14
Kedar A. Damle Thyssenkrupp Industrial Solutions India Private Limited 2nd Floor, Duggal Plaza, PremNagar, Bibwewadi Road, Pune 411037, India e-mail: [email protected] Pratik S. Gharat Thyssenkrupp Industrial Solutions India Private Limited 2nd Floor, Duggal Plaza, PremNagar, Bibwewadi Road, Pune 411037, India e-mail: [email protected] Rudolf Neufeld Department of Mechanical Engineering, Fachhochschule Sudwestfalen (University of Applied Science), Meschede 59872, Germany Wilhelm Peters Department of Mechanical Engineering, Fachhochschule Sudwestfalen (University of Applied Science), Meschede 59872, Germany Effect of Nozzle Junction and Equipment Stiffness on Absorption of Pipe Thermal Loads As an industry norm, the nozzle local loads are considered to be local and are not consid- ered in foundation design. Presently, this norm is under debate. One opinion is some per- cent of these loads are to be considered to be transferred to the foundation. The horizontal forces on the foundation are more critical than vertical forces. Attempt has been made to understand the system and create a model which will represent the system to a good approximation. A mathematical model is developed to demonstrate the actual system. It is a stiffness system consisting of equipment, nozzle junction, and connected piping. The connected pipes are heated sequentially to generate nozzle loads in axial and out plane directions. Steady-state thermal loads are calculated for the given system stiff- ness. Governing parameters are identified and altered to note the effect. The governing parameters identified are equipment diameter (D), nozzle location on equipment (x), and nozzle diameter (d). The effect is studied for pressure range (20–120 bar) and tempera- ture (100–400 C). The results of percentage loads transferred with respect to the govern- ing parameters are plotted. It is observed that nozzle loads in axial directions are transferred to the foundation almost 100%, whereas out plane loads are absorbed by the system to a greater extent. Further study is required to investigate combined effects of all such nozzle loads for single equipment. The results may be refined for different materials and effect of nozzle reinforcement. [DOI: 10.1115/1.4031719] Introduction Static equipment is connected with other equipment, pumps, packages through nozzles, and piping. The interfaces are equip- ment nozzles which are bolted or welded to the piping. The equipment is located on the ground or at elevated locations as per the process and plant layout requirements. The equipment exerts gravity loads (operating weight), horizontal shear loads (wind and seismic force), and moments on the foundation. The foundations are designed for these loads. Additionally, the con- nected piping exerts loads on the equipment at the nozzle loca- tions. The load consists of sustained (weight of pipe and fluid), thermal, and occasional loads (wind and seismic). The nozzle to equipment junction is designed to address these loads. This study is carried out to understand how much of these pipe loads are transferred to the foundation and how much is absorbed due to the system flexibility. Nozzle Loads Calculation To explain the background of the methods and calculations that are made in this study, it is required to understand how the load calculations of a pipe system are carried out. Figure 1 shows a separated system of a plant, two pressure vessels connected with pipes which are suitable supported. For simplicity, the other pipes which are connected with the vessels are not shown here. The pipes with supports are analyzed for the design conditions. The pipe end connection at the vessel is anchored and considered rigid (Fig. 2). The end forces are kept within limits of nozzle load table values (Table 1). These limit values include sustained, thermal, and occasional loads, but the highest contributor is thermal loads. Force Directions Figure 3 displays the directions of forces and moments acting on nozzle. Fig. 1 Vessel–pipe system Fig. 2 Pipe model in CAESER II Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 27, 2014; final manuscript received September 15, 2015; published online November 19, 2015. Assoc. Editor: Allen C. Smith. Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-1 Copyright V C 2016 by ASME Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Effect of Nozzle Junction and Equipment Stiffness on Absorption of

  • Upload
    dothien

  • View
    318

  • Download
    16

Embed Size (px)

Citation preview

Page 1: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

Kedar A. DamleThyssenkrupp Industrial Solutions India Private

Limited

2nd Floor, Duggal Plaza, PremNagar,

Bibwewadi Road,

Pune 411037, India

e-mail: [email protected]

Pratik S. GharatThyssenkrupp Industrial Solutions India Private

Limited

2nd Floor, Duggal Plaza, PremNagar,

Bibwewadi Road,

Pune 411037, India

e-mail: [email protected]

