TRD 301 Annex 1 Design

Edition August 1996

ICS 27.040 Technical Rules for Steam Boilers (TRD)

Calculation for cyclic loading due to pulsating internal pressure or combined changes of internal pressure and temperature

TRD 301 Annex 1 Design

The Technical Rules for Steam Boilers (TRD) reflect the present state of safety requirements for the materials, manufacture, design, equipment, erection, inspection, and testing as well as the operation of steam boilers. They are prepared and updated according to the most recent technical developments by Deutscher Dampfkesselausschuß (DDA) Reference is also made to § 6, Paragraph 2 of the Steam Boiler Decree (DampfkV) (Clause on the equivalence of technical rules and standards within the EC)

c CO

The TRD sheets are published on behalf of "Deutscher Dampfkesselausschuß" by f¿

Vereinigung der Technischen Überwachungsvereine e.V., P.O.Box 10 38 34, 45038 Essen

¿"I E S

Translated by: Fachverband Dampfkessel-, Behälter- und Rohrleitungsbau e.V., Düsseldorf If there is any doubt regarding the interpretation of this sheet, the German wording shall apply. Ú E

E =

B i

Preliminary note The calculation for cyclic loading shall be governed by local peak stresses. For static loading, these are only indirectly accounted for by the mean stress and the related efficiency coefficients which take into consideration a limited and partially plastic deformation.

15 Q.

•if »i

u o 2 cr Q. C

Contents

1

Scope

5

Allowable streses and load cycles

2

Design values and units

6

Superposition of various load cycles

3

Individual stresses

7

Literature

4

Total stress condition

m O

Ira S .y o Z3

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Q. Q.

Ö §

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^§ o E

t O £ o CD 0)

1 Scope 1.1 This Annex 1 to TRD 301 shall apply to the contirmatory calculation of components which were designed in accordance with TRD 301, with respect to cyclic loadings which are due to internal pressure, on the one hand, and due to radial temperature differentials during start-up (heating-up) and shutdown (cooling down), on the other hand, in the areas subjected to maximum loadingi). It is assumed that on components subjected to pressure and temperature the maximum local peak stresses occur on the inside of the edges of openings or on branches in cylindrical shells. Additional forces and moments of a significant magnitude shall be calculated separately (design rules in preparation).

The design rules following hereafter will be supplemented inasmuch as new knowledge is gained. 1.2 The calculation shall be based on the actual dimensions of the respective plant component which shall be determined by confirmatory measurements. If the actual wall thickness is unknown, the probable wall thickness shall be calculated as follows: If the wall thickness Se is a mean wall thickness, then the design wall thickness shall be taken as Sb = Se. If Se is a minimum wall thickness, then Sb = 1.15 • Se shall be used for seamless cylindrical shells, and Sb = Se + 1 for welded shells made of plate^). 2) Ttie factor of 1.15 is about half ttie plus tolerance of 25 % for tubes with minimum wall thickness.

^) Explanations in course of preparation

To replace the April 1975 edition of TRD 301, Annex 1 and to replace Draft TRD sheet 301, Annex 1,

edition Ivlay 1995; I = changed with respect to revtous edition This TRD sheet shall only be applied in conjunction with TRD 300 and TRD 301 :üpyright © 1997 by Vulkan-Verlag, P.O.Box 10 39 62, 45039 Essen

Page 2 TRD 301, Annex 1 At the same time, the following shall apply, depending on d or da. whichever is the nominal diameter: da = d, + 2Sb di

= da-2 Sb

dm = 0.5 (i^ + d\) 1.3 For calculation purposes, the following shall be defined as governing temperature &* during a start-up and shutdown period (load cycle) under consideration;

ctmo = 3-2 for flanged-out main bodies with welded branch; root drilled out or ground over, without residua! gap, Fig. 5 Where the requirements for the welded joint are not met. e.g. in the case of a non-machined root of the weld or a residual gap of < 1.5 mm, amo shall be increased by the factor for the influence of the root gap

U-

1

(4)

1 - 0.5 I -^ d;

1Î* = d +0,75(0-0) (1)

= 0,75 iW 0,25 0 All temperature-dependent values shall be referred to this governing cycle temperature i3* (or the respective load cycles). 1.4 Because of the approximately linear dependence of stresses on the governing internal pressure p', the calculation of the allowable temperature differentials may be limited solely to the two points of minimum and maximum pressure of the load cycle under consideration. Intermediate values shall be obtained by linear interpolation.

