.2-8) only apply ifno positive primary longitudinal stresses σa occur. In Equa-tions (A 2.2-6) to (A 2.2-8) Sm shall be replaced by (Sm - σa) if σa > 0.

A 2.3 Spherical shells

A 2.3.1Design values and units relating to Section A 2.3


da outside diameter of spherical shell mm

di inside diameter of spherical shell mm

dm mean diameter of spherical shell mm

Ck design value

fk safety factor against elastic instabil-ity

fv additional safety factor against grossplastic deformation

σk stress in confirmatory calculationagainst elastic instability

N/mm2

A 2.3.2 Spherical shells under internal pressure

A 2.3.2.1 Scope

The calculation hereinafter applies to unpierced sphericalshells under internal pressure where the ratio da/di ≤ 1.5.The calculation of pierced spherical shells under internalpressure shall be made in accordance with Section A 2.7.


(1) For the calculation of the required wall thickness s0 ofspherical shells with a ratio s0n/di greater than 0.05 one ofthe following equations applies:

sd C

Ca k

k0 2

1= ⋅

− (A 2.3-1)

or

( )sd

Cik0 2

1= ⋅ − (A 2.3-2)

with

Cp

S pkm

= +⋅

⋅ −1

22

(A 2.3-3)

(2) For the calculation of the required wall thickness of thin-walled spherical shells with a ratio s0n/di not exceeding 0.05the following applies:

sd p

Sa

m0 4

=⋅

⋅(A 2.3-4)

or

sd p

S pi

m0 4 2

=⋅

⋅ − ⋅(A 2.3-5)

(3) For the confirmatory calculation at a given wall thick-ness the following applies:

( )σVi

i n nmp

dd s s

S= ⋅⋅ + ⋅

+

≤2

0 040 5. (A 2.3-6)

A 2.3.3 Spherical shells under external pressure

A 2.3.3.1 Scope

The calculation hereinafter applies to spherical shells underexternal pressure where the ratio da/di does not exceed 1.5.

A 2.3.3.2 Safety factors

(1) The additional safety factor against gross plastic defor-mation shall be fv = 1.2 irrespective of the material used.

(2) The safety factor against elastic instability shall be takenfrom Table A 2.3-1 irrespective of the material. Where a testpressure > 1.3 ⋅ p is required then the test pressure shall beadditionally verified with ′fk from Table A 2.3-1.

2 sd

0

i

⋅ fk ′fk

0.001 5.5 4.00.003 4.0 2.90.005 3.7 2.70.010 3.5 2.6

≥ 0.1 3.0 2.2

Intermediate values shall be subject to straight interpolation.

Table A 2.3-1: Safety factors against elastic instability

KTA 3201.2


(1) General

It shall be verified by calculation that there is sufficientsafety against elastic instability and plastic deformation. Thehighest value of s0 obtained from subparagraphs 2 and 3shall be determining.

(2) Calculation against elastic instability

The required wall thickness is obtained from the followingequation:

s dp f

Eak

0 1 464= ⋅

⋅⋅.

(A 2.3-7)

For the confirmatory calculation at a given wall thicknessthe following applies:

σka

n k

p ds

Ef

= ⋅

≤

1 464 0.(A 2.3-8)

(3) Calculation against plastic deformation

The required wall thickness is obtained from:

sd p f

S p fa v

m v0 2

1 12

2= ⋅ − −

⋅ ⋅⋅ + ⋅

(A 2.3-9)

For spherical shells with a ratio s0/da ≤ 0.05 the requiredwall thickness may be calculated by approximation from

sp d f

Sa v

m0 4

=⋅ ⋅

⋅(A 2.3-10)


( )σVa

a n n

m

vp

dd s s

Sf

= ⋅⋅ − ⋅

−

≤2

0 040 5. (A 2.3-11)

A 2.4 Conical shells



da outside diameter of conical shell mm

da1 outside diameter at large end ofcone

mm

da2 outside diameter at small end ofcone

mm

di inside diameter of conical shell mm

di1 inside diameter at large end of cone mm

di2 inside diameter at small end of cone mm

e die-out length according to Fig.A 2.4-3

mm

e1 die-out length at large end of cone mm

e2 die-out length at small end of cone mm


s1 wall thickness at large end of cone mm

s2 wall thickness at small end of cone mm

Ap pressure-loaded area mm2


β shape factor in accordance with Ta-ble A 2.4-1

ϕ semi-angle of the apex of the conicalsection

degree

ϕ1 semi-angle of the apex at the largeend of the cone

degree

ϕ2 semi-angle of the apex at the smallend of the cone

degree

ψ absolute difference between thesemi-apex angles ϕ1 and ϕ2

degree

σl longitudinal stress N/mm2

r transition radius mm

A 2.4.2 Conical shells under internal pressure

A 2.4.2.1 Scope

The calculation hereinafter applies to unpierced conicalshells under internal pressure where at the large end of thecone the condition 0.005 ≤ s0n/da ≤ 0.2 is satisfied. The calcu-lation of penetrated shells under internal pressure shall beeffected in accordance with Section A 2.7.

Note:

For da - di = 2 ⋅ s0n the value da/ d i = 1.67 corresponds tos0n/ d a = 0.2.

A 2.4.2.2 General

(1) Conical shell with corner welds

Conical shells may be welded to each other or to cylindricalshells or sections without knuckle in accordance with clause5.2.3.

(2) Die-out length

For conical shells with inwardly curved transitions the wallthickness required in accordance with clause A 2.4.2.3, sub-paragraphs (2) or (4) shall be provided over the knuckle arealimited by the die-out length e (see Figure A 2.4-1).

The following applies:

e r s d sn a n1 0 020 8, ( ) tan . e2 = + ⋅ + ⋅ ⋅ψ

(A 2.4-1)

In the case of change in wall thickness within the die-outlength the respective wall thickness at run-out of curvatureshall govern the determination of the lengths e1 and e2 ac-cording to equation (A 2.4-1).

KTA 3201.2

ϕ−

ϕϕ

ϕ

ϕψ

ψ

ϕ

1

22

122 1

a1

a2

2

1

a

i2

1

i1

se

r

=

e

d

s

d

d

>

d

d

Figure A 2.4-1: Die-out lengths e1 and e2


(1) Wall thickness calculation for area without discontinu-ity of a conical shell with ϕ ≤ 70°.

The required wall thickness of the area without discontinu-ity of a conical shell (see Figure A 2.4-2) is obtained fromeither

( )sd p

S pa

m0 2

=⋅

⋅ + ⋅ cosϕ(A 2.4-2)

or

( )sd p

S pi

m0 2

=⋅

⋅ − ⋅ cosϕ(A 2.4-3)


σϕV

i

nmp

ds

S= ⋅⋅ ⋅

+

≤

20 5

0 cos. (A 2.4-4)

For da and di the diameters at the large end of the areawithout discontinuity of the conical shell shall be taken inequations (A 2.4-2) to (A 2.4-4).

For da and di there is the relation:

di = da - 2 ⋅ s0n ⋅ cos ϕ (A 2.4-5)

In the case of several consecutive conical shells with thesame apex angle all shells shall be calculated in accordancewith (A 2.4-2) or (A 2.4-3).

(2) Calculation of wall thickness of the area with disconti-nuity of inwardly curved conical shells and ϕ 70≤ °

The wall thickness shall be dimensioned separately withrespect to

a) circumferential loading in external knuckle portion

b) circumferential loading in internal knuckle portion

and

c) loading along the generating line of shell section.

The largest wall thickness obtained from a), b) and c) shallgovern the dimensioning.

Regarding the circumferential stress for inwardly curvedtransitions (Figure A 2.4-1) the required wall thickness shallbe determined by means of equations (A 2.4-2) or (A 2.4-3)for both sides of the transition.

Regarding the longitudinal stresses the wall thickness can beobtained from

sd p

Sa

m0 4

=⋅ ⋅⋅

β (A 2.4-6)

where the shape factor β shall be taken from Table A 2.4-1 independence of the angle ψ and the ratio r/da. Intermediatevalues may be subject to straight interpolation.

The largest value obtained from equation (A 2.4-2) or (A 2.4-3) and (A 2.4-6) shall be decisive. For the confirmatory calcu-lation at a given wall thickness the following applies:

σβ

la

nm

d ps

S=⋅ ⋅⋅

≤4 0

(A 2.4-7)

The angle ψ is the absolute difference of half the apex angles ϕ1 and ϕ2:

ψ ϕ ϕ= −1 2 (A 2.4-8)

Where the wall thickness changes within the die-out length(e.g. forgings, profiles) the wall thickness at run-out of cur-vature shall govern the determination of the lengths e1 ande2 according to equation (A 2.4-1).

ϕ

a

i

discontinuity Area without

discontinuity

Area with

d

s

d

Figure A 2.4-2: Area of shell without discontinuity

(3) Wall thickness calculation for the area without disconti-nuity of conical shells with outwardly curved transi-tions and ϕ 70≤ °

In the case of outwardly curved transitions (Figure A 2.4-3)basically all conditions and relationships apply as for in-wardly curved transitions.

In addition, the following condition shall be satisfied due tothe increased circumferential stress:

σσ

Vp

mpA

AS= ⋅ +

≤0 5. (A 2.4-9)

KTA 3201.2

ψ

Figure A 2.4-3: Conical shell with outwardly curvedtransition

(4) Wall thickness calculation for the area with discontinu-ity of flat conical shells with knuckle and ϕ > 70°

In the case of extremely flat cones whose angle inclination tothe vessel axis is ϕ > 70°, the wall thickness may be calcu-lated in accordance with equation (A 2.4-10) even if asmaller wall thickness than that calculated according toequations (A 2.4-2), (A 2.4-3) or (A 2.4-6) is obtained:

( )s d rp

Sam

0 0 390

= ⋅ −°

⋅.ϕ (A 2.4-10)

A 2.4.2 Conical shells under external pressure

For cones subject to external pressure the calculation shall bemade in accordance with clause A 2.4.2.3. Additionally, forconical shells with ϕ not exceeding 45° it shall be verifiedwhether the cone is safe against elastic instability. This veri-fication shall be made in accordance with clause A 2.2.3.3.2in which case the cone shall be considered to be equal to acylinder the diameter of which is determined as follows:

dd d

aa a=

+⋅1 2

2 cosϕ(A 2.4-11)

where

da1 diameter at large end of cone

da2 diameter at small end of cone.

The axial length of the cone and the adjacent cylindricalsections, if any, shall be taken unless the cylinder is suffi-ciently reinforced at the juncture in accordance with clauseA 2.2.3.

≤ 0.01 0.02 0.03 0.04 0.06 0.08 0.10 0.15 0.20 0.30 0.40 0.50

0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1

10 1.4 1.3 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1

20 2.0 1.8 1.7 1.6 1.4 1.3 1.2 1.1 1.1 1.1 1.1 1.1

30 2.7 2.4 2.2 2.0 1.8 1.7 1.6 1.4 1.3 1.1 1.1 1.1

45 4.1 3.7 3.3 3.0 2.6 2.4 2.2 1.9 1.8 1.4 1.1 1.1

60 6.4 5.7 5.1 4.7 4.0 3.5 3.2 2.8 2.5 2.0 1.4 1.1

70 10.0 9.0 8.0 7.2 6.0 5.3 4.9 4.2 3.7 2.7 1.7 1.1

75 13.6 11.7 10.7 9.5 7.7 7.0 6.3 5.4 4.8 3.1 2.0 1.1

Table A 2.4-1: Shape factor β in dependence of the ratio r/da and ψ

A 2.5 Dished heads (domend ends)



da outside diameter of dished head mm

di inside diameter of dished head mm

dAi inside diameter of opening mm

fk safety factor against elastic instabil-ity

′fk safety factor against elastic instabil-ity at increased test pressure

h1 height of cylindrical skirt mm

h2 height of dished head mm


β shape factor

pB elastic instability pressure N/mm2

l distance of weld to knuckle mm

R radius of dishing mm

A 2.5.2 Dished heads under internal pressure

A 2.5.2.1 Scope

The calculation hereinafter applies to dished heads, i.e.torispherical, semi-ellipsoidal and hemispherical headsunder internal pressure if the following relationships andlimits are adhered to (see Figure A 2.5-1):

r/da

KTA 3201.2

2

a

i

1

s

h

d

d

R

r h

Figure A 2.5-1: Dished unpierced head

a) Torispherical headsR = da

r = 0.1 ⋅ da

h2 = 0.1935 ⋅ da - 0.455 ⋅ s0n

0 001 0 10. .≤ ≤sd

n

a

b) Semi-ellipsoidal headsR = 0.8 ⋅ da

r = 0.154 ⋅ da

h2 = 0.255 ⋅ da - 0.635 ⋅ s0n

0 001 0 10. .≤ ≤sd

n

a

c) Hemispherical headsda/di ≤ 1.5

A 2.5.2.2 General

(1) Height of cylindrical skirt

For torispherical heads the height of the cylindrical skirtshall basically be h1 ≥ 3.5 ⋅ s0n, and for semi-ellipsoidal headsh1 ≥ 3.0 ⋅ s0n but shall not exceed the following dimensions:

Wall thickness s0n, mm Height of cylindricalskirt h1, mm

s0n ≤ 50 150

50 < s0n ≤ 80 120

80 < s0n ≤ 100 100

100 < s0n ≤ 120 75

120 < s0n 50

For hemispherical heads no cylindrical skirt is required.

(2) Where a dished head is made of a crown section and aknuckle welded together the connecting weld shall have asufficient distance l from the knuckle which shall be:

a) in case of differing wall thickness of crown section andknuckle:

l R s n= ⋅ ⋅0 5 0.

where s0n is the required wall thickness of the knuckle.

b) in case of same wall thickness of crown section andknuckle:

l = 3.5 ⋅ s0n for torispherical heads

l = 3.0 ⋅ s0n for semi-ellipsoidal heads.

However, the distance l shall normally be at least100 mm.

c) The determination of the transition from knuckle tocrown section shall be based on the inside diameter. Forthin-walled torispherical heads to DIN 28 011 the transi-tion shall be approximately 0 89. ⋅di and for thin-walled

semi-ellipsoidal heads to DIN 28 013 0.86 ⋅ di. Thesefactors are reduced with an increase in wall thickness.


(1) Calculation of the required wall thickness of the knuckleunder internal pressure.

For the calculation of the required knuckle wall thicknessthe following applies:

sd p

Sa

m0 4

=⋅ ⋅⋅

β(A 2.5-1)

The shape factors β for dished heads shall be taken in de-pendence of s0n/da for torispherical heads from FigureA 2.5-3, for semi-ellipsoidal heads from Figure A 2.5-4.

In any case, openings in dished heads as per Figure A 2.5-2shall meet the requirements of Section A 2.7 in which casetwice the radius of dishing shall be taken as sphere diame-ter. In the case of torispherical and semi-ellipsoidal heads,this procedure shall, however, be limited to the crown sec-tion 0.6 ⋅ da (see Figure A 2.5-2).

For unpierced hemispherical heads a shape factor β = 1.1applies irrespective of the wall thickness over the distance0.5 ⋅ R s n⋅ 0 from the connecting weld. In the case of

pierced hemispherical heads the wall thickness of the rein-forcement of the opening shall be calculated in accordancewith Section A 2.7 in which case the wall thickness shall notbe less than that determined with β = 1.1 for the unpiercedhead.

2

Ai

a

a

1

s

d i

0.6

h

d

d

R

d

hr

Figure A 2.5-2: Dished head with nozzle

(2) Wrinkling of the knuckle

For torispherical and semi-ellipsoidal heads under internalpressure it shall be additionally demonstrated that the headknuckle area is sufficiently dimensioned to withstand elastic

KTA 3201.2

instability (wrinkling of knuckle). This is the case if the elas-tic instability pressure determined by means of FigureA 2.5-5 is pB ≥ 1.5 ⋅ p.

A 2.5.3 Dished heads under external pressure

For the calculation of the required wall thickness of theknuckle under external pressure the requirements of clauseA 2.5.2 with the additional requirements given hereinaftershall apply.

The required wall thickness s0 of the knuckle shall be com-puted by means of equation (A 2.5-1). When computing therequired wall thickness s0 the allowable stress intensity Sm

shall be reduced by 20 %. In addition, it shall be verified thatthe head has been adequately dimensioned against elasticinstability in the crown section.

This is the case if

pEf

sRk

n≤ ⋅ ⋅

0 366 02

. (A 2.5-2)

The safety factor fk shall be taken from Table A 2.5-1. Wherea test pressure in excess of p´ = 1.3 ⋅ p is required, a separateverification of strength against elastic instability shall bemade. In this case the safety factor ′fk at test pressure shall

not be less than the value given in Table A 2.5-1.

sR

n0 fk ′fk

0.001 5.5 4.0

0.003 4.0 2.9

0.005 3.7 2.7

0.010 3.5 2.6

0.1 3.0 2.2

Intermediate values shall be subject to straight interpolation.

Table A 2.5-1: Safety factors against elastic instabilityunder external pressure

β

aAi

a0n

0.05

0.25

0.005

0.5 0.6

0.2

d0.40.3

0.15

0

/ d9

3

4

5

2

0.001

0

1

0.1

s / d

0.01

6

7

8

Figure A 2.5-3: Shape factors β for torispherical heads

KTA 3201.2

β

aAi

0n a

0.2

0.15

0.25

0.005 0.05

0.40.3 0.5 0.6

0

0.1

d / d

3

4

5

2

0.001

0

1

6

s / d

9

0.1

7

8

0.01

Figure A 2.5-4: Shape factors β for semi-ellipsoidal heads

6B

a0n

7

6

3

4

5

8

Semi-ellipsoidal head Torispherical head

10/E

)(

p

0 0.0005 0.001

s / d

0

0.0015 0.0035

1

2

0.002 0.0025 0.003

Figure A 2.5-5: Determination of elastic instability pressure PB

KTA 3201.2

A 2.6 Flat plates



aD gasket moment arm mm

dA opening diameter mm

dD mean diameter or diameter of gasketcontact face

mm

di inside diameter mm

dt bolt circle diameter mm

kl gasket factor mm

r transition radius mm

C factor

CA factor relating to the calculation ofopenings

FD compression load on gasket N

s0n, Pl nominal wall thickness of plate mm

s0n, Zyl nominal wall thickness of cylinder mm

A 2.6.2 Scope

The calculation rules given hereinafter apply to flat plateswith and without edge moment under pressure load for therange

0 5431

34 0

. ;,⋅ ≤ ≤

p

E

s

d d

n Pl

i i

s0n,Pl

A 2.6.3 Calculation

A 2.6.3.1 Circular flat plate integral with cylindrical section

(1) In case of a plate integral with a cylindrical section asshown in Figure A 2.6-1 the plate and cylinder shall be con-sidered a unit.

n,Pl

n,Zyl is

r

s

d

Figure A 2.6-1: Flat plate integral with cylindrical section

(2) According to footnote 1) of Table 7.7-1 there are twopossibilities of dimensioning the juncture between flatplate/cylindrical shell.

Note:

Compared to alternative 1, alternative 2 allows for thinner flat platesat greater wall thickness of the cylindrical shell.

a) Alternative 1:

Predimensioning of the plate

s dp

Si

m0 0 45, . Pl = ⋅ ⋅ (A 2.6-1)

Predimensioning of the cylindrical shell in accordancewith Section A 2.2

Check of stresses in cylindrical shell:

3 60 82 0 85

6 56 3 31

1

211

2 2 32

1

22

3 11⋅ ≥ ⋅ ⋅ ⋅

+ ⋅ ⋅

+ ⋅ ⋅+ ⋅ +

S p BB B B

B B BBm

. . /

. . /

(A 2.6-2)

with Bd s

s

i n

n1

0

02=

+

⋅,

,

Zyl

Zyl

(A 2.6-3)

Bs

s

n

n2

0

0

= ,

,

Pl

Zyl

(A 2.6-4)

Bd s

s

i n

n3

0

02=

+

⋅,

,

Zyl

Pl

(A 2.6-5)

b) Alternative 2:

Predimensioning of the plate

ss

sd

p

S

n

ni

m0

0

0

0 45 0 1,,

,

. . Pl Zyl

Pl

= − ⋅

⋅ ⋅ (A 2.6-6)

Predimensioning of the cylinder in accordance withSection A 2.2.

Check of stresses in the cylinder:

1 5 60 82 0 85

6 56 3 311

2 2 32

1

22

3 1

.. . /

. . /⋅ ≥ ⋅ ⋅ ⋅

+ ⋅ ⋅

+ ⋅ ⋅+

S p BB B B

B B Bm

+ ⋅ +

1

211B (A 2.6-7)

with Bd s

s

i n

n1

0

02=

+

⋅,

,

Zyl

Zyl

(A 2.6-8)

Bs

s

n

n2

0

0

= ,

,

Pl

Zyl

(A 2.6-9)

Bd s

s

i n

n3

0

02=

+

⋅,

,

Zyl

Pl

(A 2.6-10)

For both alternatives it may be required to increase the wallthicknesses obtained from predimensioning for plate andcylindrical shell and to repeat the check of the stresses in theshell at the transition to the plate in accordance with equa-tion (A 2.6-2) or (A 2.6-7).

A 2.6.3.2 Unstayed circular plates with additional edgemoment

(1) For flat plates provided with a gasket and bolted at theedge the deformation shall also be taken into account byusing equation (A 2.6-11) in addition to the strength calcu-lation in accordance with equation (A 2.6-14), so that thetightness of the joint is ensured in which case the bolting-up,test and operating conditions shall be considered.

(2) The required wall thickness s0 of unstayed flat circular

plates with additional edge moment in same direction inaccordance with Figure A 2.6-2 will be:

KTA 3201.2

s C dp

SD

m0 = ⋅ ⋅ (A 2.6-11)

i

t

D

d

d

d

Figure A 2.6-2: Circular flat plate with additional edgemoment

The C value shall be taken from Figure A 2.6-3 in depend-

ence of the ratio dt/dD and the δ value in which case the

ratio of the required bolt load to hydrostatic end force oninside of flange is

δ = + ⋅ ⋅ ⋅1 4

m b S

dD D

D

(A 2.6-12)

Here, as a rule SD = 1.2 is inserted and the gasket factor m is

taken from Table A 2.10-1. bD is the gasket width according

to Section 2.10.

The equation given hereinafter leads to the same C value asFigure A 2.6-3:

Cd d d dt D t D

= ⋅ +

+ ⋅ ⋅ ⋅ −

+0 063

0 72 6 0 125 0 7 1

1.

.

/, . .

/δ

( )2 6

1 2

. ln /

/

⋅

d dt D (A 2.6-13)

It is recommended to check the deflection of the plate withwall thickness s0 in accordance with equation (A 2.6-11)

with respect to the tightness requirements by use of equa-tion (A 2.6-14).

Where the deflection is limited e.g. to w = 0.001 ⋅ dD,

x = 0.001 shall be inserted in equation (A 2.6-14).

sp d

x E

F a

x ED D D

0

33 0 0435 1 05≥

⋅ ⋅⋅

+ ⋅ ⋅⋅ ⋅

. .

π(A 2.6-14)

with the compression load on gasket FD according to Section

A 2.8 and the gasket moment arm

ad d

DD= −1

2(A 2.6-15)

It is permitted to restrict, if necessary, the deflection withinthe gasket area by other means.

A 2.6.3.3 Openings in flat circular plates

Openings in flat plates as per Figure A 2.6-1 shall be rein-forced in accordance with A 2.7.2.3.1.

(2) The required wall thickness s0 of the flat plate with

additional edge moment according to clause A 2.6.3.2 isobtained by means of equation (A 2.6-11), by multiplyingthe C value as per Figure A 2.6-3 or equation (A 2.6-13) with

the factor CA. The factor CA shall be determined as follows,

where dA is the diameter of the opening:

d dA A

dC

diA

i

≤ = ⋅0 1 14. (A 2.6-16)

0 1 0 7 0 286 1 37. . . .< ≤ = ⋅ +d dA A

dC

diA

i

(A 2.6-17)

(3) At a diameter ratio dA/di > 0.7 the plate shall be calcu-

lated as flange in accordance with Section A 2.9.

(4) Off-centre openings may be treated like central open-ings.

A 2.7 Reinforcement of openings

A 2.7.1 Design values and units relating to Section 2.7


dAa outside diameter of branch mm

dA diameter of opening mm

dAe inside diameter of opening plustwice the corrosion allowance c2

mm

dAi inside diameter of opening rein-forcement plus twice the corrosionallowance c2

mm

dAm mean diameter of nozzle mm

dHi inside diameter of basic shell mm

dHm mean diameter of basic shell at loca-tion of opening

mm

eA limit of reinforcement, measurednormal to the basic shell wall

mm

eH half-width of the reinforcement zonemeasured along the midsurface ofthe basic shell

mm

′eH half-width of the zone in which twothirds of compensation must beplaced

mm

l (see Figure A 2.7-10) mm

r1, r2, r3 fillet radii mm

sA nominal nozzle wall thickness in-cluding the reinforcement, but mi-nus allowances c1 and c2

mm

sA0 minimum required nozzles wallthickness

mm

sH nominal wall thickness of vesselshell or head at the location ofopening including the reinforce-ment, but minus allowances c1 and

c2

mm

sH0 minimum required wall thickness ofbasic shell

mm

sR nominal wall thickness of connectedpiping minus allowances c1 and c2

mm

sR0 minimum required wall thickness ofconnected piping

mm

KTA 3201.2


x slope offset distance mm

y slope offset distance mm

Ae cross-sectional area of the requiredreinforcement of opening

mm2

A1, A2,

A3

metal area available for reinforce-ment

mm2

F correction factor acc. to Figure A 2.7-1

α angle between vertical and slope(see also Figures A 2.7-2, A 2.7-3 andA 2.7-4)

degree

β angle between axes of branch andrun pipe

degree

δ5 elongation at fracture %

A 2.7.2 Dimensioning of reinforcements of openings invessels

A 2.7.2.1 Scope

(1) The scope of the design rules given thereinafter corre-spond to the scopes mentioned in Sections A 2.2 to A 2.6 andA 4.6.

(2) The design rules only consider the loadings resultingfrom internal pressure. Additional forces and moments shallbe considered separately.

(3) The angle β between the axes of branch and run pipeshall be equal to or greater than 60°.

A 2.7.2.2 General

(1) Openings shall normally be circular or elliptical. Furtherrequirements will have to be met if the stress index methodin accordance with clauses 8.2.2.1 to 8.2.2.3 is applied. In thiscase the design requirements for the stress index methodaccording to clause 8.2.2 shall be met.

(2) Openings in the basic shell shall be reinforced as fol-lows.

a) by selecting a greater wall thickness for the basic shellthan is required for the unpierced basic shell. This wallthickness may be considered to be contributing to thereinforcement on a length eH measured from the axis of

opening.

b) by nozzles which, on a length eA measured from the

outside surface of the basic shell, have a greater wallthickness than is required for internal pressure loading.The metal available for reinforcement shall be distrib-uted uniformly over the periphery of the nozzle.

c) by combining the measures in a) and b) above.

Regarding a favourable shape not leading to increased loa-dings/stresses subclause c) shall be complied with.

(3) When an opening is to be reinforced the following di-ameter and wall thickness ratios shall be adhered to:

A wall thickness ratio sA/sH up to a maximum of 2 is per-

mitted for dAi not exceeding 50 mm. This also applies to

nozzles with dAi greater than 50 mm if the diameter ratio

dAi/dHi does not exceed 0.2.

