Design by Analysis

Specification of ExamplesDBADesign by Analysis

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5 Specification of examples

5.1 General

In this section the specifications are given of ten examples, dealt with by the group.

The various design checks had been assigned to the members a priori, differences discussed,and, where necessary, supplemented by additional investigations and corrected.

The results are summarized in the next section, the details in the section thereafter.

The specifications are complete, but to follow the examples in detail or to use them asbenchmarks, it is necessary to consult standards, for instance for material propertiesspecifications or other sections of prEN13455.

As a help, physical properties of materials used in the examples are collected in an annex tothis section.

The geometries specified in the drawings are already those to be used in the analyses, i. e. thethicknesses given are already analysis thicknesses, allowances – for tolerances and, ifrelevant, corrosion – have already been deducted. Should the corrosion allowance be requiredfor specifying the weld regions: A value of 1.00 mm was used for ferritic steels, and 0 foraustenitic ones.

The proposal for Detailed Fatigue Analysis states that in the (fatigue) analysis extremeoperating values of actions rather than design values should be used. For the calculation of theallowable number of action cycles an upper value for the pressure sup,opP equal to 90% of the

maximum allowable pressure PS is specified in the examples here.

In cases where the maximum allowable pressure PS can be determined by the Design byFormulae (DBF) section of the CEN TC 54 proposal of an Unfired Pressure Vessel standard,PS has not been specified here.

The maximum allowable pressure according to this DBF proposal - DBFPSmax - shall be used

as characteristic value in the design checks for Gross Plastic Deformation (GPD), ProgressivePlastic Deformation (PD) or Shakedown (SD):

DBFc PSP max=

In the other cases values for PS are specified.

Note: Unfortunately, because of the combination of ideas and designations from Euronorm 3on one hand, and those from the Pressure Equipment Directive (PED) and EN 764 on theother hand, one has to distinguish between the design values of (the action) pressure –obtained by multiplying the characteristic values of pressure by the relevant partial safetyfactors – and the design pressure dP - the maximum pressure at the top of the equipment

specified by the manufacturer and used for the determination of the calculation pressures,mainly within the framework of DBF.


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To minimize the possibility of confusing the two, the notion design pressure – relevant toDBF – is never used here. The specified values for PS or those determined by DBF shall beused as upper characteristic values; the design value for (the action) pressure shall not becalled design pressure and especially not be denoted by dP ! (It could be denoted by PdA ).

In all cases the admissibility of the design shall be checked and proven first by the simplestmeans possible for the example – to show that quite often DBA can be quite short and simple,if only the admissibility is to be be proven.

In all examples a normal hydraulic test is presupposed, i. e. the checks against GPD fortesting conditions do not require separate calculations.

Specified pressures and temperatures are to be considered as pairs. If other actions arespecified, they are considered to form, with pressures and temperatures, triplets, etc.

Should the alternative of using any primary stress field be used in the check against GPD, theprincipal strains corresponding to this primary stress field shall be limited by ± 5% - asspecified in the tangent intersection procedure. In general, this requires primary stress fieldsobtained by (inelastic) FEM.

5.2 General notations

Where possible, the notations of the CEN proposal for the Unfired Pressure Vessel Standard,prEN 13445, are used, and shall be used:

• Analysis thickness: Nominal thickness minus allowances – manufacturing, eδ , and

corrosion, erosion, c :

cee ena −−= δ

• Maximum allowable pressure: The maximum pressure (on top of the vessel) specified (bythe manufacturer) for design, for normal operating conditions: PS . This pressure PSconstitutes an upper limit for the set-pressure of the safety valve – if there is only one -, orfor the maximum pressure (at the top of the compartment) that can occur under reasonablyforeseeable conditions – if no safety valve is required. It shall be used in the design checksagainst GPD and PD, or SD.

• Maximum operating pressure: sup,opP

This value – specified directly, or as being equal to 90% of DBFPSmax - shall be used as

upper value (of full pressure cycles) for cases with cyclic pressure.

• Maximum allowable pressure according to prEN 13445-3, Annex 5.B: DBFPSmax

• Maximum allowable pressure according to DBA: DBAPSmax

For GPD and PD/SD checks, and, if relevant, for checks against instabilty (I), only.

• Characteristic value of moment: Maximum reasonably foreseeable value of externalmoment; (in general equal to the "usual" design moment): cM

• Allowable number of cycles: Number of cycles (for specified actions) allowed byprEN 13445-3, Section Detailed Fatigue Analysis.


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• Modulus of elasticity: EE at 100°C, say: 100E

• Mean coefficient of (linear) thermal expansion: αα between 20°C and 100°C, say: 100,20α

Weld symbols according to EN 22553.