2 Design values and units

Root gaps up to approximately 1.5 mm are taken into consideration by this (actor íA. However, the requirements according to (1) shall always be met for diameter ratios of dAi/d > 0.5 and simultaneously d > 300 mm or for welded-on stubs or nozzles respectively with dAi > 120 mm, provided the pertinent basic shell consists of a material having a guaranteed minimum yield strength of Os > 355 N/mm2 at 20 "C. OmO = 3.5 for expanded joints amo = 5.0 for expanded and welded joints with residual gap on the root side > 1.5 mm

Cf. TRD 301, Section 2.

3 Individual Stresses 3.1

Ideal-elastic mechanical hole-edge stresses

3.1.1 The maximum hole-edge stress for cylindrical shells with vertical branches shall be determined by using the following relation: d o¡p -a

P*

2 s.

(2)

For the stress concentration factor am the following shall apply: «m ^ «mO + f..-a.

(3)

If om or the stress concentration factor a^o cannot be determined either by measuring or by calculation, the following shall be used:

Fig. 1: Reinforcement by means of set-through and fullpenetration welded branch

(1) omo = 2.6 for set-through and full penetration welded branches as per Fig. 2, as well as for dieforged branches with conical transition and fillets as per Figs. 2 and 3; in each case without residual gap Omo = 2.9 for welded-on branches; seating surface adapted or milled plane; root drilled out or ground over, without residual gap, Fig. 4 '"

Deviating herefrom, the stress concentration factor ctmo = 2.4 may be used for dAi £ 50 mm; dAi/oS < 0.2 and 1.6 < ^ < 2.0

3) For material properties cf. VDE Guidelines 3128.

Fig. 2: Die-forged branch

Page 3 TRD 301. Annex 1 3.1.2 For the time being, cylindrical shells with oblique and/or non-radially arranged branches shall be calculated as per para 3.1.1 above. 3.1.3 In this connection, arrays of holes in cylindrical shells shall be treated like single openings as per para 3.1.1 above. 3.1.4 For the time being, cylindrical shells with Y-shaped branches under an opening angle of VA shall be calculated as follows: (6)

2 s. Here the following shall be used: Fig. 3: Branch forged from solid material and subsequently bored and turned a„ = 2.5 +

(90-VA)' 10^

(7)

but not less than 3.2. A weld root in the gusseted area shall be machined. If this is impossible, am shall be multiplied by ii = 1.2. 3.2 Ideal-elastic thermal stresses at hole edge These stresses solely depend on the radial temperature pattern within the vessel wall. For the inner wall, and assuming a rotation-symmetrical temperature characteristic (also under thermal shock), Design a Fig. 4:

Design b

Ö:,, - a.

1- V

(^m-^i)

(8)

Reinforcement by means of welded-on branch shall be used. Herein, a stress concentration factor of ati = 2 shall be used unless another value can be proved to be correct by calculation. Assuming a quasi-static nary temperature pattern for an insulated outer wail, the temperature differential will become Au = i'>rn - ^\ = const. - A-öoo and, as a function of the rate of temperature change 1/0 can be stated as follows: Ai3_ - — • 0»

(9)

In this case 5 n shall be used as basis, so as to ensure adequate reseives for start-ups from hot condition {Cf. TRD 301, Clause 6.2.1). However, if combined load cycles have to be assumed, consisting of ni start-ups from cold and nz, ns . . start-ups from hot condition (with possible differences between the initial and the finai conditions), then the incipient crack formation load cycle numbers/ii, 02- ns.etc, shall be so selected that the requirement of equation (25) is complied with. In accordance with Clause 5,1.2 the reduced alternating stress ranges shall be determined for the load cycle numbers Hi, 02, etc. 5.1.2 For unnotched bars, and in accordance with Fig. 8, the allowable alternating stress ranges of 2oa shall be determined as a function of the incipient crack formation load cycle number n. For components, these ranges shall be reduced because of surface influences. This shall be done by using the correction factor fs as per Table 1 and results in Aa* =

f.

