Inr. J. Pm. Ves. & Pqing 72 (1997) l-18 PII:SO308-0161(97 ...€¦ · the MW Kellogg Company in...

Inr. J. Pm. Ves. & Pqing 72 (1997) l-18

ELSEVfER

0 1997 Elsevier Science Limited. All rights reserved Printed in Northern Ireland

PII:SO308-0161(97)00014-8 0308~0161/97/$17.00

Nozzles-on external loads and internal pressure

C. J. Dekker Continental Engineering B.V., Joan Muyskenweg 22, 1096 CJ Amsterdam, The Netherlands

&

H. J. Bos Dynaflow Engineering B. V., Tintlaan 73, 2719 AH Zoetermeer, The Netherlands

(Received 30 January 1997; accepted 11 February 1997)

Close comparison of local load stress calculation methods reveals considerable differences. To investigate we performed many finite element analyses of nozzles on cylinders concentrating not just on the shell stresses but also on the stresses in the nozzei wall. Local load stresses were sometimes found to be much higher in the nozzle than in the shell. This led us to formulate a ‘modified improved shrink ring method’ and to devise multiplication (contour-) charts for deriving local load nozzle stresses from local load shell stresses. Being important for a proper nozzle assessment, pressure induced stresses were investigated too. This resulted in non-dimensional parameter graphs to determine pressure induced stresses at nozzles. 0 1997 Elsevier Science Ltd.

NOMENCLATURE

8 Radial thrust load on nozzle MC Circumferential moment load on nozzle

(out-of-plane bending) Ml Longitudinal moment load on nozzle

(in-plane bending) P Internal pressure Y Mean radius of nozzle

s Outside radius of nozzle, r, = r + it Mean radius of vessels

Ro Outside radius of vessel, R,, = R + :T SCF Stress concentration factor t Wall thickness of nozzle

: Wall thickness of vessel Relative nozzle size with respect to vessel size WRC definition: fi = 0.875 X rolR

Y Relative thinness of vessel, WRC definition: y = R/T

(WRC stands for WRC Bulletin 107, see references)

u Stress or stress intensity

1 INTRODUCTION

pressure is emphasized. This is mainly due to the prominence that design codes place on this aspect. But reactions from connected piping may give rise to high stresses too and these stresses are in addition to the pressure induced stresses.

The stresses due to external loads can be calculated by various analytical methods, e.g. WRC-107,’ Appendix G of BS 55002 and Wordsworth,3 but their results may differ up to a factor of 2. For a thorough comparison of these methods see Dekker.4

To resolve the question which local load calculation method gives reliable stresses we made numerous finite element analyses of radially placed nozzles on cylinders. Being important for a proper nozzle assessment the pressure-induced stresses were investigated too.

2 ASSESSMENT OF NOZZLES

2.1 General

In the assessment of nozzles the weakening effect of The raison d’&re for vessels are nozzles, afterall who nozzle openings on vessels with respect to internal needs vessels sealing forever their contents (nuclear

2 C. J. Dekker, H. J. Bos

waste industry?), and these nozzles experience two simultaneously occurring loadings:

-pressure -external loads due to piping reactions.

A proper stress assessment of a nozzle requires the superposition of the stress systems from both loadings. Then the maximum stress intensities for the various stress categories are to be determined and compared with their specific stress limits. One is referred to e.g. Article 4.1 ‘Mandatory Design Based on Stress Analysis’ in Appendix 4 of ASME VIII, div. 2,’ BS 55002 Appendix A ‘Recommendations for design where loadings and components are not covered by section three’ or sheet D 1200 ‘General Strength Assessment by Analysis’ from the Dutch ‘Rules for Pressure Vessels’.6

The various stresses occurring at nozzle/vessel junctions are to be categorized as follows:

-membrane stresses (local!) due to internal pressure are primary stresses.

-the bending stresses due to internal pressure are secondary stresses.

-membrane stresses (local) due to external loads belong to the local primary membrane stress category whether the origin of the external loading is mechanical or thermal. Though in the latter case it has all the characteristics of a secondary stress.

-bending stresses due to external loads belong always to the secondary stress category.

-stress increments due to concentration in the transition of vessel to nozzle proper belong to the peak stress category and need to be considered only when a fatigue evaluation is required. The amount of stress increment is very much dependent on the actual weld geometry.

The stress intensity limit for primary stresses due to pressure will be deemed to be satisfied by judiciously following the applicable design code for the considered vessel. Assuming that the bending stresses due to pressure and due to external loads to be at least as large as the membrane stresses, then one need only check the stress intensity due to the sum of primary stresses and secondary stresses. When this latter stress requirement is fulfilled then the other stress requirement (primary membrane stress) is fulfilled too. Note that the sum of primary stresses and secondary stresses criterion is to prevent low cycle fatigue.

If indeed a large number of load cycles occur then additionally a fatigue assessment is to be performed.

2.2 Practical implementation

Preferably one should superimpose the stress systems due to internal pressure and due to the various external load components and only then determine the maximum stress intensity. However, such an approach is feasible only when using FEM-programs (Finite Element Method). Having no access to such programs (or the time!) for such an analysis, then one has to resort to more conventional methods.

To calculate the external load’s stress intensity one could use for example WRC-107’ or the methods given in G.2.2 and G.2.3 of BS 55002 (in Appendix G). Both WRC-107 as well as Appendix G of BS 5500 distinguish between bending stresses and membrane stresses and these stresses are given in 4 different points, i.e. the two crown points and the two saddle points.

However, the stress distribution due to internal pressure at nozzle/vessel junctions is quite another matter. The only method? known to the authors is Enquiry Case 5500/19 from BS 5500 and this method gives only the maximum stress intensity due to internal pressure. No distinction in either stress type (membrane vs bending) or in position can be made.

Remarkable is that BS 5500 restricts in clause A.3.3.2 the sum of the stress intensity due to pressure (calculated in accordance with Enquiry Case 5500/19) and the stress intensity due to external loads (calculated in accordance with G.2.2 and G.2.3) to 2.25 X f with f being the basic design stress (note that 2.25 X f corresponds with 1.5 times the yield stress). Normally the stress intensity of primary and secondary stresses is limited by 3 xf (or 2 X yield stress). In contrast to BS 5500 the bulletin WRC-107 does neither mention any stress criterion nor provide any method to calculate the stress intensity due to pressure.$

2.3 Improved shrink ring method

Predating the WRC-107 Bulletin and the BS 5500 methods is the shrink ring method first published by the MW Kellogg Company in their publication ‘Design of Piping Systems’.’ The major advantages are

t Admittedly, the Dutch ‘Rules for Pressure Vessels‘” given in sheet D 1141--Appendix 1 is an approximate method for the maximum stress intensity due to pressure but the method’s applicability is restricted. $ Some people advocate to enter the longitudinal pressure force in the cylindrical shell forming the nozzle (i.e. x (r(, - t)’ xp) as the radial nozzle load in a WRC-107 calculation. The resulting stress intensity from such a calculation is thought to represent the pressure induced stresses.

External loads and internal pressure in nozzles 3

its simplicity of use and its quickness for assessment calculations. There is no need to extract data from numerous graphs which would lead inevitably to interpolation.