For nozzles with a diameter ratio dAi/dHi greater than 0.2

the ratio sA/sH shall basically not exceed 1.3. Higher values

are permitted if

a) the additional nozzle wall thickness exceeding theaforementioned wall thickness ratio is not credited forreinforcement of the opening, but is selected for designreasons, or

b) the nozzle is constructed with a reinforcement zonereduced in length (e.g. nozzles which are conical for rea-sons of improving testing possibilities) in which case thelacking metal area for reinforcement due to the reducedinfluence length must be compensated by adding metalto the reduced influence length.

Nozzles with inside diameters not less than 120 mm shall bedesigned with at least two times the wall thickness of theconnected piping in which case the factor refers to the calcu-lated pipe wall thickness. Referred to the actual wall thick-ness the factor shall be at least 1.5.

(4) Openings need not be provided with reinforcement if

a) a single opening has a diameter equal to or less than

0.2 ⋅ 0 5. ⋅ ⋅d sHm H , or, if there are two or more ope-

nings within any circle of diameter 2.5 ⋅ 0 5. ⋅ ⋅d sHm H ,

but the sum of the diameters of such unreinforced ope-

nings shall not exceed 0.25 ⋅ 0 5. ⋅ ⋅d sHm H , and

b) no two unreinforced openings have their centres closerto each other, measured on the inside wall of the basicshell, than 1.5 times the sum of their diameters, and

c) no unreinforced opening has its centre closer than

2.5 ⋅ 0 5. ⋅ ⋅d sHm H to the edge of any other locally stres-

sed area (structural discontinuity).

Note:See clause 7.7.2.2 for definition of locally stressed area.

(5) Combination of materials

Where nozzle and basic shell are made of materials withdiffering design stress intensities, the stress intensity of thebasic shell material, if less than that of the nozzle, shall gov-ern the calculation of the entire design provided that theductility of the nozzle material is not considerably smallerthan that of the basic shell material.

Where the nozzle material has a lower design stress inten-sity, the reinforcement zones to be located in areas providedby such material shall be multiplied by the ratio of the de-sign stress intensity values of the reinforcement material andthe basic shell material.

Differences up to 4 % between the elongation at fracture ofthe basic shell and nozzle materials are not regarded as

considerable difference in ductility in which case δ5 shall not

be less than 14 %.

Where the materials of the basic shell and the nozzle differin their specific coefficients of thermal expansion, this dif-ference shall not exceed 15% of the coefficient of thermalexpansion of the run pipe metal.

KT

A 3201.2

Factor C of flat circular plates with additional edge moment acting in same directionFigure A 2.6-3:

δ

δ

δ

δ

δ

δ

δ

Dt

= 2.5

1.9

= 3.0

2.0

= 1.5

= 1.25

= 1.0

= 1.75

= 2.0

0.6

0.5

0.8

0.7

C

0.4

1.0

/ dd

0.9

1.61.5 1.81.71.41.1

1.0

1.31.2

KTA 3201.2


A 2.7.2.3.1 Required reinforcement

(1) The total cross-sectional area A of the required rein-forcement of any opening in cylindrical, spherical and coni-cal shells as well as dished heads under internal pressureshall satisfy the following condition:

A ≥ dAe ⋅ sH0 ⋅ F (A 2.7-1)

where the correction factor F applies to rectangular nozzlesand shall have a value of 1 for all planes required for di-mensioning. For cylindrical or conical shells F shall be takenfrom Figure A 2.7-1 for a plane not required for dimension-ing in dependence of its angle to the plane under considera-tion.

(2) Openings in flat circular heads not exceeding one-halfthe head diameter shall have an area of reinforcement of atleast

A ≥ 0.5 ⋅ dAe ⋅ sH0 (A 2.7-2)

40˚ 60˚50˚10˚ 20˚ 30˚

Angle between the plane containing the shellgenerator and the nozzle axis and the planeunder consideration through the nozzle axis

70˚ 80˚ 90˚

1.00

0.55

0.60

0.65

F

0˚

0.50

0.85

0.90

0.95

0.70

0.75

0.80

Figure A 2.7-1: Chart for determining the correction factorF for nozzles normal to cylindrical or coni-cal shells

A 2.7.2.3.2 Effective lengths

(1) The effective length of the basic shell shall be deter-mined as follows:

eH = dAe (A 2.7-3)

or

eH = 0.5 ⋅ dAe + sH + sA (A 2.7-4)

The calculation shall be based on the greater of the twovalues. In addition two thirds of the area of reinforcement

shall be within the length 2 ⋅ ′e H (Figures A 2.7-8 to

A 2.7-10), where ′e H is the greater value of either

( )′ = ⋅ + ⋅ ⋅e d d sH Ae Hm H0 5 0 5. . (A 2.7-5)

or

′eH = 0.5 ⋅ dAe + 2/3 ⋅ (sH + sA) (A 2.7-6)

(2) The effective length for nozzles according to Figures

A 2.7-2, A 2.7-3, A 2.7-5, A 2.7-6 shall be determined as fol-lows:

( )e d s rA Am A= ⋅ ⋅ ⋅ +0 5 0 5 2. . (A 2.7-7)

where

dAm = dAi + sA (A 2.7-8)

In the case of a nozzle with tapered inside diameter accord-ing to Figure A 2.7-6 the effective length shall be obtainedby using dAi and sA values at the nominal outside diameters

of the basic shell.

(3) The effective length for nozzles according to Figures A

2.7-4 and A 2.7-7 shall be determined as follows:

sA = 0.5 ⋅ 0 5, A⋅ ⋅d sAm (A 2.7-9)

where

dAm = dAi + sA (A 2.7-10)

and

sA = sR + 0.667 ⋅ x (A 2.7-11)

In the case of a nozzle with a tapered inside diameter ac-cording to Figure A 2.7-7 the limit of reinforcement areashall be obtained using dAi and sA values at the centre of

gravity of nozzle reinforcement area. These values shall bedetermined, if required, by a trial and error procedure.

A 2.7.2.3.3 Loading scheme for metal areas available forreinforcement

(1) The metal areas A1, A2, A3 available for reinforcement

used to satisfy equation (A 2.7-1) are shown in Figures

A 2.7-8 to A 2.7-11 and shall satisfy the condition A1 + A2 +

A3 equal to or greater than A.

(2) Interaction between nozzle opening and cone to cylin-der transition shall only be taken into account if

1 < 2.5 ⋅ (d / 2) sHm H⋅ (A 2.7-12)

where dHm = dHi + sH (A 2.7-13)

KTA 3201.2

≤

α

αH

m

Ai

3

HH

i

AAe

R

2

1

Am A

= d

45˚

Offset

dd s

s

rr

s

s

r

/2

d

α

=α

Am A

Hm

1

2

R

3

Ae

HH

i

Ai A

d

Offset

r

90˚

= d

/2

s

r

d

s

s

r

d

s

≤

α

α

Hm

3

2

A

1

Hi

H

AiAe R

r

x

= d = s

30˚

r

d

r

d

s

s

Figure A 2.7-2 Figure A 2.7-3 Figure A 2.7-4

2

Am

R

1

AiAe

Aa

A

H

Hm

A

Hi

d

d

d

= d = s

s /2

d

r

s

s

d

r

H

Ae H0

2

1

A

Hm

2

Hi

1

A0

e

Ai A

H

S

A

/2A

A

/2

/2

d

r

r sd

e

e

d s

d s

s

Figure A 2.7-5 Figure A 2.7-6

H0

Ae

e

1

2

1

2

AAi

Hi

H

Hm

A

A0

H

d

/2

d

A

A

s

/2A

/2

r

r

d s

s

e

S

ds

e

′ ′

β

Ae Ai

2

A

1 e

A

2

3

1

R

A0

3

H

H

H

HH Hi

H0

2

/2

bran

ch a

xis

AA

/2

run pipe axis

/2 r

/2

A

A

A ds

e

s

e e

e e

dA /2

/2A

s

= d

s

s

Figure A 2.7-7

Figures A 2.7-2 to A 2.7-7: Allowable nozzle configurations Figure A 2.7-8: Oblique cylindrical branch

KTA 3201.2

′ ′

β

α

Ae Ai

2

3

A

A0

22

1

R

H0

H1

H

H

1

3

Hi

H

H

A

A

/2

run pipe axis

r

/2br

anch

axis

/2

/2

AA

/2 ds

e

s

e e

e e

d

A

A

A

/2

s

= d/2

s

Figure A 2.7-9: Oblique conical branch

α

′′

ϕ ≤

A0

2

3

Ae Ai

R

2

3

Hi

e

1

12

H

H

H0

A

H

H

H

d

e

/2

e

A

e

/2

45˚

e

A

run pipe axis

bran

ch a

xis

A

s

s

A /2

e

d

s

= d

/2/2

r

A

A /2

s

A

Figure A 2.7-10: Conical shell with reinforced opening

1

Hm

Ae

Hi

H0H

2

2

e

1

A0

AH

AAi

A

/2A

r

r

sd

/2

A

de

s

sd

S

/2

e

d

s

Figure A 2.7-11: Conical branch in spherical shell

A 2.7.3 Alternative dimensioning of reinforcements ofopenings

A 2.7.3.1 Cylindrical shells

Where the alternative stress index method as per clause8.2.2.2 is used, the following alternative rule applies to thecalculation of metal areas for reinforcement as per clauseA 2.7.2:

d d sAi Hi H/ /⋅ 0 2 reinforcement

< 0.2 0

from 0.2 to 0.4 4 052

1 810

0./

.⋅⋅

−

⋅ ⋅d

d sd sAi

Hi HAi H

> 0.4 0.75 ⋅ dAi ⋅ sH0

Figure A 2.7-12 applies to the effective reinforcement area.

lc (see Figure A 7.2-12) shall be determined by means of

equation (A 2.7-14):

lc = 0.75 ⋅ (sH0/dHi)2/3 ⋅ dHi (A 2.7-14)

ln (see Figure A 7.2-12) shall be determined by means of

equation (A 2.7-15):

ln = (sH0/dAi)2/3 ⋅ (dAi/dHi + 0.5) ⋅ dHi (A 2.7-15)

The design values shall be taken from clause A 2.7.1.

A 2.7.3.2 Dished heads

Where the alternative stress index method as per clause8.2.2.2 is used, the following alternative rule applies to thecalculation of metal areas for reinforcement as per clauseA 2.7.2:

KTA 3201.2

d d sAi Hi H/ /⋅ 0 2 reinforcement

< 0.2 0

from 0.2 to 0.4 5 42

2 410

0./

.⋅⋅

−

⋅ ⋅d

d sd sAi

Hi HAi H

> 0.4dAi ⋅ sH0 ⋅ cos µ

µ = sin-1 ( )d dAi Hi/

Figure A 2.7-12 applies to the effective reinforcement area.

The design values shall be taken from clause A 2.7.1.H0

c

Hi

R

A

Hi

Ai

A

H0

H

R

H

Ai

n

c or

s

Reinforcement of opening in the plane

cylindrical shell in any plane of dishedhead containing the nozzle axis

normal to the longitudinal axis of

d

Reinforcement of opening atintersection of cylindrical shell

d

ds

s

s

s

s

s

s

d

Figure A 2.7-12: Effective area of reinforcement

A 2.8 Bolted joints



a, b, c geometric values for bolt and nutthread in accordance with FiguresA 2.8-1 and A 2.8-2

mm

bD gasket seating width mm

c design allowance mm

d bolt diameter = thread outside di-ameter

mm

d2 pitch diameter of thread mm

di pipe (shell) inside diameter mm

diL diameter of internal bore of bolt mm

dD mean gasket diameter mm

dD1, dD2 mean gasket diameter formetal-O-ring gaskets

mm

dK root diameter of thread mm

dS shank diameter of reduced shankbolt

mm


k k1 11∗ ∗, ,

k12∗

gasket factors for metal-O-ring gas-kets

N/mm

l effective thread engagement lengthor nut thickness

mm

lB length of fabricated tapered nutthread end

mm

leff (Figure A 2.8-3), compare "l" mm

lges total engagement length or nutthickness

mm

n number of bolt holes A0 cross-sectional area of shank mm2

AS section under stress mm2

ASG Bolzen shear area of bolt thread mm2

ASG Bi plane of bolt shear area sections mm2

ASG Mutter shear area of nut thread mm2

ASG Mi plane of nut shear area sections mm2

ASG

Sackloch

shear area of blind hole mm2

C1, C2,

C3

strength reduction factors

D outside diameter of nut/blind holethread

mm

D1 root diameter of nut/blind holethread

mm

D2 pitch diameter of nut/blind holethread

mm

Dc inside diameter of nut bearing sur-face, diameter of chamfer

mm

Dm mean diameter of tapered nutthread end

mm

KTA 3201.2


Dmax maximum diameter of tapered nutthread end

mm

D1 max (see Figure A 2.8-2) mm

FDB required compression load on gasketfor the design condition

N

′FDB required compression load on gasketfor the test condition

N

FDVU gasket seating load N

FF difference between total hydrostaticend force and the hydrostatic endforce on area inside flange for designcondition

N

′FF difference between total hydrostaticend force and the hydrostatic endforce on area inside flange for testcondition

N

Fmax Bolzen ultimate breaking strength of freeloaded bolt thread or shank

N

Fmax G Bolzen

ultimate breaking strength ofengaged bolt thread

N

Fmax G Mutter

ultimate breaking strength of en-gaged nut thread

N

FR total hydrostatic end force N

FRM additional pipe force resulting frompipe moment

N

′FRM additional pipe force resulting frompipe moment for test condition

N

FRP hydrostatic end force due to internalpressure

N

FRZ additional pipe longitudinal force N

′FRZ additional pipe longitudinal forcefor test condition

N

FS operating bolt load (general) N

′FS operating bolt load for test condition N

FSO bolt load for gasket seating condi-tion

N

FSOU bolt load for gasket seating condi-tion (lower limit)

N

FSB bolt load for design condition N

FSBU bolt load for design condition (lowerlimit)

N

FSP bolt load for test condition N

FZ additional axial force for transfer oftransverse forces and torsional mo-ments due to friction at a certainvalue, for operating condition

N

′FZ axial tensile force for transfer oftransverse forces and torsional mo-ments due to friction at a certainvalue, for test condition

N

MB bending moment on pipe N⋅mm

Mt torsional moment on pipe N⋅mm

P thread pitch mm


Q transverse force on pipe N

RmB tensile strength of bolt material N/mm2

RmM tensile strength of nut material N/mm2

RmS tensile strength of blind hole mate-rial

N/mm2

Rp0.2T 0.2 % proof stress at operating ortest temperature

N/mm2

Rp0.2RT 0.2 % proof stress at room tempera-ture

N/mm2

RS strength ratio

SD safety factor

SW width across flats mm

α pitch angle degree

µ friction factor

σB gasket contact surface load for op-erating condition

N/mm2

σV gasket contact surface load for gas-ket seating condition

N/mm2

σBU lower limit value for σB N/mm2

σBO upper limit value for σB N/mm2

σVU lower limit value for σV N/mm2

σVO upper limit value for σV N/mm2

σzul allowable stress as perTable A 2.8-2

N/mm2

A 2.8.2 Scope

The calculation rules hereinafter apply to bolts with circularand equi-distant pitch as friction-type connecting elementsof pressure-retaining parts. These calculation rules primarilyconsider static tensile loading. The rules may also apply toflanged joints under controlled compression in which casethe design diameters and friction factors to be used in thecalculation shall be adapted accordingly. Shear and bendingstresses in the bolts resulting e.g. from deflections of flangesand covers, thermal effects (e.g. local or time-dependenttemperature gradients, different coefficients of thermalexpansion) are not covered by this section.

A 2.8.3 General

Such bolts are deemed to be reduced-shank bolts the shankdiameter of which does not exceed 0.9 times the root diame-ter and the shank length of which is at least two times, butshould be four times the shank diameter, or such bolts thedimensions of which correspond to DIN 2510-1. Shank boltswith extended shank length and a shank diameter equal toor less than the root diameter may be used as reduced-shankbolts if their yielding regarding bolt elongation and elasticbehaviour regarding bending under the given boundaryconditions corresponds to the elastic behaviour of a re-duced-shank bolt as defined above with same root diameterand minimum shaft length as specified above.

KTA 3201.2

For bolted joints to DIN 267-11 and DIN 267-13, DIN 2510-1,DIN ISO 3506 and DIN ISO 20898-1 a recalculation of thethread loading can be waived if the given nut thickness orthread engagement lengths are adhered to.

Otherwise, the calculation shall be made in accordance withA 2.8.4.

A 2.8.4 Calculation

A 2.8.4.1 Bolt load

The bolt load (FS) shall be determined for the design condi-

tion (FSB), for the test condition (FSP) and the gasket seating

condition (FS0).

a) Design condition

FSB = FR + FDB + FF (A 2.8-1)

The hydrostatic end force FR is the force transmitted

from the pipe or shell on the flange. This force is ob-tained for unpierced pipes or shells from the followingequation:

FR = FRP + FRZ + FRM (A 2.8-2)

where

Fd p

RPi=

⋅ ⋅2

4

π(A 2.8-3)

The additional pipe forces FRZ and FRM consider pipe

longitudinal forces FRZ and pipe bending moments MB,

where

FM

dRM

B

D

= ⋅4(A 2.8-4)

In the calculation of bolt stresses the bolt circle diameterdt may be used instead of the mean gasket diameter dD.

If required FRZ and MB shall be taken from the static or

dynamic piping system analysis.

FRZ and MB are equal to zero for flanged joints in vessels

and pipings to which no piping or only pipings withoutadditional longitudinal force FRZ and without additional

pipe bending moment MB are connected.

The required compression load on gasket for the designcondition (FDB) is obtained for gaskets, except for metal-

O-ring gaskets, from:

FDB = π ⋅ dD ⋅ bD ⋅ m ⋅ p ⋅ SD (A 2.8-5)

For a simple metal-O-ring-gasket from:

FDB = π ⋅ dD ⋅ k1∗ ⋅ SD (A 2.8-6)

and for a double metal-O-ring gasket from:

FDB = π ⋅ (DD1 ⋅ k11∗ + DD2 ⋅ k12

∗ ) ⋅ SD (A 2.8-7)

(for SD a value of at least 1.2 shall be taken).

For simple metal-O-ring gaskets the gasket factor k1∗

and for double metal-O-ring gasket the gasket factors

k11∗ and k12

∗ shall be taken from the manufacturer's

documents.

The required compression load on the gasket for the

design condition FDB is required to ensure tight joint

during operation. The value for m shall be taken from

Section A 2.10. If no m value is indicated it shall be taken

from the manufacturer's documents or be determined by

experimental analysis.

The allowable (maximum bearable) compression load on

the gasket for the design condition shall be

FDBO = π ⋅ dD ⋅ bD ⋅ σBO (A 2.8-8)

The difference between total hydrostatic end force andthe hydrostatic end force on area inside flange FF shall be

( )F d d pF D i= ⋅ − ⋅π4

2 2 (A 2.8-9)

This force FF is caused by the internal pressure p and is

applied on the annular area inside the flange boundedby the gasket diameter dD and the inside diameter di.

The mean gasket diameter shall be taken as gasket di-ameter dD. For weld lip seals the mean diameter of the

weld shall be taken. For concentric double gaskets themean diameter of the outer gasket shall be taken.

If required, an additional force FZ shall be applied on the

gasket to make possible transfer of a transverse force Q(normal to pipe axis) and a torsional moment Mt due to

friction at a certain value in the flanged joint.

FZ shall be

aa) for laterally displaceable flanges where transverseforces can only be transferred due to friction at acertain value

FQ M

dF

M

dZ

t

DDB

B

D

= + ⋅⋅

− − ⋅

max ; 02 2

µ µ (A 2.8-10)

ab) for laterally non-displaceable flanges where trans-verse forces can be transferred due to infinite friction

FM

dF

M

d

M

dZ

t

DDB

B

D

B

t

= ⋅⋅

− − ⋅ ⋅

max ; max ; 0

2 2 4

µ

(A 2.8-11)

Where FZ > 0 is obtained from equation (A 2.8-10) or

(A 2.8-11), this force shall be added to the required com-pression load on the gasket obtained from equation(A 2.8-5).

Note:

Metal-O-ring gaskets are not suited to withstand transverse forcesand torsional moments due to friction at a certain value.

Where no other test results have been obtained the fric-tion factors shall be taken as follows:

µ = 0.1 for graphite-reinforced gaskets

µ = 0.15 for metallic flat contact faces

µ = 0.25 for bonded asbestos gaskets.

b) Test condition

Fp

pF

F F

SF F F FSP RP

DB Z

DF RZ RM Z=

′⋅ + − +

+ ′ + ′ + ′

(A 2.8-12)

The values ′FRZ and ′FRM correspond to the additional

pipe forces at test condition. ′FZ shall be determined by

means of equations (A 2.8-10) and (A 2.9-11) in conside-

KTA 3201.2

ration of the test condition. For SD the same value as in

equation (A 2.8-7) shall be taken.

c) Gasket seating condition

The bolts shall be so tightened that the required gasketseating is obtained, pipe forces FR if any, are absorbed

and the bolted joint remains leak tight in the test andoperating conditions.

To satisfy this 3 conditions the following must be met

FS0U ≥ FDVU (A.2.8-13)

but at least

for the test condition

FS0U = FSP (A 2.8-14)

and for the operating condition

FS0U = 1.1 ⋅ FSBU (A 2.8-15)

Here, FDVU is the gasket seating load required to obtain

sufficient contact between gasket and flange facing.

FDVU = dD ⋅ π ⋅ bD ⋅ σVU (A 2.8-16)

The gasket load σVU depends on the type and shape of

the gasket and the fluid filled, and shall be taken fromSection 2.10.

At bolting-up condition the gasket shall only be loadedwith

FDVO = π ⋅ dD ⋅ bD ⋅ σVO (A 2.8-17)

d) Pre-stressing of bolts

The initial bolt prestress shall be applied in a controlledmanner. Depending on the bolt tightening procedurethis control e.g. applies to the bolting torque, the boltelongation or temperature difference between bolt andflange. Here - in dependence of the tightening procedure- the following influence factors shall be taken into ac-count, e.g. friction factor, surface finish, greased condi-tion, gasket seating.

Where the bolts are tightened by means of torquewrench, the bolting torque shall be determined by a suit-able calculation or experimental analysis, e.g. VDI 2230,Sheet 1.

A 2.8.4.2 Bolt diameter

(1) The required root diameter of thread dK of a full-shank

bolt or the shank diameter dS of a reduced shank bolt (with

or without internal bore) in a bolted connection with anumber n of bolts shall be calculated by means of the follow-ing equation:

dF

nd ck

S

zuliL or ds = ⋅

⋅ ⋅+ +4 2

π σ(A 2.8-18)

with σzul according to Table A 2.8-2.

Here, the following load cases shall be considered:

a) the load cases of loading levels 0, A, B, C, D according tolines 1 and 2 of Table A 2.8-2,

b) the load case of loading level P according to line 3 ofTable A 2.8-2.

c) the bolting-up conditions according to line 4 of TableA 2.8-2 (To consider the scattered range of forces applieddepending on the tightening procedure, the respectiverequirements of VDI 2230, Sheet 1 shall be taken into ac-count. If required, the upper or lower limit of the initialbolt stress shall be used in the calculation).

(2) Upon recalculation of the forces and deformations in aflanged joint in accordance with clause A 2.9.5, the strengthcalculation for bolts and gaskets for the load cases accordingto lines 4 and 5 of Table A 2.8-2 shall be repeated with theforces obtained from the recalculation.

(3) A design allowance c = 0 mm shall be used for re-duced-shank bolts, and for full-shank bolts the followingapplies:

a) for the load cases of loading level 0 according to lines 1and 2 of Table A 2.8-2:

c = 3 mm, if 4

20⋅

⋅ ⋅≤

F

nS

zulπ σ mm (A 2.8-19)

or

c = 1 mm, if 4

50⋅

⋅ ⋅≥

F

nS

zulπ σ mm (A 2.8-20)

Intermediate values shall be subject to straight interpo-lation with respect to

c

F

nS

zul=− ⋅

⋅ ⋅65

4

15

π σ(A 2.8-21)

b) for the load cases of the other loading levels c = 0 mmshall be taken.

A 2.8.4.3 Required thread engagement length

A 2.8.4.3.1 General

(1) When determining the required thread engagementlength in a cylindrical nut or blind hole it shall normally beassumed that the limit load based on the threadstrippingresistance of both the bolt thread and female thread isgreater than the load-bearing capacity based on the tensilestrength of the free loaded portion of the thread or of theshank in the case of reduced-shank bolts. The load-bearingcapacity of the various sections is calculated as follows:

Free loaded thread:

Fmax Bolzen = Rm Bolzen ⋅ AS (A 2.8-22)

Reduced shank:

Fmax Bolzen = Rm Bolzen ⋅ A0 (A 2.8-23)

Engaged bolt thread:

Fmax G Bolzen = Rm Bolzen ⋅ ASG Bolzen ⋅ C1 ⋅ C2 ⋅ 0.6 (A 2.8-24)

Engaged nut thread:

Fmax G Mutter = Rm Mutter ⋅ ASG Mutter ⋅ C1 ⋅ C3 ⋅ 0.6 (A 2.8-25)

(2) The calculation of the thread engagement length shallbe made for the case with the smallest overlap of flanks inaccordance with the clauses hereinafter. To this end, thesmallest bolt sizes and greatest nut sizes (thread tolerances)shall be used in the calculation of the effective cross-sec-tions.

KTA 3201.2

(3) At a given thread engagement length or nut thicknessit shall be proved that the load-bearing capacity of the freeloaded thread portion or reduced shank is smaller than thatof the number of engaging bolt or nut threads.

(4) Standard bolts are exempted from the calculation ofthe thread engagement length in accordance with the fol-lowing clauses. The calculation of the engagement length inthe clauses hereinafter including clause A 2.8.4.3.6 does notapply to bolts with saw-tooth or tapered threads.

(5) Where, in representative tests, thread engagementlengths smaller than that calculated in the following clausesare obtained, these lengths may be used.

A 2.8.4.3.2 Bolted joints with blind hole or cylindrical nutwithout chamfered inside

The required engagement length l for bolted joints withblind hole or cylindrical nut without consideration of aconical chamfer shall be the maximum value obtained fromthe equations given hereinafter. The additional considera-tion of the chamfered thread is made in clause A 2.8.4.3.5:

a) The requirement for threadstripping resistance of thebolt thread leads to the condition (see Figure A 2.8-1):

( )l

A P

C C DP

d D

S≥ ⋅

⋅ ⋅ ⋅ ⋅ ⋅ + − ⋅

0 552 2

1 2 1 2 1. tanπ α(A 2.8-26)

BoltNut

2 1

SGMi SGBi

2

1

2

2

b =- D d

a =d 1

2- D

321

3

Plane of nut shear

bb

P/ 2

D

d

d

D

P

Aarea sectionsarea sections

A

a/ 2

Plane of bolt shear

a

Figure A 2.8-1: Representation of design values for boltand female thread

In the case of reduced-shank bolts the cross-sectional area ofshank A0 may be inserted instead of the section under stress

AS.

For tapered threads with a thread angle α = 60°

tanα2

1

33

1

3= ⋅ =

b) The requirement for threadstripping resistance of the nutor blind hole thread leads to the condition (see Figure A2.8-1)

( )l

R A P

R C C dP

d D

mB S

mM

≥ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − ⋅

0 552 2

1 3 2. tanπ α

(A 2.8-27)

In the case of a blind hole the tensile strength RmS shall

be inserted in lieu of RmM.

c) The condition given hereinafter is based on currentpractice to read

l ≥ 0.8 ⋅ d (A 2.8-28)

The values C1, C2 and C3 shall be determined in accordance

with A 2.8.4.3.4.