^

If during start-up not only the temperature, but also the pressure is reduced, and the component is not regularly cooled by an additionally feeded colder fluid, and unless otherwise agreed between boiler manufacturer, purchaser and inspection body, y - 0 may be used in the calculation. Then, in this case ój = á,p and Oi ^ G¡p - AG,. Otherwise the maximum is o¡ = a,p + A 0|

(1 ) In the elastic case of Aa' < 2 ho.2/f a correction is required in order to take account of the influence of the maximum possible mean stress. The result upon using the Gerber parabola is the allowable reduced alternating stress range of the ideal-elastic stresses in the form of

AO; = 2 Or

''0.2/tí'

5.1.4 For parts in contact with water which are manufactured from non-austenitic steels, special care shall be taken to preserve the mangetite protection layer. Therefore, the stress limits for these parts are additionally restricted as follows: > Oip^ - 600 N/mm2

(16)

â| < öjp^ + 200 N/mm2

[17)

Os in N/mm2

h

355 to 600

1.2

>600

1.4

Ao*

'^02/-d' _^

Ao*

Table 1: Correction factor fe to take into account the influence of the surface as a function of the yield strength

''E

(12) Aa*

(2) In the 0 v e r e I a s t i c case of Ao* > 2 ao2/it* it must be considered that, in fact, the calculation must be made with a higher strain than that in the idealised elastic case. Then the following applies: AOi - 1/2 • f^o.s/ö* • ^° '

(13)

5.1.5 Equations (14) to (17) provide the allowable maximum and minimum stresses for the individual load cycles. Therefrom, and using equations (8) and (10), the allowable temperature differentials upon start-up and shutdown can be calculated as follows: Start-up: Ai3 = i5^-0¡

5.1.3 After the allowable reduced alternating stress ranges Aoi have been determined for the individual load cycles, the allowable maximum stresses a, and the allowable minimum stresses oi shall be determined, by means of which a, shall be limited during start-up and shutdown and finally the allowable temperature differentials are to be calculated. As the stress limits for the individual cycles can be influenced by the selection of the start-up and shutdown rate, they may be freely selected within a certain range. In this case, it is recommended to determine o¡ as follows, using a factor Y-

—

.a.

1- V

Öi - Oi,

[18)

ßu ^. Shutdown: AÛ = ^^ - oi

a,=

(15)

[11:

This alternating stress range Ao* shall be corrected as indicated in Fig. 7.

2

y > 0 is the absolute relation between the allowable thermal stress at the beginning of shutdown and the allowable thermal stresses at the beginning of start-up.

1- V

O; - O;,

5.2 Allowable number of load cycles for given stresses 5.2.1 If for a load cycle the stress limits a, and a, are known, then the incipient crack formation load cycle number n for this cycle can be determined as follows: Based on the existing alternating stress range AO: = Ó: - Ó,

there is (14)

(19)

(1 ) for the over-elastic case of Aoi < 2 • GO 2/,r

(20)

Page 5 TRD 301, Annex 1

•SH¿4?>

M

Bmmmmm

W'.f

WmMM^i^&^MM"Ae\¡

!^iLü"[!iLi!DiHííljiJllj!:!lJil!Íihi^?^

0.5x10"^

Flg. 6: Out-of-roundness factor fu

Page 6 TRD 301, Annex 1

-0.48

-0.45 ^^^

é, -0.40 ^ggíPS^;

-0.35, -0.32 Diameter ratio íJ^=-TFtg. 7:

Shape factors for cylindrical shells

AG; 2aa - ACf: • h —30,2/û*

(21 ;

(2) for the elastic case of AGí < 2

2 0a - Aa¡

oo.2/ô'

(2Öp)'

f^ •

(22)

(2 0B)^-(2GO2/,,.-AOj)^

Using the value of 2aa, the incipient crack formation load cycle number n is derived from Fig. 8. Therefrom, the allowable number of load cycles results, for start-ups from cold only, as n = —.

For combined load cycles the allowable load cycle numbers ni, n2, n3, ... shall be so selected that equation (25) is satisfied. 5.2.2 For preliminary calculations, the stress limits of ôj and Oi, based on the temperature change rates of v,ti and v-dz, assuming quasi-stationary conditions, can be assumed as follows:

G; = a m P — + a. 2 s.