However, comparing the original shrink ring method with the ‘WRC-107’ calculated stress intensities show that the stress intensity could be severely underestimated. In ‘External Loads on Nozzles” an improved shrink ring method is proposed together with a stress limit which takes into account the internal pressure stresses.

Improved shrink ring method:

u due to thrust = 4.5 VEE ~ X thurst 2mOT

l/RITXM u due to M, = 1.5~

rcrgT 1

aduetoM,= i l+?.05cT l%E grit XM,

with (T (thrust) + a(M,) + a(M,) c 1 Xf

Application range is for r,JR s 0.6 and 10 d (R/T) 8 100.

In ‘Proper Interface Design for Pressure Vessels” the improved shrink ring method is combined with the so called load fraction rule. The resulting formulation gives the piping/vessel designer an even better insight into the relative severity of each loading component:

with:

F,, act

F,, max

M,, act

M, , max

MC, act

MC, max

I MI, act F act ry MC, act

F,, max M, , max + MC, max Gl

the actual thrust load on the nozzle. the maximum allowable thrust load as calculated by means of the improved shrink ring method and in the absence of any other external load component. the actual longitudinal moment loading on the nozzle. the maximum allowable longitudinal moment as calculated by means of the improved shrink ring method and in the absence of any other external load component. the actual circumferential moment loading on the nozzle. the maximum allowable circumferential moment as calculated by means of the improved shrink ring method and in the absence of any other external load component.

3 NUMERICAL VERIFICATION OF EXTERNAL LOADS

3.1 Introductory notes

As mentioned in the Introduction the widely accepted external load calculation methods do result in quite large differences, see Dekker.4 Trying to establish the more reliable method, we embarked upon ‘finite element method’ analyses. For these analyses we used the program FE-Pipe,? a dedicated finite element program for nozzles.

The external load on the nozzles always consisted of a single load component, i.e. either a radial thrust load, a circumferential moment or a longitudinal moment. The vessel, or better said the cylinder on which the nozzles are placed, are either moderately thick or relatively thin as in the experience of the authors thick-walled vessels never pose problems with regard to local load stresses. The y-parameter being the ratio of the average cylinder radius and the wall thickness, is taken as 25 for moderately thick-walled vessels and as 50 for thin-walled vessels.

3.2 Results of cases analyzed

The nozzle geometries analyzed are listed with their resulting stresses in tables, see the Appendix. For both y-values a table is given for each specific t/T ratio. With four different t/T values (i.e. 0.5, 0.75, 1.0 and 1.5, respectively) this amounts to eight tables.

In these tables the maximum stress intensity in the cylinder proper due to the three different single load components, are given together with the load causing these stress intensities.

In addition, the so called ‘back-calculated’ SCFs are listed which were derived from the following equations:

WTXF S.I. due to thrust = SCF x -

2nr,T r

S.I. due to M, = SCF x - vRITx M nr:T

1

WTXM S.I. due to MC = SCF X -

m$T ’

7 This is a proprietary program of the Paulin Research Group, Texas. It is a dedicated FE-program for pipe configurations, i.e. for many often occuring problems, so-called mesh-generating templates are provided. For radial nozzles on cylinders the user can suffice with entering the major geometric data like radii and wall thicknesses of cylinder and nozzle, respectively and the program automatically generates the finite element mesh.


To compare with the ‘back-calculated’ SCFs are the SCFs according to the improved shrink ring method. These latter SCFs are either 4.5 (for thrust), 1.5 (for longitudinal moments) or

( 1+l.o5&T >

for circumferential moments, see Section 2.3

Last entries in the tables are the stress intensities in the branch (or nozzle) itself and these S.1.s are expressed as a percentage of the corresponding S.I. in the vessel.

Obviously, the SCFs are functions of the specific nozzle/vessel geometry characterized by the non- dimensional geometry parameters /3 and y and the t/T ratio. This enables the graphic display of the various SCFs as functions of the p-parameter:

-The back-calculated SCFs from the finite element analyses are plotted as distinct points. To show more markedly the t/T dependency, curves are drawn through ‘equal t/T’ points.

-The (continuous) SCF-curves as derived from the WRC-107 bulletin, see Dekker.*

-The SCF functions from the improved shrink rink method and the modified improved shrink ring

60

7,o

690

5,O

4,O

3,O

m 5 A

14

co

‘MIST

‘IMPROVED’

/..a .+

/ :

NRC-1 07

FE-Pipe results

*for UT = 0.50 ‘._. ..--

+for UT = 0.75

*for VT = 1 .OO

+for UT = 1.50

0 0,l 0,2 0,3 0,4 0,5 0,6 0,7

-P

Fig. 1. Stress intensity due to thrust for y = 25

8,O

7,O

60 ‘MIST’

0 0,l 0,2 0.3 0,4 0,5 0,6 0,7

-P

Fig. 2. Stress intensity due to thrust for y = 50.

method are identified by ‘improved’ and ‘mist’ respectively. For the modified improved shrink ring method see Section 5.1.

Six separate graphs are given for thrust, longitudinal moment and circumferential moment respectively at both considered y-values (Figs l-6).

3.3 Stress intensities in nozzle necks

Studying the tables with numerical results one learns that the stress intensity in the nozzle neck proper may differ considerably from the stress intensity in the shell at externally loaded nozzles. For nozzle configurations with t/T = 1.0 the stress intensities are about the same, but for t/T < 1.0 the stress intensity in the nozzle neck becomes larger than the corresponding stress intensity in the shell. For t/T > 1.0 the reverse is true: the nozzle’s S.I. becomes less than the corresponding shell’s S.I.

The reason for this is of course, that the discontinuity bending moments in the nozzle neck and in the shell must be necessarily equal at the junction. Note that this moment is not constant along the length of the junction! The resulting bending stress from this moment is inversely proportional to the square of the


60

50

4,O

3,O

ZO

14

w

+for VT = 0.50

*form= 1.00 --fort/l= 1.50

0 0,1 02 0,3 0,4 03 0,6 0,7

-P

Fig. 3. Stress intensity due to circular moment for y = 25.

local thickness (i.e. u = 6M/t2) and hence unequal thicknesses of the nozzle and of the shell cause the overall stress intensities of the nozzle neck and of the shell to differ quite substantially. Although not in proportion to the square of the t/T ratio, as not all constituent stress components of the stress intensity exhibit this ‘square t/T’ behaviour.

extrapolate in a linear way between y = 2.5 and y = 50 for other y-values.

4 NUMERICAL VERIFICATION OF INTERNAL PRESSURE STRESS

In order to quantify this potential large stress intensity raising effect due to unequal nozzle/shell thicknesses, we prepared contour charts of this factor as functions of the t/T ratio and the p-parameter (Figs. 7-8). As these factors differ only slightly for the three loading types, i.e. radial thrust, longitudinal moment and circumferential moment, the contour charts give the average value of these three factors. Hence the contour charts, given for y = 25 and y = 50, respectively, are applicable to all three loading types.

4.1 General

For a proper assessment of the stress intensity at a nozzle/vessel junction the external load on the nozzle is important, but so is the internal pressure. Afterall, the stress intensity due to primary and secondary stresses from both loadings together is limited to 3 X f (or twice the yield stress). Being able to assess the stress intensity due to external loads is not enough. It is vital to know too the stress intensity due to internal pressure.

