PVP-1279

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STIFFNESS CO EFFICIENTS FOR NOZZLES IN API 650 TANKS

Manfred Lengsfeld

Fluor Daniel Inc.

manfred.lengsfeld @fluor.com

Kanajett Hathaitham

Fluor Signature Services Inc.

ken.hathaitham @ fluor.com

Kanhaiya L. Bardia

Fluor Dan iel Inc.

[email protected]

Dona ld G. LaBounty

Fluor Dan iel Inc.

[email protected]

Jaan Taagepera

Valero Refining Co.

[email protected]

Mark C. Lengsfeld

Crane Valves

lengsfeld @yahoo.com

ABSTRACT

The analys is of tank nozzles for API S tandard 650 [1] tanks

is a comp lex problem. Appen dix P of API 650 provides a

method for determining the a l lowable external loads on tank

shel l openings . The method in Appen dix P is based on two

papers , one by Bil l imoria and Hagstrom [2] and the other by

Bil l imoria and Tam [3]. Although A ppendix P is opt ional ,

indus try has used i t for a number of years for large diameter

tanks. For tanks less than 120 feet (33.6 m) in diam eter,

Appen dix P is not appl icable .

In previous ly published papers [4-10], the authors used

fini te e lement analys is (FEA) to verify the experim ental resul ts

reported by Bil l imoria and Tam for shel l nozzles . The analys is

showed the variance between s t i ffness coeffic ients and s tresses

obtained by FEA and API 650 methods for tanks .

In this fol low-up paper, the authors present s t i ffness

coeffic ients for tank nozzles located away from a s tructural

discontinui ty. Factors to es tabl ish spring ra tes for nozzles

varying from 6 to 48 inches and tank diam eters from 30 feet to

300 feet and for nozzles a t different e levat ions on the shel l are

provided. Mathematical equat ions are provid ed together with

graphs f or the s t i ffness coeffic ient factors .

INTRODUCTION

In Appendix P of API 650 a procedure has been es tabl ished

to determine the a l lowable loads on tank shell openings . This

procedure is a pract ical solut ion to a complex problem,

especia l ly s ince low-type nozzles , as defined in API 650, are

close to the bot tom and thus are affected by the bot tom-to-shel l

junct ion (See F ig. 1). As mention ed by Bil l imoria and

Hagstr om, this procedure is conservat ive . Users in indus try

have ques t ioned the need for such conservat ism. Even though

Appendix P is not mandatory, many des igners use this method

for lack of any other guidance.

In previous ly published papers , the authors used FEA to

verify the experimental resul ts reported by Bil l imoria and

Tam. In papers by Lengsfeld, e t . a l [4-7] various degrees of

conservat ism were reported for different nozzle s izes a t tached

to tanks . S tress factors and s t i ffness coeffic ients for low-type

nozzles were published by the authors [8,9]. S tress factors for

varying nozzles heights were published by the authors [10]. In

this paper s t i ffness coeffic ients are provided for nozzles away

from a s tructural discontinui ty. The dis tance a t which a

discontinui ty has no influence o n the spring ra te of a nozzle i

defined by Welding Research Counci l (WRC) Bulle t in 297

[11]. H eight factors are used to calcula te s t i ffness coeffic ient

for nozzles located c lose to a gross s t ructural discontinui ty

With the height factors provided , the engineer is able to arr iv

at s t i ffness coeffic ients for nozzles a t any locat ion on the tan

shel l , which in turn helps to p redic t m ore accurate ly the pipin

loads at the nozzle.