à. =a.

2s.

-t-a.

ßLö •E^ 1- V ßLü

^.

1- V

, 'flt

O, 'ö2

(23)

(24)

The results as per equations (23) and (24) are conservative, because the maximum thermal stress and the maximum mechanical stress are added without considering an additional phase shift. For more accurate calculations, the actual time phasing must be taken into account. 5.2.3 For parts in contact with water, o¡ and o¡ shall not exceed the limits stipulated in clause 5.1.4 which, under certain conditions, can be achieved by limiting the idealelastic thermal stresses.

6 Superposition of different load cycles A given combination of load cycles with irregularly fluctuating stresses, regarding magnitude and frequency, is subdivided into load cycles with an identical or almost identical alternating stress range (such as, for example, start-ups from cold, or from hot condition), and evaluation is made on the basis of the linear damage rule. According to this rule, the usage factor D of all load cycles shall be limited to

D = ^ +^ + ñr>

1

ño

(25)

with a safety factor against usage So > 2.

7 Literature Makinejad, N.: Dynamische Lochrandspannungen und zulässige Temperaturdifferenzen in rotationssymmetrisch belasteten zylindrischen Bauteilen größerer Dampferzeuger. VGB Kraftwerkstechnik Vol. 54 (1974) No. 3, pp. 186-194.

Page 7 TRD 301, Annex 1

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Page 8 TRD 301, Annex 1

Form for calculating the allowable number of load cycles at specified temperature differentials or temperature change rates, respectively a) Design and calculation data 1

Type and (nominal) dimensions of vessel

2

Material

seamless longitudinally welded

3

Design wall tfiickness (without thermal stress: Sb = Sv)

Sb = (measured or average wall thickness) Sb = X 1.15 (seamless and minimum wall thickness) Sb = + 1 (longitudinally welded and minimum wall thickness)

St

mm

4

Inside diameter (for outside diameter d\^ da-2 • Sb)

a

mm

5

Maximum diameter of opening

dA\

mm

6

Out-of-roundness

U

7

Opening angle for Y-shaped branches

VA

% "

8

Working pressure (gauge)

P4

N/mm2

P

N/mm2

9

Minimum cycle pressure

10

Maximum cycle pressure Minimum cycle temperature

P Û

N/mm2

11 12

Maximum cycie temperature

Û

°C

13

Governing cycle temperature

•Ô* = 0.75 T3 + 0.25 Ü

Ô'

°C

14

Start-up rate at the beginning of start up, calculated for quasistationary condition

(at p) (positive)

Vû,

K/min

15

Temperature difference at the beginning of start-up

(at p) (negative)

AÖ1

K

16

Shutdown rate at the beginning of shutdown, calculated for quasistationary condition

(at p) (for 7=0 becomes va^ = 0, otherwise negative)

Vf,2

K/min

17

Temperature difference at the beginning of the shutdown

(at p) (for 7=0 becomes Ai32 = 0, othenwise positive)

Ai32

K

18

Modulus of elasticity

(atr)

Eö

N/mm2

19

Minimum proof stress at elevated temperature

(at r)

ao.2/d

N/mm2

20

Differential thermal expansion coefficient

(at r)

ßu^

1/K

21

Thermal diffusivity

(at Û*)

aö

mm2/min

22

Minimum tensile strength

(at room temperature)

ÓB

N/mm2

23

Factor fa

h=^.0 (if 5s Í3 = 1.2 (355 Í3=1.4(ifas

24

Theoretical stress concentration factor for membrane stresses

(for start-up from cold p = 0)

< 355 N/mm2) < as < 600 N/mm2) >600N/mm2)

amo = 2.6 (forged/set/through) Omo = 2.9 (welded on without gap) ttmo = 3.2 (flanged)

•••

"C

^

-

&itß

-

k

—

f4= ^.0 (unmachined root) 25

Factor it

'4 1-0.5 /4 = 1.2 Y-br£inch ( unmachined)

Page 9 TRO 301, Annex 1 b) Calculating procedure 26 27

28

dm = 0.5 (da + d)

dm

mm

uo= 1 + 2-f

uo

-

w

°-^^ ßL. • ^,.

