INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011 1

Abstract— Spherical heads are widely used in pressure

vessels and piping systems of petrochemical and power

plants. Under different loading conditions, the stress will

occur at the nozzle to head or shell junction area. Due to

discontinuity of the geometry, defect will occur and the

junction region will become the weakest point which will

be the failure source of the whole structure. Thus a

reliable and accurate analysis method for head or shell to

nozzle junction is necessary. In this paper, stress analysis

is carried out for nozzle to head junction subjected to

applied external load, internal pressure and moments.

Stresses at reactor nozzle to head junction are obtained

using Welding Research Council (WRC) 107 and PV-

CodeCalc software (2008) with and without stress indices.

It is observed from the analysis that with the case of stress

indices stress are very high in nature. So, an attempt is

made to do the stress analysis of reactor nozzle to head

junction using FEA software (ANSYS 12), as per ASME

Section VIII Division 2. Index terms—Stress analysis, Stress indices.

I. INTRODUCTION

ressure vessel is a closed container designed to hold gases

or liquids at a pressure substantially different from the

ambient pressure. Reactor is one type of pressure vessel.

Pressure reactor is a device or process in which chemical

reactions take place during a chemical conversion type of

process. A reactor is a vessel designed for internal pressure or

vacuum, has a heat source typically an external jacket, and is

agitated for proper mixing. Martens and Massey [1] found

stress at nozzle to shell junction using welding research

council (WRC) 107[2] and finite element analysis. Moini and

Mitchell [3] thick-walled pressure vessel with an attached

nozzle under internal pressure is analyzed by using the finite

element method. Raju P. P. [4] has presented a brief

summary of the technical basis for the recommended

stress indices for 45 degree lateral connections under internal

pressure and in-plane moment loadings.

Welding Research Council Bulletin No 107 has been one of

the most widely used Bulletins for finding local stresses in

spherical and cylindrical shell due to external loading in

WRC. The methods published in WRC107 theoretical of

Prof. Bijlaard, the formulations for calculation of the

combined stress intensity. High stresses occurred at nozzle to

head\shell junction which direct subjected to various forms of

external loading on the nozzle. WRC 107 can find local

stresses in spherical and cylindrical shells due to external

loadings; it contains curves for hollow and solid circular

junction. It determines local stresses at the eight points (Four

upper and lower points) in the shell it shown in Figure 1.

Fig.1 Local stresses in spherical shell

As such the validity of Bijlaard's work is restricted to smaller

diameter ratios (up to about d/D= 0.003). In WRC 107 the

available graphs are based partially on the work of Bijlaard

and partially on experimental data so that the ratio d/D could

be extended to values of about 0.1.

As per ASME section VIII division 2 part 5 ANNEX 5.D. [5]

stress indices may be used to determine peak stresses around

a nozzle opening. The term stresses index, is defined as the

numerical ratio of the stress components σt, σn and σr under

consideration to the computed membrane hoop stress in the

unreinforced vessel material; however, the material which

increases the thickness of a vessel wall locally at the nozzle

shall not be included in the calculation of the stress

components. These stress directions are defined in Figure 2.

Tables 5.D.5 in ASME give only the maximum stresses at

certain general locations due to internal pressure. In the

evaluation of stresses in or adjacent to vessel openings and

Stress Analysis of Reactor Nozzle to Head

Junction

A. Hardik B. Nayak and B. R. R. Trivedi

A. Assistant Professor, Mechanical Engg. Department, Faculty of Engineering, Technology and

Research, Bardoli

B. Professor, Mechanical Engg. Department, Institute of Technology, Nirma University,

Ahmedabad

P

INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, ‘NUiCONE – 2011’ 2

connections, it is often necessary to consider the effect of

stresses due to external loadings or thermal stresses.

Fig.2 Direction of Stress Components

In such cases, the combined stress at a given point may be

determined by superposition. In the case of combined stresses

due to internal pressure and nozzle loading, the maximum

stresses for a given location should be considered as acting at

the same point and added algebraically unless positive

evidence is available to the contrary.

II. MOTIVATION:

Reactor has many discontinuous regions in their structures

such as manhole connections, nozzles, supports, joints etc.