A 2.8.4.3.3 Bolted joint with tapered thread area withoutchamfer

The required engagement length l for bolted joints withtapered thread area of nut without consideration of a ta-pered chamfer shall be determined as the maximum valueobtained from the equations hereinafter. The additionalconsideration of the thread chamfer is made in clauseA 2.8.4.3.5.

a) The requirement for threadstripping resistance of thebolt thread leads to the condition (see Figures A 2.8-2and A 2.8-3):

( )

( )l l

A P C C l DP

d D

C C DP

d DB

S B m m

≥ +⋅ − ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + − ⋅

⋅ ⋅ ⋅ ⋅ ⋅ + − ⋅

0 62 2

0 552 2

1 2 2

1 3 1 2 1

. tan

. tan

π α

π α

(A 2.8-29)

b) The requirement for threadstripping resistance of the nutthread leads to the required engagement length l (seeFigures A 2.8-2 and A 2.8-3) according to equation(A 2.8-27) from clause A 2.8.4.3.2 b).

c) According to current practice the engagement length lshall satisfy equation (A 2.8-25).

The values C1, C2 and C3 shall be determined in accordance

with clause A 2.8.4.3.4.

KTA 3201.2

Nut Bolt

Detail X

≈

≈

SGBi

2

1

22 2

m

SGMi

2

1

2

1

1max

m

1

D

b

D

D

D

12- D

1.03

1.015

3

P/ 2

b

c =d

d

d

/ 2P

P

a

area sectionsPlane of bolt shear

aD

D

d

d

/ 2c

c

A

33

1 1b =

- D2

Plane of nut sheararea sectionsA

a = 2d - D

Figure A 2.8-2: Representation of design values for boltand female thread (tapered femalethread)

X

Nut

≈

eff

ges

B

ges

m

1

max

0.4

D

D

D

Figure A 2.8-3: Representation of design values for thenut (with tapered portion)

A 2.8.4.3.4 Factors C1, C2, C3

(1) The factor C1 shall be determined by means of the

following equation

CSW

d

SW

d1

2

3 8 2 61= −

+ ⋅

−

. . (A 2.8-30)

for 1 4 1 9. .≤ ≤SW

d

or in accordance with Figure A 2.8-4.

In the case of serrated nuts the width across flats SW shallbe replaced by an equivalent value.

1

1.1

1.0

0.9

Red

uctio

n fa

ctor

Referred width across flats SW/d

C1.5 1.7

0.7

1.4 1.9

0.8

1.6 1.8

Figure A 2.8-4: Factor C1 for the reduction of threadstrip-

ping resistance of bolt and nut thread dueto nut extension

(2) The factor C2 can be determined by means of equation

(A 2.8-35) or according to Figure A 2.8-5.

The required values are computed as follows:

Strength ratio RS

( )( )R

R A

R AS

m SG Mutter Sackloch

m SG Bolzen

=⋅

⋅/ (A 2.8-31)

Note:

When determining the strength ratio the quotient of the shear areasASG Mutter/Sackloch and ASG Bolzen shall be formed so that the en-

gagement length can be obtained.

The shear area ASG of the nut or blind hole thread is

( )Al

Pd

Pd DSG Mutter/Sackloch = ⋅ ⋅ ⋅ + − ⋅

π α2 2

2 tan (A 2.8-32)

The size of the shear area ASG Bolzen depends on whether a

bolted joint with blind hole or nut with straight thread or abolted joint with a nut having a tapered threaded portion isconcerned.

Therefore, the equation of the shear area ASG Bolzen for

bolted joints with blind hole or straight nut is:

( )Al

PD

Pd DSG Bolzen = ⋅ ⋅ ⋅ + − ⋅

π α1 2 1

2 2tan (A 2.8-33)

The size of the shear area ASG Bolzen of a bolt for bolted joints

with a nut having a tapered threaded portion as shown inFigure A 2.8-3 and in consideration of the relationship lB =

0.4 ⋅ l shall be:

KTA 3201.2

( )Al

PD

Pd DSG Bolzen = ⋅ ⋅ ⋅ ⋅ + − ⋅

+0 6

2 21 2 1

.tanπ α

( ) +l

PD

Pd DB

m m⋅ ⋅ ⋅ + − ⋅

π α2 2

2 tan (A 2.8-34)

Dm is obtained from Dm = 1.015 ⋅ D1 (A 2.8-35)

C2 is obtained for 1 < RS ≤ 2.2 from equation

C S S S S22 3 45 594 13 682 14 107 6 057 0 9353= − + − +. . . . . R R R R

(A 2.8-36)

and for RS ≤ 1 to C2 = 0.897

C2 may also be determined by means of Figure A 2.8-5.

(3) The factor C3 is obtained for 0.4 ≤ RS < 1 from the

equation

C S S S32 30 728 1 769 2 896 1 296= + − +. . . . R R R (A 2.8-37)

and for RS ≥ 1 to C3 = 0.897

C3 may also be determined by means of Figure A 2.8-5.

Stripping ofbolt threadnut thread

Stripping of

s

2

3

2

3an

d CC

R

C

1.61.2 2.0

0.8

0.4 0.8

1.2

CR

educ

tion

fact

ors

0.9

1.1

1.0

Figure A 2.8-5: Factor for reduction of threadstrippingresistance of bolt and nut thread due toplastic deformation of thread

A 2.8.4.3.5 Calculation of the total engagement length inconsideration of the thread chamfer

Taking the thread chamfer into account the required totalengagement length for blind holes (see Figure A 2.8-6) isobtained from:

lges = l + (Dc - D1) ⋅ 0.3 (A 2.8-38)

and for a nut chamfered on both sides

lges = l + (Dc - D1) ⋅ 0.6 (A 2.8-39)

The diameters of the chamfered portion Dc shall be taken

from Table A 2.8-1.

Thread diameterD, mm

Diameter of chamfered portionDc, mm

D < 5 1.15 ⋅ D

5 ≤ D ≤ 8 1.12 ⋅ D

D > 8 1.08 ⋅ D

Table A 2.8-1: Diameter of chamfered portion Dc

X

Detail X

c 1

on one sideDepth of chamfer

DD

45˚

Figure A 2.8-6: Fabricated chamfer of thread in the area ofthe nut bearing surface

A 2.8.4.3.6 Required engagement length for valve bodies

Alternately to the procedure given in clause A 2.8.4.3 theengagement length may be checked as follows for valvebodies. Proof is deemed to be furnished if the followingconditions are satisfied:

a) l ≥ 0.8 ⋅ d (A 2.8-40)

and

b) lF

n d Sm

≥⋅

⋅ ⋅ ⋅2

2

max

π(A 2.8-41)

where l engagement length

n number of bolts

d, d2 in accordance with Figure A 2.8-7

σzul allowable stress of valve body material for

the related loading level

Fmax FS or FS0 (most unfavourable loading condi-

tion according to Table A 2.8-2)

2

k

P

60˚

60˚

d

d

d

Figure A 2.8-7: Thread dimensions

KTA 3201.2

Loading level

0 A, B P C, D

1Average tensile stress due to internal pressureonlyFS = FRP + FF

1

30 2Rp T.

Average tensile stress due to internal pressure,required gasket load reaction and external loads D

1

1 50 2

..Rp T

1

1 50 2

..Rp T

1

1 10 2

..Rp T

FS = FRP + FF + FDB + FRZ + FRMV

1

1 80 2

..Rp T

1

1 80 2

..Rp T

1

1 30 2

..Rp T

Average tensile stress at test condition

F F F F F FSP = RP + F + DB + RZ + RM′ ′ ′ ′ ′ D1

1 10 2

..Rp T ′

V1

1 30 2

..Rp T′

Average tensile stress in the as-installed con-

dition 4) D1

1 10 2

..Rp RT

1

1 10 2

..Rp T

FS0 V1

1 30 2

..Rp RT

1

1 30 2

..Rp T

5

Average tensile stress due to internal pressure,external loads, residual gasket load, and differ-

ential thermal expansion 5), if any, taking thebolts stress and residual gasket load at the re-spective pressure load condition into accountFS = FRP + FF + FDB + FRZ + FRM

1

1 10 2

..Rp T

1) See clause A 2.8.1 for definition of notations used.2) Where the design provides reduced-shank bolts or bolts with waisted shank as per clause A 2.8.3 shall be used.3) Type of bolts D = reduced-shank bolts

V = full shank bolts4) The differing application of forces on the bolts depending on torque moment and friction shall be conservatively considered in

strength verifications.5) Consideration of differential thermal expansion at a design temperature > 120 °C. This temperature limit does not apply to combina-

tions of austenitic and ferritic materials for flange and bolts.

Table A 2.8-2: Allowable stresses σzul for bolts

A 2.9 Flanges



a moment arm, general mm

a1 distance between bolt hole centre tointersection C-C

mm

aD distance between bolt hole centre topoint of application of compressionload on gasket FD

mm

aF distance between bolt hole centreand point of application of force FF

mm

aR distance between bolt hole centreand point of application of total hy-drostatic end force FR

mm

b radial width of flange ring mm

d1 loose flange ring I. D. mm

d2 loose flange ring O. D. mm

dD mean diameter or diameter of gasketcontact face

mm


dD1, dD2 mean diameter for double O-ringgasket

mm

dF flange or stub-end outside diameter mm

dL bolt hole diameter mm

′dL bolt circle design diameter mm

di inside diameter of pipe, shell, orflange ring

mm


dt∗ fictitious bearing surface diameter of

loose flangesmm

e1, e2 distance to centroid of flange mm

f height of flange facing mm

h flange thickness mm

hA height of tapered hub mm

hF effective flange thickness mm

hL thickness of loose flange ring mm

hS flange thickness required to with-stand shear stress

mm

Type of

bolt 2)3)Bolt loading 1)Ser.

no.

2

3

4

KTA 3201.2


n number of bolt holes r, r1 transition radius, see cl. 5.2.4.1 (3) mm

s1 required pipe or shell wall thicknessfor longitudinal force

mm

sF thickness of hub at transition toflange

mm

sR pipe or shell wall thickness mm

sx wall thickness at section X-X mm

t bolt pitch mm

A cross-sectional area mm2

A1, A2 partial cross-sectional areas accord-ing to Figure A 2.9-1

mm2

CB spring stiffness of blank N/mm

CD spring stiffness of gasket N/mm

CM spring stiffness of flange N/mm

CS spring stiffness of bolts N/mm


FDB compression load on gasket for op-erating condition

N

FF difference between total hydrostaticend force and the hydrostatic endforce on area inside flange

N

Fi hydrostatic end force N

FR total hydrostatic end force N

FRP hydrostatic end force due to internalpressure

N

FS bolt load N

FSO bolt load for gasket seating condi-tion

N

FSB operating bolt load N

K, L factors SP1,

SP2

centroids of partial cross-sectionalarea, A1 = A2

W flange section modulus mm3

WA flange section modulus for sectionA-A

mm3

WB flange section modulus for sectionB-B

mm3

Werf required flange section modulus mm3

Wvorh available flange section modulus mm3

Wx flange section modulus for sectionX-X

mm3

A 2.9.2 Scope

(1) The calculation hereinafter applies to the strengthcalculation of steel flanges which as friction-type joints aresubject to internal pressure with the gaskets not being undercontrolled compression (flange without controlled contactland). It may also apply to flanged joints with gaskets undercontrolled compression in which case the design diametersand friction factors to be used in the calculation shall beadapted accordingly. The flanges hereinafter comprise

welding-neck flanges, welding stubs, welded flanges andstubs as well as lap-joint flanges and cover flanges.

(2) Flanges designed in accordance with the equationshereinafter meet the strength requirements. The verificationby calculation of the strength and deformation conditions toensure the tightness of the joint shall be made in accordancewith clause A 2.9.5.

A 2.9.3 Construction and welding

(1) Vessel flanges may be forged or rolled without seam.

(2) Welding and heat treatment, if required, shall be basedon the component specifications.

A 2.9.4 Calculation

A 2.9.4.1 General

(1) The strength calculation shall always consider theinteracting parts of a bolted flanged joint (flanges, bolts andgaskets). The flanged joint shall be so dimensioned that theforces during assembly (gasket seating condition), pressuretesting, operation and start-up and shutdown operationsand incidents, if any, can be withstood.

Where the test pressure pzul operat

′ ⋅ > p zul test condition

ing condition

σσ

the calculation shall also be made for this load case.

(2) The flanges shall be calculated using the equationsgiven in the paragraphs hereinafter. The effects of externalforces and moments, if any, shall be considered and verifiedseparately.

(3) The flange thickness hF or hL on which the calculation

is based shall be provided on the fabricated component.Grooves for normal tongue or groove or ring joint facingsneed not be considered.

(4) The required flange section modulus Werf obtained

from equations (A 2.9-1) to (A 2.9-3) and (A 2.9-4) shall gov-ern the flange design.

(5) For the determination of the required section modulusfor the operating condition of flanges as per clauses A 2.9.4.2and A 2.9.4.3 in Sections A-A and B-B and for flanges as perclause A 2.9.4.4 in section A-A the following applies

WF a F a F a

erfDB D R R F F

zul

= ⋅ + ⋅ + ⋅σ

(A 2.9-1)

For the mentioned flanges in section C-C the following ap-plies

WF a

erfSB

zul

=⋅ 1

σ(A 2.9-2)

For the flanges as per clause A 2.9.4.5 the following applies.

WF a

erfSB D

zul

=⋅

σ(A 2.9-3)

KTA 3201.2

For the gasket seating condition the following applies toflanges as per clauses A 2.9.4.2 to A 2.9.4.5 irrespective ofthe sections

WF a

erfS D

zul

=⋅0

σ(A 2.9-4)

where σzul allowable stress as per Table A 2.9-1.

The equations (A 2.9-1) to (A 2.9-3) shall be applied accord-ingly for the test condition.

The forces F shall be determined in accordance with SectionA 2.8.

The moment arms (for gaskets in flange rings without con-trolled contact land) shall be:

ad d

Dt D=

−2

(A 2.9-5)

ad d s

Rt i R=

− −2

(A 2.9-6)

ad d d

Ft D i=

⋅ − −2

4(A 2.9-7)

For stubs dt may be inserted as bolt circle diameter dt∗ (see

Figure A 2.9-3 and A 2.9-5).

For lap-joint flanges the following applies:

a ad d

Dt t= = − ∗

2(A 2.9-8)

(6) The flange section modulus shall meet the generalcondition for any arbitrary section X-X (Figure A 2.9-1).

( ) ( ) ( )W A e e d s s sx i x x= ⋅ ⋅ ⋅ + + ⋅ + ⋅ −

21

81 1 2

21

2π (A 2.9-9)

Here, s1 is the wall thickness required due to the longitudi-

nal forces in the flange hub, and is calculated by means ofthe following equation:

( )sF

d s SR

i R m1 =

⋅ + ⋅π(A 2.9-10)

With e1 and e2 the centroids of the partial cross-sectional

areas A1 = A2 (shown in Figure A 2.9-1 as differing hatched

areas) adjacent to the neutral line 0-0 are meant, with thisneutral line being applicable to the fully plastic conditionassumed. The weakening of the flange by the bolt holes shallbe considered in the calculation by means of the design

diameter ′dL in the following equation:

For flanges with di ≥ 500 mm

′dL = dL/2 (A 2.9-11)

and

for flanges with di < 500 mm

′dL = dL ⋅ (1 - di/1000) (A 2.9-12)

21e

e

1

2

1

x

2

R

1

i

SP

s

SPa

C

0

AA

sd

0

X

A

A

C

X

B B

Figure A 2.9-1: Flange cross-section

A 2.9.4.2 Welding-neck flanges with gasket inside boltcircle and tapered hub according to Fig. A 2.9-2

The flange shall be checked with regard to the sections A-A,B-B and C-C where the smallest flange section modulusshall govern the strength behaviour.

D

F

L

D

R

F

F D

F

S

R

t

R

A

i

1

F hh

a

d

F

fh

d

a

a

sd

d

F

s

r

dF F

Figure A 2.9-2: Welding-neck flange with tapered hub

The flange section modulus available in section A-A is ob-tained from:

( ) ( ) ( )[ ]W d d d h d s s s WA F i L F i F F erf= ⋅ − − ⋅ ′ ⋅ + + ⋅ − ≥π4

2 2 21

2

(A 2.9-13)

Equation (A 2.9-13) may also be used for the determinationof hF.

The flange section modulus available in section B-B is ob-tained from:

( ) ( ) ( )

( )W d d d e e e d s

s s W

B F i L i R

R erf

= − − ⋅ ′ ⋅ + + + ⋅

⋅ −

≥

π 2 21

41 1 2

21

2 (A 2.9 - 14)

KTA 3201.2

The centroids e1 and e2 for flanges with tapered hub are:

( )e h

h s s

d d dF

A F R

F i L1

1

4 2= ⋅ +

⋅ +− − ⋅ ′

(A 2.9-15)

eK

L2 = (A 2.9-16)

where:

( ) ( )K d d d h eF i L F= − − ⋅ ′ ⋅ − ⋅ +0 5 2 2 12

.

( ) ( ) ( )h h e s s

hs sA F F R

AF R⋅ − ⋅ ⋅ + + ⋅ + ⋅2

321

2

(A 2.9-17)

L = (dF - di - 2 ⋅ ′dL ) (hF - 2 ⋅ e1) + hA ⋅ (sF + sR) (A 2.9-18)

The flange thickness hS required to absorb the shear stress is

obtained as follows:

for the gasket seating condition

( )hF

d sS

S

i F zul0

02

2=

⋅⋅ + ⋅ ⋅π σ

(A 2.9-19)

for the operating condition

( )hF

d sSB

SB

i F zul

=⋅

⋅ + ⋅ ⋅2

2π σ(A 2.9-20)

where σzul allowable stress as per Table 2.9-1.

The flange section modulus in section C-C is obtained from:

( ) ( )[ ]W h d d h d sC F F L S i F= − ⋅ ′ − + ⋅π4

2 22 2 (A 2.9-21)

In this case, the external moment shall be

MC = FS ⋅ a1 (A 2.9-22)

A 2.9.4.3 Welding stubs with tapered hub according toFigure A 2.9-3

The calculation shall be made in accordance with clause

A 2.9.4.2 with ′dL = 0.

*

FDD

D

S

R

R

F

t

R

F

F

i

F

1

Ah

=

a

s

F

d

=

h

d

Fd

a

a

s

r

F

F

d

Figure A 2.9-3: Welding stub with tapered hub

A 2.9.4.4 Flanges and stubs with gasket inside bolt circleand cylindrical hub in accordance with FigureA 2.9-4 and Figure A 2.9-5

The flange shall be checked with regard to sections A-A andC-C. The flange section modulus available in section A-A isobtained from:

( ) ( ) ( )[ ]W d d d h d s s s WA F i L F i R R erf= ⋅ − − ⋅ ′ ⋅ + + ⋅ − ≥π4

2 2 212

(A 2.9.-23)

The flange section modulus available in section C-C is ob-tained in accordance with clause A 2.9.4.2.

For the calculation of welding stubs ′dL = 0 shall be taken.

S

F

t

DF D

D

L

R

F

R

R

F

i

1r

d

a

h

F

d

a

d

sd

F

F

Fad

Figure A 2.9-4: Welding-neck flange with cylindrical hub

*

S

F

R

DF

DD

F

R

R

t

F

1

i

r

h

=

a

F

=

d

a

d

sd

F

F

Fad

Figure A 2.9-5: Welding stub with cylindrical hub

KTA 3201.2

A 2.9.4.5 Lap-joint flanges to Figure A 2.9-6

The required flange thickness shall be

( )hW

d d dL

erf

L

= ⋅⋅ − − ⋅ ′

4

22 1π(A 2.9-24)

with Werf obtained from equation (A 2.9-3).

*t

S

D

t

S

L

L

1

2

=

d

d

=

d a

d

d

h

F

F

r

Figure A 2.9-6: Lap-joint flange

A 2.9.4.6 Cover flange for reactor pressure vessel accordingto Figures A 2.9-7 and A 2.9-8

(1) The flange may be considered as lap-joint flange. Inaddition, the circumferential stress resulting from internalpressure must be considered. As this flange joint is aflange-spherical shell connection, the membrane force shallbe divided into its components (see Figure A 2.9-7).

ϕ

∆

F

i

s

R

F

2

F

m

1

SP

D

i

RH

t

F

D

S

L

D

h

FR

a

FF

dSP

a

F

a

d

d

d

d

F

a

F

r

d

a

hh

r h

Figure A 2.9-7: Cover flange of reactor pressure vessel

(2) To determine the centroid of flange, the area of bolt holesshall be distributed evenly over the circumference and anequivalent diameter shall be formed:

h n d d d hL t L⋅ ⋅ ⋅ = ⋅ ⋅ ′ ⋅π

π4

2 (A 2.9-25)

′ = ⋅⋅

dn d

dL

L

t

2

4(A 2.9-26)

(3) Thus the following external moments are obtained:

MS = FS ⋅ aS = FS ⋅ 0.5 ⋅ (dt - dSP) (A 2.9-27)

MR = FR ⋅ aR = FR ⋅ 0.5 ⋅ (dSP - di) (A 2.9-28)

( )M F a F

d d dF F F F

SP i D= ⋅ = ⋅⋅ − +2

4(A 2.9-29)

MD = FD ⋅ aD = FD ⋅ 0.5 ⋅ (dSP - dD) (A 2.9-30)

M F a F hH H H R= ⋅ = ⋅ ⋅ −

cot hFϕ2

∆ (A 2.9-31)

and the total moment is as follows:

M = MS + MR + MF + MD + MH (A 2.9-32)

(The signs are as follows: positive sign where the momentsare applied clockwise)

(4) The flange section modulus is then:

( )W d d d hF i L F= ⋅ − − ⋅ ′ ⋅π4

2 2 (A 2.9-33)

The required effective flange thickness thus is:

( )hW

d d dF

erf

F i L

=⋅

⋅ − − ⋅ ′4

2π(A 2.9-34)

(5) The circumferential stress caused by twisting of theflange ring is obtained from the following equation:

σuvorh

M

W1 =

.

(A 2.9-35)

(6) The hydrostatic end force on the flange is:

Fi = π ⋅ di ⋅ hF ⋅ p (A 2.9-36)

(7) The horizontal force applied by the connected spheri-cal shell is

FH = FR ⋅ cot ϕ (A 2.9-37)

(8) The resulting horizontal force then is:

Fres = Fi - FH (A 2.9-38)

(9) The wall thickness of the weakened radial width offlange ring is

b = 0.5 ⋅ (dF - di - 2 ⋅ ′dL ) (A 2.9-39)

(10) The resulting horizontal force corresponds to anequivalent internal pressure of

pF

d häq

res

i F

=⋅ ⋅π

(A 2.9-40)

(11) The mean circumferential stress thus is obtained fromthe following equation:

σπu

äq i res

F

p d

b

F

h b2

0

2=

⋅ ⋅=

⋅ ⋅ ⋅

.5(A 2.9-41)

(12) The total stress then is:

σ = σu1 + σu2 (A 2.9-42)

KTA 3201.2

(13) In addition, the seating stress between cover flangeand mating component shall be verified by calculation (seeFigure 2.9-8).

The facing is considered to be only the face between theinternal diameter of the external O-ring-groove and theinside diameter of the mating flange part.

The contact face thus is:

( ) ( )[ ]A d d d d= ⋅ − − −π4

62

32

52

42 (A 2.9-43)

The effective seating stress is:

pF

AA

S= max (A 2.9-44)

The allowable seating stress shall be verified in dependenceof the combination of materials used.

D2

4

i

3

D1

6

5

d

d

d

d

d

d

d

Figure A 2.9-8: Facing of reactor pressure vessel

A 2.9.5 Verification by calculation of the strength and de-formation conditions in flanged joints

Note:

Formulae to calculate the angle of flange ring slope arecontained in DIN 2505-1 (E04/90) and guide values formaximum angles of slope are contained in DIN 2505-2(E04/90).

A 2.9.5.1 General

(1) During start-up and shutdown, the relation betweenbolt load, pressure load and gasket load in the flangechanges due to internal pressure, additional forces and mo-ments independent of operation, temperature-dependentchange of elastic moduli, differential thermal expansion,seating of the gasket, especially of non-metallic gaskets.

(2) Based on the selected initial bolt stress and in consid-eration of the elastic deflection characteristics of the flangedjoint with consistent bolt elongation the bolt load and theresidual gasket load shall be evaluated for each governingload case.

In the case of identical flange pairs, consistent bolt elonga-

tion means the sum of the deflections of the flange 2 ⋅ ∆F, the

bolts ∆S and the gasket ∆D, in case of temperature effects, ofthe differential thermal expansion in the flange and the bolt

∆W as well as, in the case of seating of the gasket, in the

bolted joint and in the gasket ∆V. Taking these

magnitudes into account, the bolt elongation in the assemblycondition E will be consistent for each operating condition x:

2 ⋅ ∆FE + ∆SE + ∆DE = 2 ⋅ ∆Fx + ∆Sx + ∆Dx +∆Wx + ∆Vx

(A 2.9-45)

In the case of non-identical flange pairs, 2 ⋅ ∆F is substitutedby the sum of deflections of the individual flanges

∆F1 + ∆F2, in the case of flange-cover joints 2 ⋅ ∆F is substi-

tuted by the sum of deflections of the flange and the cover ∆F + ∆B.

In the case of flanged joints with extension sleeves the stiff-ness of the extension sleeves shall also be taken into account.

(3) By means of the bolt and gasket loads resulting fromthe verification by calculation of the strength and deforma-tion conditions for the governing load cases the evaluationof strength of the total flanged joint (flange, blank, bolts andgasket) shall be controlled.

(4) The allowable stresses shall be taken from Table A 2.9-1.

A 2.9.5.2 Simplified procedure for verification by calcula-tion of the strength and deformation conditions inflanged joints

A 2.9.5.2.1 General

(1) For some cases where internal pressure, additionalforces and moments, temperature-dependent changes inelastic moduli, different thermal expansion in the flange andthe bolts, as well seating of the gasket occurs, equations aregiven in the following clauses to determine the bolt loads FS,

the compression loads on the gasket FD as well as the de-

flections ∆F, ∆S and ∆D for the respective conditions.

(2) Alternatively, an approximate calculation for verifyingthe strength and deformation conditions may be made byother procedures for a detailed evaluation of the

a) torsional rigidity of flanges

b) radial internal pressure

c) effective bolt circle diameter

d) effective gasket diameter.

Note:

Such a procedure is given, e.g. in DIN EN 1591 (E11/94). Whenusing this procedure, however, the additional load due to torsion andtransverse forces shall be considered additionally.

A 2.9.5.2.2 Calculation of spring constants

A 2.9.5.2.2.1 Bolts

The elastic elongation of bolts can be calculated from

∆SF

CS

S

= (A 2.9-46)

For full-shank bolts the following applies approximately

( )Cn E d

l dS

S N

N

= ⋅ ⋅ ⋅⋅ + ⋅

π 2

4 0 8.(A 2.9-47)

KTA 3201.2

For reduced-shank bolts the following applies

( )C

n E d d

d l d l dS

S K S

K S S N

= ⋅ ⋅ ⋅ ⋅⋅ + ⋅ ′ ′ ′ + ⋅

π4 0 8

2 2

2 2 +l .(A 2.9-48)

″′

N

N

K

s

s

N

N

N

K

N0.