5.3 Designations

DBA. Design by Analysis

DBF Design by Formulae

GPD Gross Plastic Deformation

PD Progressive Plastic Deformation

SD Shakedown

I Instability

F Fatigue

NLG Non-Linear GeometryPS Maximum alloxable pressure

PSmaxDBF Maximum allowable pressure according to prEN 13445-3 Section DBF

PSmaxGPD Maximum allowable pressure according to Gross Plastic Deformation usingDBA

PSmaxSD: Maximum allowable pressure according to Progressive Plastic Deformationusing DBA

sup,opP Maximum operating pressure.

PdA Design value for the pressure action

Pap Applied pressure to elastic compensation analysis

Mc Characteristic value of moment

Tc Calculation temperature

E Modulus of elasticity

α Mean coefficient of (linear) thermal expansion

λ Heat conduction coefficient

h Heat transfer coefficient

a Thermal diffusivity (temperature conductivity)

σ Stress..... nomeeiij σσσσσ ,,,, max,

ε Strain..... eij εε ,


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5.4 Specifications of examples

Example No. 1.1: Thick unwelded flat end

1. Material: P280GH according to EN 10222-2The relevant heat treatment dimension is specified as101.6 mm (in deviation from EN 10222-1).

2. Actions: Pressure MPaPSPS DBF 17max == x)

Temperature CTc °= 20

3. Operational cycles: constT = , p varying from 0 to PSPop ⋅= 9.0sup,

4. Geometry: See Fig. 5.1

Fig. 5.1

x) A not very reasonable result: The end thickness is large and the ratio of admissible pressure tonominal design stress is outside the graphs and the scope of DBF. Extrapolation was necessary.


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Example No. 1.2: Thin unwelded flat end

1. Material: P280GH according to EN 10222-2The relevant heat treatment thickness is specified as101.6 mm (in deviation from EN 10222-2).

2. Actions: Pressure MPaPSPS DBF 2.4max ==




Fig. 5.2


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Example No. 1.3: Welded-in flat end without nozzle

1. Material: P265GH according to EN 10028-2




4. Geometry: See Fig. 5.3 and 5.4

Fig. 5.3


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Fig. 5.4

Example No. 1.4: Welded-in flat end with nozzle

1. Material: Plate and Shell: P265GH according to EN 10028-2Nozzle: P265 according to prEN 10216-2




4. Geometry: See Fig.5.5, 5.6 and 5.7


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Fig. 5.5

Fig.5.6 Fig. 5.7


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Example No. 2: Storage tank (cone-cylinder junctions)

1. Material: Shell: X6CrNiTi 18-10 (1.4541) according to prEN 10028-7Reinforcing ring, foot ring: P235GH according to EN 10028-2;Note: the different thermal expansion coefficients shall be

considered.

2. Actions: Hydrostatic pressure Hp , medium density 31000 mkgM =ρminimum medium level hMIN and maximum medium level hMAX see Fig. 5.8. Note:

no longitudinal stress in the main cylindrical shell caused byhydrostatic pressure.

Temperature in service CTc °= 60 ;

Temperature before complete filling of thevessel 20°C.

Internal pressure during draining (see also Fig. 5.9) MPaPS 06.0= ;

Note: longitudinal stress in the main cylindrical shell causedby internal pressure acting on the upper end of the vessel.

Dead load (self weight and insulation): Insulation:2220 mNqd = (weight force / surface of the vessel),

insulation thickness 200 mm; dead weight of roof includinginsulation and reinforcing ring 26,15 kN.

Wind load (limit value): stagnation pressure qW depending onheight h: :60 mhm ≤≤ 2/81.0 mkNqW =

:106 mhm ≤< 2/88.0 mkNqW =

:1510 mhm ≤< 2/94.0 mkNqW =

:2515 mhm ≤< 2/02.1 mkNqW =Wind force: iiWi AqcW ⋅⋅= ,

where 44.0=c and iA = projection of the surface of

the vessel in wind direction.

3. Detail to be investigated: wide and narrow ends of cone

4. Operational cycles: See Figure 5.9.Note: It is ascertained that internal pressure can be increased only if the medium height is below hMIN. The internal pressure increases slowly; for safety reasons bothextremes shall be considered, the very slow (dotted line) and very

fast (full line) pressure increases.

5. Geometry: See Fig.5.8.


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Fig. 5.8


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Fig. 5.9

Example No. 3.1: Thin-walled cylinder-cylinder intersection

1. Material: P295GH according to EN 10028-2


Nozzle longitudinal moment NmM c 4.15644=(moment vector normal to plane through both cylinder axes).


3. Operational cycles: A) constT = , p varying from 0 to ,9.0sup, PSPop ⋅=

constM c =

and B) constT = , M varying from 0 to 26400 Nm,

MPaconstp 28.1==(for comparison with experimental results).