Having established in one way or another the stress intensity in the shell at the nozzle/shell junction of an

Analytical methods to calculate the stress intensity

externally loaded nozzle, the stress intensity in the due to internal pressure are ‘Enquiry Case No.

nozzle wall proper can be obtained by multiplying the 5500/19’ from BS 55002 and the ‘approximate method’

former with the factor read from these contour charts. from the Dutch ‘Rules for Pressure Vessels’,6 sheet

Where necessary one could interpolate or even D 1141-Appendix 1. However, the method ‘Enquiry Case No. 5500/19’ is apparently regarded with some

890

67’3

5,O

4.0

3,O

24

D

I

I,0

w

*for UT = 0.50

4for VT = 0.75

+forl/r= 1.00

--fort/T= 1.50

0 0,l 0,2 0,3 0,4 0,5 0,6 0,7

-P

Fig. 4. Stress intensity due to circular moment for y = 50.

C. J. Dekker, H. J. Bos 6

*for f/T = 1 .OO

+for VT = 1.50

0,3 0.4 05 0.6 0.7

Fig. 5. Stress intensity due to longitudinal moment for y = 25.

suspicion because, as already mentioned in Section 2.2, BS 5500 limits then the total stress intensity to 2.25 Xf instead of 3 Xf Comparing the resulting stress intensities from both methods revealed fairly large differences of about 25%.

All this combined with the results from some earlier finite element analyses made us pursue internal pressure in a similar systematic way with FE Pipe as was the case with external loadings.

4.2. Results and graphical representation

The results from the internal pressure calculations are presented in tables, see the Appendix. In these tables are listed the geometric data, resulting non- dimensional parameters, the actual stress intensity in both the cylindrical shell as well as the nozzle (branch) and an abstracted SCF factor. This abstracted SCF factor for internal pressure is derived from

P.R SI. pressure = SCF,,,,,,,, X - T

For each of the four different y (= R/T) values graphs were made of these FEM-determined SCFs for internal

‘390

7,O

690

*for VT = 0.50 *for VT = 0.50

+for VT = 0.75 +for VT = 0.75

*for UT = 1 .OO *for UT = 1 .OO .-.m;: :.-I+ +forVT= 1.50 +forVT= 1.50 I

.- .- .-..,.

: ‘IMPRQVED’ + ‘I.+1 ‘IMPRQVED’ + ‘I.+1

I I

0,3 OS4 0,5 096 0,7

Fig. 6. Stress intensity due to longitudinal moment for y = 50.

pressure as a function of the p-parameter (= relative nozzle size) and the t/T parameter (thickness ratio) (Figs 9-12). As in general the pressure stress intensity absorbs the lion’s share of the available stress limit of 3 XL an error in this pressure stress intensity has a more serious consequence than a similar (relative) error in the external load’s stress intensity. So it is imperative to estimate the pressure’s stress intensity as accurately as possible, hence the separate graphs for y = 20, 30, 40 and 50, respectively.

The graphs are based on the highest occurring stress intensity due to internal pressure in either the cylindrical shell or in the nozzle wall. Reading off the appropriate SCF and multiplying this with p X R/T gives directly the highest occurring stress intensity due to pressure.

Remark The SCFs given in these graphs can easily be compared with the corresponding SCFs from both mentioned analytical methods. Enquiry Case No. 5500119 from BS 5500 can be transformed into:


w 0.2 0.3 0,4 0,5 0,6 0,7 0,8 0,9 1 I,1 1,2

-t/T

Fig. 7. Factor for nozzle stress, y = 25.

where

is a function depending on non-dimensional parameters. The approximate method from the ‘Rules’ is:

2.5 p. R ~pressure = [ 1 --

z T

where z is the strength reduction coefficient of the nozzle opening to be determined in accordance with chapter D 0501 of the ‘Rules’.

The expression between square brackets can be interpreted as a stress concentration factor for the stress intensity due to internal pressure at nozzles.

P.R S.1. pressure = SCF,,,,,,,, x - T

To illustrate the differences between these various determined pressure SCFs, let us consider a vessel, O.D. = 2020 mm and T = 20 mm (i.e. y = 50), and a nozzle with O.D. nozzle = 685.7 mm and t = 20 mm (i.e. p = 0.3). A ssuming the nozzle material to be

096

0,2 0,3 0,4 0,5 0,6 0,7 038 099 1 lo1 182

-t/T

Fig. 8. Factor for nozzle stress, y = 50.

equal in strength to the vessel material, then one finds:

-Using the graphs as presented here: SCF,,,,,,re = 4.74

-Based upon enquiry case no. 5500119: SCF,,,,,,,e = 3.40

-Approximate method from the ‘Rules’: SC$m,,,re = 4.08

-Nozzle’s longitudinal pressure force as thrust load in a WRC-107 calculation and transforming the found stress intensity into an SCF: SCF,,.,,,,,, = 4.91

5 DISCUSSION AND CONCLUSIONS

5.1 MIST

Though we think that the performance of the improved shrink ring method is fair, certainly when one includes from the contour charts as given in 3.3, the factor for the stress intensity raising effect that thin nozzle walls have, it may underestimate nevertheless the stress intensity in the shell wall by

C. J. Dekker, H. J. Bos

IO,0

7,O

60

5,O

480

I,0 0,05 0,l 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

-P

Fig. 9. Maximum stress intensity due to pressure for R/T = 20.

about 25%. In case one prefers to use a simple local load stress method which is conservative over its entire range, then we recommend using the Modified Improved Shrink ring method (or MIST for short), which was devised just for that purpose:

u due to thrust = 6.0 X VEE ~ x thrust 2nro T

v’Ii7Tx, u due to A4r = l-5 X-

7i7$T 1

u due to M, = (1415m) X 2 X M, 0

with u (thrust) + a(M1) + a(M,) s 1 Xflfactor

and factor obtained from the contour charts as given in 3.3, but not less than 1.0.

Range of application of this MIST approach is 10 d y(= R/T) < 100 with r,/R 6 0.8 (or p G 0.7).

84

630

5,O

4,O

p 3,0

t

2,0 1

1,o 0,05 0,l 0,15 0,2 0,25 0,3 0,35 0,4 0,45 005

-P

Fig. 10. Maximum stress intensity due to pressure for R/T =30.

5.2 Proposed design and assessment method for nozzles

Nozzles which will experience external loads from connecting (process) piping should of course conform to the applicable design code.

Next, with the internal pressure SCF-graphs one should establish that the S.I. due to internal pressure is not more than 2 Xf (twice the design stress) and so leaving a stress margin of 1 Xf for external load stresses. Where necessary, nozzle and/or vessel thicknesses are to be increased to achieve this.