Rudolf NeufeldDepartment of Mechanical Engineering,

Fachhochschule Sudwestfalen

(University of Applied Science),

Meschede 59872, Germany

Wilhelm PetersDepartment of Mechanical Engineering,

Fachhochschule Sudwestfalen

(University of Applied Science),

Meschede 59872, Germany

Effect of Nozzle Junctionand Equipment Stiffnesson Absorption of PipeThermal LoadsAs an industry norm, the nozzle local loads are considered to be local and are not consid-ered in foundation design. Presently, this norm is under debate. One opinion is some per-cent of these loads are to be considered to be transferred to the foundation. Thehorizontal forces on the foundation are more critical than vertical forces. Attempt hasbeen made to understand the system and create a model which will represent the systemto a good approximation. A mathematical model is developed to demonstrate the actualsystem. It is a stiffness system consisting of equipment, nozzle junction, and connectedpiping. The connected pipes are heated sequentially to generate nozzle loads in axial andout plane directions. Steady-state thermal loads are calculated for the given system stiff-ness. Governing parameters are identified and altered to note the effect. The governingparameters identified are equipment diameter (D), nozzle location on equipment (x), andnozzle diameter (d). The effect is studied for pressure range (20–120 bar) and tempera-ture (100–400 �C). The results of percentage loads transferred with respect to the govern-ing parameters are plotted. It is observed that nozzle loads in axial directions aretransferred to the foundation almost 100%, whereas out plane loads are absorbed by thesystem to a greater extent. Further study is required to investigate combined effects of allsuch nozzle loads for single equipment. The results may be refined for different materialsand effect of nozzle reinforcement. [DOI: 10.1115/1.4031719]

Introduction

Static equipment is connected with other equipment, pumps,packages through nozzles, and piping. The interfaces are equip-ment nozzles which are bolted or welded to the piping.

The equipment is located on the ground or at elevated locationsas per the process and plant layout requirements. The equipmentexerts gravity loads (operating weight), horizontal shear loads(wind and seismic force), and moments on the foundation. Thefoundations are designed for these loads. Additionally, the con-nected piping exerts loads on the equipment at the nozzle loca-tions. The load consists of sustained (weight of pipe and fluid),thermal, and occasional loads (wind and seismic). The nozzle toequipment junction is designed to address these loads.

This study is carried out to understand how much of these pipeloads are transferred to the foundation and how much is absorbeddue to the system flexibility.

Nozzle Loads Calculation

To explain the background of the methods and calculations thatare made in this study, it is required to understand how the loadcalculations of a pipe system are carried out. Figure 1 shows aseparated system of a plant, two pressure vessels connected withpipes which are suitable supported. For simplicity, the other pipeswhich are connected with the vessels are not shown here.

The pipes with supports are analyzed for the design conditions.The pipe end connection at the vessel is anchored and consideredrigid (Fig. 2). The end forces are kept within limits of nozzle loadtable values (Table 1).

These limit values include sustained, thermal, and occasionalloads, but the highest contributor is thermal loads.

Force Directions

Figure 3 displays the directions of forces and moments actingon nozzle.

Fig. 1 Vessel–pipe system

Fig. 2 Pipe model in CAESER II

Contributed by the Pressure Vessel and Piping Division of ASME for publicationin the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 27,2014; final manuscript received September 15, 2015; published online November 19,2015. Assoc. Editor: Allen C. Smith.

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-1Copyright VC 2016 by ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 2: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

In this paper, the emphasis is on the forces, therefore themoments are not considered. The important forces are the hori-zontal forces, i.e., axial and out plane (Fig. 4). They act as shear-ing forces on the support and therefore are the most critical for thefoundation design.

In-plane forces act in gravity direction and therefore are notcritical. Hence, the in-plane forces are not further considered inthis study.

Solution

To simulate axial and out plane forces, a simple mathematicalmodel as shown in Fig. 5 is considered. The pipes 1 and 2 lengthsare suitably selected to ensure the forces (axial and out plane) gen-erated are kept within limits of values in Table 1. The thicknessand diameter of the pipe are same as the connected nozzledimensions.

Problem Analysis

To demonstrate effect of thermal expansion, the system may beconsidered as an assembly of stiffness. The equipment may be

replaced by a cantilever beam, and the nozzle–shell junction as aspring and piping as another spring. This system will be reviewedfor thermal expansion loads. In the cold system, no force arises.When the pipe is heated, the pipe will expand and every springwill be deflected as shown in Fig. 6. Thermal effect on shell lengthis ignored for simplicity.

The resultant force which acts on the vessel support depends onthe stiffness (the vessel, the junction, and the pipe). The stiffnessdepends on parameters, such as pressure, temperature, nozzlelocation, vessel diameter, and nozzle diameter. These parametersmust be examined for the effects on stiffness and thus on theresultant force.

Stiffness Determination

Vessel Stiffness. The vessel has a simple geometric form. Forsimplicity, the vessel is considered as cylinder of uniform thick-ness fixed at foundation (Fig. 7). The parameters for the vesselstiffness are the modulus of elastic, the diameter, the thickness,

Fig. 3 Forces and moments on nozzles

Fig. 4 Force directions

Table 1 Maximum allowable forces and moments on nozzles

Forces (N) Moments (N�m)

Nozzle size (in.) F VL VC MT ML MC

1/8 240 180 180 5.4 4.32 4.321/4 320 240 240 9.6 7.68 7.68: : : : : : :24 20,000 15,000 15,000 37,500 36,300 36,30042 20,000 15,000 15,000 37,500 36,300 36,300

Fig. 5 Mathematical model

021601-2 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 3: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

and lever arm of the nozzle. The deflection xV can be calculatedwith the formula

xV ¼Fx3

3EI(1)

Therefore, the formula for the vessel stiffness is

KVA ¼F

xV¼ 3EI

x3(2)

where

I ¼ p64

D4O � D4

I

� �(3)

Nozzle–Shell Junction Stiffness. The stiffness of thenozzle–shell junction is an important part of the whole stiffness.