^ 29

30

31

w

' " 8 V -

f In \ 'u (P4 )

(u¡ - 1} (u^ - 1)2

^••'

1 "^1 1-^

\

U

D -*

(d f

1 + 0.455 ÍP4

32

Obtain from diagram or compute!

1 (u^ - 1) (3 u¡ - 1) - 4 u^ In u^

m

mm^ K N

Of

-

V

1/min

AJ(P4)

-

100

i^b j

«m(P4) = «mo''4 +2-.'u(P.)

Of

«m =

10^

J

•^A

am(p4)

-

Ojp4

N/mm2

m)

-

«mÍP)

-

(Tip

N/mm2

am > 3.2 33 1

^b J

34

L/ 3

1 + 0.455 'P1

35

100

«m(P) = «mû'^4+2 i,(p)

or

•u

«m =

am > 3.2 36

óip=cx,(p)-P'|f

/ 37 1 + 0.455

38

dm] «b J

u

ÍPI ¡dm'

a^(p)^a^o-^4+2-/,(p)

3

íiÍP)

-

100

Ub> or

am(p)

-

üip

N/mm2

(quasi-stationary case!)

Wúl

N/mm^

{quasi-stationary case!)

CT¡i52

N/mm2

Oi

N/mm2

2.5 +

r

•u

am > 3.2 39

ó,=ajp).p.^

40

41

'i>2

w

V

42

a\ = Ojp + Oifl, *)

43

Oj = Oip + OiiÍ2 ')

W

(at the beginning of shutdown and Y = 0 become o,-,^^ = 0)

N/mm2

Page 10 TRD 301, Annex 1

44

AOi = CTi - (Tj "^a -ACT, ACT .03

/Í3

o„

f

^""^ 2.5^^^^

N/mm2

2 0a

N/mm2

ñ

-

n

-

ifAai>2CT0.2/fl

45 A„

Aö(

(205)"

if AOi > 2 00^0

(25Br-(25o.2/ö-Ao^f 46

Incipient crack formation load cycles n for 2 Oa at 1"^' only start-up from cold: n < —

47

Allowable number of cycles

Combined cycle loading: select m

48

Si = Gip4 -600

49

S2 = öip, + 200

50

For parts wetted by water, the additional requirements are: Si < Ci

Si

N/mm2

S2

N/mm2

S2>Ôi

See also notes to clause 5.2.2 of Annex 1.

.•iJH?,

.' •••••îift^-.v

•^!,'.--îjr.:-: „.^-í^V.'-flI^flí'í^:-

,-.í;Ír.

•J^v^Tí'^'^í

J

Page 11 TRD 301, Annex 1

Form for calculating the allowable temperature differentials and temperature change rates at specified number of load cycles a) Design and calculation data 1

Type and (nominal) dimensions of vessel

2

Material

3

Design wall thickness

Sb = (measured or minimum wall thickness Sb = X 1,15 (seamless or minimum wall thickness Sb = + 1 (seamless or minimum wall thickness

4

Inside diameter

(for outside diameter d\ == da - 2 • Sb)

5

Maximum diameter of opening

6

Angle of opening

7

Working pressure (gauge)

8

Minimum cycle pressure

9

Maximum cycle pressure

10

seamless longitudinally welded

for Y shaped branches (for start-up from cold p = 0)

Minimum cycle temperature

11

Maximum cycle temperature

12

Specified number of load cycles

13

Incipient crack formation number of load cycles

mm

oi

mm

C^Ai

mm

VA

°

P4

N/mm2

P

N/mm2

P

N/mm2

•&

°C

%

°C

(for start-up from cold n > 2000)

n

-

only start-up from cold combined loading:

h

-

xV

X

5 • n sele ct n¡

A) 14

Governing cycle temperature

iV = 0,75 i3 + 0.25 i^

15

Modulus of elasticity

(at xV)

16

(Minimum) proof stress at elevated temperature

(at xr)

Differential thermal expansion coefficient

(at i3")

18

Thermal diffusivity

19

(Minimum tensile strength

20

Ratio Y

21 22

17

Sb

< 0.5

E,.