4 d

0.4

d

reduced-shank boltull-shank bolt

d

d

dd

0.4

d

d

0.4

d

Figure A 2.9-9: Bolts

A 2.9.5.2.2.2 Flanges

The deflection ∆F of the individual flange in the bolt circle is

∆FM

CM

= (A 2.9-49)

When determining the relation between bolt load, pressureload and gasket load of a pair of identical flanges, twice the

value of ∆F shall always be taken

( )( )C

E h h W

d d aM

F F B

F i D

=⋅ ⋅ + ⋅

⋅ + ⋅4

3(A 2.9-50)

For flanges with tapered hub W = WA according to equation

(A 2.9-13). In addition, the following applies

hd

shB

i

FA= ⋅

⋅0 58

0 29

.

.

(A 2.9-51)

For welded flanges where the pipe or shell is connected tothe flange without tapered hub, the following applies

( ) ( ) ( )[ ]W d d d h d s s sF i L F i R R= ⋅ − − ⋅ ′ ⋅ + + ⋅ −π4

2 2 21

2

(A 2.9-52)In addition, the following applies

( )h . B = ⋅ + ⋅0 9 d s si R R (A 2.9-53)

For lap joint flanges the following applies

( )W d d d hL L= ⋅ − − ⋅ ′ ⋅π4

22 12 (A 2.9-54)

and

hB = 0

A 2.9.5.2.2.3 Blanks

The deflection ∆B of the blank in the bolt circle for the gasketseating condition (condition 0) shall be:

∆BF

C

S

B

00

0

= (A 2.9-55)

with FS0 = FD0 bolt load for gasket seating condition

and CB0 spring constant for gasket seating condition

and for and for the operating condition (condition x):

∆Bp

dF

C

F

Cx

DBZ

Bxp

Dx

BxFD

=⋅ ⋅ +

+

2

4

π

(A 2.9-56)

where the force FBx on the cover shall be

F pd

F F F FBxD

BZ RP F RZ= ⋅ ⋅ + = + +2

4

π(A 2.9-57)

and

CBxp = spring constant for the loading due to force on cover

and

C C spring constant for the loading due tocompression load on the gasket F

BxFD B0

Dx

= ⋅ =E

Eϑ

20

The spring constants for the various types of loading maye.g. be taken from

a) Markus [5]

b) Warren C. Young, case 2a, p. 405 [6]

c) Kantorowitsch [7]

or be determined by suitable methods.

A 2.9.5.2.2.4 Gaskets

The elastic portion of compression (spring-back) of the gas-

ket ∆D can be assumed to be, for flat gaskets

∆DF

CD

D

= (A 2.9-58)

where

CE d b

hD

D D D

D

= ⋅ ⋅ ⋅π(A 2.9-

59)

Depending on the load case ED is the elastic modulus of the

gasket material at seating condition or operating tempera-ture, and can be taken from Table A 2.10-2.

For metal gaskets of any type the springback of the gasket isso low in comparison with the flange deflection that it canbe neglected.

A 2.9.5.2.2.5 Differential thermal expansion and additionaltime-dependent gasket loads

The equations for calculating the bolt loads and gasket com-pression loads according to clause A 2.9.5.2.2 may also con-sider differential thermal expansions between flange, blank,bolts, and gasket as well as time-dependent seating

( ) ( )( ) ( )

∆W l h

h

x k S Sx F F F x F

F x D D Dx

= ⋅ − ° − ⋅ − ° − ⋅ ⋅

⋅ − ° − ⋅ − °

α ϑ α ϑ α

ϑ α ϑ

20 20

20 20

1 1 1 2

2

h

(A 2.9 - 60)

F2

where

∆Wx differential thermal expansion of flange, blank, bolt,

and gasket. The indices 1 and 2 refer to the flangeand the mating flange or blank

lk grip length (distance between idealized points of

effective bolt elongation)

∆Vx time-dependent gasket seating (to be considered for

metal groove gaskets only in which case the manu-facturer's data shall be taken as a basis).

KTA 3201.2

A 2.9.5.2.3 Calculation of bolt loads and compression loadson the gasket

A 2.9.5.2.3.1 Case of identical flange pairs

For identical flange pairs the following applies:

F

C

a

C C

FC

a

C C

C

a

a

a

C C

a

a

a

CW V

DBx

Sx

D

Mx Dx

SS

D

M D

Sx

R

D

D

Mx Sx

F

D

D

Mxx x

=+ ⋅ +

+ ⋅ +

⋅

⋅ + ⋅ ⋅

− + ⋅ ⋅

− −

11 2 1

1 2 1

1 2 1 2

00 0 0

- F

F

Rx

Fx ∆ ∆

(A 2.9-61)and

FSx = FDBx + FRx + FFx (A 2.9-62)

A 2.9.5.2.3.2 Case of non-identical flange pairs

For flanged joints with non-identical flanges 1 and 2 thefollowing applies:

F

C

a

C

a

C C

FC

a

C

C C C

a

a

a

C

a

a

a

C

C

a

a

a

C

a

a

a

CW V

DBx

Sx

D

M x

D

M x Dx

SS

D

M

M D Sx

R

D

D

M x

R

D

D

M x

Sx

F

D

D

M x

F

D

D

M xx x

=+ + +

+ +

+ + + ⋅

− ⋅ ⋅

+ ⋅

⋅ ⋅ − −

11 1

1

1 1

1

1 2

00 10

20 0

1

1

2

2

1

1

2

2

a-F F -

-F - F

DR1x R2x

F1x F2x ∆ ∆

(A 2.9-63)


and

FR1x + FF1x = FR2x + FF2x (A 2.9-65)

A 2.9.5.2.3.3 Flange-blank combination

For flanged joints consisting of a flange and a blank thefollowing applies:

F

C

a

C C C

FC

a

C

C C C

a

a

a

C

C

a

a

a

CF

CW V

DBx

Sx

D

Mx BxFD Dx

SS

D

M

B D Sx

R

D

D

Mx

Sx

F

D

D

MxBx

Bxpx x

=+ + +

+ +

+ + + ⋅

−

− + ⋅

− ⋅ − −

11 1 1

1

1 1 1

1 1

00 0

0 0

- F

F

Rx

Fx ∆ ∆

(A 2.9-66)

and


Ser. Loading levels

no. 0 A, B P C, D

1

Stress resulting from internal pressure, required

gasket load reaction and external loads 2)

FS = FRP + FF + FDB + FRZ + FRM

Sm Sm

1

1 10 2

..Rp T

8)9)

2Stress at test condition 3)

F F F F F FSP = RP + RZ + RM + F + DB′ ′ ′ ′ ′1

1 10 2

..Rp T ′

8)

3Stress at gasket seating 4) 5)

FS0

1

1 10 2

..Rp RT

8) 1

1 10 2

..Rp T

8)

4

Stress due to internal pressure, external loads, re-sidual gasket load and differential thermal expan-

sion 6) , if any, taking the relation between bolt loadand residual gasket load at the respective pressure

condition into consideration 7)

FS = FRP + FF + FDB + FRZ + FRM

1

1 10 2

..Rp T

8)

For diameter ratios dF/di > 2 all stress intensity limits shall be reduced by the factor

( )Φ = +

+0 6

1

5 252

.

. /d dF i

1) See clause A 2.8.1 for definition of notations used.2) If equations (A 2.9-1) to (A 2.9-3) are used.3) If equations (A 2.9-1) to (A 2.9-3) with Rp0.2T´/1.1 instead of Sm are used.

4) If equation (A 2.9-4) is used.5) The different application of forces on the bolts depending on torque moment and friction shall be conservatively considered in

strengths verifications.6) Consideration of differential thermal expansion at a design temperature > 120 °C. This temperature limit does not apply to combina-

tions of austenitic and ferrritic materials for flange and bolts.7) In the case of calculation as per clause A 2.9.5.8) For cast steel 0.75 ⋅ Rp0.2T instead of Rp0.2T/1.1

9) This stress limit only applies if it is not required to verify the tightness of the flanged joint.

Table A 2.9-1: Allowable stresses σzul for pressure-loaded flanged joints made of steel

Type of stress 1)

KTA 3201.2

A 2.10 Gaskets

A 2.10.1 General

(1) The gasket factors shall be taken from Table A 2.10-1and the elastic moduli of the gasket materials from TableA 2.10-2.

The gasket factors apply to the flange calculation in accor-dance with Section A 2.9 for gaskets in flanges without con-trolled contact land.

The factors given in Table A 2.10-1 are design factors basedon general experience, and have to be observed by the gas-ket manufacturer unless the latter proves the usability ofother values. Other gasket factors that have been sufficientlyjustified may be used.

Note:

The values given in Tables A 2.10-1 and A 2.10-2 were taken fromDIN 2505-2 (E 04/90) by adhering to the respective position num-bers of that standard.

(2) The most important condition for the leak tightness ofthe flanged joint is a sufficient gasket seating with a gasketcontact surface load of at least σVU .

Where, at a given flanged joint, σVU is not obtained the

following corrective changes are possible:

a) Reduction of the gasket area AD by reducing the effec-

tive gasket width (strength calculation required)

b) Selection of another gasket.

A 2.10.2 Gasket factors for design

Note:

See DIN 28 090-1 (09/95) for definition of gasket factors.

A 2.10.2.1 Lower limit value for gasket seating σVU

The minimum gasket contact surface load σVU refers to the

compression load on the gasket, related to the gasket areaAD with land not under controlled compression, on the

mean circumference and the gasket width to be used in thecalculation.

σπVU

DVU

D

DVU

D D

F

A

F

d b= =

⋅ ⋅(A 2.10-1)

D

Db

d

Figure A 2.10-1: Gasket width bD

The minimum gasket surface load σVU serves to compress

the gasket to contact the flange surface such that the com-pression load FDB for the operating condition then will only

depend on the internal pressure.

A 2.10.2.2 Upper limit value for gasket seating σVO

At ambient temperature, σVO is the greatest mean contact

surface load at which the gasket is still undeformed, i.e. atwhich it has still its characteristic shape.

A 2.10.2.3 Lower limit value for operating condition σBU

σBU is the smallest mean gasket contact surface load re-

quired during operation to maintain leak lightness. Whenthe gasket seating load has at least achieved the lower limit

value σVU, σBU shall be proportional to the internal pres-

sure.

σBU = F

ADBU

D

= m ⋅ p (A 2.10-2)

A 2.10.2.4 Upper limit value for operating condition σBO

σBO is the greatest mean contact surface load at operating

temperature at which the gasket is still undeformed, i.e. atwhich it has still its characteristic shape.

A 2.10.2.5 Tabular values

(1) Table A 2.10-1 contains factors for the selection of

gaskets. The tabulated values for σVU apply to gases and

vapours. In the case of non-metallic gaskets or combinedseals it is possible to use lower values for non-corrosivefluids with a surface tension equal to that of water.

These values as well as the gasket factors not contained inTable A 2.10-1 shall be agreed with the manufacturer.

(2) Due to the non-linear behaviour of the elastic modulusin dependence of the gasket surface contact load, approxi-

mate values for the assumed operating range (between σVU

and σBO) - as far as known - have been given for non-

metallic gaskets and combined seals.

Note:

Literaturea) Bierl, A. and Kremer, H.: Berechnung der gasförmigen Leckagen

aus Flanschverbindungen mit It-Dichtungen,Chemie-Ing.-Technik 1978

b) Tückmantel, H. J.: Optimierung statischer Dichtungen,2nd. Edition, Kempchen 1984

ed

a b c

f

R

R

RR R R

1

b2

b

b bDDb D

b

1

b

bbDb

2

70˚

Figure A 2.10-2: Gasket profiles for metallic gaskets withcurved surfaces

KTA 3201.2

KTA 3201.2

Elastic modulus ED, in N/mm2 at a temperature of

20 °C 200 °C 300 °C 400 °C 500 °C

Bonded asbestos (It) 1 000 to 1 500 2 200

PTFE600647

45(at 260 °C)

Graphite EDRT ≅ 5 000

Spiral-wound gasket 10 000

Grooved metal gasket 20 000

Mild steelCarbon steelLow-alloy steel

212 000 200 000 194 000 185 000 176 000

Cr-Ni steel 18.8 200 000 186 000 179 000 172 000 165 000

Table A 2.10-2: Elastic moduli of gasket materials

A 3 Valves

A 3.1 Valve bodies



a, a1, a2 distance mm

b1, b2 clear width of non-circular cross sec-tions

mm

c1, c2 wall thickness allowances mm

dAi inside diameter of branch mm

dHi inside diameter of main body mm

l length of transition from circular toelliptical cross-section

mm

e, l´ die-out length mm

eA effective length of branch mm

eH effective length in main body mm

s0 calculated wall thickness withoutallowances

mm

sA0 calculated wall thickness of branchwithout allowances

mm

sAn nominal wall thickness of branch mm

sH0 calculated wall thickness of mainbody excluding allowances

mm

sHn nominal wall thickness of main body mm

′sH wall thickness at transition of flangeto spherical shell

mm

sn nominal wall thickness mm

sRn nominal wall thickness of pipe mm

y cylindrical portion in oval bodies mm

Ap pressure-loaded area mm2


Bn factor for oval cross-sections CK factor C effectiveness of edge reinforcement α angle between axis of main body and

branch axisdegree

Subscripts

b bending u circumferencel longitudinal m mean/averager radial B operating conditiont torsion 0 as-installed condition

A 3.1.2 Scope

The calculation hereinafter applies to valve bodies subject tointernal pressure.

A 3.1.3 Calculation of valve bodies at predominantly staticloading due to internal pressure

A 3.1.3.1 General

(1) The valve bodies may be considered to be a main bodywith a determined geometry with openings or branches andbranch penetrations. The calculation of the wall thicknesstherefore comprises the main body lying outside the areainfluenced by the opening and the opening itself. The mainbody is considered to be that part of the valve body havingthe greater diameter so that the following applies:

dHi ≥ dAi or b2 ≥ dAi.

(2) The transitions between differing wall thicknesses shallnot show any sharp fillets or breaks to minimize disconti-nuity stresses and show a good deformation behaviour.Depending on the chosen stress and fatigue analysis addi-tional design conditions shall be satisfied, e.g. with regard tothe transition radii (see Section 8.3).

The main body wall thickness sHn and the branch thickness

sAn shall be tapered to the connected pipe wall thickness sRn

on a length of at least 2 ⋅ sHn or 2 ⋅ sAn, respectively. In addi-

tion, the condition of clause 5.1.2 (2) regarding the transi-tional area shall be taken into account.

(3) For the total wall thickness including allowances thefollowing applies

sHn ≥ sH0 + c1 + c2 (A 3.1-1)

and

sAn ≥ sA0 + c1 + c2 (A 3.1-2)

Gasket material

KTA 3201.2

where sHn and sH0 apply to the main body and sAn and sA0

to the branches.

(4) For the recalculation of as-built components the follow-ing applies

sH0 ≤ sHn - c1 - c2 (A 3.1-3)

and

sA0 ≤ sAn - c1 - c2. (A 3.1-4)

A 3.1.3.2 Calculation of the main body outside the openingor branch area and without any influences at theboundary

A 3.1.3.2.1 General

The geometric configuration of the main body of valve bod-ies may be cylindrical, spherical, conical or oval. Accord-ingly, the wall thicknesses can be determined within bodyareas remote from discontinuities.

A 3.1.3.2.2 Determination of the required wall thickness s0

of cylindrical main bodies

The required wall thickness s0 of cylindrical main bodies

shall be determined in accordance with clause A 2.2.2.


of spherical main bodies

The required wall thickness s0 of spherical main bodies shall

be determined in accordance with clause A 2.3.2.


of conical main bodies

The required wall thickness s0 of conical main bodies shall

be determined in accordance with clause A 2.4.2.


of oval main bodies

(1) In the case of oval-shaped cross-sections (FigureA 3.1-1) the additional bending loads in the walls shall beconsidered.

2

11

2

s

b

b

Figure A 3.1-1: Oval-shaped valve body

(2) The theoretical minimum wall thickness for such bod-ies subject to internal pressure is obtained as follows:

′ =⋅⋅

⋅ + ⋅ ⋅sp b

SB

S

pB

m

mn0

202

2

4(A 3.1-5)

(3) The wall thickness shall be calculated at the locations 1and 2 shown in Figure A 3.1-1 for oval cross-sections, sincehere the bending moments obtain maximum values andthus have essential influence on the strength behaviour.

(4) The factor B0 depending on the normal forces shall be

for location 1: B0 = b1/b2

for location 2: B0 = 1

(5) Bn shall be taken from Figure A 3.1-2.

(6) The factors Bn depending on the bending moments are

shown in Figure A 3.1-2 for oval cross-sections at locations 1

and 2 in dependence of b1/b2. The curves satisfy the follow-

ing equations:

Bk K

E

kE E1

2 21

6

1 2

6=

−⋅

′′

−−

(A 3.1-6)

Bk k K

EE E

2

2 21

6

1

6= + − − ⋅ ′

′(A 3.1-7)

with kb

bE2 1

2

2

1= −

(A 3.1-8)

Note:

K´ and E´ are the full elliptical integrals whose values can be taken independence of the module of the integral kE from Table books such as

�Hütte I, Theoretische Grundlagen, 28 th edition, Publishers: W.Ernst u. Sohn, Berlin.�

0.1

0.05

0.6 0.8 1.0

0.3

0.35

0.25

0.15

0.2

0

0

0.40.2

2

1

n2

2

1

n

2

b4

B

Bp

b / b

B

B

=M

Fig. A 3.1-1

Figure A 3.1-2: Factor Bn for oval cross-sections

KTA 3201.2

(7) For the factors relating to b1/b2 ≥ 0.5 the followingapproximate equations may be used

Bbb

bb1

1

2

1

21 0 625 0 435 1= −

⋅ − ⋅ −

. . (A 3.1-9)

Bbb

bb2

1

2

1

21 0 5 0 125 1= −

⋅ − ⋅ −

. . (A 3.1-10)

(8) The factors also apply to changes in cross-section in ovalmain bodies, e.g. for gate valves according to Figure A 3.1-3,design a and b where the side length b1 from the crown ofthe inlet nozzles (flattened oval shape) increases over thelength l to obtain b2 (circular shape). The value b1 in sectionB-B at 1/2 shall govern the determination of Bn where l isobtained from

l H yd

s lHiH= − − +

− ′2

(A 3.1-11)

with H being a design dimension as per Figure A 3.1-3.

For the length ′l influenced by the inlet nozzle the follow-ing applies:

l d sm n′ = ⋅ ′ ⋅1 25. (A 3.1-12)

where ′ =′ +

db b

m1 2

2(A 3.1-13)

in which case ′b1 and b2 shall be determined at section A-Aon a length ′l from the inlet nozzle. sn is the wall thicknessavailable for ′l . In general, ′b1 and ′l shall be determined

by iteration.

′

′ ′

′

H

H

Hi

b

y

d

2

b

d

H

B

H

Ry

Hi

ABB

AB

A A

2b

11

b1 b1A

b

s

s s

Design a Design b

Figure A 3.1-3: Examples for changes in cross-section ofoval bodies

(9) For short bodies (e.g. Figure A 3.1-3, design a or b) withthe length l remote from discontinuity, corresponding to thedesign geometry, the supporting effect of the componentsconnected at the end of the body (e.g. flanges, heads, covers)may be credited. Thus, the required minimum wall thick-ness is obtained by using equation (A 3.1-5) to become:

s s k0 0= ′ ⋅ (A 3.1-14)

(10) The correction factor k shall be obtained, in corres-pondence to the damping behaviour of the loadings in cy-lindrical shells, in consideration of experimental test resultsfrom non-circular bodies as follows

kl

d sm= ⋅

⋅ ′0 48

2

03. (A 3.1-15)

with 0.6 ≤ k ≤ 1

The function is shown in Figure A 3.1-4 in dependence ofl2/ d sm ⋅ ′0 .

′

0.4

0.2

6

1.0

0.8

0.6

2

0

1 4 53

2

0m s

k

d

Figure A 3.1-4: Correction factor k for short bodies

(11) For dm dm = (b1 + b2)/2 shall be taken, and ′s0 corres-

ponds to equation (A 3.1-5). For changes in cross-sectionover a length l, e.g. according to Figure A 3.1-3, design a orb, the dimensions b1 and b2 shall be taken from Section B-B(at l/2). Local deviations from the body shape irrespectivewhether they are convex or concave, shall, as a rule, be ne-glected.

(12) The strength criterion is satisfied if the required wallthickness is locally available provided that the wall thick-ness transitions are smooth.

A 3.1.3.2.6 Valve bodies with branch

(1) The strength of the body containing a branch shall becalculated considering the equilibrium of external and inter-nal forces for the highly loaded areas which are the transi-tions of the cylindrical, spherical or non-circular main bodyto the branch. The diameter dH and the wall thickness sH

refer to the main body, and the diameter dA and the wallthickness sA to the branch. The following shall apply:dHi > dAi.

(2) In the case of cylindrical main bodies, see Figure A 3.1-5,the section I located in the longitudinal section through themain axis as a rule is subject to the greatest loading with theaverage main stress component σ1 . In the case of nozzle to

main body ratios ≥ 0.7, however, the bending stresses oc-curring in the cross-sectional area to the main axis (SectionII) cannot be neglected anymore, i.e. this direction has alsobe taken into account.

(3) A recalculation of section II can be omitted if the wallthickness differences within the die-out length of this sectionand compared to section I do not exceed 10 %.

KTA 3201.2

(4) In the case of non-circular bodies with branches andgenerally in the event of additional forces acting in the di-rection of the main axis the greatest loading may be ob-tained in the section with the average main stress compo-nent σII (section II).

Figure A 3.1-5: Calculated sections for valve bodies withbranch

(5) In these cases, the calculation shall be effected for bothsection I and II.

(6) The calculation procedure hereinafter applies to valvebodies with vertical branch, see Figures A 3.1-6 to A 3.1-12as well as with oblique branch if the angle α is not less than45°, see Figure A 3.1-14, provided that sA does not exceedsH. Where these conditions cannot be satisfied by certaindesigns, the wall thickness sA can only be used in accor-dance with this equation in the calculation of the effectivelength and effective cross-sectional area Aσ.

Note:

In Figures A 3.1-5 to A 3.1-14 the wall thickness shown is thenominal wall thickness minus the allowances c1 and c2.

(7) For the equilibrium of forces in the longitudinal sectionaccording to Figures A 3.1-6 to A 3.1-12 the following rela-tionship applies

p A ApI I I⋅ = ⋅σ σ (A 3.1-16)

where p ⋅ ApI is the total external force acting upon the pres-sure-loaded area ApI (dotted) whereas the internal forceσ σI IA⋅ is the force acting in the most highly loaded zone of

the wall with the cross-sectional area AσI (cross-hatched)and in the cross-section the average main stress σI .

(8) The strength condition to be satisfied in accordance withTresca´s shear stress theory is:

σ σ σσ

VI I IIIpI

Imp

A

Ap

S= − = ⋅ + ≤2

(A 3.1-17)

(9) In the case of non-circular bodies with branches thefollowing strength condition shall be satisfied to considerthose bending stresses exceeding the bending stresses al-ready covered by the calculation of the wall thicknessesaccording to equations (A 3.1-5) or (A 3.1-14):

σ σ σσ

VI I IIIpI

I

mpA

Ap S= − = ⋅ + ≤2 1 2.

(A 3.1-18)

(10) In equations (A 3.1-17) and (A 3.1-18) the stress σIII

acting normal to wall is considered to be the smallest mainstress component which on the pressure-loaded side isσIII = - p and on the unpressurized side is σIII = 0, that is amean value σIII = - p/2.

Accordingly, the following applies to the equilibrium offorces in section II (see Figure A 3.1-6)

p A ApII II II⋅ = ⋅σ σ (A 3.1-19)

The strength condition in this case is

σ σ σσ

VII II IIIpII

IImp

A

Ap

S= − = ⋅ + ≤2

(A 3.1-20)

and for non-circular bodies

σVIImS≤

1 2.(A 3.1-21)

σ σ

′

H

H

Hi

A

1

A1

Ai

AA2

H

pI

A3

2

pII

2

II

H

I

e

A

s

b

A

e

b/ 2

s

A

sb

d

e

e

A

es

d

Section IISection I

Figure A 3.1-6: Valve bodies

(11) For cylindrical valve bodies with dAi/dHi ≥ 0.7 andsimultaneously sA0/sH0 < dA/dH the following conditionshall be satisfied in section II:

pd s

sd s

sd s

sSHi H

H

Ai A

A

Hi H

Hm⋅ +

⋅+ ⋅ + ⋅ +

≤ ⋅0

0

0

0

0

020 2 1 5. .

(A 3.1-22)

(12) For non-circular valve bodies the condition shall be:

pb s

sd s

sb s

sSH

H

Ai A

A

H

Hm⋅ ⋅ +

⋅+ ⋅ + ⋅ +

≤ ⋅252

0 25 1 52 0

0

0

0

2 0

0. .

(A 3.1-23)

(13) For the cases shown in Figures A 3.1-7 to A 3.1-14 thegeneral strength condition applies:

σσ

= ⋅ +

≤p

A

ASp

m0 5. (A 3.1-24)

The pressure-loaded areas Ap and the effective cross-sec-tional areas Aσ are determined by calculation or a drawingto scale (true to size).

The effective length of the considered cross-sectional areasAp and Aσ shall be determined as follows (except for spheri-

KTA 3201.2

cal bodies to Figure A 3.1-11 and branches with obliquenozzles to Figure A 3.1-14).

e = (d + s ) sH Hi H0 H0⋅ (A 3.1-25)

e = 1.25 (d + s ) sA Ai A0 A0⋅ ⋅ (A 3.1-26)

(14) For the design shown in Figure A 3.1-6, section I thefollowing applies:

e = (b + s ) sH 1 H0 H0⋅ (A 3.1-27)

e = 1.25 (d + s ) sA1 Ai A0 A0⋅ ⋅ (A 3.1-28)

eA2 in accordance with subclause (21).

For section II applies:

′ ⋅e = (b + s ) sH 2 H0 H0 (A 3.1-29)

e = 1.25 (b + s ) sA3 2 A0 A0⋅ ⋅ (A 3.1-30)

(15) At a ratio of nozzle opening to main body openingexceeding 0.8 the factor ahead of the root is omitted inequations (A 3.1-26), (A 3.1-28) and (A 3.1-30).

(16) For branches in spherical main bodies with a ratiodAi1/dHi or dAi2/dHi ≤ 0.5 the effective length in the spheri-cal portion according to Figure A 3.1-11, design a, can betaken to be:

e = (d + s ) sH Hi H0 H0⋅ (A 3.1-31)

however, shall not exceed the value obtained by the bisect-ing line between the centrelines of both nozzles. For theeffective length the following applies:

e = (d + s ) sA Ai A0 A0⋅ (A 3.1-32)

At ratios of dAi1/dHi or dAi2/dHi exceeding 0.5 the effectivelength shall be determined in accordance with FigureA 3.1-11, design b, where eA1 or eA2 shall be determined inaccordance with equation (A 3.1-32).

(17) Valve bodies with oblique nozzles (α ≥ 45°) may also becalculated by means of equation (A 3.1-17) in which case thepressure-loaded area (dotted) and the pressure-loadedcross-sectional area (cross-hatched) are distributed in accor-dance with Figure A 3.1-14.

Here, the effective length shall be determined as follows:

e = (d + s ) sH Hi H0 H0⋅ (A 3.1-33)

( )e d s sA Ai A A= + ⋅

⋅ + ⋅1 0 2590 0 0.α

(A 3.1-34)

In the case of oblique branches the area shall be limited tothe pressure-loaded area bounded by the flow passage cen-tre lines. At a ratio of branch opening to main body openingexceeding 0.8 the factor ahead of the root shall be omitted inequation (A 3.1-34).