Mathematical simplification is not possible to calculate thisstiffness.

The stiffness of the junction is influenced by the shell diameter,length and thickness, and the nozzle diameter and thickness.Ratios like the shell diameter to the shell thickness or the shelldiameter to the nozzle diameter are affecting the stiffness. Thegeometry is very complicated and cannot be simplified. Therefore,an finite element analysis (FEA) program, “NOZZLE PRO” [1] isused to obtain the junction stiffness.

NOZZLE PRO analysis. NOZZLE PRO is an FEA program to calculatestresses and stiffness at vessel attachments, such as nozzles, sad-dles, pipe shoes, attachments, and skirts [2–6].

In our paper, we have used it to obtain the stiffness of thenozzle–shell junction.

We used NOZZLE PRO v8.6, produced by the Paulin ResearchGroup, Houston, TX.

Axial Loads

Axial Pipe Stiffness and Geometry. For the study of the axialloads, only pipe 1 is heated to create a thermal force. To simplifythe calculation, the elbow is considered as a hinge. With thesesimplifications, the deflection of the pipe is shown in Fig. 8. Here,the vessel and nozzle–shell junction are considered rigid.

The thermal expansion Dl1 is shown in Fig. 8. Because of thestiffness of pipe 2, pipe 1 is not allowed to expand the wholelength Dl1 as shown in another schematic representation (Fig. 9).

Fig. 6 Schematic representation

Fig. 7 Deflection cantilever beam Fig. 8 Pipe deflection axial

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-3

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 4: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

Figure 9 shows that the whole thermal expansion is absorbedby the two springs which represent the pipes. Therefore, the forcemust be calculated with the combine stiffness KPA of both pipes.Hence, the formula for the maximum allowable force is

FMax;A ¼ KPA � Dl1 (4)

Dl1 ¼ a� l1 � DT (5)

where FMax;A is known and equal to maximum nozzle load (Table1). The expansion Dl1 depends on the length l1. The requiredpipe stiffness can be generated with various combinations of thelength l1 and l2. Therefore, it is necessary to assume one parame-ter (l1 in this case). Now the axial pipe stiffness can be calculatedwith the formula

KPA ¼FMax;A

Dl1

(6)

Pipe Geometry. To obtain the length l2, it is required to sepa-rate the pipe stiffness KPA into two parts KP1A (for pipe 1) andKP2A (for pipe 2). Due to the thermal expansion, pipe 1 is undercompression. Therefore, the formula for the stiffness for part 1 is

KP1A ¼EA

l1

(7)

Pipe 2 is bent and must therefore be calculated with the formulafor a cantilever beam

KP2A ¼3EI

l32

(8)

The two pipes act like two springs in series. Therefore, the for-mula for the whole pipe stiffness is

KPA ¼KP1A � KP2A

KP1A þ KP2A

(9)

With this formula, the stiffness of pipe 2 KP2A is determined andused to calculate the length l2

l2 ¼ffiffiffiffiffiffiffiffiffiffi3EI

KP2A

3

r(10)

Calculation of the Real Force. In reality, the vessel andnozzle–shell junction are not rigid. As a result of this additionalflexibility in the system, the resultant force will be less thanFMax;A.

In this system, the thermal expansion Dl1 is absorbed by thefour springs of the system. The displayed system in Fig. 10 is sim-ilar to the system in Fig. 8 but in this system, two stiffnesses areadded. A schematic representation is shown in Fig. 11. Therefore,the final resultant force will be related to combined stiffness of thewhole system.

First, the stiffness of the vessel and nozzle shell junction mustbe computed. The unit of the axial vessel stiffness KVA and the

Fig. 9 Schematic representation of the thermal deflection ofthe pipe

Fig. 10 Schematic representation of the axial deflection

Fig. 11 Schematic representation of the thermal deflection with springs

021601-4 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 5: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

axial nozzle–shell junction stiffness KJA is ðN=mmÞ. Therefore,they can be combined by the formula

KVJ ¼KVA � KJA

KVA þ KJA

(11)

The axial stiffness for the whole system is a combination of thestiffness of the vessel and nozzle–shell junction KVJ and the pipestiffness KPA

KTotal;A ¼KVJ � KPA

KVJ þ KPA

(12)

With the total stiffness KTotal;A and the thermal expansion Dl1, thereal force FRA which arises can be calculated as follows:

FRA ¼ KTotal;A � Dl1 (13)