N/mm2

Ô0.2/Î)

N/mm2

ßu

1/K

(at Ú-)

ai)

mm2/min

(at room temperature)

OB

N/mm2

(cf. clause 5.1.3)

Y

-

Factor /b

fe = 1.0 fe = 1.2 fa = 1.4

h

-

Allowable alternating stress range

(2 oa for ñ at xV)

2aa

N/mm2

U

%

ClmO

-

U

-

23

Out-of-roundness

24

Theoretical stress concentration factor for membrane stresses

(if Os < 355 N/mm2) (355 < Os < 600 N/mm2> (if Gs > 600 N/mm2)

amo = 2.6 amo = 2.9 amo = 3.2

forged/set-through welded-on without gap flanged

f4 = 1.0 (ma :;hined root) 25

Factor U

(unmachined)

f4= 1-0.5

f4 = 1.2 Y-br anch (unmachined)

Page 12TRD301, Annex 1

b) Calculation procedure 26

drr, = 0.5 (da + a,)

dm

27

üo=1 +2 -^ = d.

uo

28

W=

^1 (üg - 1) (3 ug - 1) 4 üg In ÜQ 8 {Uo^ - 1) . (üo - 1}'

Obtain from diagram or compute!

.

1/min

s^ 2 0, Í.

Aa¡ = ^2 • CTo.2/0 • ^^ ' - 2 Or

AGZUI

N/mm2

AOi

N/mm2

(for the over-elastic case) Ao* > 2 ÓQ2/O)

32 AG,

mm^K

a>t

V = ^^ *f

31

W

ßLfl-^ö

29

30

0.35

mm

Ao*

+ .1-H

"B

Ao'

O

Ao*

^0.2/It O,'B

(for the elastic case)

33

Ü

K'^b

^u(P4)-1-5

ii(p4)

100 1 - 0.455 V^b ; 2 \

am(P4) = «mO-^4+2./,(p4)

or

a^ - 2.5 + ID'

34

-^ am(p4)

ttm > 3.2 35

^'ip. =«m(P4)P4' 2s. /"w

36

Oipa \

f.(p) = 15/•

N/mm2

=

\

^w A^

U 100

/u(p)

1 -H 0.455 v^«. 37 «m(P)= «mO

^ +2/u(P)

a„ =

or

2.5-H

(90-VA)' 10^

am{p)

am > 3.2 38

ô^p -a^(p).p

Oip

2 s.

N/mm2

/^ \ 39

U

i,(p)-1.5 1 + 0.455

f •^L \

(M

l^oj

», =»6

«m(P)-«mO-^4 +2 /-.(p)

^^

or

^u(p)

100

a„ -

2.5 + (90-n'A)'

10^

40

am(p)

am > 3.2 41

r. - rf. Oin ip =an-(p)p""m" 2S.

Oip

N/mm2

Page 13 TRD 301, Annex 1

Aa¡ 42

S ^1 -5 "ip +' ^'P

43

S2 = OifM - 600

44

6\ = S^ 5i = S2

1 + y

Oi= Si 45

S3 = ACT¡ + Ói

46

SA

47

ai = S3 ai = S4 6i=S3

48 49 50

(not wetted by water) " • (if wetted by water) if S2 > Si if Si > S2

= aip4 + 200 (not wetted by water) " • (if wetted by water) if SA < S3 if S3 < S4 -

AO1 = W • (ói - 5ip) Ai^r = W- im- Sip)

51

= W • (Si - áip) Ai32' = W • (ai - 5ip)

52

Vù, = V • A\h

53

v,i, = V • Atír

54

W'^ = V • AÔ2

55

VtV = V • Ai32'

AT32

*) *) *) *)

Si

N/mm2

S2

N/mm2

Oi

N/mm2

S3

N/mm2

S4

N/mm2

Oi

N/mm2

A•ö^

K

A^r

K

A1Î2

K

Ai^-

K

v^

K/min

V^r

K/min

v^

K/min

V^^:

K/min

See also notes to para 5 2.2 of Annex 1

»'•î K/min ^•1

^^ .

9

^

Í

Internal près sure

P*

^^3

-^^^^ ^ »^•4

Fig. 1 : Allowable temperature differences

Fig. 2: Allowable temperature change rate, calculated for quasi-stationary condition

' • ^^^^4>•