NOMENCLATURE

B = 2(12*Dt) in , height from tank bot tom per WR C,

Bulle t in 297 where tank bot tom has no influence

on stiffness on nozzles (see Figure 1), in

D = nominal diameter of tank, f t

Do = outs ide diameter of re inforcing pad, in

FR = radial load, lbs

KBc = s t i ffness coeffic ient due to c ircumferent ia l

mom ent a t dis tance B, in-lbs /radian

Kc = s t i ffness coeffic ient for c ircumferent ia l mom ent ,

in-lbs/radian

KBL = s t i ffness coeffic ient due to longitudinal mom ent

at dis tance B, in-lbs /radian

KL = s t i ffness coeffic ient for longitudinal mome nt , in-

lbs /radian

KBR = stiffness coeff icient due to radial force at

dis tance B, lbs / in

KR = stiffness coeff icient for shell thrust (radial) load,

lbs/in

L = vert ical dis tance from nozzle centerl ine to tank

bottom (see F igure 1), in

LB = vert ical dis tance of nozzle centerl ine where tank

bottom has no influence on nozzle s t i ffness

= B + ½Do

Mc = c ircumferent ia l mom ent , in-lbs

ME = longitudinal mom ent , in-lbs

a = outs ide radius of opening connect ion, in

d = outs ide diameter of nozzle (2a), in

h = height factorL/L B

mc = s t i ffness ra t io for c ircumferent ia l mom ent

Proceedings of PVP20022002 ASME Pressure Vessels and Piping Conference

August 5-9, 2002, Vancouver, BC, Canada

PVP2002-1279

1 Copyright © 2002 by ASME

wnloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 06/03/2015 Terms of Use: http://asme.org/terms

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Y

..... ~ 1 ~LONGrlIlJDINALOMENTM~,

l X .

+M~

Figure 1: Dimensions for nozzles per API 650

mL = stiffness ratio for longitudinal moment

m R - stiffness ra tio for radial force

t = shell thickness of tank, in

t. = thickness of nozzle wall, in

tp = thickness of reinforcing pad, in

DESCRIPTION

Figure 2 shows a detail of the nozzle area. Each tank was

assumed to be at ambient temperature of 70 ° Fahrenheit. The

bottom of the shell course for each model had the nodes fixed

in all displacements while rotations were not fixed. This

assumes that the annular ring provides little resistance to shell

rotation due to imposed piping loads. Only an 180 ° section of

each tank was modeled, utilizing symmetry to reduce model

size. Stiffness coefficients were calculated from the deflection

of the nozzle after the loads were applied.

For the FEA, COSMOS software developed by Structural

Research and Analysis Corporation was used to construct

three-dimensional models of the tanks and the nozzles. Large

tanks (D>30 feet) were modeled with 4 node shell elements

Smaller tanks were modeled using 8 node solid elements

Each variation of tank and nozzle diameter had differen

numbers of elements. The analyses were performed on

Silicon Graphics Workstation and PC's.

Figure 3a represents stiffness coefficients due to a radia

force for tanks from 30 feet to 300 feet in diameter with a wa

thickness of 3/4 . Figure 3b gives the stiffness ratio due to

radial force to be used for nozzles located closer to a structura

discontinuity. Figures 4a and 4b are for circumferentia

moments where as Figures 5a and 5b for longitudina

moments. Actual stiffness ratios mi conform to a relativ

narrow scatter band. For simplicity these bands were combine

into single lines in Figures 3b, 4b and 5b. Stiffness coefficien

for above figures 3a, 4a and 5a are for nozzles 6 to 48

diameter located away from a gross structural discontinuity

Nozzles were chosen to have reinforcing pads with equivalen



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Figure 2: Detail of a typica l nozzle and shell area

dimensions of Table 3-6, column 5 of API 650. The tanks

modeled were 30 feet to 300 feet in diameter and 64 feet high.

Several shell-th ickness were investigated for each tank. The

mathematical method of least-square fits for polynomial curves

was used to smooth these curves and derive mathematical

equations.

Table 1 lists the equations for tank diameters and

thickness presently available. These equations were then used

to produce the graphs of Figures 3a through 5b. Using the

mathematical equations will simp lify the creation of computer

programs for the calculation of nozzle stiffness coefficient at

the nozzle-to-shell junction.

LOADING

The same loadings were applied to all finite element models,

namely

Radial,

P = 1,000 lbs

Longitudinal Moment,

ML = 10,000 in-lbs

Circumferential Moment,

Mc = 10,000 in-lbs

The loadings were applied independently. In excess of 100

combinations of loading, tank, thickness, and nozzle sizes

were evaluated.

RESULTS

Stiffness coefficients vary with the location of the nozzle in

height on the tank wall. Stiffness coefficients increase as the

nozzle moves closer to a gross structural discontinuity. Factors

have been established to calculate spring rates for nozzles a

any location on the tank wall using as a basis the rates for

nozzles away from a discontinuity . Stiffness coefficients are

inverse proportional to the height, the lower the location on the

tank, the higher is the spring rate. Depending on the location o

the nozzle, the value for the stiffness coefficients from Figures

3a, 4a or 5a wil l be divided by the height factor from Figures

3b, 4b or 5b respectively.