Percentage of the Axial Loads. Percentage of the axial loadstransferred is the ratio between the real force FRA and the maxi-mum force FMax;A, which shows percentage of load transferred tothe foundation

FRA

FMax;A¼ KTotal;A � Dl1

KPA � Dl1

¼ KTotal;A

KPA

¼ KVJ � KPA

KPA KVJ þ KPAð Þ (14)

After simplification, the final formula for the percentage of theaxial force transferred to foundation is

Percentage %½ � ¼ FRA

FMax;A¼ KVJ

KVJ þ KPA

(15)

Out Plane Loads

Out Plane Pipe Stiffness and Geometry. For the study of theout plane loads, now pipe 2 (Fig. 5) is heated. The elbow isconsidered as a hinge and the deflection of the pipe is shown inFig. 12. Here, the vessel and nozzle–shell junction are consideredrigid.

The maximum load limit is known as per Table 1. The pipedimensions are to be selected such that the load generated will beequal to this limit. The formula is similar to Eq. (4)

Fmax;O ¼ KPO � Dl2 (16)

KPO ¼Fmax;O

Dl2

(17)

Dl2 ¼ a� DT � l2 (18)

where the maximum load Fmax;O is known and equal to the VCload in Table 1. Here, a pipe 2 length is assumed and pipe 1 lengthis computed.

Pipe Geometry. The maximum allowed force Fmax;O, the lengthl2, and the stiffness of the pipe model KPO are known. From this,pipe 2 stiffness is

KP2O ¼EA

l2

(19)

The combined pipe stiffness is

KPO ¼KP1O � KP2O

KP1O þ KP2O

(20)

KP1O ¼KP2O � KPO

KP2O � KPO

(21)

Now the length of pipe 1 could be calculated

KP1O ¼3EI

l31

(22)

l1 ¼ffiffiffiffiffiffiffiffiffiffi3EI

KP1O

3

r(23)

Calculation of the Real Force. In reality, the vessel andnozzle–shell junction are not rigid. This additional flexibility willresult in the reduction of final resultant force in the system.

Individual stiffness considerations are as follows:

� Pipe stiffness: KPO is calculated based on the selected length� Junction stiffness: KJO is from NOZZLE PRO

� Vessel stiffness: KV is ignored because it is much higher thanthe junction stiffness (for springs in series, this is validapproximation).

The thermal expansion Dl2 is a combination of junction deflec-tion ½dNO� and pipe 1 ½dPO� (Fig. 13)

Dl2 ¼ dPO þ dNO (24)

The stiffness of the pipe and nozzle–shell junction has differentunits

Calculated! KPO

N

mm

� �; Nozzle PRO! KJO

N mm

deg

� �

Therefore, the unit of the junction stiffness must be transformed.The deflection dNO is calculated by pipe 1 and the angle u

dNO ¼ l1 � tan u ¼ l1 � u (25)

Fig. 12 Pipe deflection out plane Fig. 13 Out plane deflection

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-5

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 6: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

The whole formula for the deflection Dl2 is

Dl2 ¼FRO

KPO

þ FRO � l12 � p

KJO � 180(26)

FRO

Dl2

¼ 1

1

KPO

þ l21 � pKJO � 180

(27)

The combine stiffness for the whole system is determined by

KTotal;O ¼FRO

Dl2(28)

With Eqs. (27) and (28), we are able to calculate the stiffness ofwhole system

KTotal;O ¼1

1

KPO

þ L12 � p

KJO � 180

(29)

The real resultant force is calculated by

FRO ¼ KTotal;O � Dl2 (30)

Percentage of the Out Plane Loads. Percentage of the out planeloads transferred to foundation is the ratio between FRO andFmax;O

Percentage %½ � ¼ FRO

Fmax;O(31)

Design Parameter Analysis. Following design parameters arevaried and different scenarios are studied.

The vessel and nozzle thickness are dependent on the pressure, tem-perature, and vessel/nozzle diameters. The thicknesses are selectedas the nearest next commercially available standard thicknesses.

Table 2 displays considered scenario for axial as well as outplane condition.

Results and Discussion

Axial Analysis

Scenario: Temperature Effect on Percentage of Loads Trans-ferred to Foundation

Geometric data

vessel: diameter, 2000 mm; length, 7000 mm; and thickness,10–94 mm

Fig. 14 Percentage of loads transferred to the foundation for varied design temperature(axial case)

Table 2 Scenarios for parameter analysis

Scenarios 1. Design temperature 2. Vessel diameter 3. Nozzle position 4. Nozzle diameter

Pressure Change Change Change ChangeTemperature Change Constant Constant ConstantVessel diameter Constant Change Constant ConstantVessel thickness Change Change Change ChangeNozzle position Constant Constant Change ConstantNozzle diameter Constant Constant Constant ChangeNozzle thickness Change Change Change Change

021601-6 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 7: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

nozzle: diameter, 24 in. and thickness, 9–30 mmdesign temperature: 100–500 �CD, x, and d kept constant

Design pressure and temperature conditions are varied and per-centage of load transferred is calculated. The results are plotted inFig. 14. Percentage of loads transferred to the foundation is plot-ted on Y-axis versus design pressure on X-axis for each tempera-ture case to analyze effect of design temperature. Though designtemperature significance seen below 40 bar pressure is marginal,above 40 bar, design temperature has no effect and �100% loadsare transferred to foundation.