(18) Where flanges or parts thereof are located within thecalculated effective length they shall be considered not to becontributing to the reinforcement, as shown in FiguresA 3.1-6, A 3.1-7, A 3.1-9, A 3.1-12.

(19) Where effective lengths of reinforcements of openingsextend into the tapered portion of the flange hub, only the

cylindrical portion shall be considered for the determinationof the area of the opening contributing to the reinforcement.

Figure A 3.1-7: Valve body

σ

σ

2

A

H

A

Hi

Hi

p

Ai

A

2H

1

Hp

Ai

H

H

A

1

A

ds

e

d

s

e

sa

a

A

ae

A

d

A

a

d

e

e

right side

left side

s A

sa

/2

a

Figure A 3.1-8: Cylindrical valve body

KTA 3201.2

Figure A 3.1-9: Angular-type body


≤ >

σσ

A2

A2

A2

A1

Ai2

Ai1

A1

HiAi2Ai1 HiAi2Ai1

H

HiHi

Hi

Ai2

A1

HH

Hi

A1

Ai1

0.5withwith d

d

0.5

e

s

dBranch in spherical body

d

Design b

dd

e

d ord

s

d

p

s

p

d

d

s

e

d

Design a

dBranch in spherical body

or

e

d

s

s

AA

AA

Figure A 3.1-11: Spherical bodies


(20) Where within the boundary of the effective cross-sec-tional area Aσ or within the area of influence of 22.5° to thesectional area boreholes (bolt holes) are provided, thesecross-sectional areas shall be deducted from Aσ.

(21) Metal extending to the inside shall be credited to theeffective cross-sectional area Aσ up to a maximum length ofeH/2 or eA/2.

(22) In the case of a design to Figure A 3.1-13 where a gas-ket is arranged such that the pressure-retaining area Ap issmaller than the area obtained from the die-out lengths eH

or eA, the centre of the gasket may be used to set theboundaries for the area Ap whereas the metal area Aσ islimited by the calculated length eH or eA.

In the case of designs with pressure-retaining cover plateswhere the split segmental ring is located within the die-outlength, eH or eA may be used for the determination of theeffective cross-sectional area Aσ but only up to the centre ofthe segmental ring in order to limit the radial forces inducedby the gasket and the bending stresses at the bottom of thegroove.

σ

HH

iH A

A

pA

A Ai

d

s

s

Cen

tre

ofga

sket

d

e

e

Figure A 3.1-13: Example for cover

Figure A 3.1-14: Cylindrical body with oblique branch

KTA 3201.2

A 3.2 Valve body closures



a1, a2, aD,aF, aH, aS,aV

lever arms in acc. with FigureA 3.2-1

mm

b effective width of flange mm

c1 wall thickness allowance for consid-eration of fabrication tolerances

mm

c2 wall thickness allowance for consid-eration of wall thickness reductiondue to chemical or mechanical wear

mm

d1 diameter at intersection of flangering and spherical section

mm

da outside diameter of flange mm

′da outside diameter of spherical crownsection

mm

dD mean diameter or diameter of gasketcontact circle

mm

di inside diameter of flange mm

′di inside diameter of spherical crownsection

mm

dL bolt hole diameter mm

′dL calculated diameter of bolt hole mm

dp centroid of flange when subject totwisting

mm


hF thickness of flange ring mm

m gasket factor

′ra outside radius of curvature of sphe-rical crown section

mm

′ri inside radius of curvature of spheri-cal crown section

mm

s0 wall thickness of spherical crownsection

mm


FDB compression load on gasket to en-sure tight joint (gasket load differ-ence between design bolt load andtotal hydrostatic end force)

N

FDV gasket seating load N

FF difference between total hydrostaticend force and the hydrostatic endforce on area inside flange

N

FH horizontal force N

FS operating bolt load (required boltload for the design condition)

N

FSO bolting-up condition (bolt load forgasket seating condition)

N

FV vertical force N

Ma moment of external forces N mm


MaB moment of external forces for op-erating conditions

N mm

Ma0 moment of external forces for gasketseating condition

N mm

Mb bending moment N mm

Mt torsional moment N mm

Q transverse force N

σBO upper limit value of gasket bearingsurface load for operating conditions

N/mm2

σVO upper limit value of gasket bearingsurface load for gasket seatingcondition

N/mm2

σVU lower limit value of gasket bearingsurface load for gasket seatingconditions

N/mm2

µ friction factor

A 3.2.2 Spherically dished heads with bolting flanges

A 3.2.2.1 General

(1) Spherically dished heads with bolting flanges consist ofa shallow or deep-dished spherical shell and a boltingflange. Therefore, the strength calculation comprises thecalculation of the flange ring and the spherical shell.

(2) (2) According to the geometric relationships distinc-tion is made between type I to Figure A 3.2-1 as shallow-dished spherical shell (y > 0) and type II to Figure A 3.2-2 asdeep-dished spherical shell (y = 0).

A 3.2.2.2 Calculation of the flange ring

(1) The strength conditions for the flange ring are::

Fb h

SH

Fm2π ⋅ ⋅

≤ (A 3.2-1)

( )M

bh

ds s

Fb h

Sa

F e

H

Fm

24 8

32 1 20

2π π⋅ ⋅ + ⋅ −

+⋅ ⋅

≤ (A 3.2-2)

with

se = sn - c1 - c2

The wall thickness s0 of the spherical shell without allow-ances shall be, at a diameter ratio ′ ′d da i/ ≤ 1.2, as follows:

sr pS p

i

m0 2

=′ ⋅

⋅ −(A 3.2-3)

or

sr p

Sa

m0 2

=′ ⋅⋅

(A 3.2-4)

with ′da = 2 ⋅ ′ra and ′di = 2 ⋅ ′ri

For 1.2 ≤ ′da / ′di ≤ 1.5 the following equations shall be used

for calculating the wall thickness s0 of the spherical shell:

s rp

S pim

0 12

21= ′ ⋅ +

⋅⋅ −

−

(A 3.2-5)

KTA 3201.2

s r

pS p

pS p

am

m

0

12

21

12

2

= ′ ⋅+

⋅⋅ −

−

+⋅

⋅ −

(A 3.2-6)

The equations (A 3.2-3) to (A 3.2-6) lead to the same resultsif ′ = ′r ri a - s0.

(2) The moment Ma resulting from external forces referredto the centroid of flange PS shall be for the operating condi-tion:

M F a F FM

da F a F a

F a

aB S S V axB

V F F D D

H H

= ⋅ + + + ⋅

⋅ + ⋅ + ⋅

+ ⋅

4

1

(A 3.2 - 7)

The compression load FD on the gasket, in the case of appli-cation of a transverse force due to friction at a certain valueshall be determined by:

FQ M

dM

dFD

t

D

b

DDB= + ⋅

⋅− ⋅

max ;µ µ

2 2(A 3.2-8)

The compression load FD on the gasket, in the case of appli-cation of a transverse force due to infinite friction shall bedetermined by:

FMd

Md

Md

FDt

D

b

D

b

tDB= ⋅

⋅− ⋅ ⋅

max max ; ;

2 2 4µ

(A 3.2-9)

The moment Ma for the bolting-up condition shall be:

Ma0 = FS0 (aS + aD) (A 3.2-10)

The moments applied clockwise shall be inserted withnegative signs in equations (A 3.2-7) and (A 3.2-10). Thestrength condition in equation (A 3.2-2) shall be calculatedwith both moments MaB and Ma0 where for the bolting-upcondition s0 = 0 shall be taken.

(3) The forces are obtained from the following equations

a) Operating bolt load

F F F F FM

dFS V F DB ax

b

tZ= + + + + ⋅ +4

(A 3.2-11)

In the case of application of a transverse force due tofriction at a certain value FZ shall be determined by:

Fd

FM

dZD

DBb

D= ⋅

⋅− − ⋅

max 0; Q

+2 Mt

µ µ2

(A 3.2-12)

In the case of application of a transverse force due toinfinite friction FZ shall be determined by:

FMd

FM

dM

dZt

DDB

b

D

b

t= ⋅

⋅− − ⋅ ⋅

max ; max ;0

2 2 4µ

(A 3.2-13)

b) Vertical component of force on head

F p dV i= ⋅ ⋅π4

2 (A 3.2-14)

c) Difference between total hydrostatic end force and thehydrostatic end force on area inside flange

( )F p d dF D i= ⋅ ⋅ −π4

2 2 (A 3.2-15)

d) Compression load on gasket to ensure tight joint

FDBU = p ⋅ π ⋅ dD ⋅ bD ⋅ m ⋅ SD (A 3.2-16)

withSD = 1.2

FDBO = dD ⋅ bD ⋅σBO

m from Table A 2.10-1bD is the gasket width according to section A 2.10.

e) Horizontal component of force on head

F p d rd

Hi= ⋅ ⋅ ⋅ −π

2 412

2(A 3.2-17)

with

rdi= ′2

For the bolting-up condition, the bolt load FS0 for gasketseating condition shall be the higher value of the gasketseating load FDV or F xS ⋅ , where FS is obtained from equa-tion (A 3.2-11) and x = 1.1 ⋅ FDV shall be determined from:

FDVU = π ⋅ dD ⋅ bD ⋅ σVU (A 3.2-18)

FDVO = π ⋅ dD ⋅ bD ⋅ σVO

σVU, σVO according to Table A 2.10-1

(4) The lever arms of the forces in the equations used fordetermining the moments (A 3.2-7) and (A 3.2-10) are ob-tained from Table A 3.2-1.

Spherically dished head

Type I Type II

aS 0.5 (dt - dp)

aV 0.5 (dp - d1)

aD 0.5 (dp - dD)

aH determine graphically 0.5 ⋅ hF

aF aD + 0.5 (dD - di)

Table A 3.2-1: Lever arms for equations (A 3.2-7) and(A 3.2-10)

(5) The effective width of the flange shall be:

b = 0.5 ⋅ (da - di - 2 ⋅ ′dL ) (A 3.2-19)

with′dL = v ⋅ dL

For inside diameters di equal to or greater than 500 mmv = 0.5 and for di less than 500 mm v = 1 - 0.001 ⋅ di (di inmm).

(6) The centroid of flange dp is obtained from:

dp = da - 2 ⋅ Sa (A 3.2-20)

with

( )S

a a a d a

a aaL=

⋅ + ⋅ + + ⋅+

0 5 0 512

2 1 2

1 2

. .(A 3.2-21)

and

Lever arm

KTA 3201.2

a1 = 0.5 ⋅ (da - dt - dL) (A 3.2-22)a2 = 0.5 ⋅ (dt - di - dL) (A 3.2-23)

σ

′

′

′

′

L 2

a

1

H

p

s

v

i

0

0

a

A

s

p

1

A

DD

1

F

t

a

F

1

s

D

v

i

F

1

HP

d

F

s

d

A

A

Determination of d :

d = intersection of flange

y

and spherical shell

inte

rsec

tion

with

rFF

d

F

F

a

d

h

d

da

d

a

s

dd

a

d

a

a ad

Figure A 3.2-1: Spherically dished head with shallow-dished spherical shell (type I, y > 0)

Figure A 3.2-2: Spherically dished head with deep-dishedspherical shell (type II, y = 0)

A 3.2.2.3 Calculation of the wall thickness of unpenetratedspherical shell and the transition of flange tospherical shell under internal pressure

(1) The wall thickness s0 of the unpenetrated spherical shellis obtained from equations (A 3.2-3) to (A 3.2-6).

(2) For the wall thickness se at the transition of flange tospherical shell the following applies:se ≥ ′se = s0 ⋅ β (A 3.2-24)

The shape factor β takes into account that for a large portionof bending stresses an increased support capability can beexpected in case of plastic straining. Where the strain ratio δof dished heads is assumed, which characterises the supportcapability, β = 3.5 may be taken for flanges with inside boltcircle gasket in accordance with Figures A 3.2-1 and A 3.2-2,a value which is obtained by approximation of β = α/δfrom Figure A 3.2-3.

δ

β

α

α, β

, δ

9

0,03

7

8

1,00,5 10,00,05 0,20,1 2,0 5,0

1

2

5

6

3

4

2

2F

0id

hb

s

Figure A 3.2-3: Shape factor β for the transitionflange/spherical shell

A 3.2.2.4 Reinforcement of opening at gland packing spaceof valves under internal pressure

The reinforcement shall be calculated like for heads withopenings according to the area replacement approachmethod. The strength condition then is:

pA

AS

pm⋅ +

≤

σ

12

(A 3.2-25)

The effective lengths are

( )l r s s0 0 02= ⋅ + ′ ⋅ ′ (A 3.2-26)

( )l d s sA A A1 = + ⋅ (A 3.2-27)

with ′s0 as actual wall thickness in spherical portion minus

allowances c.

A 3.2.3 Dished heads

The calculation of dished heads shall be made in accordancewith Section A 2.5.

A 3.2.4 Flat plates

Closures designed as flat plates are often used as external orinternal covers of valve bodies. Here, primarily flat circular

KTA 3201.2

plates or annular ring plates are concerned as shown inclauses A 2.6.3.2 and A 2.6.3.3. Other plate types (e.g. rec-tangular or elliptical) are special cases to be referred to in thepertinent literature. In the case of valves, a superposition ofload cases may occur resulting from internal pressure load-ing and additional forces. The load cases then can be consid-ered to originate from individual loadings, as was donebefore, and be covered by a summation of moments. In thiscase, however, it shall be taken into account that the maxi-mum moments of the individual loadings will not result inthe maximum total moment in any case. In this case, thelocation and size of the maximum shall be determined con-sidering the course of the load cases.

The strength condition is either contained in the wall thick-ness formulae or is written explicitly as follows:

σ σr t mM

sS, .max= ⋅ ≤ ⋅6

1 52 (A 3.2-28)

The dimensioning of flat plates shall be made in accordancewith Section A 2.6.

A 3.3 Bolts for valves

Bolts for valves shall be calculated according to SectionA 2.8.

A 3.4 Self-sealing cover plates

(1) Design values and units relating to Section A 3.4


a width of bearing mm

b width of spacer mm

bD width of raised facing mm

da outside diameter of body mm

d0 inside diameter of body mm

d1 inside diameter of ring groove mm

d2 diameter of cover plate mm

h0 minimum height of bearing surface mm

hD minimum height of facing mm

hv thickness of cover plate mm

h1 thickness of lap ring R mm

s1 body wall thickness at location ofring groove

mm

Fax axial force N

FB axial force distributed uniformlyover the circumference

N

FZ additional axial force N

MB bending moment N⋅mm

(2) The strength calculation is intended to examine theweakest section (section I-I or II-II in Figure A 3.4-1). At thesame time, the most important dimensions of the cover plateshall be calculated by elementary procedure, e.g. the ring Rinserted in the groove. In the event of dimensions deviatingfrom the geometric conditions shown in Figure A 3.4-1 theformulae given hereinafter may be applied accordingly.

D

1

D

0

1

D

B

2

v

1

a

F

d

h

R

h

h

a

d

d

d

b

h

s

b

Figure A 3.4-1: Self-sealing cover plates

The axial force distributed uniformly over the circumferenceis calculated as follows:

F p d FB Z= ⋅ ⋅ +π4 0

2 (A 3.4-1)

FZ is an additional axial force acting in the same direction(equation A 3.4-3 to A 3.4-8: force applied over cover; equa-tion A 3.4-9 and A 3.4-10: additional loadings applied overthe body, e.g. axial force, bending moment). In the case of abending moment and an axial force, FZ is determined asfollows:

F FM

d sZ axB= +

⋅+

4

1 1(A 3.4-2)

(4) The minimum width of the pressure-retaining areas onthe bearing surface and on the spacer are obtained consider-ing frictional conditions and sealing requirements:

ad Sm

,.

b FB≥

⋅ ⋅ ⋅1 5 0π(A 3.4-3)

(5) The minimum thickness of the lap ring R is obtainedfrom the calculation against shear and bending, and themaximum value obtained shall be inserted.

Regarding shear the following applies:

hF

d SB

m1

0

2≥

⋅⋅ ⋅π

(A 3.4-4)

Regarding bending the following applies:

( )h

F a bd S

B D

m1

01 38

2≥ ⋅

⋅ +⋅

./

(A 3.4-5)

KTA 3201.2

(6) The minimum height of the bearing surface (sectionII - II) is obtained from the design against shear

hF

d SB

m0

1

2≥

⋅⋅ ⋅π

(A 3.4-6)

and against bending

hF a

d SdB

m0

1

01 132

≥ ⋅ ⋅⋅

−. with a =

d1 (A 3.4-7)

(7) For the minimum thickness of the raised face the follow-ing applies:

hF b

d SDB D

m≥ ⋅ ⋅

⋅1 13

2

2.

/(A 3.4-8)

(8) The minimum thickness hv of the cover plate can bedetermined by assuming an idealized, simply supportedcircular plate or annular ring plate (case 1, case 7 or case 8from Table 5 of DIN 3840).

(9) Strength condition for section I - I

( ) ( ) ( )[ ]F as

h d d d s s s SB a a m⋅ +

≤ ⋅ − + − ⋅ − ⋅10

20 1 1

22

2

2 4π

(A 3.4-9)

and ( )sF

d s SsB

a m2

11=

⋅ − ⋅≤

π(A 3.4-10)

A 3.5 Valve flanges

Valve flanges shall be calculated according to Section A 2.9.

A 4 Piping systems

A 4.1 General

(1) The design rules hereinafter apply to the dimensioningof individual piping components subject to internal pressureloading where the internal pressure is derived from thedesign pressure. Additional loadings, e.g. external forcesand moments, shall be considered separately in which casethe rules contained in Section 8.4 may apply to the pipingcomponents.

(2) Where within dimensioning a recalculation is made ofcomponents with actual nominal wall thickness sn , the wallthickness s0n = sn - c1 - c2 shall be used in the calculation inthis Annex A4.

(3) The figures in this Annex do not show allowances.

A 4.2 Cylindrical shells under internal pressure

The calculation shall be made in acc. with clause A 2.2.2.

A 4.3 Bends and curved pipes under internal pressure

A 4.3.1 Scope

The calculation hereinafter applies to bends and curvedpipes subject to internal pressure where the ratio da/di ≤ 1.7.Diameter ratios da/di ≤ 2 are permitted if the wall thicknesss0n ≤ 80 mm.

A 4.3.2 Design values and units relating to Section A 4


dm mean diameter (see Figure A 4-1) mm

di inside diameter mm

da outside diameter mm

r, R bending radii (see Figure A 4-2) mm

s0i calculated wall thickness at intrados mm

s0a calculated wall thickness at extrados mm

Bi factor for determining the wallthickness at the intrados

Ba factor for determining the wallthickness at the extrados

σi mean stress at intrados N/mm2

σa mean stress at extrados N/mm2

hm depth of wrinkle mm

a distance between any two adjacentwrinkles

mm

a2

m

a3a4 6

8

7

a

d

5

9

d

dd

1

4

3

2

Figure A 4-1: Wrinkles on pipe bendNote:The wrinkles in Figure A 4-1 are shown excessively for clarity´ssake.

a

ii

a

a

i/2

ss

d/2

/2 /2dd

d

r

R

Figure A 4-2: Notations used for pipe bend

KTA 3201.2

A 4.3.3 Allowable wrinkling

Wrinkles the dimensions of which meet the requirementshereinafter, need not be recalculated:

a) Depth of wrinkling

hd d

d dma a

a m= + − ≤ ⋅2 432

0 03. (A 4-1)

b) Ratio of distance a to depth hm of wrinklea

hm≥ 12 (A 4-2)

A 4.3.4 Calculation

(1) For the calculation of the wall thickness of bends orcurved pipes under internal pressure the requirements ofclause A 2.1 apply in which case it shall be taken into ac-count that the loading at the intrados is greater by the factorBi and at the extrados is smaller by Ba than at straight cylin-drical shells.

(2) The calculated wall thickness at the intrados is obtainedfroms0i = s0 ⋅ Bi (A 4-3)

(3) The calculated wall thickness at the extrados is obtainedfroms0a = s0 ⋅ Ba (A 4-4)

(4) Determination of the factor Bi

For bends and curved pipes with given inside diameters thefollowing applies:

Br

sd

sr

sd

sr

sd

sii i i= −

⋅− −

⋅

− ⋅ +

⋅0 0 0 0

2

0 02 22

2(A 4-5)

The factor Bi may also be taken from Figure A 4-3 in depen-dence of r/di and s0/di.

For bends and curved pipes with given outside diameter thefollowing applies:

Bd

sr

sd

sr

sia a=

⋅+ −

⋅+ −

⋅

2 21

0 0 0 0

⋅

−

⋅

−

⋅⋅

⋅−

rs

ds

rs

ds

ds

a

a a

0

2

0

2

0

2

0 0

2

2 21

(A 4-6)

The factor Bi may also be taken from Figure A 4-4 in depen-dence of R/da and s0/da.

(5) Determination of the factor Ba

For bends and curved pipes with given inside diameter thefollowing applies:

Br

sd

sr

sd

sd

sr

sai i i= −

⋅

+ ⋅ +

⋅−

⋅−

0 0

2

0 0 0 022

2 2(A 4-7)

The factor Ba may also be taken from Figure A 4-5 in depen-dence of r/di and s0/di.

For bends and curved pipes with given outside diametersthe following applies:

Bd

sr

sd

sr

saa a=

⋅− −

⋅− −

⋅

2 21

0 0 0 0

⋅

−

⋅

−

⋅⋅

⋅−

rs

ds

rs

ds

ds

a

a a

0

2

0

2

0

2

0 0

2

2 21

(A 4-8)

The factor Ba can be taken from Figure A 4-6 in dependenceof R/da and s0/da.

(6) Calculation of stresses

In the equations (A 4-9) to (A 4-12) either the nominal di-ameters dan and din in connection with the wall thicknessess0na and s0ni, respectively or actual diameters in connectionwith actual wall thicknesses minus allowances c1 and c2

shall be used.

The strength condition for the intrados at given inside di-ameter shall be

σ ii

i

i

i im

p ds

r dr d s

pS=

⋅⋅

⋅⋅ − ⋅⋅ − −

+ ≤2

2 0 52 20 0

,(A 4-9)

The strength condition for the intrados at given outside dia-meter shall be

σia i a

i

a i a

a im

p d s ss

R d s sR d s

pS

=⋅ − −

⋅⋅

⋅ ⋅ − ⋅ + ⋅ − ⋅⋅ − +

+ ≤

( 0 0

0

0 0

0

22 0 5 1 5 0 5

2 2

)

. . ,(A 4-10)

The strength condition for the extrados at given inside di-ameter shall be

σai

a

i

i am

p ds

r dr d s

pS=

⋅⋅

⋅ ⋅ + ⋅⋅ + +

+ ≤2

2 0 52 20 0

.(A 4-11)

The strength condition for the extrados at given outside dia-meter shall be

σaa i a

i

a i a

a am

p d s ss

R d s sR d s

pS

= ⋅ − −⋅

⋅

⋅ ⋅ + ⋅ + ⋅ − ⋅⋅ + −

+ ≤

( 0 0

0

0 0

0

22 0 5 0 5 1 5

2 2

)

. . . (A 4-12)

A 4.4 Bends and curved pipes under external pressure

For bends and curved pipes under external pressure allrequirements of clause A 2.2 apply with the following addi-tional requirements:

a) The buckling length l shall be determined over the de-veloped length of the bend or curved pipe.

b) In the calculation against plastic deformation as perSection A 2 the additional safety factor fv = 1.2 shall bereplaced by fvB according to the following equation:

f f

rd

rd

vB va

a

= ⋅−

−

0 25

0 5

.

.(A 4-13)

A 4.5 Reducers

Reducers shall be calculated in accordance with the re-quirements of clause A 2.4.2.

KTA 3201.2

≈

ii 0

i

B

0.5

1.2

1.3

1.0

1.1

0.1

0.15

0.05

0

/ ds

0.2

= 0.25

1.4

1.7

1.8

5

1.6

1.9

/ dr

2.0

Fact

or

1.5 2.0

1.5

1.0 2.5 4.0 4.53.0 3.5

Figure A 4-3: Factor Bi for the intrados at given inside diameter

KTA 3201.2

≈

0 a/ d = 0.25

i

s

0.05

a

0

0.2

0.15

0.1

1.05

1.1

1.15

B

0.5

1.0

1.2

1.35

1.4

5

1.3

1.45

/ dR

1.5

Fact

or

1.5 2.0

1.25

1.0 2.5 4.0 4.53.0 3.5

Figure A 4-4: Factor Bi for the intrados at given outside diameter

KTA 3201.2

≈

i

a

0

i

B

0.5

0.80

0.825

0.75

0.775

0.2

0.15

0

= 0.25/ ds

0.1

0.05

0.85

0.925

0.95

5

0.90

0.975

/ dr

1.00

Fact

or

1.5 2.0

0.875

1.0 2.5 4.0 4.53.0 3.5

Figure A 4-5: Factor Ba for the extrados at given inside diameter

KTA 3201.2

≈

i

a

0

a

B

0.5

0.80

0.825

0.75

0.775

0.1

0.15

0

0.05

/ ds

0.2

= 0.25

0.85

0.925

0.95

5

0.90

0.975

/ dR

1.00

Fact

or

1.5 2.0

0.875

1.0 2.5 4.0 4.53.0 3.5

Figure A 4-6: Factor Ba for the extrados at given outside diameter

KTA 3201.2

A 4.6 Butt welding tees

A 4.6.1 Butt welding tees forged from solid

A 4.6.1.1 Scope

(1) These calculation rules apply to butt welding tees forgedfrom the solid as well as bored and turned butt welding teeswith nominal diameter not exceeding DN 100. They onlyconsider loadings resulting from internal pressure. Addi-tional forces and moments shall be considered separately.

(2) The dimensions a and b shall not be less than the valuesgiven in DIN 2615-2.

(3) The external transition radius r2 shall be at least0.1 ⋅ dAa.

(4) A wall thickness ratio sA/sH not exceeding 2 is permit-ted for dAi not exceeding 50 mm. This also applies to nozzleswith dAi greater than 50 mm, provided that the diameterradio dAi/dHi does not exceed 0.2. For branches with a di-ameter radio dAi/dHi greater than 0.2 the ratio sA/sH shallbasically not exceed 1.3. Higher values are permitted if

a) the additional nozzle wall thickness exceeding theaforementioned wall thickness ratio is not credited forreinforcement of the nozzle opening but is selected fordesign reasons

orb) the nozzle is fabricated with reinforcement area reduced

in length (e.g. nozzles which are conical to improve testconditions for the connecting pipe) in which case thelacking metal area for reinforcement due to the reducedinfluence length may be compensated by adding metalto the reduced influence length

orc) the ratio of nozzle diameter to run pipe diameter does

not exceed 1 : 10.

A 4.6.1.2 General

The weakening of the run pipe may be compensated by anincrease of the wall thickness in the highly loaded zone atthe opening (see Figure A 4-7) which can be obtained byforging or machining.

A 4.6.1.3 Design values and units

See clause A 4.7.3 and Figure A 4-7 with respect to the de-sign values and units. In addition, the following applies.


dHa nominal outside diameter of runpipe at outlet

mm

dAa nominal outside diameter for branchconnection

mm

s1 nominal wall thickness of run pipeat outlet

mm

s2 nominal wall thickness for branchconnection

mm

sA+ equivalent wall thickness for branch

connectionmm

sH+ equivalent wall thickness for run

pipe at outletmm

p+ allowable internal pressure in tee N/mm2


(1) For the calculation of the effective lengths of the run andthe branch clause A 4.7.4.2 shall apply.