They subjected to different types of loadings such as internal

pressure, external pressure, thermal loads, lateral loads, etc.

These discontinuous regions will become weakest points and

more chance to failure of the whole structure. Thus a reliable

and accurate analysis method for shell nozzle junction is

necessary and there is scope for research stress analysis of

reactor nozzle to head junction.

.

III. METHODOLOGY:

Porter and Martens have presented methodology to calculate

stresses and acceptance criteria for loads on nozzle to shell

junctions on pressure vessels. First stage of present work

finds stresses at nozzle to head junction by WRC 107 with

and without stress indices.

In the general case, all applied loads & moments must be

resolved (at attachment shell interface) in the three principal

direction; i.e. they must be resolved into components P, VL,

VC, ML, MC and MT membrane, bending and shear stresses

can be evaluated at eight distinct points in the shell at its

juncture with the attachment. These eight points are shown in

figure 1. All the nozzle loads and moments are considered to

be acting at the same time, on conservative front. Nozzles

external are shown in figure 3.

Fig.3.Nozzle loads

The radial membrane and bending stress at eight points on

nozzle to head junction are obtained using equation 1 to 6.

Radial membrane stress (P) )/)(/( 2TPPTNk xn ..(1)

Radial bending stress (P) )/6)(/( 2TPPMk xb …..(2)

Radial membrane stress (Mc)

2/12

11

2/1 )(/)/)(( TRTMMTRTNkn mmx …..(3)

Radial bending stress (Mc)

2/12

11

2/1 )(/6)/)(( TRTMMTRMkb mmx …..(4)

Radial membrane stress (ML)

2/12

22

2/1 )(/)/)(( TRTMMTRNk mmxn …..(5)

Radial bending stress (ML)

2/12

22

2/1 )(/6)/)(( TRTMMTRMk mmxb ….(6)

The tangential membrane and bending stress at eight points

on nozzle to head junction are obtained using equation 7 to

12.

Tangential membrane stress (P) )/)(/( 2TPPTNk yn

.. (7)

Tangential bending stress (P) )/6)(/( 2TPPMk yb ..(8)

Tangential membrane stress (Mc)

2/12

11

2/1 )(/)/)(( TRTMMTRTNkn mmy …..(9)

Tangential bending stress (Mc)

2/12

11

2/1 )(/6)/)(( TRTMMTRMkb mmy …..(10)

Tangential membrane stress (ML)

2/12

22

2/1 )(/)/)(( TRTMMTRNk mmyn …..(11)

Tangential bending stress (ML)

2/12

22

2/1 )(/6)/)(( TRTMMTRMk mmyb …..(12)

Local and general primary and secondary stresses at nozzle to

head junction can be obtained with help of above equation’s

results.

After validated this WRC 107 stress results with PV-

CodeCalc 2008 software results with and without stress

indices. With the case of considering stress indices the

stresses at junction are very high in nature. So design is

failed. Thus, stresses calculation at nozzle to head junction is

carried out by finite element analysis using Ansys 12. Finite

element model of nozzle on head is shown in figure 4.

INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011 3

Fig.4 Finite element model

All the geometries are mapped meshed because the mapped

mesh has very structured and ordered elements. The necessary

partitions are made for accurate meshing which satisfies the

quality check on the elements. Same mesh is used for static

analysis. For evaluating the stresses due to structural loads,

the top nodes of the vessel are fixed in axial and longitudinal

directions.

Stress classification line (SCL) is obtained by reducing two

opposite sides of a Stress classification plane (SCP) to an

infinitesimal length. SCL has been placed in the areas of the

structure where the critical equivalent stress intensity is

expected. Refer figure 5, for the location of SCL on the

structure. Acceptance criteria acceptance criterion is taken as

per ASME VIII, Division 2, Ed' 2007, ADD 2008. Part-5,

paragraph 5.2.2.

Fig 5. Stress classification line.

IV. DESIGN DATA:

Max. Allowable working pressure: 10 MPa

Design Temperature: 426 °C (699 °K)

Material of construction:

Shell & Head: SA 387M GR.22 CL.2 [6]

Nozzles: SA 336M GR.F22 CL.