Similarly, other scenarios are represented here in graphical form.

Scenario: Vessel Diameter Effect on Percentage of LoadsTransferred to Foundation

Geometric data

vessel: diameter, 1000–5000 mm; length, 7000 mm; and thick-ness, 6–272 mm

nozzle: diameter, 24 in. and thickness, 9–34 mm

design temperature: 300 �CT, x, and d kept constant

Figure 15 shows the percentage of loads as a function of vesseldiameter. Each curve corresponds to specific vessel diametersunder consideration. The temperature is kept constant at 300 deg(for this comparison).

The curve for the vessel diameter 1000 mm rises quickly till 60 barand further more slowly to 120 bar. The other curves show similar pat-tern. The curve for the vessel with a diameter 1500 mm has a kink at15 bar. The reason is that the increment of the vessel thickness, whichis rounded to a regular plate thickness, is very high at this point.

Similar to Fig. 14, Fig. 15 also shows discrimination betweenlow- and high-pressure vessels. Especially for the vessels with di-ameter of 3000 mm, and greater, at high pressures (>40 bar), thepercentage of loads for the various diameters converge and all areabove 90%. Below 40 bar, there are some differentiations becauseof the nozzle–shell junction stiffness. For vessels with diametersabove 3000 mm, the combined stiffness for the vessel and thenozzle–shell junction is governed by the junction. The percentage

Fig. 15 Percentage of loads transferred to the foundation for varied vessel diameters(axial case)

Fig. 16 Percentage of loads transferred to the foundation for varied nozzle positions(axial case)

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-7

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 8: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

of loads for the vessel with the diameter of 1000 mm are quite dif-ferent from the other. Here, the combined stiffness is ruled by thevessel stiffness because vessel required thickness is less whichreduces the vessel stiffness below junction stiffness.

Scenario: Nozzle Position Effect on Percentage of Loads Trans-ferred to Foundation

Geometric data

vessel: diameter, 2000 mm; length, 5000–18,000 mm; and thick-ness, 10–110 mm

nozzle: diameter, 24 in. and thickness, 9–34 mmdesign temperature: 300 �CT, D, and d kept constant

Figure 16 shows the effect of nozzle position on the absorp-tion of loads and percentage of loads transferred to thefoundation.

The stiffness for the short vessel is high making the systemrigid. Only in case of higher x values, the effect can be seen(x¼ 17,000 mm and above).

Scenario: Nozzle Diameter Effect on Percentage of LoadsTransferred to Foundation.

Geometric data

vessel: diameter, 2000 mm; length, 7000 mm; and thickness,10–110 mm

nozzle: diameter, 200–1050 mm and thickness, 9–34 mmdesign temperature: 300 �CT, D, and x kept constant

Figure 17 shows the behavior of the percentage of loads due tothe pressure for the different nozzle diameters.

The curves rise rapidly, like exponential curve, until the pres-sure reaches 40 bar. Above 40 bar point, they are nearly flat.

The discrimination of the low (<40 bar) and high (>40 bar)pressure vessels is also similar to Fig. 15. But in Fig. 17, the dis-crimination is clearer than in the earlier figures.

The reason is that the curves are closely packed together andmaximum forces are proportional to increase in the nozzle diame-ter. Therefore, the pipe stiffness and the maximum force changein the same relation.

With higher diameters, the percentages of loads decrease,except for the nozzle with diameter 42 in. This is because themaximum forces for the diameter 24 in. and 42 in are same, asshown in Table 1. For diameter 42 in., the stiffness increases, butthe maximum force is the same as that for diameter 24 in.(20,000 N).

Out Plane Analysis

Scenario: Temperature Effect on Percentage of Loads Trans-ferred to Foundation

Geometric data

vessel: diameter, 2000 mm; length, 7000 mm; and thickness,10–124 mm

nozzle: diameter, 600 mm and thickness, 9–30 mmD, x, and d kept constant

Figure 18 shows the percentage of loads transferred to the foun-dation as a function of design temperature. On the vertical axis,the percentage of loads is plotted, and on the horizontal axis, thedesign pressure is plotted.

The curves with the temperature from 100 �C until 300 �C risevery slow and nearly linear. The curve with the temperature400 deg is almost linear.

Below the temperature of 300 �C, the stiffness of the vesseland nozzle–shell junction is low and thus percentage loadstransferred to the foundation is significantly low (<40%).Above 300 �C, the percentage of loads increases; as at thattemperature, material allowable stresses decrease significantly,leading to higher thicknesses and thus increased junctionstiffness.