(2) The required area of reinforcement shall be determinedaccording to clause A 4.7.4.1.

Ha

Aa

Ai

A

Hi

H

2

2

1d

s

ba a

r

d

s

d

s

s

d

Figure A 4-7: Branch forged from solid, bored or turned

A 4.6.1.5 Equivalent wall thicknesses for connection atbranch and run pipe outlet

The wall thicknesses sH+ and sA

+ required by Section 8.4 for

stress analysis are those wall thicknesses obtained for pipeswith the outside diameters dHa and dAa if they are dimen-sioned with the allowable internal pressure p+ for tees.Then, the following applies.

sp d

S pHHa

m

++

=⋅

⋅ +2(A 4-14)

s s d dA H Aa Ha+ += ⋅ / (A 4-15)

For simplification p+ = p can be taken.

A 4.6.2 Die-formed butt welding tees

A 4.6.2.1 Scope

(1) These calculation rules apply to seamless tees fabricatedby die-forming from seamless, rolled or forged pipes (seeFigure A 4-8).

2

1

Ha

Aa

2

d

a

b

a

s

r

d

s

Figure A 4-8: Die-formed butt-welding tee

KTA 3201.2

(2) The dimensions a and b shall not exceed the valuesgiven in DIN 2615-2. For tees with nominal diameters excee-ding DN 300 the following equations apply for the dimen-sions a and b:

a ≥ 0.75 dHa (A 4-16)

and

b ≥ 0.5 dHa + 0.25 dAa (A 4-17)

(3) The external transition radius r2 shall be at least0.1 ⋅ dAa.

(4) At no location shall the wall thickness of the tee be morethan twice and not less than 0.875 times the connecting wallthickness s1. Only at the branch outlet the wall thicknessmay be reduced to 0.875 ⋅ s2 on a maximum length of 2 ⋅ s2.

A 4.6.2.2 Design values and units

See clause A 4.7.3 and Figure A 4-8 regarding the designvalues and units. In addition, the following applies:


Ap pressure loaded area according toFigure A 4-9

mm2

Aσ effective cross-sectional areas acc. toFigure A 4-9 upon deduction of wallthickness

mm2

dHa nominal outside diameter of runpipe at outlet

mm

dAa nominal outside diameter of branchconnection

mm

sH+ equivalent wall thickness of run

pipe at outletmm

sA+ equivalent wall thickness for branch

connectionmm

s1 nominal wall thickness for run pipeat outlet

mm

s2 nominal wall thickness for branchconnection

mm


(1) With eH as maximum value of

eH = dAi (A 4-18)

eH = 0.5 ⋅ dAi + sH + sA (A 4-19)

eH = 0.5 ⋅ dAi + sA + r2 ⋅ (1 - sin α), (A 4-20)

however, not to exceed eH = a and with eA as the greatervalue of

eA = 0.5 ⋅ ( )0 5 2. + r⋅ ⋅d sAm A (A 4-21)

eA = r2 ⋅ cos α (A 4-22)

however not to exceed

eA = b - (r2 + sH) ⋅ cos α - 0.5 ⋅ dHi (A 4-23)

the following condition shall be satisfied

σα

σV

p p p pmp

A A A A

AS≤ ⋅

+ + ++

≤1 2 3 4 0 5

/cos.

(A 4-24)

(2) With ′eH as maximum value of

′eH = 0.5 ⋅ ( )d d sAi Hm H+ ⋅ ⋅0 5. (A 4-25)

′eH = 0.5 ⋅ dAi + 2/3 ⋅ (sH + sA) (A 4-26)

′eH = 0.5 ⋅ dAi + sA + r2 ⋅ (1 - sin α), (A 4-27)

however, not to exceed ′eH = a, and with eA as computed

above the following condition shall be satisfied additionally

′ ≤ ⋅′ + ⋅ + +

′+

≤σ

α

σV

p p p pmp

A A A A

AS1 2 3 42 3

0 5/cos /

.

(A 4-28)

The areas Ap and Aσ are shown in Figure A 4-9.

σ σ

′

′

α

′

p2

A

2

H

A

Ai

Aa

H

Ha

p3

01

Hi

p1

p4

p1

02

H

r

ss

da

e

e

e or

A

AA

A

or AA

or

ds

s

d

A

b

d

Figure A 4-9: Reinforcement area dimensions for buttwelding tees

A 4.6.2.4 Equivalent wall thickness for connection of runpipe and branch outlet

(1) The connecting wall thicknesses sH+ and sA

+ required by

Section 8.4 for stress analysis then lead to a value S being thegreater value obtained from σV and ′σV

, (see clause

A 4.6.2.3) to become

sp d

S pHHa+ =

⋅⋅ +2

(A 4-29)

sp d

S ps d dA

AaH Aa Ha

+ +=⋅⋅ +

= ⋅2

/ (A 4-30)

(2) As S ≤ Sm must be satisfied, sH+ and sA

+ can also be

determined with Sm instead of S.

KTA 3201.2

A 4.7 Reinforcement of openings in pipe run

A 4.7.1 Scope

(1) The scope of the calculation rules hereinafter is given inclause A 2.2.2.1

(2) The rules consider the loadings resulting from internalpressure. Additional forces and moments shall be consid-ered separately.

A 4.7.2 General

(1) Openings shall be circular or elliptical. Further require-ments are to be met when using the stress intensity valuesaccording to Section 8.4.

(2) The angle β (see Figure A 2.7-8) between nozzle axis andrun pipe axis shall not be less than 60° , but shall not exceed120°.

(3) Openings in a run pipe may be reinforced as follows:

a) by selecting a greater wall thickness for the run pipethan is required for an unpierced run. This wall thick-ness shall be provided at least up to a length eH meas-ured from the axis of the opening,

b) by branches which, on a length eA measured from thesurface of the run, have a greater wall thicknesses than isrequired for internal pressure loading. The material re-quired for reinforcement shall be distributed uniformlyover the periphery of the branch,

c) by a combination of the measures shown in a) and b)above.

Regarding a favourable shape not leading to increased loa-dings/stresses subclause c) shall be complied with.

(4) In the case of several adjacent openings the conditionsfor the area of reinforcement shall be satisfied for be planesthrough the centre of the opening and normal to the surfaceof the run pipe.

(5) When an opening is to be reinforced the following di-ameter and wall thickness ratios shall be adhered to:

A wall thickness ratio sA/sH not exceeding 2 is permitted fordAi not exceeding 50 mm. This also applies to branches withdAi greater than 50 mm, provided that the diameter radiodAi/dHi does not exceed 0.2. For branches with a diameterradio dAi/dHi greater than 0.2 the ratio sA/sH shall basicallynot exceed 1.3. Higher values are permitted if

a) the additional branch wall thickness exceeding theaforementioned wall thickness ratio is not credited forreinforcement of the nozzle opening, but is selected fordesign reasons or

b) the branch is fabricated with reinforcement area reducedin length (e.g. branches which are conical to improve testconditions for the connecting pipe) where the lackingmetal area for reinforcement due to the reduced influ-ence length may be compensated by adding metal to thereduced influence length or

c) the ratio of branch diameter to run pipe diameter doesnot exceed 1 : 10.

(6) Openings need not be provided with reinforcement ifthe following requirements are met:

a) A single opening has a diameter not exceeding

0 2 0 5. .⋅ ⋅ ⋅d sHm H , or, if there are two or more openings

within any circle of diameter 2 5 0 5. .⋅ ⋅ ⋅d sHm H , but the

sum of the diameters of such unreinforced openings

shall not exceed 0 25 0 5. .⋅ ⋅ ⋅d sHm H and

b) no two unreinforced openings shall have their centrescloser to each other, measured on the inside wall of therun pipe, than the sum of their diameters, and

c) no unreinforced opening shall have its edge closer than

2 5 0 5. .⋅ ⋅ ⋅d sHm H to the centre of any other locally

stressed area (structural discontinuity).

Note:See clause 7.7.2.2 for definition of locally stressed area.

(7) Combination of materials

Where run pipe and branch are made of materials withdiffering design stress intensities, the stress intensity of therun pipe material, if less than that of the branch, shall gov-ern the calculation of the entire design provided that theductility of the branch material is not considerably smallerthan that of the run pipe material.

Where the branch material has a lower design stress inten-sity, the reinforcement zones to be located in areas providedby such material shall be multiplied by the ratio of the de-sign stress intensity values of the reinforcement material andthe run pipe material.

Differences up to 4 % between the elongation at fracture ofthe run pipe and branch material are not regarded as con-siderable difference in ductility in which case δ5 shall not beless than 14 %.

Where the materials of the run pipe and the branch differ intheir specific coefficients of thermal expansion, this differ-ence shall not exceed 15 % of the coefficient of thermal ex-pansion of the run pipe metal.

A 4.7.3 Design values and units

(See also Figures A 2.7-8 and A 4-10 to A 4-13)


dAi inside diameter of opening plustwice the corrosion allowance c2

mm

dAm mean diameter of branch mm

dHi inside diameter of run pipe mm

dHm mean diameter of run pipe mm

dn nominal diameter of tapered branch mm

r1 inside radius of branch pipe mm

r2 minimum radius acc. to clause 5.2.6 mm

sA nominal wall thickness of branchincluding reinforcement, but minusallowances c1 and c2

mm

KTA 3201.2


sA0 calculated wall thickness of branch mm

sH nominal wall thickness of shell, ves-sel or head at the opening includingthe reinforcement, but minus allow-ances c1 and c2

mm

sH0 calculated wall thickness of run pipe mm

sR nominal wall thickness of branchpipe minus allowances c1 and c2

mm

sR0 calculated wall thickness of con-nected piping

mm

y slope offset distance mm

α angle between vertical and slope(see also Figures A 4-10, A 4-11 andA 4-13)

degree

The following notations can be taken from Figures A 2.7-8and A 2.7-9.


eA limit of reinforcement measurednormal to the run pipe wall

mm

eH half-width of the reinforcementzone measured along the midsurfaceof the run pipe

mm

′eH half-width of the zone in which twothirds of compensation must beplaced

mm

A1, A2,A3

metal areas available for reinforce-ment

mm2

β angle between axes of branch andrun pipe

degree

A 4.7.4 Calculation

A 4.7.4.1 Required reinforcement

(1) The total cross-sectional area A of the reinforcementrequired in any given plane for a pipe under internal pres-sure shall satisfy the following condition:

A ≥ dAi ⋅ sH0 ⋅ (2 - sinβ) (A 4-31)

(2) The required reinforcing material shall be uniformlydistributed around the periphery of the branch.

A 4.7.4.2 Effective lengths

(1) The effective length of the basic shell shall be deter-mined as follows:

eH = dAi (A 4-32)

or

eH = 0.5 ⋅ dAi + sH + sA (A 4-33)

The calculation shall be based on the greater of the twovalues. In addition two thirds of the area of reinforcementshall be within the length 2 ⋅ ′eH (Figure A 2.7-8 and A 2.7-9)

where

′eH is the greater value of either

′eH = 0.5 ⋅ [dAi + (0.5 ⋅ dHm ⋅ sH)1/2] (A 4-34)

and

′ = ⋅ + +e ds

sH AiA

H0 5.sinβ

(A 4-35)

(2) The effective length of a cylindrical branch shall be de-termined as follows:

eA = 0.5 ⋅ [(0.5 ⋅ dAm ⋅ sA)1/2 + r2] (A 4-36)

where

dAm = dAi + sA (A 4-37)

See also Figures A 4-10, A 4-11, A 4-12.

(3) The effective length of a tapered branch shall be deter-mined as follows:

eA = 0.5 ⋅ (0.5 ⋅ dn ⋅ sA)1/2 (A 4-38)

where

dn = dAi + sR + y ⋅ cosα (A 4-39)

See also Figure A 4-13.

For branches with tapered inside diameter dn shall be de-termined by trial and error procedure.

A 4.7.4.3 Loading scheme for metal areas available for rein-forcement

The metal areas A1, A2, A3 available for reinforcement usedto satisfy equation (A 4-31) are shown in Figures A 2.7-8 andA 2.7-9, and shall satisfy the condition A1 + A2 + A3 equal toor greater than A.

KTA 3201.2

αH

m

Rm

Hi

A

H

Aa

3

2

Ai

1

Ra

Am

R

R

H

Branch pipe

s

d

/2

d

d Offset

d

s /2

rr

s

sd

d

d

r

s

Figure A 4-10: Branch

α

=α

2

Rm

R

1

Ra

Aa

Ai A

3

H

H Hi

R

Am

Hm

d

d

Branch pipe

/2

s

d

/2

s

s

r

d

Offset

ds

r

90˚

d

d

s

r


2

Am

R

1

Ai

H

Aa

A

Hm

A

Hi

Hds

d

Branch pipe

/2

= sd

d

d

s /2

r

s

s

r


α

H

1

RRm

Ra

RAi

3

Hm

HH

i

Ha

H2

d /2

ds

d

s

/2

/2

d

rr

ds

r

Branch pipe

Branch

s

y

sd

Figure A 4-13 Branch

KTA 3201.2

Annex B

Calculation methods

The methods described hereinafter are intended to deter-mine the influence coefficients (e.g. unit shear forces andunit moments, stresses, deformations) characterizing themechanical behaviour due to loadings. These methods arebased on relationships derived theoretically or experimen-tally for the mechanical behaviour of the structure.

The calculation methods to be dealt with differ by the rela-tionships on which they are based, the adaptability to thegeometry, the type of loading and the mechanical behaviourof the materials, by the type of approach for solutions andtreatment of the systems of equations, by the expressivenessof the results obtained and the extent of methods applied.

B 1 Freebody method

B 1.1 Scope

B 1.1.1 General

The freebody method makes possible the calculation ofcoefficients influencing the mechanical strength (e.g.stresses) and the deformation behaviour (displacements androtations). The subdivision of the total structure in severalelements (bodies) assumes that for each element the rela-tionship between its edge deformations on the one hand andthe loadings as well as the unit shear forces and momentsacting on its edges on the other hand can be given. Whenapplying differential equations the subdivision into ele-ments is generally made such that the solutions of the ap-plied differential equations apply to the total freebodystructure.

The freebody method assumes that the distribution of de-formations and unit shear forces and unit moments over acertain cross-section can be represented by the respectiveunits in a defined point of this cross-section and from theserepresentative units the local units can be derived by meansof assumptions (e.g. linear distribution through the wallthickness). These assumptions shall be permitted for solvingthe problem.

The freebody method is primarily used to solve linearproblems.

B 1.1.2 Component geometry

The freebody method is primarily used for the structuralanalysis of components comprising shells of revolutions,circular plates, circular disks, and rings subject to twistingmoments.

Geometric simplifications of the free bodies (elements) andthe treatment of given structures by means of differentialequations for suitable substitute structures are permitted ifthis type of idealisation leads to sufficiently exact or conser-vative results.

Regarding the cross-sectional geometry of the elements it ispossible to consider anisotropy, e.g. double-walled shellswith stiffenings, orthotropic shells etc.

B 1.1.3 Mechanical loadings and edge conditions

Except for the prerequisites of clause B 1.1.1 the freebodymethod principally does not further restrict the considera-tion of mechanical loadings and boundary conditions. How-ever, only in conjunction with rotationally symmetric load-ings and boundary conditions relatively simple equationsapply to the stress and deformation condition of the variousrotationally symmetric freebody elements. Non-rotationallysymmetric loadings and boundary conditions may also beconsidered by the aid of Fourier series; the extent of calcula-tion grows with an increase in the number of the requiredFourier coefficients.

In addition, initial distortions, such as thermal strains, canbe taken into account.

B 1.1.3.1 Local distribution of loadings

The mechanical loadings can be considered as point, line,area or volume loads.

B 1.1.3.2 Time history of loading

Any time-dependent loadings can principally be analysedby means of the freebody method in which case the usualmethods of dynamics can be applied.

B 1.1.4 Kinematic behaviour of the structure

When applying the freebody method a fully linear kinematicbehaviour can generally be assumed. This means that thedeformations are small with regard to the geometric dimen-sions and the conditions of equilibrium are set for the unde-formed element (1st order theory).

B 1.1.5 Material behaviour

In most cases, linear material behaviour (stress-strain rela-tionship) is assumed, and if required, the temperature de-pendence of the constants and initial strains is considered.The material is mostly assumed to be homogenous andisotropic.

Non-linear material behaviour may principally be consid-ered in which case the extent of calculation generally in-creases.

B 1.2 Principles

B 1.2.1 Preliminary remark

The principles of the freebody method will be explainedhereinafter because they are important for its applicationand the evaluation of the calculation results. These explana-tions also serve to define the terms used in this Annex.

Like for each thermo-mechanical calculation method thefreebody method is based on the physical principles of con-tinuum mechanics. These principles will be satisfied fully orby approximation when applying the freebody method.

KTA 3201.2

B 1.2.2 Basic terms and physical principles

B 1.2.2.1 Fields

The continuum theories describe the physical properties ofbodies by means of fields (e.g. displacement field, velocityfield, temperature field, and others) which at least in piecescan be considered a steady function of the fixed coordinatesand of the time, if required.

As indicated in B 1.1.1, the fields are only given by represen-tative units assigned to the respective cross-section.

B 1.2.2.2 Kinematic relationships

Where a structure behaves like a continuum the displace-ment field in its interior is steady at any time. By kinematicboundary conditions values for displacement magnitudes atthe edges of the area to be calculated are prescribed.

The steadiness of a displacement field for structures thedeformation of which is only described by displacementmagnitudes of an area or a line (plates and shells or beams)also means that at any point of the referred section or linenot only the displacements but also the rotations about thetwo axes lying in the cross-section or about the three-dimensional axes are steady.

Where a displacement field is steady and satisfies the kine-matic boundary conditions it is termed kinematically com-patible.

Examples for kinematic edges are:

- rigid restraints

- rigid supports

- prescribed edge displacement magnitudes.

In the case of free supports the condition of zero displace-ment normal to the free surface, and in the case of hingedsupports the condition of zero displacement of the hinges iskinematic (however, not the condition of freedom fromstress or forces).

The deformation in the proximity of any point of the struc-ture is described by distortions (change in length of a lineelement, change in angle between two line elements). Theprerequisite for a linear relationship between the displace-ments are small distortions or rotations where the order ofmagnitude of the rotations is, at maximum, equal to theorder of magnitude of the squared distortions; where theseprerequisites are satisfied, we can speak of geometric line-arity.

B 1.2.2.3 Conservation laws

For a portion or the total of a structure the impulse or mo-mentum principle as well as static boundary conditions aresatisfied. For quasi-steady mechanical events this leads tothe internal conditions of equilibrium:

a) sum of forces on the (deformed) volume element equalszero

b) sum of moments on the (deformed) volume elementequals zero.

These relationships connect the volume forces with thederivation of stresses from the coordinates. In the case ofdynamic problems the portions of the inertial forces addedto the volume forces must be considered.

Boundary conditions prescribing values for magnitudes offorce are called static boundary conditions.

Examples for static boundary conditions are:

- edge loaded by area load, line load or point load

- load-free edge without further conditions

- condition for frictional forces in free supports

- condition for freedom from momentum of a hingedsupport.

At all points with static boundary conditions there will beequilibrium between external concentrated or distributedforces and moments on the one hand and the respectiveinternal forces and moments or stress components on theother hand; here the external forces may be equal to zero.

The conditions of equilibrium are equivalent to the principleof virtual work which can be formulated as follows:

Where a body is in equilibrium the external virtual workdone by the external loading (including volume forces) withvirtual displacements is equal to the internal virtual workdone by the stresses with virtual distortions.

Here, virtual displacements are small kinematically admis-sible distortions of any magnitude. Virtual distortions can bederived from virtual displacements by means of the usualdisplacement-distortion-relationships. For dynamic prob-lems the Lagrange-d'Alembert principle applies additionallywhich is obtained from the principle of virtual work andaddition of the inertial forces.

Where the structure is also subject to thermal loads(temperature balance) in addition to mechanical loads, theimpulse and momentum principle shall be supplemented bythe equation of energy to describe a physical behaviour,where the energy equation can be formulated as follows:

The change in time of the sum of internal and kinematicenergy of the volume element is equal to the sum of themagnitudes of surface and volume forces on the elementand the thermal energy added per unit of time.

This condition establishes, by incorporation of the impulseand momentum principles, the relationship between thechange in time of temperature in the element and the three-dimensional derivations of the heat fluxes.

Where loadings of a structure are also due to fluidic occur-rences (e.g. in piping), the conservation law of mass (conti-nuity equation) shall be satisfied for the fluid in addition tothe impulse and momentum conservation laws.

The differential formulation of the conservation laws leadsto generally partial differential equations for the instantane-ous condition of the fields describing the physical system(displacement, displacement velocity, temperature, etc.).

B 1.2.2.4 Material laws

For the mechanical behaviour of a material the material lawsshow the linear relationship between stresses and strains,whereas e.g. in the case of elasto-plastic behaviour the ma-terial law is non-linear. In the case of elastic isotropic mate-rials the material behaviour can be described by two inde-pendent coefficients. Elastic anisotropic materials are prin-cipally not considered by the freebody method.

Additional parameters are required in the case of thermalloading (coefficient of thermal expansion, thermal diffusivi-

KTA 3201.2

ty, temperature-dependent elastic moduli, etc.) and in thecase of flowing fluids (heat transfer coefficients, viscosity,etc.).

B 1.2.3 Principles of the method

B 1.2.3.1 Basic idea

The basic idea of the freebody method is to consider thestructure to be evaluated a statically or dynamically inde-terminate system of partial structures (freebodies) whichunder the given loadings and boundary conditions are sub-ject to deformation not in dependence of each other, butunder the additional effect of mutual mechanical influences.

B 1.2.3.2 Mechanical behaviour of the individual body

The freebody method uses matrix relations between magni-tudes of deformation and force. These relationships can bedetermined theoretically or experimentally.

The pertinent differential equations shall be derived fromthe impulse and momentum laws, the kinematic relation-ship between distortions and deformations as well as fromthe material law.

Besides the given loads (external forces) and the pressureand temperature distributions additional statically determi-nate forces shall be applied, if required, at one edge or sev-eral edges of the considered freebody to obtain equilibriumof forces for this body. These additional forces therefore arealso known and shall be applied on the adjacent edge of theconnecting freebody element in order to maintain the equi-librium of the total freebody structure.

The deformations resulting from the given loads, the pres-sure and temperature distributions and the known addi-tional forces are called known deformations.

Where differential equations are available for the pertinentfreebody element describing its mechanical behaviour, ana-lytical or numerical solutions can be developed by integra-tion when the boundary conditions are maintained. Thesesolutions, in the form of matrix relations, will show therelationship between the known physical parameters(forces, moments, displacements and rotations) at any pointof the pertinent freebody element. These relationships mayalso be found by means of other mathematical methods orby experiments.

B 1.2.3.3 Mechanical cooperation of freebody elements inthe system

Where the individual elements of a system are subjected togiven loads and additional forces, each element - seen for itsown - undergoes deformations as per clause B 1.2.3.2.

The loads and additional forces applied on each element arein equilibrium with each other, however, the deformationsof adjacent elements generally do not satisfy the compatibil-ity conditions at first.

To obtain compatibility therefore the application of suitableadditional indeterminate forces and deformation parametersis required the magnitude and orientation of which shall bedetermined from the mutual mechanical influences of allelements of the freebody system. The equations of this sys-tem are derived by means of equilibrium conditions or by

the aid of the principle of virtual work, but here are appliedon the entire freebody system.

Depending on the calculation method, the relationships forthe unknown forces and deformation parameters form asystem of simultaneous equations for all force and deforma-tion parameters of the entire structure or if transfer-functionmatrices are used, a system of equations for combining thestate vectors at the edges (e.g. beginning and end) of thestructure. In such a case, the unknown parameters withinthe entire structure can be determined one after the other ifthe prevailing boundary conditions and calculated statequantities at the edges of the entire structure are adhered to.

B 1.2.3.4 Resulting force and deformation parameters

The solutions resulting from the system of equations for theunknown force and deformation parameters, together withthe known force and deformation parameters, will lead tothe resulting force and deformation parameters. Deforma-tions and pertinent stresses shall be evaluated.

B 1.2.3.5 Properties of the solutions

The solutions obtained by the freebody method representapproximations for general reasons:

a) The differential equations may contain simplificationsmade either to make an analytical solution possible or toobtain a simplified analytical solution (e.g. continuumregarded as thin shell). The simplifications in the differ-ential equations themselves shall be based on physicalgeometric conditions which are permitted with respectto the problem finding and calculation method.

b) The composite solution of the differential equation mayrepresent an approximation e.g. with respect to theboundary conditions or the loading, or it will only applyin a limited range of definition.

c) If the solution of the differential equations is found bynumerical integration, the exactness depends on the or-der of approximation and the step size.

d) The system of equations for the elastic cooperation offreebody elements in the system may be conditioned un-favourably, e.g. in the case where the element length issmall with respect to the die-out length.

B 1.3 Application

B 1.3.1 Idealisation

B 1.3.1.1 Idealisation of the structure

The total structure is substituted, by way of approximation,by a number of adjacent freebody elements the mechanicalbehaviour of which corresponds to that of the structure asfar as required by the intended expressiveness of the resultsobtained. The meridional lengths of the elements shall beselected in dependence of the approximate character of thedifferential equations used and their approximate solutionsas well as of the die-out lengths of edge discontinuities andthe numerical character of the pertinent systems of equa-tions.

KTA 3201.2

B 1.3.1.2 Idealisation of loads

At first the individual freebody elements are consideredindependently of each other and subjected to the givenexternal influences, e.g. pressure and temperature distribu-tions, as well as the given loads (external edge forces andmoments). If the physical model used does not make possi-ble the exact consideration of the given load applied, theload may also be substituted by approximation by a suitablestatically equivalent system of forces; simplifications madehere shall be permitted with regard to the problems to besolved.

The distribution of edge loads on the edges of adjacent ele-ments in the common cross-sectional area of which they areapplied can be made arbitrarily.

Besides the given loads additional statically determinateforces shall apply, if required on an edge or several edges ofthe element under consideration to obtain equilibrium offorces for this element. Accordingly, the additional forcesare also known and shall be applied with inverted signs onthe adjacent edge of the connecting element to maintain theequilibrium of forces of the entire structure.

B 1.3.1.3 Idealisation of boundary conditions

The static and kinematic boundary condition cannot beidealised exactly if the pertinent boundary conditions can-not be dealt with exactly by the approximate calculationsapplied. This applies e.g. to

a) rotationally non-symmetric boundary conditions withslight deviation of rotational symmetry in case of ap-proximate calculations for purely rotationally symmetricloadings

b) loadings of areas with little extension in one direction ifthe loadings are idealised as line loads

c) displacements along a curve approximated by draft oftraverse (progression).

Such approximations shall be permitted for the problems tobe solved.

B 1.3.1.4 Control of input data

A control of the input data is indispensable and should bemade, as far as possible by means of the data stored by theprogram.

Routines to check the input data as well as graphic represen-tations of input data, e.g. of the geometry, boundary condi-tions and loadings are purposeful.

B 1.3.2 Programs

B 1.3.2.1 General

Calculations made by means of the freebody method aregenerally made by programs on data processing systems.

B 1.3.2.2 Documentation of programs

Each program used shall be documented.

The following items shall be documented or indicated:

a) identification of the program including state of change

b) theoretical principles

c) range of application and prerequisites

d) description of program organisation as far as requiredfor the use and evaluation of the program

e) input instructions for program control and problemdescription

f) explanation of output

g) examples of application

The theoretical part of the documentation shall contain alltheoretical principles on which the program is based.