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ANALYSIS PROCEDURE

The procedure for the evaluation of stiffness coefficients is

as follows:

1. Calculate the distance B

2. Establish the height LB

3. Establish the height factor h

4. For a given nozzle on a tank with established wall

thickness read the stiffness coefficient from Figures

3a, 4a or 5a for the corresponding loading

5. Fro m Figures 3b, 4b or 5b establish the stiffness ratio

factors mi

6. Divide the value of the spring rate from (4) by the

stiffness ratio factor from (5) to arrive at the stiffness

coeff ic ient for the nozzle under cons iderat ion

DISCUSSION

The graphs presented in this paper were cons tructed to be on

the conserv ative side.

The presented results may be interpolated to establish

stiffness coefficients for other nozzles, tank diameters and

shell thickness.

The purpose of this paper is to give the des igner a s imple

means to arrive at a spring rate at a nozzle to tank shell

connect ion.

For more complex or critical applications, i t is

recommended to perform an FEA analys is including the

complete piping sys tem.

CONCLUSION

The method presented in this paper provides the des ign

engineer a means to calculate stiffness coefficients at the shell

to nozzle junction . With these rates applied piping loads can

be established.

Once accurate piping loads have been established, stresses at

the nozzle-shell junctio n can be calculated using the metho ds

published previously [10].

The use of the finite element analysis models in determining

the stiffness coefficients for tank nozzles is recommended

when piping loads indicated by the method provided in this

paper are excessive and would result in expensive piping

systems.

Additional data for other tank sizes are being developed

Time and size constrains prevent the authors from

investigation of several mo re shell thickness.

ACKNOWLEDGMENTS

The authors grateful ly acknowledge the support of th

managements of Fluor Daniel , Valero Refining Co and CCI t

prepare and publish this paper. Special thanks to Gilber

Chen, Avtar S. Mann and Dennis Mitchell for their review o

the manuscript and their encouragement.

REFERENCES

[1] American Petroleum Institute, API Standard 650 tent

Edition, Novem ber 1998 Welded Steel Tanks for Oil Storage

[2] Billimoria, H.D., and Hagstrom, K .K, Stiffnes

Coeff ic ients and Allowable Loads for Nozzles in Flat Bot tom

Storage Tanks Paper 77-PVP-19. ASME 1977

[3] Billimoria, H.D., Tam, K.K., 1980, Experim enta

Investigation of Stiffness Coefficients and Allowable Load

for a Nozz le in a Flat Bott om Tank ASM E Publication 80

C2/PVP-5

[4] Lengsfe ld, M., Bardia, K.L, Taagepera, J ., 1995 Nozz l

Stresses Resul t ing fro m Piping Load s a t Lo w-Type Nozzles i

API 650 Storage Tanks ASME PVP-Vol . 315

[5] Leng sfeld, M., Bardia, K.L, Taagepera, J ., 1996 FEA v

API 650 for Low Tank Nozzles ASME PVP-Vol . 336

[6] Lengsfe ld, M., Bardia, K.L, Taagepera, J ., 1997 FEA v

API 650 for Low Tank Nozzles (2) ASME PVP-Vol . 359

[7] L engsfeld , M., Bardia, K.L, Taagepera, J ., 1998 Sprin

Rates for Low Tank Nozzles ASME PVP-Vol . 368

[8] Lengsfeld, M., Bardia, K.L, Taagepera, J ., Hathaitham

K., 1999 Stress Factors for Low-Typ e Nozzles in API 65

Tanks ASME PVP-Vol. 388

[9] Lengsfeld, M., Bardia, K.L, Taagepera, J ., Hathaitham

K., 1999 Spring Rates for Low Tank Nozzles in API 65

Tanks ASME PVP-Vol . 388

[10] Lengsfeld, M., Bardia, K.L., Taagepera, J ., Hathaitham

K., LaBo unty, D.G., Lengsfe ld, M.C., 2001 Analysis o

Loads for Nozzles in API 650 Tanks ASME PVP-Vol . 430

Il l ] Bu l le t i n 297, September1987, Local Stresses

Cylindrical Shells due to External Loadings on Nozzle

Welding Research Counci l (WRC), New York



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S TIFFN E S S C O E FFIC IE N T D U E TO R A D IA L FO R C E

400

350

300

250

o ~ 200

150

100

5O

0

30'Dia.x3/4

. . . . .

