openings –principles of reinforcement - pixis.cl · pdf fileopenings in vessels and...

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September, 27th - 29th, 2010 1

Openings in vessels and their reinforcement

Principles used in the various Pressure Vessel codes

A comparison of the methods used

Author: Ray Delaforce

Openings – principles of reinforcement

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There are three basic methods in use today

� Area replacement� Pressure Area� Stress Concentration Factor (scf)

Area replacement is the oldest method – used first

It was in the 1925 edition of ASME Section VIII

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This is how the codes uses the various methods

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Area replacement

Pressure Area

Stress Concentration

ASME Division 1

ASME Division 2

PD 5500 EN 13445

These details are repeated later in the presentation

Area replacement UG-37

Pressure Area Appendix 1-10

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Area Replacement method

First, we look at the Area Replacement method

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Here is a nozzle in a shell

Basic principle: Area removed = Area put back

Excess shell thickness

There is also excess nozzle thickness available

Calculated thickness

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Pressure Area method

The Pressure Area method is slightly different

This is the Pressure Area – area where internal pressure acts

This is the Metal that restrains the pressure force

The forces should at least balance

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Another view will make the pressure area method clearer

The pressure force is counteracted by the metal force

Pressure Area x Pressure < Metal area x allowable stress

That is the principle of the Pressure Area method

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Stress concentration method

The Stress Concentration method is entirely different

Consider a plate with a hole subject to a tensile force

The stress increases as we approach the hole

Average Stress S

Increased Stress Sa

Sa/S is known as the Stress Concentration Factor scf

But, what is that concentration factor

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Stress concentration method

The scf is defined by the Inglis equation

Half (crack) opening length a

For a circle: a = r therefore scf = 3

The stress concentration method is only used by PD 5500

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Large nozzle in a cylinder

A large nozzle in a cylinder poses a special problem

It tends to twist when pressure is applied

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Large nozzle in a cylinder

A large nozzle in a cylinder poses a special problem

It tends to twist when pressure is applied

Because of the hoop stress that is pulling on the nozzle

This causes a bending moment to exist, twisting the nozzle

ASME Division 1 is the only code that analyses this

This is in Appendix 1-7

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Area replacement in more detail

When we insert a nozzle in a vessel, we first cut a hole

Then the nozzle is installed

The hole is a weakness we have to take into account

The hole must be reinforced to render is strong enough

The ASME code has a procedure for Nozzle Reinforcement

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Nozzle reinforcement in accordance with ASME VIII, Division 1:

When we cut a hole in a shell we weaken it as just stated

Principle in ASME: metal Removed must be replaced

We now consider the area of metal that is removed

Calculate the required thickness of nozzle for pressure trn

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t

t is the actual plate thickness

tr

tr is the calculated (required) thickness of the shell

Install a nozzle This is the area to reinforce A

A

Extra shell thickness is available as reinforcement A1

A1 A1


trn

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t

t is the actual plate thickness

tr A

A1 A1


trn

Calculate the area of the nozzle available A2

A2 A2

Calculate the area of the nozzle inside A3

A3 A3

And if there is a reinforcement pad A5

A5 A5

Finally, the welds can also be included A4

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All the reinforcement must be within a credit envelope

That is the principle of Area Replacement


This is the simple requirement for area replacement:

ttr A

A1 A1

A2 A2

A3 A3

A5 A5

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All the reinforcement must be within a credit envelope

That is the principle of Area Replacement


This is the simple requirement for area replacement:

A1 + A2 + A3 + A4 + A5 > A

This is the illustration of the principle from ASME VIII, Division 1

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Figure UG-37


This is the illustration of the principle from ASME VIII, Division 1

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Consider a nozzle installed in a cylinder

dtn

R

t

This is area over which the pressure acts Ap

Lr

Lh

This the metal area resisting the pressure As

LR is actually the decay length of the stress as shown here

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dtn

R

t

Lr

Lh

Decay length

The pressure tries to split the shell, and metal holds it together

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dtn

R

t

Lr

Lh


This is the basic principle of Pressure Area method

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This is the basic principle of Pressure Area method

Pressure x AP < Allowable Stress x AS

Area over which the pressure acts

Area over which metal resists

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Stress Concentration method

The scf is a little more complicated than shown before

For a circle scf = 3

ASME Section VIII, Division 2 shows that it depends what part of the nozzle (hole) we are considering