Scenario: Vessel Diameter Effect on Percentage of LoadsTransferred to Foundation

Geometric data

vessel: diameter, 1000–5000 mm; length, 7000 mm; and thick-ness, 6–272 mm

nozzle: diameter, 600 mm and thickness, 9–34 mmdesign temperature: 300 �CT, x, and d kept constant

Fig. 17 Percentage of loads transferred to the foundation for varied nozzle diameters(axial case)

021601-8 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 9: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

Figure 19 shows the variation in the percentage of loadstransferred to the foundation for change in vessel diameter as afunction of design pressure.

Though the junction stiffness reduces with increase in diameter,the required thickness increases which leads to increase in thejunction stiffness.

Figure 19 shows the significant effect of vessel diameter on per-centage of loads transferred to the foundation.

Scenario: Nozzle Position Effect on Percentage of Loads Trans-ferred to Foundation

Geometric data

vessel: diameter, 2000 mm; length, 5000–18,000 mm; andthickness, 10–110 mm

nozzle: diameter, 600 mm and thickness, 9–34 mmdesign temperature: 300 �CT, D, and d kept constant

Figure 20 shows the variation in percentage of loads as a func-tion of variation in nozzle position for different design pressures.The curves in this diagram are nearly overlapping and show noeffect of nozzle position. This is because vessel stiffness was notincluded in the calculation. Vessel stiffness being significantlyhigher than out plane junction stiffness has little effect on the stiff-ness of the system.

Scenario: Nozzle Diameter Effect on Percentage of LoadsTransferred to Foundation.

Geometric data

vessel: diameter, 2000 mm; length, 7000 mm; and thickness,10–110 mm

nozzle: diameter, 200–1050 mm and thickness, 9–58 mmdesign temperature: 300 �CT, D, and x kept constant

Fig. 19 Percentage of loads transferred to the foundation for varied vessel diameters(out plane case)

Fig. 18 Percentage of loads transferred to the foundation for varied design temperature(out plane case)

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-9

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 10: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

Figure 21 shows the variation in percentage of loads as effectof nozzle diameter for different design pressures.

As nozzle diameter increases, for the same D, the junction stiff-ness reduces. The system becomes more flexible. This is reflectedin Fig. 21.

Figure 21 clearly shows that the difference between the nozzlewith 8 in. and 14 in. diameter is much higher than the differencebetween the 24 in. and 42 in. diameter. The reason is that the max-imum allowable forces are significantly different for 8 in. and14 in. Diameter, however, allowable loads are same for 24 in. and42 in. diameters.

Conclusions

Axial Loading. From the scenarios described in the Results andDiscussion section, following influential parameters are identified

� design pressure (P)

� vessel diameter (D)� nozzle location on vessel (x)

The effect of these parameters is combined and represented inFig. 22. The diagram is created with a design temperature at300 �C. For vessel with other design temperatures (200–500 �C),there will be very nominal difference, as design temperature hasminimal effect, as evident earlier.

Appendix 2 provides details on development of this graph.It is evident from the diagram that the system is highly rigid

and nearly most of the nozzle axial load is transferred to the foun-dation. Only vessels with a high ratio x/D and at low pressures areabsorbing more thermal loads. Such situations are not common.

Out Plane Loading. The influential parameters for the percent-age of loads in out plane case are as follows:

� design pressure (P)

Fig. 20 Percentage of loads transferred to the foundation for varied nozzle positions (outplane case)

Fig. 21 Percentage of loads transferred to the foundation for varied nozzle diameters(out plane case)

021601-10 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 11: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

� design temperature (T)� vessel diameter (D)� nozzle diameter (d)

Appendix 2 provides details on development of this graph.Figure 23 shows the variation in percentage of loads as a func-

tion of ratio of vessel diameter and nozzle diameter for variousdesign pressures.

The percentage of loads is plotted on the vertical axis, whileratio of the vessel diameter to nozzle diameter is plotted on hori-zontal axis. Each curve corresponds to particular design pressure.The pressures vary from 10 bar to 120 bar. To create final diagram,the curves from Fig. 23 is changed to linear trend lines.

To account for the effect of temperature, two separate diagramsare required, the first for temperature up to 300 �C and the secondfor temperatures above 300 �C and 400 �C.

Figure 24 shows the result for temperature up to 300 �C, andFig. 25 for temperature in the range above 300–400 �C.

Verification With Software CAESAR II

The results are verified and compared using CAESAR II model forboth axial and out plane loads.

About CAESAR II. CAESAR II 2013 Version 2013 R1 (6.10) wasprovided by the Intergraph CADWorx & Analysis Solutions, Inc.,Houston, TX.

Five cases each for axial and out plane condition are modeledin CAESAR II. The model includes vessel, pipe1, and pipe 2. Tem-perature values are assigned to pipes as applicable. The junctionand vessel are considered rigid and loads are noted. Further thejunction stiffness is introduced and vessel rigidity is removed andfinal loads on foundation are calculated. Thus, percentages ofloads transferred on foundation are calculated as ratio of result insecond case by first case.