Then once the external load on the nozzle is known (by means of a pipe stress analysis or otherwise) the stress intensity due to this load is to be assessed by means of a suitable method, e.g. improved shrink ring method or the MIST-approach. Hereby one should take into account the sometimes higher stress levels in the nozzle necks, i.e. to include the multiplication factor from the contour charts. This external load’s S.I. is not to exceed 1 Xf as this is the margin left by setting the pressure’s S.I. at 2 Xc

Remark It is possible to reserve a larger stress range than just 1 Xf for the external load’s S.I., but then one has to


60

50

4,O

3,O

zo

l,O 0,05 0,l 0,15 0,2 0,25 0,3 0,35 0,4

-P

0,45 0,5

Fig. 11. Maximum stress intensity due to pressure for RIT =4Q.

lower simultaneously the stress range for the internal pressure’s S.I., as the limit for the combined S.I. is fixed at 3 X & In our experience the suggested 2 X ,f for the internal pressure is not a bad choice as the S.1.s of realistic nozzle loads seldom exceed 1 Xc In this way the vessel design can be finalized before the pipe stress analysis reveals the actual external load on the nozzle. In the rare cases that the nozzle load proves too large then pipe lay-out changes have to solve the problem.

5.3 Conclusions

-The local load stresses in cylindrical shells at nozzles with external loads are dependent too on the ratio of nozzle wall thickness and shell wall thickness. The thicker the nozzle wall is in comparison with the shell wall, the more the nozzle behaves like a rigid insert and, consequently, locally steeper deformation gradients in the shell wall occur and hence the larger the stresses in the shell wall are. This effect is reflected neither in WRC-107 nor in the improved shrink ring method. The sometimes up to 25% underestimation of stresses by the

10,o

7,O

630

50

4,O

8 rn 3,O I

I 1 2,0

18 0,05 0,l 0,15

-P 0,2 0,25 0,3 0,35 0,4 0,45 0,5

Fig. 12. Maximum stress intensity due to pressure for R/T = 50.

improved shrink ring method made us formulate the modified improved shrink ring method.

-The stress intensity from local load stresses due to externally loaded nozzles is sometimes larger in the wall of the nozzle than in the shell’s wall. This is the case when the thickness of the nozzle wall is less than the thickness of the shell. This stress raising effect is more or less the same for thrusts, longitudinal moments and circumferential moments. To quantify this effect we devised contour charts for this magnification factor which apply equally to all three load types. Note that these contour charts are independent of the used local load stress calculation method and could be used, if so desired, in conjunction with e.g. the ‘Appendix G’ method of BS 5500. Needless to say that we recommend the far easier (modified) improved shrink ring method.

-The bending stresses are always larger than the (local) membrane stresses for both internal pressure as well as external loads. Though the membrane stresses are not included separately in the tables with FE-Pipe results we do confirm the correctness of this assumption made in Section 2.1 for the whole range of nozzles considered here.


-The stress intensity due to internal pressure is larger than predicted by analytical methods like Enquiry Case No. 5500/19 of BS 5500. Here too the maximum stress intensity in the nozzle wall is sometimes higher than in the shell wall, this is the case when the thickness of the nozzle wall is less than the thickness of the shell. As in general the internal pressure induced S.I. takes up the larger part of the allowable stress range of 3 x f, it is imperative to use accurate pressure S.1.s. For this purpose we made graphs of the (maximum) SCF due to internal pressure for y = 20, 30, 40 and 50, respectively.

-Following our proposed design/assessment method for nozzles, i.e. using the here-given pressure graphs and contour charts in conjunction with either the improved shrink ring method or the MIST- approach, will result in soundly designed nozzles. Admittedly, our proposed design method is sometimes a bit conservative in that it adds up algebraically the various load component’s maximum stress intensities which do not necessarily occur at the same position, but the resulting nozzle design will be safe from low cycle fatigue. In the exceptional case that you are designing a pressure vessel from gold then use FE-techniques in order to save as much material as possible, but otherwise use the relatively simple and quick design method for nozzles as proposed by us.

-As shown, the stresses at nozzle/vessel junctions may be much higher than predicted by ‘conventional’ methods. Especially due to the stress raising effect of a nozzle with a wall much thinner than the vessel wall. This applies both to pressure induced stresses as well as to extenal load induced stresses. One might wonder why in the daily practice of plant operating this has never been noticed through nozzle failures due to overstressing. Well, in our opinion the following explanation deals with that objection (plus operating conditions being less severe than the design conditions and the yield stresses of materials often being higher than their specified minimum yield stresses).

In case such a vessel with a thin walled nozzle does not experience many pressure-cum-load cycles, then failure need not occur as the failure mode is low cycle fatigue for too large ‘primary-and-secondary’ stress intensities. But if enough cycles occur to result in failure of the nozzle then the true nature of the failure is often not recognized. At the point of failure (or very near to it) will also be the weld between nozzle

and vessel. The plant manager will call in a weld specialist and that is quite understandable! However, as minor defects and blemishes are always present in a weld, the weld specialist is indeed able to pinpoint such a weld irregularity and blame it for having caused the failure. After welding a new nozzle in the vessel, the vessel will operate well for many years to come as the plant’s operators are experienced by now. The smooth way of operating the plant results in few (start-stop) load cycles and low cycle fatigue does not get a second chance.

It is our opinion that many nozzle failures masquerade as weld defects while in reality the nozzle design (or better said: the nozzle design method) is to blame. One would be wise to also consult a stress specialist at nozzle failures to establish the true cause of the failure!

ACKNOWLEDGEMENT

Much of the here-presented material is from studies undertaken in cooperation with the authors’ com- panies under commission by NAM (Assen, The Netherlands). We would like to thank Mr W. J. Stikvoort of NAM, business unit Groningen, for allowing us to use this material and for his encouragement in preparing this paper.

REFERENCES

1.

2.

3.

4.

5.

6.

I.

8.

9.

Wichman, K. R., Hopper, A. G. and Mershon, J. L., Local stresses in spherical and cylindrical shells due to external loadings. WRC Bulletin 107/August 1965, Revision March 1979. BS 5500: 1991, Specification for Unfired Fusion Welded Pressure Vessels. British Standards Institution, London, 1991. Wordsworth, A.C., Stresses in cylindrical pressure vessels due to local loads. In Structural Zntegrity Assessment, ed. P. Standley. Elsevier Applied Science, London, 1992. Dekker, C. J., Comparison of local load stress calculation methods for nozzles on cylinders. Znt. J. Pres. Ves. & Piping, 1994, 58, 203-213. ASME Boiler and Pressure Vessel Code, Section VIII-Division 2, 1995 edition. The American Society of Mechanical Engineers, New York, 1995. Rules for Pressure Vessels, Issue 96-02. Published on behalf of Stoomwezen B.V. bv SDU Publishers, The Hague. The MW Kellogg Co., Design of Piping Systems, 2nd edition. John W%.y, New York, 1956. Dekker, C. J., External loads on nozzles. Znt. J. Pres. Ves. & Piping, 1993, 53,335-350. Stikvoort, W. J., Proper interface design for pressure vessels. Chemical Engineering, 1994, 133-134.

APPENDIX: TABLES WITH NUMERICAL RESULTS FROM FE-PIPE CALCULATIONS

Tables with the main results from our FE-Pipe analyses, for both external loads as well as internal pressure, are included here for reference purposes.

There are eight external load tables and four internal pressure tables.