[.

30'Dia.xl/2

10

20

KBR = 3.4604X + 70,876

1 gO'Dia.xa/4

KBR = 2.3202x + 47.251

300'Dia.x3/4

KBR = 0.4032X + 4.4569

30 40 50

Z

Note 3/4 thicknesses are solid line

Nozzle Size in)

Figure 3a

STIFFNESS RATIO DUE TO RAD IAL FORCE

0.9

0,8

0.7

0.6

0.5-

I¢ 0.4-

0.3-

0 . 2

0.1

0

,,, , .. .. ,

0.1 0.2

0.3 0.4 0.5 0.6

h=L/L B

mR = -0.2504h 2 + 1.2516h - 0.0086

, , , , , ,

0.7 0.8 0.9

Figure 3b



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S T I F F N E SS C O E F F I C I E N T D U E T O C IR C U M F E R E N T I A L M O M E N T

200 -

180

160 -

1 4 0

o8 ~

2o

7 1oo.

f f , -

~.~ 80-

60

40 . . . . .

0 . . . . . . .

180'Dia.x,3/4

KBC = 0 .0243x = + 0 .0 707x + 2 .221 8

3 O ' D i a , x l / 2

P

120 'D ia .x3 /4 KBc = 0 .0421 x2 - 0 .272 3x + 9 .9571

KBC = 0 .036 4x ~ + 0 .106 x + 333 27 ~ I = .

3O'Oia .x3 /4

K~ = 0 .0622 x 2 + 0 .451 lx + 9 .1617

t 300 'D ia .x3 /4

K e c = 0 . 0 0 7 5 x2 + 0 .2921x + 4 .1626

i ........

1 0 2 0 3 0 4 0 5 0

x

Nozzle Size in)

Note 3 /4 th ickn esses are so lid l ine

Figure 4a

S T I F F N E S S R A T I O D U E T O C I R C U M F E R E N T I A L M O M E N T

0.9

0.8

07

0.6

~ 05

E 0.4

0.3

0.2

0.1

0

mc = -0.2947h2 + 1.0205h +

0.2751

0.1 0.2 03 0.4 0.5 06 0.7 0.8 0.9

h=L/LB

Figure 4b



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SPRING RATE DUE TO LONGITUDINAL MOMENT

: e l i _

/ / - ~ K ,L = o .2~ o o , - o .o 88 3 ,+ 2o . , ~

/

I - /

00 - - - 30'Dia.xl/2 - . . . . . . .

~ ~ 300 1 I ~ ,20'Dia.x3/4

I / ~

2 ° 1 . . . . . / . . . . , , ~ = o . , 3 , ~ e - o . , , , x + , . o , , ~ . . . . . -

. . . .

50 1 ~ ~ ~ - 300'Dia.x3/4

o | ~,L= o o249x~ + o 2o8,x +

, , , ~ 9

0 t 0 20 30 40 50

Nozzle Size (In) Note 3/4 thicknesses are solid ine

Figure 5a

STIFFNESS RATIO DUE TO LONGITUDINAL MOMENT

0.9

0.8

0 . 7

. j 0.6 . . . . . . . . . .