If required, the respective literature shall be referred to.

In the examples of application part demonstrative andchecked calculation examples for application shall be con-tained.

B 1.3.2.3 Reliability of programs

In case of extensive freebody method programs it cannot beassumed that all possible calculation methods are free fromerrors. Therefore the following items shall be considered toevaluate the reliability of the program:

a) modular program build-up

b) standardized program language

c) central program maintenance

d) large number of users and extensive use of the program,especially for the present range of application.

The program can be expected to operate reliably to the ex-tent where the aforementioned items are satisfied for therespective program version.

B 1.3.3 Evaluation of calculation results

B 1.3.3.1 General

The first step to evaluate calculation results is the checkwhether the results are physically plain. This plausibilitycontrol is a necessary but not sufficient condition for theusability of the results obtained. Therefore, the calculationmodel, the correctness of the data and the proper perform-ance and use of the program is to be checked additionally.

B 1.3.3.2 Physical control

For the freebody method the physical control of the resultscovers the check of the following solution results:

a) Consistency conditions

b) equilibrium conditions

c) edge conditions

d) symmetry conditions

e) stresses and deformations in locations remote from dis-continuities

f) die-out of edge discontinuities.

KTA 3201.2

B 1.3.3.3 Numerical control

B 1.3.3.3.1 Examination of results obtained by numericalsolution procedures

A method often used to numerically solve differential equa-tions is e.g. the Runge-Kutta method which, with generalother approximation methods to be performed step-by-stephas in common that the exactness of the solution stronglydepends on the order of the derivations considered and thestep sizes selected. Therefore, it is not possible to evaluatethe absolute error within the Runge-Kutta method. Where,however, the approximate solutions converge with decreas-ing step sizes to obtain an exact solution, a relative exactnesscan be demonstrated by comparison of two approximatesolutions obtained by different step sizes.

B 1.3.3.3.2 Check of the calculation method

When applying the freebody method numerical errors mayoccur especially when solving large systems of equationsdue to the use of numerical solution methods for the indi-vidual freebody element (e.g. numerical integration) or dueto the application of transfer-function matrices on the free-body system. In such cases, the numerical exactness shall beexamined.

B 1.3.3.3.3 Examination of the solution vectors

Where the elements of the solution vector are inserted in theoriginal equations, information is obtained on the order ofmagnitude of the numerical error if the coefficient matrixhas been conditioned to a sufficient extent.

B 1.3.3.4 Comparison with results obtained from otherexaminations

B 1.3.3.4.1 General

To evaluate the results from freebody method calculationsthe following may substitute or supplement other examina-tions:

a) comparison with other calculations made to the freebodymethod

b) comparison with calculations made to other methods

c) comparison with experimental results.

The selection of the examination method to be used for thecomparison depends on where the emphasis of examinationis to be placed (theoretical formulation, programming, ide-alisation, input data and, if required, numerical exactness).

For the comparative calculation it is possible to use equiva-lent or differing programs, operating systems, data process-ing plants and idealisations.

B 1.3.3.4.2 Comparison with other calculations made to thefreebody method

By comparison of results obtained from a calculation to thefreebody method with results obtained from other calcula-tions made to the freebody method, the theoretical formula-tion, programming, idealisation, input data, and numericalexactness of the calculation can be evaluated in dependenceof the program used and the idealisation selected.

Under certain circumstances, the numerical exactness of thecalculation may be improved if the number of digits is in-creased or, in case of numerical integration, the step size isdecreased.

The quality of idealisation may be examined by comparativecalculations with other generally more precise idealisationsor idealisations covering the mechanical behaviour of thecomponent more exactly.

The theoretical formulation can be examined together withthe programming by comparative calculations using pro-grams with other theoretical bases if the same idealisationand number of digits is used.

Comparative calculations made with the same or differentprograms and the same idealisations serve to control theinput data if the latter have been established independently

B 1.3.3.4.3 Comparison with calculations made to other cal-culation methods

Where other calculation methods, e.g. the finite differencesmethod (FDM) according to Section B 2 or the finite elementmethod (FEM) according to Section B 3 satisfy the condi-tions for treating the respective problem, they may be usedfor comparative calculations. Such calculations then serve toevaluate the sum of all properties of both solutions.

B 1.3.3.4.4 Comparison with results obtained by experi-ments

The evaluation of results obtained from calculations to thefreebody method may be made in part or in full by compari-son with the experimental results in which case the particu-larities and limits of the measuring procedure shall be takeninto account.

The measuring results may be obtained by measurements onthe model (e.g. photoelastic examinations) or measurementson the components (strain or displacement measurements) ifall essential parameters can be simulated. When usingmodels they shall be representative for the problem to besolved.

This comparison especially serves to evaluate the admissi-bility of assumptions on which the freebody method isbased.

B 2 Finite differences method (FDM)

B 2.1 Scope

The finite differences method (FDM) makes possible thecalculation of coefficients influencing the mechanicalstrength (e.g. stresses) and the deformation behaviour (dis-placements and rotations). The requirements laid downhereinafter mainly for problems of structural mechanics canbe applied accordingly to problems of heat transfer, fluidmechanics and coupled problems.

With this method it is possible to cover any type of geome-try and loading as well as of structural and material behav-iour.

Simplifications for performing calculations with respect tothe geometric model, the material behaviour, the loadings

KTA 3201.2

assumed, and the kinematic behaviour shall be purposefullyadjusted to the problem to be solved.


The geometry of the component to be analysed may be one-dimensional, two-dimensional or three-dimensional.

The capacity of the data processing plant or of the individ-ual program as well as the extent required may be limited tocover the entire geometry.

B 2.1.3 Mechanical loadings and boundary conditions

When applying the finite differences method there are prac-tically no limitations as to the type of mechanical loadingand boundary conditions of a component.

In addition, initial distortions, such as thermal strains, maybe taken into account.


The mechanical loadings may be considered as point, areaand volume loads.


Any time-dependent loadings can principally be analysedby means of the finite differences method in which case theusual methods of dynamics can be applied.


Kinematic behaviour of the structure can principally bedemonstrated in which case large rotations and distortions,if any, as well as plays have to be considered.

Generally the method is limited to a kinematically full-linearbehaviour of the structure.

If required, primary instabilities (buckling) may be consi-dered.


In most cases, the method is limited to linear material behav-iour (linear stress-strain relationship) and, if required, thetemperature dependence of the constants and initial strainsis considered.

The consideration of non-linear material behaviour (e.g.rigid-plastic, linear elastic-ideally plastic, general elasto-plastic, viscoelastic) is possible, entailing, however, greatexpense.

B 2.2 Principles of FDM


The principles of FDM will be explained hereinafter only tothe extent essential for FDM application and the assessmentof the calculation. These explanations also serve to definethe terms used in this Annex.

Like for each thermo-mechanical calculation method theFDM is based on the physical principles of continuum me-chanics. Depending on the type of discretization method,these principles will be satisfied fully or by approximationwhen applying the finite differences method.


B 2.2.2.1 Fields

The continuum theories describe the physical properties ofbodies by means of fields (e.g. displacement field, velocityfield, temperature field, and others) which at least in partscan be considered a steady function of the fixed coordinatesand of the time, if required; in this case fixed three-dimen-sional or body coordinates may be used (Euler or Lagrangecoordinates).


Where a structure behaves like a continuum the displace-ment field in its interior is steady at any time. By kinematicboundary conditions values for displacement magnitudes atthe edges of the area to be calculated are prescribed. Wherea displacement field is steady and satisfies the kinematicboundary conditions it is termed kinematically compatible.



a) rigid restraints

b) rigid supports

c) prescribed edge displacement magnitudes.


The deformation in the proximity of any point of the struc-ture is described by distortions (change in length of a lineelement, change in angle between two line elements). Theprerequisite for a linear relationship between the displace-ments are small distortions or rotations where the order ofmagnitude of the rotations is, at maximum, equal to theorder of magnitude of the squared distortions; where theseprerequisites are satisfied, we can speak of geometric line-arity.

B 2.2.2.3 Conservation laws and equilibrium conditions



KTA 3201.2



Boundary conditions prescribing values for magnitudes offorce are called static boundary conditions.


a) edge loaded by area load, line load or point load

b) load-free edge without further conditions

c) condition for frictional forces in free supports

d) condition for freedom from momentum of a hingedsupport

At all points with static boundary conditions there will beequilibrium between internal stresses and forces and theexternal loadings applied which may be equal to zero.




Where the structure is also subject to thermal loads (tempe-rature balance) in addition to mechanical loads, the impulseand momentum principle shall be supplemented by theequation of energy to describe a physical behaviour, wherethe energy equation can be formulated as follows:



Where loadings of a structure are also due to fluidic occur-rences (e.g. in piping), the conservation law of mass (conti-nuity equation) shall be satisfied for the fluid in addition tothe impulse and momentum conservation laws.



For the mechanical behaviour of a material the material lawsshow the relationship between stresses and strains. In thecase of linear-elastic material behaviour this relationship islinear, whereas e.g. in the case of elasto-plastic behaviour

the material law is non-linear. In the case of linear-elasticisotropic materials the material behaviour can be describedby two independent coefficients. In the case of linear-elasticanisotropic materials up to 21 independent coefficients maybe required.

The material law for a fluid gives the relationship betweenphysical states, e.g. for an ideal gas, between pressure, den-sity and temperature (thermal state equation).

Additional parameters are required in the case of thermalloading (coefficient of thermal expansion, thermal diffusiv-ity, temperature-dependent elastic moduli, etc.) and in thecase of flowing fluids (heat transfer coefficients, viscosity,etc.).

B 2.2.3 Discretization

B 2.2.3.1 Procedure

The representation of the structure as a mathematical modelis termed idealisation.

The base for the FDM are the differential equations describ-ing the problem. These differential equations are solvednumerically by substituting the differential quotients bydifference quotients thus reducing the problem of integrat-ing a differential equation system to the solution of an alge-braic equation system (discretization).

According to the type of solution of the equation systemdistinction is made between indirect and iterative differ-ences methods.

In addition, distinction is made as to the type of differenceexpressions i.e. to the degree of formulation between com-mon and improved differences methods.

The system to be examined is considered either a uniformlycalculation area or divided into partial areas which arecoupled. This calculation area is covered by a mesh of pointsof supports.

In the case of certain methods differing points of supportsare used for the various fields because this makes the con-struction of differential quotients easier.

The vector continuously changing according to the infini-tesimal theory thus is replaced by a finite set of discretevectors which are only defined at the points of support ofthe mesh (junction nodes). Accordingly, continuous fieldsare approximated by finite discrete sets of functional values(discrete field components) at the junction nodes and, ifrequired, also at intermediate points.

The exactness of the solution of differential equations de-pends, among other things, on the algebraic combination ofthe discrete field components. Which degree of exactness isto be attributed to a three-dimensional differential quotientcan be identified by the fact that the differential operationand the assigned differences operation is applied to a three-dimensional wave (Fourier method) and the results arecompared. Where the results only differ in square andhigher exponent terms of the ratio of the three-dimensionalextension of a mesh cell to the wavelength of the mode, thisapproximation is termed 2nd order approximation. At suf-ficiently small values of this ratio the 2nd order approxima-tion will suffice in most cases.

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The maximum allowable mesh width depends on the small-est wavelength of the field to be approximated (long waveapproximation).

This decision aid is not limited to linear problems as in mostcases non-linear problems can be approximated piecewiseto linear states of change. However, in the case of non-linearbehaviour it shall be credited that due to the dependence ofthe material characteristics (such as modules and density) ofthe extent of loading the wavelengths are also influenced.With respect to the exactness it can also be said that thesmallest wavelength occurring governs the mesh width ofthe point of support mesh.

For the discretization of the time variables at occurrenceswhich depend both on the three-dimensional coordinatesand the time, similar criteria can be won by applying thedifferences equation to a Fourier mode changing three-dimensionally and in time. The resulting relationship be-tween dispersion velocity and wavelength (dispersion rela-tionship) depends on the mesh width of the (three-dimensional) point of support mesh and additionally fromthe step in time (i.e. from the points of supports in the timedomain). By a suitable selection of the step in time the dis-persion relationship can approach the differential equation(at least in certain in frequency areas).

Depending on the form of algebraic combination of thediscrete field components in the differences equation explicitor implied procedures for the solution of differences equa-tions are obtained. A solution method is termed explicit ifthe discrete field components at any point of time can becalculated directly from values known for earlier points oftime of the components without the need of solving anequation system; if this is not the case, one speaks of impliedsolution methods.

Implied algorithms generally require an increased extent ofcalculation than explicit methods do; this higher extent may,however, be justified with respect to the exactness and sta-bility of the solutions (see clause B 2.3.2).

B 2.2.3.2 Characteristics of the solutions

The solutions calculated by FDM are approximate solutionsin two respects:

(1) Physical discretization

On account of the limited number of possible degrees offreedom due to the discretization of the continuum theproblem-relevant physical principles cannot generally besatisfied exactly. The following requirements for a differ-ences method shall be made so that the approximate solu-tions can reflect the physical occurrences to a sufficientlyexact extent:

a) Compatibility

The differences equations shall bring back marginaltransitions to infinitesimal cell extensions and time in-tervals to the differential equations to be solved. Here itshall be taken into account that there are three-dimensional and time step dependent differences equa-tions which among certain circumstances and dependingon the selection of increments converge to differing dif-ferential equations (inflexible diagram of differences ver-sus flexible diagram of differences).

b) Stability

The difference algorithm shall be established such thatthe discretization errors do not accumulate. In the case oftime-dependent problems a matrix (amplification ma-trix) can be given for any differences method, whichlinks the error at a certain point of time with the error atan earlier point of time. The stability of the solutions isensured if the amounts of all eigenvalues of the amplifi-cation matrix is smaller than or equal to unity.

This requirement cannot always be met (especially in thecase of non-linear differences systems) for eachrange of values of the relevant parameters or parameterfunctions (time step, cell size, constitutive equations,etc.), but in most cases only for certain limited ranges ofthese values. In such cases the difference algorithm isonly conditionally stable.

c) Convergence

The solution of the differences equations shall convergeagainst the exact solution if the three-dimensional andtime increments tend to zero. Where the differentialequations of a problem with correct start and boundaryconditions are approximated by consistent differencesequations, the stability of the differences solution is re-quired and will suffice for the convergence.

Where the shape of the discretized shape clearly deviatesfrom the actual shape of the structure, this may lead to inac-curacies. In many cases the approximation of curved con-tours changes the discrete field components by piecewisestraight or plane elements only incidentially, howevermagnitudes derived from the field components, such asdistortion and stress components can only hardly be inter-preted at such artifical kinks.

(2) Numerical approximation

For a given physical discretization the numerical solutiondeviates from the exact solution. This deviation is due to thefollowing two causes:

a) Due to the limited number of digits in the data process-ing system initial truncate errors and rounding errorswill occur. This may especially effect systems with ex-tremely differing physical characteristics in the calcula-tion model. By the calculation of conditioning figureswhich make possible an estimation of the amplificationof the initial truncate error by the rounding errors, onecan obtain a lower, often very conservative limit for thenumber of numerically exact digits.

b) In the case of certain algorithms, e.g. iterative solution ofequation or iterative solution of the eigenvalue problem,one error will remain which depends on the given limitof accuracy.

B 2.3 Application of FDM

B 2.3.1 Idealisation

B 2.3.1.1 Extent of idealisation

Mechanical problems may be calculated both globally and ina detailed manner. The requirements for the results to beobtained are decisive for the extent of idealisation. By theselection of the differences approximation, fixation of thethree-dimensional and time-based points of support and

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idealisation of the boundary conditions the quality of theapproximation is influenced decisively.

B 2.3.1.2 Differences approximation

The suitability of the differences approximation for theproblem class and problem-induced boundary conditions(e.g. application of load, distribution of load, support) is tobe taken into account with respect to the problem to besolved.

B 2.3.1.3 Determination of points of support

The location and number of points of support shall be se-lected such that the calculation result is sufficiently exact forthe respective problem to be solved. For the arrangement ofthe points of support the influence of the differences ap-proximation shall also be considered. Here, the followingshall be taken into account:

a) Where the calculation problem requires knowledge ofstrongly varying field components, e.g. strains orstresses, the fineness of the point of support mesh shallbe selected accordingly.

b) The limits between various governing material charac-teristics shall be considered.

c) Extensive irregularities in the (three-dimensional) ar-rangement of the points of support as well as differencesin the governing characteristics from point of support topoint of support may effect the deterioration of theconditioning of the equation matrix.

d) Within the problem to be solved the point of supportmesh shall make possible an exact representation of theapplied forces and other loadings and the boundaryconditions.

e) For dynamic problems the network shall be so designedthat the dynamic behaviour of the structure is made ac-cessible to calculation. The number and type of degreesof freedom shall be selected such that the type of move-ments which are of interest can be described.

f) The structure shall be idealised such that neither localnor global singularities of the stiffness matrix occur.Otherwise, they shall be credited by the solution algo-rithm.

The treatment of local near-singularities (according tothe conditioning and calculation exactness) shall not leadto an adulteration of the physical behaviour of thestructure. In the case of near-singularities the sufficientnumerical exactness of the results shall be checked.

g) For physical reasons, e.g. cutting-off of material orpenetration, or for numerical reasons (bad conditioningof the equation system, e.g. in strongly distorted meshesin a Lagrange representation) it may become necessarythat the points of support mesh is fixed anew partially orin full in the course of calculation operation.

B 2.3.1.4 Formulation of boundary conditions

The boundary conditions may comprise conditions for ex-ternal force and displacement magnitudes; they may alsoconsist of conditions for unit forces and moments on imagi-nary intersections. This is e.g. the case for detailed examina-tions and when using symmetry conditions; by this the

results however, shall not be changed inadmissibly withrespect to the problem to be solved. Boundary conditionswith changes in load shall be taken into account especiallywith respect to non-linearities.

B 2.3.1.5 Determination of load and time increments

The load or time increments shall be selected such that thecourse of the discrete field components over the load pa-rameters or over the time is sufficiently covered with respectto the problem to be solved, and that the numerical stabilityof the solution is ensured. The increments may be changedwithin the course of a calculation, in which case it will beuseful, depending on the problem class and differencesapproximation, to admit only gradual changes.


Due to the large number of input data a control of the inputdata is indispensable and should be made, as far as possibleby means of the data stored by the program.


B 2.3.2 Programs

B 2.3.2.1 General

Calculations made by means of the finite differences method(FDM) are only made by programs on data processing sys-tems due to the large number of computing operations.


Each program used shall be documented. The followingitems shall be documented or indicated:







g) examples of application.

The theoretical part of the documentation shall contain alltheoretical principles on which the program is based. Ifrequired, the respective literature shall be referred to.



In case of extensive FDM programs it cannot be assumedthat all possible calculation methods are free from errors.Therefore the following items shall be considered to eva-luate the reliability of the program:

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B 2.3.3.1 General

The first step to evaluate calculation results is the checkwhether the results are physically plain. The better the to-tality of the results obtained can be evaluated, the moreexpressive is the check. This plausibility control is a neces-sary condition for the usability of the results obtained. Inaddition, the calculation model, the correctness of the dataand the proper performance and use of the program is to bechecked additionally.

As each solution obtained with each discretizing numericalprocedure is an approximation of the physical behaviour itshall be checked whether the quality of the approximation issufficient for the problem to be solved. Where the validity ofthe discretization and the numerical procedures is to beproved by such checks the latter may be omitted when theyhave already been performed within other calculations thatare directly comparable. Problems are directly comparablewhere both the structure and the loadings are qualitativelythe same and where all parameters strongly characterisingthe calculation are nearly coincident.


B 2.3.3.2.1 Preliminary remark

As already shown in clause B 2.2.3.1 the finite differencesmethod leads to components of the considered field unitsonly at discrete locations. If required, this may necessitate aninterpretation of the given discrete solution by interpolationor extrapolation (Example: boundary condition or couplingof partial calculation areas).

B 2.3.3.2.2 Steadiness and monotony requirements for dis-crete field components

In most of the problem classes of the considered FDMrange of application the field components shall show asteady or piecewise monotonous three-dimensional courseand time history in areas with continuous geometry as wellas with constant or continuously varying material character-istics and loadings. For some problems this shall also applyto certain derivations of the field components (see clauseB 2.2.2.2). Where, in such ranges, the respective discrete fieldcomponents or their respective derivations show strongoscillations it shall be checked whether instability is present.Exceptions to the abovementioned course of field compo-nents are, e.g. extensive discontinuities at certain shells orshock waves.

B 2.3.3.2.3 Fulfilment of conservations laws and materiallaws

The conservation laws are fulfilled locally and globally bythe exact solution, however only globally by the FDM solu-tion except for certain methods. This may be both due to thediscretization and the special selection of the differencesoperations. At least in the latter case it shall be checkedwhether the error lies within the conservation magnitudes,e.g. in the impulse or energy, at least globally in a rangesuited to the respective problem. Such a check of the conser-vation magnitudes shall also be made if during thecourse of calculation the points of support mesh is definedanew (see clause B 2.3.1.3 g). Where discontinuities arefound in the solution, a local check shall be made addition-ally to the global check the extent of control of which con-tains the respective discontinuity. In the case of problemswith non-linear material laws it shall be ensured that theselaws are satisfied.



Principally the error is diminished by a finer subdivision ofthe structure to be examined due to the physical discretiza-tion and the susceptibility for numerical error is generallyincreased. At least in the case of explicit methods an im-proved discretization in the three-dimensional range alsonecessitates a decrease of the time or load steps for reasonsof stability.

Where due to the discretization numerical errors may beexpected, the numerical quality of the solution must bechecked. (Errors due to the physical discretization are notdealt with in this connection, see clause B 2.2.3.2).

The influence of the initial truncate and rounding errors canbe dininished if the entire calculation is performed with ahigher number of valid digits from the beginning (and not atthe time of solution of the system equation)


Where the elements of the solution vector are inserted in theoriginal equation system, information is obtained on theorder of magnitude of the numerical error in the case ofimplied differences methods.

B 2.3.3.3.3 Control for numerical instability

Numerical instability due to unsuitably selected discretiza-tion generally leads to results which infringe on the monot-ony requirements laid down in clause B 2.3.3.2.2. Therefore,numerical instability can be detected easily. In certain prob-lem classes (dissipative systems) hidden instability mayoccur. This can be checked e.g. by a confirmatory calculationwith an improved discretization in which case care shall betaken that numerical methods may also show dissipativecharacteristics.

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B 2.3.3.3.4 Control by means of condition figures

Condition figures permit the indication of upper boundariesfor the magnitude of the entirety of initial truncate androunding errors, however not for errors in the individualcomponents of the solution vector.

B 2.3.3.4 Comparison with calculations made by othermethods

B 2.3.3.4.1 General

To evaluate the results from calculations made to FDM thefollowing comparisons may be made to supplement orsubstitute the examinations made in accordance withclauses B 2.3.1.6, B 2.3.2.3, B 2.3.3.1, B 2.3.3.2, and B2.3.3.3:

a) comparison with other FDM calculations



The selection of the examination method to be used forcomparison depends on where the emphasis of examinationis to be placed (theoretical formulation, programming, ide-alisation, input data or numerical exactness).

B 2.3.3.4.2 Comparison with other FDM methods

By comparison of the results obtained from a calculation toFDM with results obtained from other FDM calculationsindividual or all characteristics of the FDM solution can beevaluated depending on the idealisation selected as well asthe program, data processing system and operating system.

When checking the program reliability by comparative cal-culations an independent program and the same discretiza-tion shall be used.

The numerical exactness may be improved if the number ofdigits is increased accordingly.

The validity of the idealisation may be checked by means ofcomparative calculations with other idealisations.

Comparative calculations made with the same or differentprograms and the same idealisations serve to control theinput data if the latter have been established independently.

B 2.3.3.4.3 Comparison with calculations made to othercalculation methods

Where other calculation methods, e.g. the finite elementmethod (FEM) or the freebody method satisfy the conditionsfor treating the respective problem, they may be used forcomparative calculations. Such calculations then serve toevaluate the sum of all properties of the FDM solutions.


The evaluation of results obtained from calculations to thefinite differences method may be made in part or in full bycomparison with the experimental results in which case theparticularities and limits of the measuring procedure shallbe taken into account. The measuring results may be ob-tained by measurements on the model (e.g. photoelastic

examinations) or measurements on the components (strainor displacement measurements) if all essential parameterscan be simulated. When using models they shall be repre-sentative for the problem to be solved. This comparisonespecially serves to evaluate the admissibility of physicalassumptions on which the idealisation is based.

B 3 Finite element method (FEM)

B 3.1 Scope

B 3.1.1 General

The finite element method (FEM) makes possible the calcu-lation of coefficients influencing the mechanical strength(e.g. stresses) and the deformation behaviour (displacementsand rotations). The requirements laid down hereinaftermainly for problems of structural mechanics can be appliedaccordingly to problems of heat transfer, fluid mechanicsand coupled problems.

With this method it is possible to cover any type of geome-try and loading as well as of structural and material behav-iour.

Simplifications for performing calculations with respect tothe geometric model, the material behaviour, the loadingsassumed, and the kinematic behaviour shall be purposefullyadjusted to the problem to be solved.


The geometry of the component to be analysed may be one-dimensional, two-dimensional or three-dimensional.

The capacity of the data processing plant or of the individ-ual program as well as the extent required may be limited tocover the entire geometry.

B 3.1.3 Mechanical loadings and boundary conditions

When applying the finite element method there are practi-cally no limitations as to the type of mechanical loading andedge conditions of a component In addition, initial distor-tions, such as thermal strains, may be taken into account.


The mechanical loadings may be considered as point, areaand volume loads.


Any time-dependent loadings can principally be analysedby means of the finite element method in which case theusual methods of dynamics can be applied.


Kinematic behaviour of the structure can principally bedemonstrated in which case large rotations and distortions,if any, as well as clearance have to be considered.

Generally the method is limited to a kinematically full-linearbehaviour of the structure.

If required, primary instabilities (buckling) may be consid-ered.

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In most cases, linear material behaviour (linear stress-strainrelationship) is assumed and, if required, the temperaturedependence of the constants and initial strains are consid-ered.

The consideration of non-linear material behaviour (e.g.rigid-plastic, linear elastic-ideally plastic, general elasto-plastic, viscoelastic) is possible, entailing, however, greatexpense.

B 3.2 Principles of FEM


The principles of FEM will be explained hereinafter only tothe extent essential for FEM application and the assessmentof the calculation. These explanations also serve to definethe terms used in this Annex.

Like for each thermo-mechanical calculation method theFEM is based on the physical principles of continuum me-chanics. Depending on the type of discretization method,these principles will be satisfied fully or by approximationwhen applying the finite element method.


B 3.2.2.1 Fields

The continuum theories describe the physical properties ofbodies by means of fields (e.g. displacement field, velocityfield, temperature field, and others) which at least in piecescan be considered a steady function of the fixed coordinatesand of the time, if required.


Where a structure behaves like a continuum the displace-ment field in its interior is steady at any time. By kinematicboundary conditions values for displacement magnitudes atthe edges of the area to be calculated are prescribed. Wherea displacement field is steady and satisfies the kinematicboundary conditions it is termed kinematically compatible.



a) rigid restraints

b) rigid supports

c) prescribed edge displacement magnitudes.


The deformation in the proximity of any point of the struc-ture is described by distortions (change in length of a lineelement, change in angle between two line elements).

The prerequisite for a linear relationship between the dis-placements are small distortions or rotations where theorder of magnitude of the rotations is, at maximum, equal tothe order of magnitude of the squared distortions; wherethese prerequisites are satisfied, we can speak of geometriclinearity.