External loads and internal pressure in nozzles

Gamma ratio: t/T ratio:

Local load stresses, i.e. FE-pipe versus the improved shrink ring method

25.00 Mean shell radius: 400.00 mm 0.50 Thickness of shell: 16.00 mm

Thickness of nozzle: 8.00 mm

Identification Results from ‘FE-pipe’ calculations

Load type Load (kN, kNm) (;II’a)

SCF (back calculated)

SCF act. improved

shrink ring method

Stress in branch

S.I. Stress in (MPa) header (%)

beta 0.100 r-0 [mm] 45.714

beta 0.150 r-o [mm] 68.571

beta r-o [mm]

beta 0.250 r-o [mm] 114.286

beta 0.350 r-0 [mm] 160.000

0.200 91.429

Thrust 50 171 3.143 4,500 211 123.4 M-circ. 50 3997 1.697 1.600 5338 133.6 M-long. 50 3358 1.411 1.500 4254 126.7

Thrust 50 135 3.723 4.500 187 138.5 M-circ. 50 2471 2.336 1.900 3606 145.9 M-long. 50 1681 1.589 1.500 2354 140.0


Thrust 50 80 3.677 4.500 14.5 181.3 M-circ. 50 1134 2.987 2.500 2078 183.2 M-long. 50 617 1.620 1.500 979 158.7

Thrust 50 54 3.474 4.500 116 214.8 M-circ. 50 622 3.202 3.100 1375 221.1 M-long. 50 303 l-560 1.500 516 170.3





Identification Results from ‘FE-pipe’ calculations SCF act. Stress in branch improved

Load type Load (kN, kNm) (;;a)

SCF (back shrink Stress in calculated) ring method (;:a) header (%)

beta 0.250 Thrust 50 81 3.723 4500 113 139.5 r-0 [mm] 114.286 M-circ. 50 989 2.597 2.500 1452 146.8

M-long. 50 511 1,342 1.500 657 128.6

beta 0.350 Thrust 50 59 3.796 4.500 85 144.1 r-0 [mm] 160.000 M-circ. 50 614 3.160 3.100 927 151.0

M-long. 50 254 1.307 1.500 349 137.4 beta 0.450 Thrust 50 44 3.640 4.500 65 r-0 [mm]

147.7 205.714 M-circ. 50 405 3.446 3.700 623 153.8

M-long. 50 147 1.251 1.500 213 144.9 beta 0.550 Thrust 50 34 3.438 4.500 50 r-0 [mm]

147.1 251.429 M-circ. 50 276 3.508 4.300 428 155.1

M-long. 50 93 1.182 1.500 138 148.4



Gamma ratio: 25.00 Mean shell radius: 400.00 mm t/T ratio: 1.00 Thickness of shell: 16.00 mm



Load type Load (kN, kNm) (I’&I’a)

SCF (back shrink Stress in calculated) ring method (;:a) header (%)

beta 0.200 r-o [mm] 91.429

beta 0.250 r-o [mm] 114.286

beta 0.350 r-o [mm] 160.000

beta 0.450 r-o [mm] 205.714

beta 0.550 r-o [mm] 251.429

beta 0.700 r-o [mm] 320.000

Thrust 50 110 M-circ. 50 1415 M-long. 50 801 Thrust 50 93 M-circ. 50 1076 M-long. 50 535

Thrust 50 67 M-circ. 50 671 M-long. 50 267

Thrust 50 51 M-circ. 50 454 M-long. 50 154

Thrust 50 38 M-circ. 50 306 M-long. 50 98 Thrust 50 28 M-circ. 50 190 M-long. 50 63

4.044 2.378 1.346

4.274 2.826 1.405

4.311 3.454 1.374

4.219 3.863 1.310

3.842 3.889 1.246

3603 3.912 1.297

4.500 97 2.200 1309 1.500 651 4.500 79 2.500 968 1.500 448 4.500 60 3.100 628 1.500 233

4.500 46 3.700 426 1.500 144

4.500 34 4.300 281 1.500 93 4.500 27 5.200 183 1.500 63

88.2 92.5 81.3

84.9 90.0 83.7

89.6 93.6 87.3

90.2 93.8 93,5

89.5 91.8 94.9

96.4 96.3

100.0






Load type Load (kN, kNm) (;:a)


SCF act. Stress in branch improved

shrink Stress in ring method (&;a) header (%)

beta 0.200 Thrust 50 117 4.302 4.500 54 46.2 r-o [mm] 91.429 M-circ. 50 1412 2.373 2.200 691 48.9

M-long. 50 789 1.326 1.500 356 45.1 beta 0.250 Thrust 50 98 4.504 4.500 45 45.9 r-o [mm] 114.286 M-circ. 50 1085 2.849 2.500 520 47.9

M-long. 50 533 1.400 1.500 250 46.9 beta O-350 Thrust 50 72 4.632 4.500 34 47-2 r-o [mm] 160.000 M-circ. 50 707 3.639 3,100 339 47.9

M-long. 50 274 1.410 1.500 133 48.5 beta 0.450 Thrust 50 54 4.467 4.500 26 48.1 r-o [mm] 205.714 M-circ. 50 475 4,042 3.700 232 48.8



M-long. 50 71 1.462 1.500 40 56.3




50.00 .Mean shell radius: 800.00 mm 0.50 Thickness of shell: 16.00 mm





SCF act. improved

shrink ring method

Stress in branch

S.I. Stress in (MPa) header (%)

beta 0.100 r-o [mm] 91,429

beta 0.150 r-o [mm] 137.143

beta 0.195 r-o [mm] 178.286

beta 0.250 r-0 [mm] 228.571

beta 0.350 r-o [mm] 320.00



Thrust 50 76 3.853 4500 163 214.5 M-circ. 50 620 2.802 2.655 1398 225-5 M-long. 50 337 1.523 1.500 620 184.0










SCF act. improved

shrink ring method

Stress in branch

S.I. Stress in NW header (%)

beta 0.250 r-o [mm] 228.571

beta 0.350 r-0 [mm] 320.000

beta 0.450 r-o [mm] 411,429

beta 0.550 r-o [mm] 502.857

Thrust 50 70 4.550 M-circ. 50 468 3.476 M-long. 50 194 1.441



Thrust 50 27 3.861 M-circ. 50 122 4.386 M-long. 50 37 1,330

4.500 3.121 1.500

4.500 3.970 1.500

'4.500 4.818 l-500

4.500 5.667 1.500

101 144.3 697 148-9 257 132.5

72 144.0 427 149.3 136 143.2

52 144.4 275 149.5

80 140.4

39 144.4 182 149.2 53 143.2



Gamma ratio: SO-00 Mean shell radius: 800.00 mm t/T ratio: 1.00 Thickness of shell: 16.00 mm




SCF (back shrink Stress in calculated) ring method (;;a) header (%)

beta r-0 [mm]

beta r-o [mm]

beta r-o [mm]

beta r-0 [mm]

beta r-0 [mm]

beta r-0 [mm]