Let us look at what Division 2 has to say

There are number of parts to the nozzle

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Inside corner

Outside corner

Division 2 calls scf ‘Pressure Index’ Each stress has its own scf

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Division 2 calls scf ‘Pressure Index’The greatest scf

That is very near the 3 we obtained from the Inglis equation

Only the British PD 5500 code uses the scf method

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Only the British PD 5500 code uses the scf method

It uses a graphical method to determine the scf

These numbers basically

represent the scf values

Let us look at the method PD 5500 uses in detail

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D

ers


Let us look at the method PD 5500 uses in detail

First we compute a value called ρ d

Next we compute the value called

Where C = 1 or 1.1 and eps is the computed shell thickness

These are the values we need to interrogate the PD 5500 graph

First we locate the curve whose value is ρ

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First we locate the curve whose value is ρ

Next, we find the Cers/eps value

Then we drop down to find the ratio erb/ers

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Then we drop down to find the ratio erb/ers

From that ratio we find the required nozzle thickness

Computers cannot work with graphs, they need numerical data

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Computers cannot work with graphs, they need numerical data

PD 5500 provides the graph data in digitised form

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Nozzles of special shape

Consider a rectangular nozzle in a cylinder

This type of nozzle has special problems that round ones don’t

The forces acting on the sides of the nozzle are the problem

Consider this example:

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There are tangential forces from the hoop stresses from the pressure that pull on the sides of the nozzle like this

The opening as a consequence gets distorted

The forces are easy to calculate

There is a uniformly distributed load (udl) acting on the opening

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There is a uniformly distributed load (udl) acting on the opening

That udl is simply P x R

The only way of reinforcing this nozzle is with a beam

Here is a beam placed at the side of the nozzle

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Here is a beam placed at the side of the nozzle

X

X

The beam must have a sufficient section modules to take the udl

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External Forces and Moments

The nozzle might have to sustain external forces from pipe work

Consider a nozzle subject to an external moment

It deforms as a result

There are bending stress

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There are bending stress

And there are membrane stress too

The combined stress is different on the outside and inside of the vessel shell (cylinder or head)

Consider just four points around the nozzle (WRC 107 method)

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Consider just four points around the nozzle (WRC 107 method)At each point there are membrane and bending stresses

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At each point there is a membrane and bending stresses

There are actually 8 points to consider:

� Four points on the inside surface, and,

� Four points on the outside surface

The WRC 107 bulletin provides a method of assessing the stresses induced in the shell from the external force and moments

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The WRC 107 method

Radial Force P

Longitudinal Force VL

VL

Circumferential Force VC

VC

MC

P

Circumferential Moment MC

Longitudinal Moment ML

ML

Torsional Moment MT

MT

AU

DU

BU

CUAL BLCLDL

Look more closely at the hole

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The WRC 107 method

Radial Force P

Longitudinal Force VL

Circumferential Force VC

Circumferential Moment MC

Longitudinal Moment ML

Torsional Moment MT

AU

DU

BU

CUAL BLCLDL

Look more closely at the hole

WRC 107 computes the membrane and bending stresses at these 8 points

The membrane stresses are summed, and then the bending stresses are summed and compared to the allowable stresses

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The WRC 107 method

Here is a sample final calculation from PV Elite

Pm is the General Primary Membrane stress

Pl is the Local Primary Membrane stress

Q is the Secondary stress

However, these are the stresses in the vessel wall only

We have to consider the stresses induced in the nozzle wall

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Stress in the Nozzle Wall

There is a membrane stress, and a bending stress in the wall

PV Elite uses the method from the piping code ASME B31.3

Radial force

Bending moment

Here is a typical sample calculation from PV Elite

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Stress in the Nozzle Wall

There is a membrane stress, and a bending stress in the wall

PV Elite uses the method from the piping code ASME B31.3

Here is a typical sample calculation from PV Elite

Summary of the discussion

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There are basically three methods of considering reinforcement

� Area replacement

� Pressure area method

� Stress Concentration

Area replacement Pressure Area Stress Concentration

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Special problems associated with Large nozzle in cylinders

Only ASME VIII, Division 1 has the analysis in Appendix 1-7

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Special problems associated with Rectangular nozzle in cylinders

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Stresses induced in the vessel from external forces and moments

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Stresses induced in the Nozzle Wall from external loads

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openings –principles of reinforcement - pixis.cl · pdf fileopenings in vessels and...

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