Geometry Inputs:

Vessel thickness 72.1 mm

Vessel Mean Radius 2187.0 mm

Nozzle thickness 60 mm

Nozzle Mean Radius 131.5 mm

Nozzle Outside Radius 161.5 mm

Nozzle OD 323 mm

Nozzle ID 203 mm

Vessel OD 4410 mm

Vessel ID 4338 mm

Nozzle external loads applied at top of the nozzle neck.

Nozzle loads are shown in Table I.

Table I. Nozzle loads

Nozzle Loads At Top Of the

Nozzle Neck

Fx, N 14398

Fy, N

0

Fz, N

0

Mx, N-mm

0

My, N-mm 7490845

Mz, N-mm 0

V. RESULT AND DISCUSSION:

The following methodologies have been considered for

nozzle to head junction under nozzle external loading,

internal pressure and moments.

1. Stress analysis using WRC 107 with and without

stress indices.

2. Stress analysis using PV-CodeCalc with and without

stress analysis. PV-CodeCalc 2008 software (version

of PV-Elite) is employed to calculate stresses of

various components at attachment of reactor as per

ASME.

3. Stress analysis using FE analysis in ANSYS 12.

Table II. Results by WRC 107 and PV-CodeCalc software

without stress indices.

INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, ‘NUiCONE – 2011’ 4

Type of

Stress Int.

Max. S.I

WRC

107

(MPa)

Max. S.I

PV-

CodeCalc

(MPa)

S.I.

Allowable

(MPa)

Result

Pm

(SUS)

153 152.79 155.14 Passed

Pm+Pl

(SUS)

176 176.03 232.71 Passed

Pm+Pl+Q

(Total)

241 242.24 491.27 Passed

As already shown in Table II value of that maximum stress

intensity obtained from WRC 107 and PV-CodeCalc

software. WRC 107 results are validated with PV-CodeCalc

results. Both results are meeting the requirements of Part 5 of

ASME Section VIII, Div 2, Ed' 2007, ADD 2008.

Table III. Results by WRC 107 and PV-CodeCalc software

with stress indices.

Type

of

Stress Int.

Max. S.I

WRC107

(MPa)

Max. S.I

PV

CodeCalc

(MPa)

S.I.

Allowable

(MPa)

Result

Pm

(SUS)

331 336.13 155.14 Failed

Pm+Pl

(SUS)

342 347.11 232.71 Failed

Pm+Pl+Q

(Total)

389 395.02 491.27 Passed

The stress evaluation is performed using WRC 107 & PV-

CodeCalc software with stress indices. WRC 107 results are

validated with PV-CodeCalc results. General primary

membrane equivalent stress (Pm) and General primary

membrane equivalent stress plus local primary membrane

equivalent stress (Pm+Pl) are not meeting the requirements of

Part 5 of ASME Section VIII, Div 2, Ed' 2007, ADD 2008.

As already shown in Table III value of that maximum stress

intensity obtained from WRC 107 and PV-CodeCalc software

does not fall under the allowable limits.

In the case of considering stress indices, the design is failed.

Nozzle to head junction analysis need to be done by finite

element method. All the nozzle loads & moments are

considered to be acting at the same time, on conservative

front. Equivalent stress intensity plot for internal pressure

plus nozzle load is shown figure 6.

Fig 6. Equivalent stress intensity plot for pressure plus nozzle loading.

Maximum & minimum stress intensity for internal pressure

plus nozzle load is 329 MPa & 12.5 MPa respectively.

Fig 7. Linearized stress intensity plot for pressure plus nozzle loading.

The accurate stress distance pattern for internal pressure plus

nozzle load at the junction is shown figure 7. Here maximum

membrane stress is 214.6 MPa, Maximum Membrane plus

bending stress is 311.6 MPa at starting stress classification

line (SCL) thickness & minimum is 135.1 MPa at 91 mm

thickness. Maximum total stress is 323 MPa at starting SCL

thickness and minimum is 160 MPa at 88 mm thickness.

Linearization of stresses: The stress evaluation for each of the

SCL and at the end nodal points of SCL is done as per Part

5.2.2.2 of code ASME Section VIII, Div 2, Ed' 2007, ADD

2008. The equivalent stress intensity at SCL and nodal end

point of SCL is categorized as primary and primary plus

secondary stresses as per code and the stress intensity are

INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011 5

checked with allowable limits. A computer program is made

membrane and bending component is found along each

defined path. The detail stress evaluation is as given below

table IV.