0.200 Thrust 50 99 5.147 4.500 82 82.8 182.857 M-circ. 50 706 3.356 2.697 616 87.3

M-long. 50 322 1.531 1.500 257 79.8 0.250 Thrust 50 80 5.199 4.500 69 86.3

228.571 M-circ. 50 512 3.803 3.121 461 90.0 M-long. 50 203 1.508 1.500 173 85.2

0.350 Thrust 50 56 5.095 4.500 49 87.5 320.000 M-circ. 50 313 4.557 3.970 285 91.1

M-long. 50 103 1.500 1.500 90 87.4

0.450 Thrust 50 41 4.796 4.500 34 82.9 411.429 M-circ. 50 205 4.934 4.818 176 85.9

M-long. 50 60 1.444 1.500 53 88.3

0.550 Thrust 50 31 4.433 4.500 24 77.4 502.857 M-circ. 50 138 4.961 5.667 111 80.4

M-long. 50 38 1.366 1.500 34 89.5

0.700 Thrust 50 22 4.004 4.500 18 81.8 640.000 M-circ. 50 79 4.600 6-940 68 86.1

M-long. 50 25 1.456 1.500 22 88.0






Load type Load (kN, kNm) (;:a)


SCF act. improved

shrink ring method

Stress in branch

Stress in (&!‘a) header (%)

beta 0.200 r-o [mm] 182.857

beta 0.250 r-o [mm] 228.571

beta 0.350 r-o [mm] 320.000

beta r-o [mm]

beta 0.550 r-o [mm] 502-857

0.450 411.429






beta 0.700 Thrust 50 25 4.550 4.500 10 40.0 r-o [mm] 640+000 M-circ. 50 92 5.358 6.940 38 41.3

M-long. 50 27 1.572 1.500 13 48.1


R/T-parameter = 20

Nozzles in cylindrical shells under internal pressure

Internal pressure = 10 MPa All dimensions in table below are in [mm] and all stresses are given in [MPa]

Nozzle dimensions Vessel dimensions Geometry parameters FE-pipe results Maximum stress

O.D. t O.D. T dlD beta tlT Stress in SCF back Stress in Percentage intensity header calculated branch of stress as SCF

in header

13.14 3.20 658.0 16.0 0.1089 0.0997 0.20 546 2.721 395 72.3 2.721

109.72 3.20 658.0 16.0 0.1659 0.1495 0.20 674 3.360 538 79.8 3.360 182.86 3.20 658.0 16.0 0.2798 0.2492 0.20 966 4.815 875 90.6 4.815

256.00 3.20 658.0 16.0 0.3938 0.3489 0.20 1219 6.076 1249 102.5 6.226 329.14 3.20 658.0 16.0 0.5077 0.4486 0.20 1447 7.212 1586 109.6 7.905

13.14 5.60 658.0 16.0 0.1052 0.0997 0.35 490 2.442 313 76.1 2.442

109.72 5.60 658.0 16.0 0.1622 0.1495 0.35 562 2.801 471 83.8 2.801

182.86 5.60 658.0 16.0 0.2761 0.2492 0.35 793 3.953 805 101.5 4.012 256.00 5.60 658.0 16.0 0.3900 0.3489 0.35 1009 5.029 1150 114.0 5.732

329.14 5.60 658.0 16.0 0.5040 0.4486 0.35 1202 5.991 1453 120.9 7.242

73.14 8.00 658.0 16.0 0.1015 0.0997 0.50 447 2.228 356 19.6 2.228 109.72 8.00 658.0 16.0 0.1584 0.1495 0.50 507 2.527 430 84.8 2.521 182.86 8.00 658.0 16.0 0.2724 0.2492 0.50 681 3.394 115 105.0 3.564 256.00 8.00 658.0 16.0 0.3863 0.3489 0.50 856 4.267 1014 118.5 5.054

329.14 8.00 658.0 16.0 0.5002 0.4486 0.50 1029 5.129 1279 124.3 6.375

13.14 12.00 658.0 16.0 0.0952 0.0997 0.75 396 1.974 337 85.1 1.974 109.72 12.00 658.0 16.0 0.1522 0.1495 0.75 435 2.168 398 91.5 2.168 182.86 12.00 658.0 16.0 0.2661 0.2492 0.75 582 2.901 544 93.5 2.901 256.00 12.00 658.0 16.0 0.3801 0.3489 0.75 739 3.683 755 102.2 3.763 329.14 12.00 658.0 16.0 0.4940 0.4486 0.75 891 4.441 943 105.8 4.700

73.14 16.00 658.0 16.0 0.0890 0.0997 1.00 356 1.774 317 89.0 I.774 109.72 16.00 658.0 16.0 0.1460 0.1495 1.00 393 1.959 380 96.7 1.959 182.86 16.00 658.0 16.0 0.2599 0.2492 1.00 483 2.407 458 94.8 2.407 256.00 16.00 658.0 16.0 0.3738 0.3489 1.00 625 3.115 585 93.6 3.115 329.14 16.00 658.0 16.0 0.4878 0.4486 1.00 761 3.794 714 93.8 3.793

73.14 20.00 658.0 16.0 0.0828 0.0997 l-25 320 1.595 293 91.6 1.595 109.72 20.00 658.0 16.0 0.1398 0.1495 1.25 356 1.774 362 101.7 1.804 182.86 20.00 658.0 16.0 0.2537 0.2492 1.25 405 2.019 435 107.4 2.168 256.00 20.00 658.0 16.0 0.3676 0.3489 1.25 516 2.572 492 95.3 2.572 329.14 20.00 658.0 16.0 0.4815 0.4486 1.25 634 3.160 580 91.5 3.160

73.14 24.00 658.0 16.0 0.0765 0.0997 109.72 24.00 658.0 16.0 0.1335 0.1495 182.86 24.00 658.0 16.0 0.2474 0.2492 256.00 24.00 658.0 16.0 0.3614 0.3489 329.14 24.00 65X.0 16.0 0.4753 0.4486

1.50

1.50 1.50

1.50

1.50

2.00 2.00

2.00 2.00

2.00

294 1.465 267 90.8 1.465 330 1.645 340 103.0 1.695 368 1.834 414 112.5 2.064 421 2.128 466 109.1 2.323 524 2.612 514 98.1 2.612

73.14 32.00 658.0 16.0 0.0641 0.0997 109.72 32.00 658.0 16.0 0.1211 0.1495 182.86 32.00 658.0 16.0 0.2350 0.2492 256.00 32.00 658.0 16.0 0.3489 0.3489 329.14 32.00 658.0 16.0 0.4628 0.4486

258 1.286 214 82.9 1.286 291 1.450 295 101.4 1.470 336 1.675 369 109.8 1.839 367 1.829 418 113.9 2.083 385 1.919 460 119.5 2.293



R/T-parameter = 30 Internal pressure = 10 MPa All dimensions in table below are in [mm] and all stresses are given in [MPa]

Nozzle dimensions Vessel dimensions Geometry parameters

O.D. t O.D. T dlD beta t/T

109.72 3.20 976.0 16.0 0.1110 0~1000 0.20 942 164.58 3.20 976.0 16.0 0.1681 O~lSOO 0.20 1213 274.28 3.20 976.0 16.0 0.2824 0.2500 0.20 1759

384.00 3.20 976.0 16.0 0.3967 0.3500 0.20 2204 493.72 3.20 976.0 16.0 0.5110 0.4500 0.20 2613

109.72 5.60 976.0 16.0 0.1085 0~1000 0.35 772 164.58 5.60 976.0 16.0 0.1656 0.1500 0.35 1000 274.28 5.60 976.0 16.0 0.2799 0.2500 0.35 1450 384.00 5.60 976.0 16.0 0.3942 0.3500 0.35 1822