Crotch corner surface machined: mRz µ50=


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4. Geometry: See Fig.5.10.

Note: Checks against GPD and PD, or SD, to be performed for constantlongitudinal moment only.

Fig. 5.10


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Example No. 3.2: Thick-walled cylinder-cylinder intersection

1. Material: Shell: P265GH according to EN 10028-2Nozzle: 11CrMo9-10 according to prEN 10216-2


Nozzle longitudinal moment NmM c 1.711=(moment vector normal to plane through both cylinder axes).


3. Operational cycles: A) constT = , p varying from 0 to ,9.0sup, PSPop ⋅= constM c =and

B) constT = , M varying from 0 to1200 Nm, MPaconstp 24==

(for comparison with experimental results).

Crotch corner surface machined: mRz µ50=

4. Geometry: See Fig 5.11.

Note: See note in Example No. 3.1.

Fig. 5.11

Fig. 5.11


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Example No. 4: Dished end with nozzle in knuckle region

1. Material: X6CrNiMoTi 17-12-2 (1.4571) according to prEN 10028-7




4. Geometry: See Fig. 5.12 and 5.13.

Fig. 5.12

Fig. 5.13


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Example No. 5: Nozzle in spherical end with cold medium injection

1. Material: Shell: 11CrMo9-10 according to EN 10028-2Nozzle reinforcement: 11CrMo9-10+QT according to

prEN 10216-2Nozzle: P265 according to prEN 10216-2

2. Actions: Pressure MPaPSPS DBF 71.1101.139.09.0 max =⋅=⋅=

Temperature of medium inside the vessel CTS °= 325 (constant

in operation).Temperature of injected cold medium CTN °= 80 .

Location of different heat transfer coefficient for cold medium injection see Fig. 5.15. The outer surface of the vessel is insulated ideally.

Heat transfer coefficients:-) medium to vessel wall, and to nozzle if there is no injection: KmkWhS

216.1=-) cold (injection) medium to nozzle wall during injection: KmkWhN

28.10= .

3. Operational cycles: See Fig. E 5.15.Cold medium injection takes place for 10 minutes. The time between the injection cycles is long enough such that temperature

reaches , stationarity. After 500 injection cycles one shutdown (and startup) should beconsidered. At shutdown and startup, pressure and temperature are decreased orincreased in phase, respectively. Temperature changes during shutdown and

startup are slow, and therefore thermal stresses can be neglected.



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Fig. 5.14

Fig. 5.15


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Example No. 6: Jacketed vessel with jacket on cylindrical shell only, and flat annularend plates

1. Material: X6CrNiTi 18-10 (1.4541) according to prEN 10028-7

2. Actions: Inner space: Pressure MPaPS 3.1/1.0 +−=Temperature CTSTc °== 160

Outer space: Pressure MPaPS 5.0/0 +=Temperature CTSTc °== 160

3. Operational cycles: See Fig. 5.18.Inner space: MPaPop 1.1sup, = MPaPop 0inf, =

TSTop =sup, CTop °= 20inf, .

Outer space: MPaPop 45.0sup, = MPaPop 0inf, =

TSTop =sup, CTop °= 10inf,

A pressure in the inner space below atmospheric can occur independently and repeatedly in operation, and an underpressure will occur concurrently with an outer space temperature of 10°C(whereby an inner space temperature value of 160°C shall beused). This case shall be included as a normal operating condition in the check against GPD, I, PD, or SD, but not in the fatigue check. A pressure in the outer space below atmospheric cannot occur, but a minimum pressure of 0 bar cannot be excluded. This case shall also be included as a normal operating condition in the check against GPD, I, PD, or SD (with temperatures in the inner and outer space of 160°C).

Note: sup,opT and inf,opT are medium temperatures. The wall

temperatures shall be determined using heat transfer coefficientsof KmkWh

i

216.1= on inside of inner vessel wall and

KmkWho

24.14= on all surfaces of the inside of the jacket. Jacket

and main vessel outside of jacket are insulated ideally.

Note: checks against GPD, I, PD or SD shall be performed usingthe PSvalues.

Note: only steady state thermal stresses shall be considered.

The maximum allowable out-of-roundness of the inner cylindrical shellis specified in prEN13445-3 as (D+1250) / 200 = (2780 + 1250) / 200 = 20,15 mm, where Dis the mean shell diameter.

4. Details to be investigated: Jacket and jacketed part of inner vessel

5. Geometry: See Fig. 5.16 and 5.17.


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Fig. 5.16

Fig. 5.17


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Fig. 5.18

160°C

160°C


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5.5 Appendix: Physical properties of some materials

P 235 GH

P 265 GH


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P 295 GH

11CrMo9-10


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1.4541

1.4571

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