Table IV. Stress analysis Results by Ansys

Type

Of

Stress Int.

Stress Int.

Allow

(MPa)

Max. S.I

Ansys

(MPa)

Result

Pm+Pl 232.71 221.1 Passed

Pm+Pl+Q 491.27 313.8 Passed

The stress evaluation is performed and the stresses intensity

are meeting the requirements of Part 5 of ASME Section VIII,

Div 2, Ed' 2007, ADD 2008. It is also shown that the design

of shell, head & nozzle are adequate as the stresses are within

allowable limits.

Table V. Stress analysis Results

Type

Of

Stress Int.

Stress

Int.

Allow

(MPa)

Max.S.I

PV-Code

Calc

(MPa)

Result Max.

S.I

Ansys

MPa

Result

Pm+Pl 232.71 347.11 Failed 221.1 Passed

Pm+Pl+Q 491.27 395.02 Passed 313.8 Passed

As already shown in Table V value of that maximum stress

intensity obtained from PV-CodeCalc and Ansys. General

primary membrane equivalent stress plus local primary

membrane equivalent stress (Pm+Pl) are not within allowable

limits. Nozzle to head junction is failed because WRC 107

calculated stresses due to pressure thrust by the convectional

formula of membrane theory and it is added to stress due to

local load algebraically.

General and Local primary membrane equivalent stresses are

not allowable limit in WRC 107 and PV-CodeCalc at nozzle

to head junction. General and Local primary stress depend on

head thickness, internal pressure & head diameter of reactor.

For obtaining stress analysis results within allowable limit,

decreased head diameter with same thickness or increased

thickness of head with same head diameter.

In Finite elements analysis nozzle to head junction analysis

General primary membrane equivalent stress plus local

primary membrane equivalent stress (Pm+Pl) are meeting

within allowable limits. Nozzle to head junction is passed

because it considered the nozzle loads along with internal

pressure. It’s also gives the accurate stress distance pattern at

the junction.

VI. CONCLUSION

The general solution obtained for nozzle to head junction

have not given the results in allowable limits for WRC 107 &

PV-CodeCalc software, because it does not take pressure into

account while calculating the local and general primary

membrane equivalent stress. It provides same nozzle load

whether the nozzle is working under ambient pressure or

working at high pressure.

The stress evaluation of nozzle to head junction using FE

analysis provides considerably more accurate stress data than

closed form calculations such as WRC 107 as it gives results

of stress profile around nozzle to head junction compared to

results given at eight points by WRC107.

VII. REFERENCES

[1] Martens D.H. and Massey S.R. "FEA analyses at

nozzle/shell junctions subject to external load".

International Journal of Pressure Vessels and Piping

(Kansas), 1996.

[2] Wichman K.R., Hooper A. G., and Mershon J.L. "local

stresses in spherical and cylindrical shells due to external

loadings." WRC bulletin no 107". Welding Research

Councile bulletin 107, 1979.

[3] Moini H and Mitchell P. T. "Stress analysis of a thick

walled pressure vessel nozzle junction". International

Journal of Pressure Vessels and Piping 46 (1991) 67-74

(California), pages 312-317, 1991.

[4] Raju P. P. "development of stress indices for nonradial

branch connections.". Nuclear Engineering and Design

98 (1987) 421-435, 198.

[5] The America Society of Mechanical Engineers. "ASME

boiler and pressure vessel code", section viii, division 2".

The America Society of Mechanical Engineers, pages

674-728, 759-767, 2007.

[6] The America Society of Mechanical Engineers. "ASME

boiler and pressure vessel code", section ii, part d,

division 2". The America Society of Mechanical

Engineers, pages 440-449, 2007.

[7] Moss. D. R. Pressure vessel design manual. Third Edition,

pages 2-11,22-38, 2007.

[8] I-deas NX-12 Modeling Software.

[9] Ansys 12 Help.

[10] Solid Edge ST2 Help.

[11] PV-CodeCalc 2008 COADE Engineering Software.