Tables 3 and 4 show comparison with values obtained fromfinal graphs.

Axial. Table 3 shows that the results from Fig. 22 are alwayshigher than the results from CAESAR II. One reason is that the curvesfrom the diagram are lifted up for 3% safety factor. The second rea-son is the inexactness of the calculation for high flexible vessels.

Out Plane. The results for the percentage of loads from Fig. 24are higher than the real results from CAESAR II. The results are not

Fig. 22 Final diagram for axial loads

Fig. 23 Percentage of loads due to D/d

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-11

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 12: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

exact because the curves in the final diagrams were simplified asstraight line segments.

So the diagram includes a safety and can be followed to calcu-late percentage of loads transferred to the foundation.

Final Conclusion

Axial. For almost all vessels, the maximum axial nozzle loadsmust be considered for the vessel foundation calculation, espe-cially for high-pressure vessels above 40 bar. For very flexiblevessels at low temperature, Fig. 22 can be used to evaluate thetransfer of axial loads.

Fig. 24 Final diagram for temperatures up to 300 �C—out plane

Fig. 25 Final diagram for temperatures above 300 �C—Out plane

Table 3 Final solution review—axial

% of loads

P(bar)

Ratio(L/D)

Designtemperature (�C)

CAESAR

II Diagram%

difference

20 7 300 83.74 92 9.8630 2.5 300 99.15 100 0.8630 6 300 95.33 98 2.840 3.5 500 99.75 100 0.2560 3.5 300 99.71 100 0.29

Table 4 Final solution review—out plane

% of loads

P(bar)

Ratio(D/d)

Designtemperature (�C)

CAESAR

IIDiagram %

difference

20 1.7 300 4.84 8 65.2920 8.3 300 22.61 23 1.7230 3.3 300 9.28 17 83.1960 10 300 63.19 82 29.77

021601-12 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 13: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

Out Plane. Out plane loads are absorbed by the system to agreater extent than axial loads. Figures 24 and 25 provide guide-lines for evaluation of loads transferred to the foundation for ves-sels with various temperatures and pressures. Percentage of loadsfor vessels with design pressures between the values displayedcan be obtained by interpolation.

Based on these diagrams, effect of all process nozzle loads onfoundation can be calculated easily for single equipment. Nozzleorientation (#) consideration should be given for final summation.

One representative case is explained below.design pressure, P: 14.5 bardesign temperature, T: 249 degvessel diameter, D: 5200 mm

Axial Loading

Nozzle d (in.) x # F FRA FRA*(sin #) FRA *(cos #)

N1 10 15,925 0 14,280 14,280 0 14,280N2 8 33,350 90 11,420 6852 6852 0N3 6 39,525 45 8570 5142 3636 3636Total 10,488 17,916

Load in X-direction—FRA*(sin #)

Load in Y-direction—FRA*(cos #)

Out Plane Loading

Nozzle d (in.) x # VL FRO FRO*(sin #) FRO*(cos #)N1 10 15,925 0 10,710 2892 2892 0N2 8 33,350 90 8570 1972 0 1971N3 6 39,525 0 6420 1349 953 953Total 3845 2924

Load in X-direction—FRO*(sin #)Load in Y-direction—FRO*(cos #)Total loads in each direction:X-component¼ 14,333 N and Y-component¼ 20,840 N

Nomenclature

A ¼ cross-sectional area of the piped ¼ nozzle outside diameterD ¼ vessel outside diameterE ¼ elastic modulusF ¼ nozzle load in axial direction

FMax;A ¼ maximal force axialFMax;O ¼ maximal force out plane

FRA ¼ real force axialFRO ¼ real force out plane

I ¼ moment of inertia of pipeKJA ¼ axial stiffness of the nozzle–shell junctionKJO ¼ out plane stiffness of the nozzle–shell junctionKPA ¼ axial stiffness of the pipe modelKPO ¼ out plane stiffness of the pipe model

KP1A ¼ axial stiffness of pipe 1KP2A ¼ axial stiffness of pipe 2KP1O ¼ out plane stiffness of pipe 1KP2O ¼ out plane stiffness of pipe 2

KTotal;A ¼ combined stiffness of the vessel, nozzle shell–junction,and pipe axial

KTotal;O ¼ combined stiffness of the vessel, nozzle shell–junction,and pipe out plane

KVA ¼ axial stiffness of the vesselKVJ ¼ axial stiffness of the vessel and nozzle–shell junction

L ¼ vessel lengthl1 ¼ length of pipe 1l2 ¼ length of pipe 2

MC ¼ circumferential moment on the nozzleML ¼ longitudinal moment on the nozzleMT ¼ torsional moment on the nozzle

P ¼ design pressureT ¼ design temperature

thk ¼ nozzle thicknessThk ¼ vessel thicknessVC ¼ nozzle load in circumferential directionVL ¼ nozzle load in longitudinal direction

x ¼ nozzle location on the vesselxV ¼ deflection of the vessela ¼ temperature expansion coefficient

Dl1 ¼ linear thermal expansion of pipe 1Dl2 ¼ linear thermal expansion of pipe 2DT ¼ temperature differencedVJ ¼ axial deflection of the nozzle–shell junctiondNO ¼ out plane deflection due to the nozzle–shell junction

stiffnessdPO ¼ out plane deflection due to the pipe stiffness

u ¼ angle of deflection due to the nozzle–shell junctionstiffness

Appendix 1

This appendix explains how graphs in Figs. 14–21 are devel-oped for each scenario.