0 . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E 0.4

0.3

0.2

0.1

0.1 0.2 0.3

0.4 0.5

h=L/LB

m L = - 0 . 25 12h 2 + 0 . 641 h + 0 . 60 34

0.6 0.7 0.8 0.9

Figure 5b



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Table

F o r m u la e

KBC = 0. 052 9x 2 + 4.040 5X - 26.14 6

KBL = 0.266 2X 2 + 4.3 491X - 35.67 8

KBR = 0.0079X + 0.19 19

KBC = 0. 0421 X 2 - 0.272 3X + 9 .9571

KBL = 0.15X 2 1.0719X + 6.463 2

KBR = 4.1196 X + 50. 97

Kac = 0.0421X 2 - 0.27 23x + 9.9571

K B L = 0 . 1 5 X 2 1.0719x + 6 .4632

KBR = 4.1196 X + 50. 97

K B C = - 0 . 0 5 8 9 X 2 +

4 .9 4 4 7 x + 2 .4 0 1 6

KBL = 0.1462X 2 - 3.7726X + 54 .295

KBR =

0.5828x + 88 .103

KBc = -010199x 2 + 1.66 14x - 4.0694

KBL = 0.0215X 2 + 0.22 08X + 5 .321 3

KBR = 0.3677X + 38.3 96

KBC = 0.0364X 2 + 0.106X 3.332 7

KBL = 0. 1373 X 2 - 0.798X - 9.0 685

KBR = 3.4804X + 70. 876

KBC = 0-008 9X 2 + 0.77 1X + 1 3.23 6

KBL = 0.0393X 2 + 0 .5196X + 13.023

KBR = 0.1211 X + 3 4.9 77

KBC = 0.0 421X 2 - 0.27 23X + 9.95 71

KBt_ = 0 . 15 X 2 - 1.0719x + 6 .4632

KBR = 4.1196 X + 50. 97

S i z e

30' Tank, 1 Wal l

30 ' Tank, 1 Wal l

30 ' Tank , 1 Wa l l

30 ' Tank, 1/2 Wal l

30 ' Tank, 1/2 Wa l l


30 ' Tank , 3 /4 Wa l l

30 ' Tank, 3/4 Wa l l


120 ' Tan k 1 W al l

120' Tank. 1 Wal l

120 ' Tan k 1 W al l

120' Tank. 1/2 Wal l


1 2 0 ' T a n k 1 /2 W a l l

120 ' Tan k 3 /4 Wa l l


120' Tank, 3/4 Wal l

300 ' Tank , 1 Wa l l

300 ' Tank , 1 Wa l l

300 ' Tank , 1 Wa l l

300 ' Tank , 3/4 Wa l l

300 ' Tank , 3 /4 Wa l l

300 ' Tank , 3/4 Wa l l

SAMPLE PROBLEM

Calcula te the spr ing ra te for the fo l lowing tank:

Mater ia l : A36

D = 30 feet (360 in)

t = %i n

d = 30 in

t, = 3/4 in

L = 2 8 in ( r e gu la r p e rA PI 6 5 0 )

The nozz le has a re inforc ing p la te in accordance wi th API

650.

Do = 49.5 in

t = ½ in

= 32.8 6 in

2) Establish the centerline dis tance of the

nozz le of no d iscont inui ty inf luence

LB = B+0.5*D0

= 32.86 + 0.5 * 49.5

= 57.61 in

3) Establ ish the he ight fac tor

h = L/LB

28/57.61

0.486

4) From Figure 3a , 4a , 5a read the s t i f fness

coeff ic ien ts

KBR = 280 ,000 lbs/in (Fig. 3a)

KBC = 80 ,000 in-lbs/rad (Fig. 4a)

KBL = 200 ,00 0 in-lbs/rad (Fig. 5a)

5) From Figure 4 , 5 , 6 read the coeff ic ien t

fac tor

mr = 0.6 for Kr ( Fig. 3b)

mc = 0 .68 for Kc (Fig. 4b)

mE = 0.88 for KL (Fig. 5b)

6) Divide the stiffness coefficients

established in step 4 by the factors from step

5 to arrive at the stiffness coefficients for the

nozz le under invest iga t ion .

K R = KB R m R

280,000 / 0 .6

466,000 lbs/ in

K c = K B c / m c

80,000 / 0 .68

117,600 in-lbs/rad

KL = KBL me

200,000 / 0 .88

227,000 in- lbs/ rad

Thus for th is sample problem the above ca lcula ted s t i f fness

coeff ic ien ts should be used when establ ish ing the loads for the

pip ing system a t tached to the nozz le , namely:

KR= 466 ,00 0 lbs/in for a radial load

Kc = 117,600 in- lbs/ rad for a c i rcumferent ia l mom ent

KL = 227,0 00 in- lbs/rad for a longi tudina l mo ment

SOLUTION

1) Calcula te the d is tance where the bot tom

discont inui ty has no inf luence on the spr ing

rate

B = 2(12*D t) °5

= 2* (12 3 0 0.7 5) 0.5


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PVP-1279