493.72 5.60 976.0 16.0 0.5085 0.4500 0.35 2159

109.72 8.00 976.0 16.0 0.1060 0~1000 0.50 712 164.58 8.00 976.0 16.0 0.1631 0.1500 0.50 871

274.28 8.00 976.0 16.0 0.2774 0.2500 0.50 1212

384.00 8-00 976.0 16.0 0.3917 0.3500 0.50 1531

493.72 8.00 976.0 16.0 0.5060 0.4500 0.50 1839

109.72 12.00 976.0 16.0 0.1018 0~1000 0.75 616

164.58 12.00 976.0 16.0 0.1589 0.1500 0.75 758

274.28 12.00 976.0 16.0 0.2732 0.2500 0.75 1075

384.00 12.00 976.0 16.0 0.3875 0.3500 0.75 1370

493.72 12.00 976.0 16.0 0.5018 0.4500 0.75 1644

109.72 16.00 976.0 16.0 0.0976 0~1000 1.00 562

164.58 16.00 976.0 16.0 0.1548 0.1500 1.00 646

274.28 16.00 976.0 16.0 0.2690 0.2500 1.00 931

384.00 16.00 976.0 16.0 0.3833 0.3500 1.00 1203

493.72 16.00 976.0 16.0 0.4976 0.4500 1.00 1454

109.72 20.00 976-O 16.0 0.0935 0~1000 1.25 510

164.58 20.00 976.0 16.0 0.1506 0.1500 1.25 551

274.28 20.00 976.0 16.0 0.2649 0.2500 1.25 785

384.00 20.00 976.0 16.0 0.3792 0.3500 1.25 1028

493,72 20.00 976.0 16.0 0.4935 0.4500 1.25 1253

109.72 24.00 976.0 16.0 0.0893 0~1000

164.58 24.00 976.0 16.0 0.1464 0.1500

274.28 24.00 976.0 16.0 0.2607 0.2500

384.00 24.00 976.0 16.0 0.3750 0.3500

493.72 24.00 976.0 16.0 0.4893 0.4500

109.72 32.00 976.0 16.0 0.0810 0~1000 164.58 32-00 976.0 16.0 0.1381 0.1500

274.28 32-00 976.0 16.0 0.2524 0.2500

384.00 32.00 976.0 16.0 0.3667 0.3500

493.72 32.00 976.0 16.0 0.4810 0.4500

1.50 1.50

1.50 1.50

1.50

2.00 2.00

2.00

2.00 2.00

473

512 654

864

1066

419 458

523 643

760

Stress in

header

FE-pipe results Maximum

stress SCF back Stress in Percentage intensity calculated branch of stress as SCF

in header

3.140 706 4.043 990

5.863 1773

7.347 2422

8.710 3006

2.573 635

3.333 981

4.833 1758 6.073 2394

7.197 2953

2.373 591

2,903 869

4.040 1517 5.103 2059

6.130 2536

2.053 560

2.527 669

3.583 1110

4.567 1486

5.480 1818

1.873 541

2.153 608

3.103 853

4.010 1113

4,847 1344

1.700 519

1.837 585

2.617 704

3.427 891 4.177 1056

1.577 492

1.707 560

2.180 652

2.880 753

3.553 877

1.397 430

1.527 504

1.743 589

2.143 657

2.533 718

74.9 3.140 81.6 4.043

100.8 5.910

109.9 8.073 115.0 10.020

82.3 2.573

98.1 3.333 121.2 5.860 131.4 7.980 136.8 9.843

83.0 2.373

99.8 2.903 125.2 5-057 134.5 6-863

137.9 8.453

90.9 2.053

88.3 2.521 103.3 3.700 108.5 4.953

110.6 6.060

96.3 1.873

94.1 2.153 91.6 3.103

92.5 4.010 92.4 4.847

101.8 1.730 106.2 1.950

89.7 2.617

86.7 3.421 84.3 4.177

104.0 1.640 109.4 1.867

99.7 2.180

87.2 2.880

82.3 3.553

102.6 1.433 110.0 1.680 112.6 1.963

102.2 2.190

94.5 2.533

17 External loads and internal pressure in nozzles


R/T-parameter = 40 Internal pressure = 10 MPa AI1 dimensions in table below are in [mm] and all stresses are given in [MPa]


O.D. t O.D. T d/D beta tlT Stress in SCF back Stress in Percentage intensity

header calculated branch of stress as SCF in header

146.28 3.20 1296.0 16.0 0.1118 0~1000 0.20 1414 3.535 1054 74.5 3.535

219.42 3.20 1296.0 16.0 0.1689 0.1500 0.20 1832 4.580 1660 90.6 4.580

365.72 3.20 1296.0 16.0 0.2832 0.2500 0.20 2655 6.638 2842 107.0 7.105

512.00 3.20 1296.0 16.0 0.3975 0.3500 0.20 3314 8.285 3791 114.4 9.478

658.28 3.20 1296.0 16.0 0.5118 0.4500 0.20 3940 9.850 4663 118.4 11.658

146-28 5.60 1296.0 16.0 O-1099 0~1000 0.35 1171 2.928 1081 92.3 2,928

219.42 5.60 1296.0 16.0 0.1670 0.1500 0.35 1520 3.800 1712 112.6 4.280

365.72 5.60 1296.0 16.0 0.2813 0.2500 0.35 2191 5.478 2935 134.0 7.338

512.00 5.60 1296.0 16.0 0.3956 0.3500 0.35 2736 6.840 3896 142.4 9.740

658.28 5.60 1296.0 16.0 0.5099 0.4500 0.35 3244 8.110 4756 146.6 11.890

146.28 8.00 1296.0 16.0 0.1080 0~1000 0.50 1045 2.613 958 91.7 2.613 219.42 S-00 1296.0 16.0 0.1652 0.1500 0.50 1290 3.225 1486 115-2 3-715

365.72 8.00 1296.0 16.0 0.2795 0.2500 0.50 1838 4.595 2496 135.8 6.240 512.00 8.00 1296.0 16.0 0.3938 0.3500 0.50 2320 5.800 3307 142.5 8.268 658.28 8.00 1296.0 16.0 0.5080 0.4500 0.50 2787 6.968 4032 144.7 10.080

146.28 12.00 1296.0 16.0 0.1049 0~1000 0.75 914 2.285 781 85.4 2.285 219.42 12.00 1296.0 16.0 0.1620 0.1500 0.75 1161 2.903 1109 95.5 2.903 365.72 12.00 1296.0 16.0 0.2763 0.2500 0.75 1665 4.163 1790 107.5 4.475

512.00 12.00 1296.0 16.0 0.3906 0.3500 0.75 2115 5.288 2348 111.0 5.870 658.28 12.00 1296.0 16.0 0.5049 0.4500 0.75 2529 6.323 2846 112.5 7.115

146.28 16.00 1296.0 16.0 0.1018 0~1000 1.00 778 1.945 758 97.4 1.945 219.42 16.00 1296.0 16.0 0.1589 0.1500 1.00 1000 2.500 880 88.0 2.500 365.72 16.00 1296.0 16.0 0.2732 0.2500 1.00 1477 3.693 1347 91.2 3.693 512.00 16.00 1296.0 16.0 0.3875 0.3500 1.00 1895 4.738 1732 91.4 4.738 658.28 16-00 1296-O 16.0 0.5018 0.4500 I .oo 2276 5.690 2077 91.3 5.690