B 3.2.2.3 Conservation laws and equilibrium conditions





Edge conditions prescribing values for magnitudes of forceare called static boundary conditions.


a) edge loaded by area load, line load or point load

b) load-free edge without further conditions

c) condition for frictional forces in free supports

d) condition for freedom from momentum of a hingedsupport.

At all points with static boundary conditions there will beequilibrium between internal stresses and forces and theexternal loadings applied which may be equal to zero.




Where the structure is also subject to thermal loads(temperature balance) in addition to mechanical loads, theimpulse and momentum principle shall be supplemented bythe equation of energy to describe a physical behaviour,where the energy equation can be formulated as follows:


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Where loadings of a structure are also due to fluidic occur-rences (e.g. in piping), the conservation law of mass(continuity equation) shall be satisfied for the fluid in addi-tion to the impulse and momentum conservation laws.



For the mechanical behaviour of a material the material lawsshow the relationship between stresses and strains. In thecase of linear-elastic material behaviour this relationship islinear, whereas e.g. in the case of elasto-plastic behaviourthe material law is non-linear. In the case of linear-elasticisotropic materials the material behaviour can be describedby two independent coefficients. In the case of linear-elasticanisotropic materials up to 21 independent coefficients maybe required.

The material law for a fluid gives the relationship betweenphysical states, e.g. for an ideal gas, between pressure,density and temperature (thermal state equation).

Additional parameters are required in the case of thermalloading (coefficient of thermal expansion, thermal diffusiv-ity, temperature-dependent elastic moduli, etc.) and in thecase of flowing fluids (heat transfer coefficients, viscosity,etc.).

B 3.2.3 Discretization

B 3.2.3.1 Procedure

The representation of the structure as mathematical model istermed idealisation. According to the finite element method(FEM) the structure to be examined is divided into a numberof relatively simple areas, the finite elements (discretization).Each finite element contains an approximation for the fields.By the use of an integral principle the various approxima-tion functions are adjusted to each other so that an exact aspossible solution is obtained. Depending on the approachand the integral principle distinction is made between sev-eral principles. In clauses B 3.2.3, B 3.3.1 and B 3.3.3 onlythe displacement method is considered. In the displacementmethod the approximation refers to the displacement typeswithin the finite elements. Each element type is based on acertain element shape. Example: triangular flat-plate ele-ment with six junction nodes: i.e. the three corner nodes andthe three subtense junction point nodes.

With respect to a possible estimation of errors the displace-ment approximation of the individual elements should meetthe following requirements:

a) kinematic compatibility within the elements and acrossthe element boundaries: the latter requirement is fulfilledby suitable assignment of displacement distributions todiscrete degrees of freedom, the node displacements:

b) the displacement shapes shall exactly describe any pos-sible rigid displacement or distortion of an element, and

the displacements derived from the distortions shall beequal to zero.

Now it is assumed that the stresses can be calculated bymeans of the material laws from the distortions which arederived from the approximate displacements. Thus, theaforementioned element type can describe a linear course ofdistortions due to the squared displacement approximationand thus also describe a linear course of stresses in case of alinear material law: at a linear displacement approximationthe stress would be constant within an element as shown inthis example.

By the use of the principle of virtual work that approximatesolution is determined the external and internal virtual workof which nears the exact values as closely as possible. Herekinematic essential boundary condition are satisfied exactly.The static (natural) boundary conditions and internal load-ings are considered to be kinematically compatible(kinematically equivalent), i.e. the respective junction nodeforces are calculated from the actual loads such that withreference to the selected displacement types, the virtualwork of the actual loads and the junction node forces areequal.

B 3.2.3.2 Characteristics of the solutions

The solution calculated this way is an approximate solutionin two respects:

a) Physical discretization

Due to the limited number of possible degrees of free-dom by the selection of finite elements the local equilib-rium and static boundary conditions cannot generally befulfilled exactly. Where the two conditions in clause B3.2.3.1 are considered displacement approximation in theelements, and disregarding the numerical influences inthe first step, the calculated solution represents the bestsolution for the selected elements with respect to the factthat the virtual work (and therefore the equilibrium to alarge extent) are covered as exactly as possible; for thejunction node forces assigned to the degrees of freedomthe equilibrium condition is satisfied exactly if the dis-placement approximations contain all rigid body dis-placements and rotations. The calculated solution leadsto a too stiff behaviour representation of the structure.For a given loading it is more likely that the calculateddisplacement is too small, the calculated inherent vibra-tion frequencies represent upper boundaries.

Where elements are selected that are not fully consistentthere is no more the danger that the calculated solutionis a best possible approximation for the purpose of theabovementioned. The infringement on the kinematiccompatibility effects that an overestimation of the stiff-ness is made, and the solution thus calculated may, incertain cases, lead to more exact solutions, especially forthe displacements, than a fully compatible model: thesolution thus found, however, does not have the effect toestablish the abovementioned boundary.

Examples for non-fully compatible elements: Where flatplate elements are connected with several approxima-tions for the displacement components in the elementplane and vertically by intersections, the kinematic com-patibility is infringed at these intersections.

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Where the shape of the structure idealized by finiteelements considerably deviates from the true shape ofthe structure, this may give rise to incertainties. In manycases the approximation of curved contours by piecewiselinear or straight elements does only slightly change thetotal deformation behaviour, but it is extremely difficultto interprete the local displacements and especially dis-tortion and stress components at such artificial intersec-tions.

b) Numerical approximation

For a given physical discretization the numerical solu-tion deviates from the exact solution. This deviation isdue to the following two causes:

- Due to the limited number of digits in the data proc-essing system initial truncate errors and rounding er-rors will occur. This may especially effect systemswith extremely differing physical characteristics inthe calculation model.

By the calculation of conditioning figures whichmake possible an estimation of the amplification ofthe initial truncate error by the rounding errors, onecan obtain a lower, often very conservative limit forthe number of numerically exact digits.

Where the elements used exactly cover displace-ments and rotations of the rigid body (the second re-quirement of clause B 3.2.3.1 with respect to the ele-ment approximation), the exact fulfilment of theequilibrium of the nodal forces is a necessary but notsufficient condition for the exactness of the numericalsolution for static problems.

- In the case of certain algorithms, e.g. iterative solu-tion of equation or iterative solution of the eigen-value problem, one error will remain which dependson the given limit of accuracy.

B 3.3 Application of FEM

B 3.3.1 Idealisation of geometry and loading

B 3.3.1.1 Extent of idealisation

Mechanical problems may be calculated both globally and ina detailed manner. The requirements for the results to beobtained are decisive for the extent of idealisation. By theselection of suitable element types, determination of junc-tion nodes and idealisation of the boundary conditions thequality of the approximation is influenced decisively.

B 3.3.1.2 Selection of element types

The elements shall be selected with respect to the problem tobe solved. The following items shall be taken into account:

a) representation of the geometry in due respect of theproblem

b) suitability of the element approximation for the prob-lem-related and kinematic boundary conditions (e.g.load application, load distribution, support)

c) Type and exactness of the results with respect to the taskset

B 3.3.1.3 Determination of junction nodes

The location and number of junction nodes shall be selectedsuch that the calculation result is sufficiently exact for therespective problem to be solved, in which case the items ofclause B 3.3.1.2 shall be considered accordingly. In additionthe following shall be taken into account:.

a) Where the calculation problem requires knowledge ofstrongly varying field components, e.g. strains orstresses, the fineness of the mesh shall be selected ac-cordingly.

b) At the limits between various governing material charac-teristics element boundaries shall be placed, if possible,unless a homogenous distribution of the material charac-teristics can be considered within an element.

c) In dependence of the element type selected the influenceof the lateral conditions on the conditioning of the sys-tem shall be considered. Generally adjacent elementsshall also show the same magnitudes of geometry andstiffness, i.e. the transitions from large to small or stiff toless stiff elements shall be gradual, since strong differ-ences in the stiffness from element to element may effectthe deterioration of the conditioning of the equationmatrix.

d) Within the problem to be solved the mesh shall makepossible an exact representation of the applied forcesand other loadings and the boundary conditions.

e) For dynamic problems the mesh shall be so designedthat the dynamic behaviour of the structure is made ac-cessible to calculation. The number and type of degreesof freedom shall be selected such that the type of move-ments which are of interest can be described. This espe-cially applies to the compensation of the degrees of free-dom

f) The structure shall be idealised such that neither localnor global singularities of the stiffness matrix occur.Otherwise, they shall be credited by the solution algo-rithm. The treatment of local near-singularities(according to the conditioning and calculation exactness)shall not lead to an adulteration of the physical behav-iour of the structure. In the case of near-singularities thesufficient numerical exactness of the results shall bechecked.

B 3.3.1.4 Formulation of boundary conditions

B 3.3.1.4.1 Types of boundary conditions

The boundary conditions may comprise conditions for ex-ternal force and displacement magnitudes; they may alsoconsist of conditions for unit forces and moments on imagi-nary intersections. This is e.g. the case for detailed examina-tions and when using symmetry conditions; by this theresults however, shall not be changed inadmissibly withrespect to the problem to be solved.

Boundary conditions with changes in load shall be takeninto account especially with respect to non-linearities.

B 3.3.1.4.2 Kinematic boundary conditions

Kinematic boundary conditions shall be formulated directlyby the degrees of freedom. Where elements are used that are

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not kinematically compatible, care shall be taken that theseboundary conditions are described sufficiently.

B 3.3.1.4.3 Static boundary conditions

The static boundary conditions given at the junction nodeforces shall be inserted directly as junction node loadings.Point loads not applied at the junction nodes as well as areaand volume loads shall be converted to kinematic equiva-lent junction node forces. Where element types are used thedisplacement approximation of which is incomplete regard-ing rigid displacements and rotations, care shall be taken toensure that the static equivalence is satisfied.

B 3.3.1.5 Determination of load and time increments

The load or time increments shall be selected such that thecourse of the displacements and the units derived therefromover the load parameter or over the time is sufficiently cov-ered with respect to the problem to be solved, and that thenumerical stability of the solution is ensured. In the case ofmaterial non-linearities care shall be taken to ensure that thematerial law is exactly satisfied, and in the case of geometricnon-linearities the equilibrium conditions shall be taken intoaccount.


Due to the large number of input data a control of the inputdata is indispensable and should be made, as far as possibleby means of the data stored by the program.


B 3.3.2 Programs

B 3.3.2.1 General

Calculations made by means of the finite element method(FEM) are only made by programs on data processing sys-tems due to the large number of computing operations.


Each program used shall be documented. The followingitems shall be documented or indicated:







g) examples of application.

The theoretical part of the documentation shall contain alltheoretical principles on which the program is based. Ifrequired, the respective literature shall be referred to.



In case of extensive FEM programs it cannot be assumedthat all possible calculation methods are free from errors.Therefore the following items shall be considered to evalu-ate the reliability of the program:







B 3.3.3.1 General

The first step to evaluate calculation results is the checkwhether the results are physically plain. The better the to-tality of the results obtained can be evaluated, the moreexpressive is the check. This plausibility control is a neces-sary condition for the usability of the results obtained. Inaddition, the calculation model, the correctness of the dataand the proper performance and use of the program is to bechecked additionally.

As each solution obtained with each discretizing numericalprocedure is an approximation of the physical behaviour itshall be checked whether the quality of the approximation issufficient for the problem to be solved. Where the validity ofthe discretization and the numerical procedures is to beproved by such checks the latter may be omitted when theyhave already been performed within other calculations thatare directly comparable. Problems are directly comparablewhere both the structure and the loadings are qualitativelythe same and where all parameters strongly characterisingthe calculation are nearly coincident.


In the displacement FEM distinction is made between physi-cal conditions that have been satisfied exactly or approxi-mately. Therefore, the following criteria can be given for thecontrol of the calculated solution.

When using kinematically compatible elements, the localequilibrium conditions in the internal and at the edge aresatisfied approximately by the method. Criteria for thequality of the approximation are:

a) the magnitude of the discontinuities in the stress com-ponent calculated for each element of adjacent elements

b) correspondence of the respective stress components withapplied distributed loading on loaded or free edges.

Where non-compatible elements are used, the exactness ofthe fulfilment of the internal kinematic compatibility condi-tions shall be checked. Since in the case of non-compatible

KTA 3201.2

elements the compatibility is only satisfied at the junctionnodes, the fineness of the division of the elements shall beselected accordingly.

The exactness of the fulfilment of the equilibrium of junctionnode forces shall be checked in the following cases:

a) where elements are used which do not satisfy the condi-tion of clause B 3.2.3.1 with respect to the rigid bodydisplacement shapes

b) in the case of local singularities, near-singularities orartificial supports due to suppression of near-singulardegrees of freedom.

c) in the case of all non-linear problems.

In the case of problems with non-linear behaviour of thematerial it shall be checked additionally whether the mate-rial law has been satisfied.



Principally the error is diminished by a finer subdivision ofthe structure to be examined due to the physical discretiza-tion and the susceptibility for numerical error is generallyincreased. At least in the case of explicit methods an im-proved discretization in the three-dimensional range alsonecessitates a decrease of the time or load steps for reasonsof stability.

Where due to the discretization numerical errors may beexpected, the numerical quality of the solution must bechecked. (Errors due to the physical discretization are notdealt with in this connection, see clause B 3.2.3.2).

The influence of the initial truncate and rounding errors canbe diminished if the entire calculation is performed with ahigher number of valid digits from the beginning (and not atthe time of solution of the system equation).


Where the elements of the solution vector are inserted in theoriginal equation system, information is obtained on theorder of magnitude of the numerical error. In the case ofstatic problems the condition for a sufficient satisfaction ofthe equilibrium of junction node forces is a necessary (butnot sufficient) condition for sufficient exactness of the dis-placement magnitude.

B 3.3.3.3.3 Control by means of condition figures

Condition figures permit the indication of upper boundariesfor the magnitude of the entirety of initial truncate androunding errors, however not for errors in the individualcomponents of the solution vector.

B 3.3.3.4 Comparison with calculations made by othermethods

B 3.3.3.4.1 General

To evaluate the results from calculations made to FEM thefollowing comparisons may be made to supplement or

substitute the examinations made in accordance withclauses B 3.3.1.6, B 3.3.2.3, B 3.3.3.1, B 3.3.3.2, and B3.3.3.3:

a) comparison with other FEM calculations



The selection of the examination method to be used forcomparison depends on where the emphasis of examinationis to be placed (theoretical formulation, programming, dis-cretization, input data and numerical exactness).

B 3.3.3.4.2 Comparison with other FEM methods

By comparison of the results obtained from a calculation toFEM with results obtained from other FEM calculation in-dividual or all characteristics of the FEM solution can beevaluated depending on the idealisation selected as well asthe program, data processing system and operating system.

For the comparative calculation it is possible to use the sameor differing programs, operating systems, data processingplants as well as the same or differing idealisations.

When checking the program reliability by comparative cal-culations an independent program and the same discretiza-tion shall be used.

The numerical exactness may be improved if the number ofdigits is increased accordingly.

The validity of the idealisation may be checked by means ofcomparative calculations with other idealisations.

Comparative calculations made with the same or differentprograms and the same idealisations serve to control theinput data if the latter have been established independently.

B 3.3.3.4.3 Comparison with calculations made to othercalculation methods

Where other calculation methods, e.g. the finite differencesmethod (FDM) or the freebody method satisfy the condi-tions for treating the respective problem, they may be usedfor comparative calculations. Such calculations then serve toevaluate the sum of all properties of the FEM solutions.


The evaluation of results obtained from calculations to thefinite element method may be made in part or in full bycomparison with the experimental results in which case theparticularities and limits of the measuring procedure shallbe taken into account. The measuring results may be ob-tained by measurements on the model (e.g. photoelasticexaminations) or measurements on the components (strainor displacement measurements) if all essential parameterscan be simulated. When using models they shall be repre-sentative for the problem to be solved. This comparisonespecially serves to evaluate the admissibility of physicalassumptions on which the idealisation is based.

KTA 3201.2

Annex C

Brittle fracture analysis procedures

C 1 Drawing-up of the modified Porse diagram with ex-ample

(1) By means of the reference temperature RTNDT deter-mined in accordance with KTA 3201.1 and the qualitativerelationship between critical crack length and stress, whichwas found by Pellini, the diagram shown in Figure C 1-1 forthe non-irradiated and analogously the irradiated conditioncan be drawn up. According to Pellini brittle fracture neednot be expected above the crack arrest temperature TDT atany crack length. This statement leads to the vertical line inthe diagram.

The lower boundary of the diagram is obtained from themodified Porse concept.

The brittle fracture diagram for the irradiated condition maybe drawn up under the same condition if the adjusted refer-ence temperature RTNDT is to be used (see KTA 3203).

In addition to the brittle fracture diagram Figure C 1-1 alsocontains a start-up/shut-down diagram (stress as functionof temperature) This diagram shows the relationship be-tween temperature and loading in the cylindrical vesselwall. The loading considers the stresses due to internal pres-sure and the unsteady thermal stresses due to membranestress on the most highly loaded part of the reactor pressurevessel. The start-up/shut-down diagram shall always beoutside the area marked by the Porse diagram.

Figure C 1-1: Brittle fracture transition concept and modified Porse diagram (Example)

(2) Drawing-up of the modified Porse diagram

Basis data:

Proof stress Rp0.2 at T = 20° C

RTNDT temperature: ∆TNDT = ∆T41

Non-irradiated:

Point 1 T = (RTNDT + 33 K) - 110 K

σ = 0.1 ⋅ Rp0.2

Point 2 T = RTNDT

σ = 0.2 ⋅ Rp0.2

Point 3 Intersection of

T = RTNDT + 33 K with extended straight line 12;

Point 4 T = RTNDT + 33 K

σ = 1.0 ⋅ Rp0.2

KTA 3201.2

Irradiated:

Point 1´ T = (RTNDT + 33 K) - 110 K + ∆TNDT

σ = 0.1 ⋅ Rp0.2

Point 2´ T = RTNDT + ∆TNDT

σ = 0.2 ⋅ Rp0.2

Point 3´ Intersection of

T = RTNDT + 33 K + ∆TNDT with extended

straight line 1´2´;

Point 4´ T = RTNDT + 33 K + ∆TNDT

σ = 1.0 ⋅ Rp0.2

C 2 Calculation method to determine the KI values

C 2.1 General

This Annex shall apply in connection with Section 7.9. Themethod described hereinafter makes possible the calculationof KI values for effective or postulated internal or externaledge cracks on components of simple geometry.

C 2.2 Prerequisites

(1) This calculation method is based on linear-elastic frac-ture mechanics.

(2) This calculation method applies to plates and shellswith little curvature. Where the method is used on compo-nents of other geometries, this shall be justified.

(3) The KI values are determined from membrane andbending stresses for the crack-free component.

(4) In the case of non-linear stress distribution, the stressesshall be determined in accordance with Figure C 2-1, and isas follows:

Two vertical lines are drawn at the crack edges and the linethrough the intersection of this vertical lines showing theeffective non-linear stress distribution results in the linear

stress distribution. The fictitious membrane stress σm* is the

value of the linear stress distribution at the location s/2. The

fictitious bending stress σb* is equal to the value of the

maximum total stress of the non-linear stress distribution

minus σm* .

Note:

The fictitious membrane and bending stresses thus determined donot correspond to the definitions as per clause 7.7.2.2.

C 2.3 Calculation

Where the conditions as per Section C 2.2 are satisfied for acomponent, the stress intensity factor can be calculated bymean of the following equation

[ ]K a Q M MI m m b b= ⋅ ⋅ ⋅ + ⋅π σ σ/ * *

where

σm* fictitious membrane stress

σb* fictitious bending stress

a half the depth for internal cracks or depth of edgecracks

Q crack shape factor as per Figure C 2-2; here Q isobtained from the geometry of the crack and thequotient of

( )σ σm b p TR* *./+ 0 2

Mm corrective factor for the membrane stresses; seeFigure C 2-3 (internal crack) or Figure C 2-4 (edgecrack)

Mb corrective factor for the bending stress; see Fig-

ure C 2-5 (internal crack) or Figure C 2-6 (edgecrack)

Rp0.2T proof stress at temperature at crack tip

C 2.4 Alternative methods

Besides the method described above there are further meth-ods to determine the stress intensity factors. These methodscan be applied if the prerequisites for the application ofthese methods are satisfied.

ba

∗∗ σσ

∗

σ∗

σ

effective ( non-linear ) stress distribution

wall thickness

s/2

2a

linearized stress distribution

internal crack

a

edge crack

s/2

s =

b

m

crack

m

crack

s

s/2s/2

s

b

Figure C 2-1: Linearization of stresses

KTA 3201.2

a

b

σ+ ∗∗σ p0.2 Tb

0.0

0

edge crack

0.6

m

internal crack

1.00.8

0.30.5

( ) / R

2.2 2.42.01.6 1.8

0.4

0.5

0.3

0.1

0.2

a

s

2aa /

s

1.2 1.41.0

Crack shape factor Q

0.8

Figure C 2-2: Determination of crack shape factor Q

2a/s =

e

0.65

2a/s = 0.55

Crack eccentricity factor 2e/s

s = wall thickness

in relation to the walle = eccentricity of crack

2a/s =

0.25

0.15

Point 1Point 20.452a/s =

0.35

2a/s =

2a/s =

0.30.2 0.4 0.60.5

1.0

0.0

2a

0.1

s

Cor

rect

ive

fact

or M

1.6

m

Point 2

Point 1

1.2

1.1

1.3

1.5

1.4

Figure C 2-3: Corrective factor for membrane stress for internal cracks

KTA 3201.2

= 0.05= 0.0

a /= 0.1a /

2.0

1.5

1.6

1.7

1.9

1.8

= 0.25a /

= 0.2

0.35 <

a /

a /

a / = 0.15

a /

= 0.3

< 0.5

1.4

s

= crack length

a

0.1

a /

s = wall thickness

1.0

0.0

Cor

rect

ive

fact

or M

Ratio of crack depth to wall thickness a/s

m

0.90.8

1.1

1.3

1.2

0.70.30.2 0.4 0.60.5

Figure C 2-4: Corrective factor for membrane stress for edge cracks

0.7

AxisNeutral

2a/s =

2a/s =0.52a/s =

Side under pressurePoint 2

e = eccentricity of crack

s = wall thickness

Point 1Side under tension

2a

s

0.72a/s =2a/s = Note:

of the bending stress shall be negative.is on the side under pressure the signWhere the centre line of the crack

0.5

0.12a/s =0.3

0.12a/s = 0.32a/s =

0.60.50.4 0.7

-0.1

-0.2

-0.3

0.3

Cor

rect

ive

fact

or M

-0.4

0.0

b

0.20.1

Crack eccentricity factor 2e/s

1.0

0.9

0.8

Point 2

to neutral axis

e

Point 1

0.7

0.2

0.1

0.0

0.3

0.6

0.5

0.4

Figure C 2-5: Corrective factor for bending stress for internal cracks

KTA 3201.2

Figure C 2-6: Corrective factor for bending stress for edge cracks

KTA 3201.2

Annex D

Regulations and Literature Referred To in this Safety Standard

(The references exclusively refer to the version given in this annex.Quotations of regulations referred to therein refer to the version available

when the individual reference below was established or issued.)

AtG Act on the Peaceful Utilization of Atomic Energy and the Protection against its Hazards(Atomic Energy Act) of December 23, 1959 as Amended and Promulgated on July 15, 1985,last Amendment by the Act of July 19, 1994

Pressure Vessel Order Order on Pressure Vessels, Gas Pressure Vessels and Filling Plants (Pressure Vessel(DruckbehV) Order - DruckbehV) of 27 February 1980, amended by the First Order amending the Pres-

sure Vessel Order of 21 April 1989 (BGBl. I, 1989, Page 830), at last amended by the Act ofSeptember 14, 1994 (BGBl. I, 1994, Page 2325)

StrlSchV Ordinance on the Protection against Damage and Injuries Caused by Ionizing Radiation(Radiological Protection Ordinance) as promulgated on June 30, 1989 and corrected onOct. 16, 1989, at last amended by the Act of August 16, 1994 (BGBl. I, 1994, Page 1963)

KTA 2201.4 (06/90) Design of Nuclear Power Plants against Seismic Events;Part 4: Requirements for Procedures for Verifying the Safety of Mechanical and Electrical

Components against Earthquakes

KTA 3201.1 (06/90) Components of the Reactor Coolant Pressure Boundary of Light Water Reactors;Part 1: Materials and Product Forms

KTA 3201.3 (12/87) Components of the Reactor Coolant Pressure Boundary of Light Water Reactors;Part 3: Manufacture

KTA 3201.4 (06/90) Components of the Reactor Coolant Pressure Boundary of Light Water Reactors;Part 4: Inservice Inspections and Operational Monitoring

KTA 3203 (03/84) Monitoring Radiation Embrittlement of Materials of the Reactor Pressure Vessel of LightWater Reactors

KTA 3205.1 (06/91) Component Support Structures with Non-integral Connections;;Part 1: Component Support Structures with Non-integral Connections for Components of

the Reactor Coolant Pressure Boundary

DIN 267-4 (08/83) Fasteners: Technical specifications: property classes of nuts (previous classes)

DIN 267-13 (08/93) Fasteners; technical specifications; parts for bolted connections with specific mechanicalproperties for use at temperatures ranging from -200 °C to +700 °C

DIN 2510-1 (09/74) Bolted connections with reduced shank: survey, range of application and examples of instal-lation

DIN 2510-2 (08/71) Bolted connections with reduced shank: metric thread with large clearance, nominal di-mensions and limits

DIN 2615-2 (05/92) Steel butt-welding fittings; tees for use at full service pressure

DIN ISO 3506 (12/92) Corrosion-resistant stainless steel fasteners; technical conditions of delivery; identical withISO 3506 : 1979

DIN 3840 (09/82) Valve bodies; strength calculation in respect of internal pressure

DIN EN 20 898-1 (04/92) Mechanical properties of fasteners; Part 1: Bolts, screws and studs; (ISO 898 Part 1: 1988);German edition of EN 20 898-1: 1991

DIN 28 011 (01/93) Dished heads; torispherical heads

KTA 3201.2

DIN 28 013 (01/93) Dished heads; semi-ellipsoidal heads

VDI 2230 , Sheet 1 (07/86) Systematic calculation of high duty bolted joints; joints with one cylindrical bolt

AD A5 (07/95) Openings, closures and special closure elementsMerkblatt

Literature

[1] H. HübelErhöhungsfaktor Ke zur Ermittlung plastischer Dehnungen aus elastischer Berechnung (Stress intensification factorKe for the determination of plastic strains obtained from elastic design), Technische Überwachung 35 (1994), No. 6,pp. 268 - 278

[2] WRC Bulletin 297 (September 1987)Local Stresses in Cylindrical Shells due to External Loadings on Nozzles-Supplement to WRC Bulletin No. 107(Revision I)

[3] WRC Bulletin 107 (August 1965, Revision März 1979)Local Stresses in Spherical and Cylindrical Shells due to External Loadings

[4] British Standard BS 5500:1985Unfired Fusion welded Pressure Vessels

[5] MarkusTheorie und Berechnung rotationssymmetrischer Bauwerke (Theory and design of structures having form of surfaceof revolution), 2nd corrected edition, Düsseldorf 1976

[6] Warren C. YoungRoark´s Formulas for Stress and Strain, 6th edition McGraw-Hill, New York 1989

[7] KantorowitschDie Festigkeit der Apparate und Maschinen für die chemische Industrie (The strength of apparatus and machines forthe chemical industry), Berlin 1955

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