Let us take example of Fig. 14, where effect of design tempera-ture is studied for axial load case for percentage of loads trans-ferred to the foundation. Design pressure is also varied in thisscenario.

In the first case, design pressure is selected as 10 bar and designtemperature as 100 �C. Vessel diameter and nozzle diameters areconstant. Based on the vessel, junction, and pipe stiffness, realload generated in the system is calculated. This real load is com-pared with max load as per Table 1 and percentage of load trans-ferred to the foundation is calculated. In this case, percentage ofload is 91.2%. This point is plotted on the Y-axis. Similarly designpressure is varied from 10 bar to 100 bar for each design tempera-ture (100–500 �C) and these points are plotted on the Y-axis.Curves are plotted for each design temperature case by connectingthese points.

On similar lines, the other figures are developed.

Appendix 2

This appendix describes methodology used for the developmentof final graphs shown in Figs. 22–24.

Axial Load Case. For the axial load case (Fig. 22), the influen-tial parameters are identified as

(a) vessel diameter (D)(b) nozzle position (x)

x and D are combined by taking x/D ratio. From all the scenarios,x/D is calculated and for each x/D, for certain pressure (P), per-centage of load transferred to foundation is noted. These valuesare plotted on Y-axis, against x/D values on X-axis for specificpressure conditions. The points are enveloped by linear envelop.This envelope ensures conservative estimate on percentage ofloads transferred to foundation and also helps to make the grapheasy to use. To cover the effect of nozzle diameter and designtemperature, these graphs are further elevated to include 3%safety margin.

Out Plane Load Case. For the out plane load case(Figs. 23–25), the influential parameters are identified as

Journal of Pressure Vessel Technology APRIL 2016, Vol. 138 / 021601-13

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 14: Effect of Nozzle Junction and Equipment Stiffness on Absorption of

(a) design temperature (T)(b) vessel diameter (D)(c) nozzle diameter (d)

To cater with above parameters, final graphs are generated forD/d ratio. It is observed from Fig. 18 that the effect of design tem-perature is substantial when it increases above 300 �C. Hence, twoseparate graphs are generated for design temperature up to 300 �Cand above 300 �C.

Percentage of loads are obtained for each D/d ratio from all thecases of Figs. 19–21 generated for varying vessel diameters andthese percentage of loads were plotted on Y-axis against each D/dfor separate design pressure.

These nonlinear graphs are converted into linear trend line (Fig.23) and are raised by a safety constant of 3% at the first point at theleft side. Percentage of loads are back calculated from these lineargraph for values of D/d¼ 1 and D/d¼ 20 for each case of designpressure. Now, we have two separate values of percentage of loadsfor each ratio of D/d¼ 1 and D/d¼ 20 for each design pressure.

For generation of final graphs, minimum value of percentage ofload is considered for D/d¼ 1 and maximum value of percentageof load is considered for D/d¼ 20. This graph generated is a linearone that ensures conservative estimate on percentage of loads trans-ferred to foundation and also helps to make the graph easy to use.

References[1] PRG, 2007, “NOZZLE PRO Program Manual,” Paulin Research Group, Houston,

TX.[2] PRG, 2011, “FE107: If You Can Run a WRC Analysis, You Can Run This FEA

Analysis,” Paulin Research Group, Houston, TX, www.paulin.com/FE107.pdf[3] Wichman, K. R., Hopper, A. G., and Mershon, J. L., 1979, “WRC 107: Local

Stresses in Spherical and Cylindrical Shells Due to External Loadings onNozzles,” Welding Research Council, New York.

[4] Mershon, J. L., Mokhtarian, K., Ranjan, G. V., and Rodabaugh, E. C., 1987,“Revised Bulletin 297: Local Stresses in Cylindrical Shells Due to ExternalLoadings on Nozzles—Supplement to WRC No. 107,” Welding Research Coun-cil, New York.

[5] Integraph, 2012, “CAESER II Users Guide,” Intergraph Corporation, Huntsville, AL.[6] Stephen, P., and Timoshenko, S. W.-K., 1959, Theory of Plates and Shells,

McGraw-Hill, Singapore.

021601-14 / Vol. 138, APRIL 2016 Transactions of the ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 11/19/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use