146.28 20.00 1296.0 16.0 0.0987 0~1000 1.25 700 1.750 733 104.7 1.833 219.42 20.00 1296.0 16.0 0.1558 0.1500 1.25 846 2.115 809 95.6 2.115 365.72 20.00 1296.0 16.0 0.2701 0.2500 1.25 1271 3.178 1085 85.4 3.178 512.00 20.00 1296.0 16.0 0.3844 0.3500 1.25 1651 4.128 1362 82.5 4.128 658.28 20.00 1296.0 16.0 0.4987 0.4500 1.25 2000 5.000 1610 80.5 5.000

146.28 24.00 1296.0 16.0 0.0955 0-1000 219.42 24.00 1296.0 16.0 0.1527 0.1500 365.72 24.00 1296.0 16.0 0.2670 0.2500 512.00 24.00 1296.0 16.0 0.3813 0.3500 658.28 24.00 1296.0 16.0 0.4955 0.4500

1.50

1.50 1.50 1.50

1.50

2.00

2.00 2.00

2.00

2.00

652 1.630 704 108-O I.760 718 1.795 777 108.2 1.943

1074 2.685 926 86.2 2.685 1410 3,525 1133 80.4 3.525 1734 4.335 1318 76.0 4.335

146.28 32.00 1296.0 16.0 0.0893 0~1000 219.42 32.00 1296.0 16-O 0.1464 0.1500 365.72 32.00 1296.0 16.0 0.2607 0.2500 512.00 32.00 1296.0 16.0 0.3750 0.3500 658.28 32.00 1296.0 16.0 0.4893 0.4500

582 1.455 633 108.8 1.583 634 1.585 708 Ill.7 I.770 815 2.038 817 100.2 2.043

1025 2.563 916 89.4 2.563 1259 3.148 1003 79.7 3.148



R/T-parameter = 50 Internal pressure = 10 MPa All dimensions in table below are in [mm] and all stresses are given in [MPa]


O.D. t O.D. T a/o beta r/T Stress in SCF back Stress in Percentage intensity

header calculated branch of stress as SCF

in header

182.86 3.20

274.28 3.20

457.14 3.20

640.00 3.20

822.86 3.20

182.86 5.60 274.28 5.60

457.14 5.60

640.00 5.60

822.86 5.60

182.86 8.00

274.28 8.00 457.14 8.00

640.00 8.00

822.86 8.00

182.86 274.28

457.14

640.00 822.86

2i4,28 457.14

640.00

822.86

12.00

12.00

12.00 12.00

12.00

16.00

16.00

16.00 16.00

182.86 20.00

274.28 20.00

457.14 20.00

640.00 20.00

822.86 20.00

182.86 24.00

274.28 24.00

457.14 24.00

640.00 24.00

822.86 24.00

182.86 32.00

274.28 32.00

457.14 32.00

640.00 32.00

822.86 32.00

1616.0

1616.0 1616.0

1616.0

1616.0

1616.0

1616.0 1616.0

1616.0 1616.0

1616.0

1616.0 1616.0

1616.0

1616.0

1616.0 1616.0

1616.0

1616.0 1616.0

1616.0 1616.0

1616.0 1616.0

1616.0

1616.0 1616.0

1616.0

1616.0

1616.0

1616.0

1616.0 1616.0

1616.0

1616-O

1616.0 1616.0

1616.0 1616.0

16.0 0.1123 0~1000 0.20 1930 3.860 1582 82.0 3.860 16.0 0.1694 0.1500 0.20 2508 5.016 2456 97.9 5.016 16.0 0.2837 0.2500 0.20 3621 7.242 4183 115.5 8.366 16.0 O-3980 0.3500 0.20 4524 9.048 5480 121.1 10.960 16.0 05123 0.4500 0.20 5404 10.808 6663 123.3 13.326

16.0 0.1108 0~1000 0.35 1610 3.220 1672 103.9 3.344

16.0 0.1679 0.1500 0.35 2088 4.176 2581 123.6 5.162 16.0 0.2822 0.2500 0.35 2992 5.984 4276 142.9 8.552 16.0 0.3965 0.3500 0.35 3734 I.468 5601 150.0 11.202 16.0 0.5108 0.4500 0.35 4444 8.888 6805 153.1 13,610

16.0 0.1093 0~1000 0.50 1403 2.806 1456 103.8 2.912 16.0 0.1664 0.1500 0.50 1690 3.380 1972 116.7 3.944 16.0 0.2807 0.2500 0.50 2518 5.036 3605 143.2 7.210 16.0 0.3950 0.3500 0.50 3203 6.406 4715 147.2 9.430

16.0 0.5093 0.4500 0.50 3854 7.708 5724 148.5 11.448

16.0 0.1068 0~1000 0.75 1255 2.510 1106 88.1 2.510 16.0 0.1639 0~1500 0.75 1615 3.230 1619 100.2 3.238

16.0 0.2782 0.2500 0.75 2328 4.656 2556 109.8 5.112

16.0 0.3925 0.3500 0.75 2950 5.900 3313 112.3 6.626

16.0 0.5068 0.4500 0.75 3524 7.048 4002 113.6 8.004

16.0 0.1614 0~1500 1 .oo 1421 2.842 1258 88.5 2.842

16.0 0.2754 0.2500 1.00 2063 4.126 1713 83.0 4.126

16.0 0.3900 0.3500 1.00 2673 5.346 2421 90.6 5.346

16.0 0.5043 0.4500 1.00 3210 6.420 2940 91.6 6.420

16.0 0.1018 0~1000 1.25 913 1.826 945 103.5 1.890

16.0 0.1589 0~1.500 1.25 1210 2.420 1051 86.9 2.420

16.0 0.2732 0.2500 1.25 1832 3.664 1510 82.4 3.664

16.0 0.3875 0.3500 1.25 2360 4.720 1887 80.0 4.720

16.0 0.5018 0.4500 1.25 2858 5.716 2229 78-O 5.716

16.0 0.0993 0~1000

16.0 0.1564 0~1500

16.0 0.2707 0.2500

16.0 0.3850 0.3500

16.0 0.4993 0.4500

1.50

1.50 1.50 1.50

1.50

2.00

2.00 2.00

2.00 2.00

826 1.652 910 110.2 1.820

1021 2.042 999 97.8 2.042

1569 3.138 1271 81.0 3.138 2042 4.084 1555 76.2 4.084

2511 5.022 1812 72.2 5.022

16.0 0.0943 0~1000 16.0 0.1514 0~1500

16.0 0.2657 0.2500

16.0 0.3800 0.3500

16.0 0.4943 0.4500

741 1.482 829 111.9 1.658

802 1.604 912 113.7 1.824

1168 2.336 1058 90.6 2.336

1504 3.008 1193 79.3 3.008

1864 3.728 1346 72.2 3.728

Inr. J. Pm. Ves. & Pqing 72 (1997) l-18 PII:SO308-0161(97 ...€¦ · the MW Kellogg Company in...

Documents

Transcript of Inr. J. Pm. Ves. & Pqing 72 (1997) l-18 PII:SO308-0161(97 ...€¦ · the MW Kellogg Company in...