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CETIM Practical guide for boiler making and pipework 1

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Performance
Practical guide for boiler
making and pipework
General pressure vessel
design principles
Performance
Sommaire
Practical guide for boiler
making and pipework
General pressure vessel
design principles
AUTHORS:
Jean-Louis Iwaniack, Matthieu Durand,
Florent Chazelat, Camille Plaisant,
Anthony Poirier
Cetim’s Boiler Making and Pipework Commission
Handbook release dates
Handbook no. 1: General pressure vessel design principles
Published in 2021
Handbook no. 2: Units and Conversions
Published in 2017
Handbook no. 3: Analytic SoM formulas
Published in 2017
Handbook no. 4: Component, support and anchor bolt design
To be released soon
Handbook no. 5: Vertical pressure vessel design
Published in 2017
Handbook no. 6: Horizontal pressure vessel design
To be released soon
Handbook no. 7: Spherical pressure vessel design
To be released soon
© CENTRE TECHNIQUE DES INDUSTRIES MÉCANIQUES (CETIM), 2022
ISSN 1767‑2546
ISBN 978‑2-36894‑244‑4
“Any full or partial reproduction or representation of this work by whatever process without CETIM’s
authorisation is illegal and constitutes an infringement. Only the reproductions strictly reserved for the private
use of the copier not intended for collective use, on the one hand and, on the other hand, analyses and short
quotations justified by the scientific or informative nature of the work in which they are incorporated, are
authorised” (French Intellectual Property Code, Articles L.-122‑5 and L.-335‑2).
Preamble
V
ia the Boiler Making and Pipework Professional Commission, Cetim
launched a study and research programme in order to compile a “Strength
of Materials” collection consisting of several handbooks. The aim is to
merge theoretical knowledge, Cetim’s expertise and the know-how of
industrial manufacturers in order to provide simple and clear guidelines for the
design of their equipment.
This instructive, functional and practical handbook no. 1 summarises the basics
of engineering for the design of pressure vessels, via many concrete examples in
order to be used as a model for sector players. It presents the principles used to
design all components of the vessel, from support to access equipment and outlines
for each category of stresses, the loading conditions to be taken into account. As the
boiler maker has to be familiar with the applicable codes and standards, the various
stresses and loadings, the main failure modes of the vessels and has to be able
to determine the maximum allowable stress, the writers of this work were careful to
meticulously address the information provided in the many chapters – terminology;
calculation method; failure and fracture mode; basic practice and calculations in
relation to the vessels. The guide also includes bibliographical references which
cite applicable codes and standards.
Mohammed Cherfaoui
Boiler Making, Pipework and
Sheet Metal Working Commission Head
Jean-Louis Iwaniack
Calculation Manager for pressure equipment
3
Contents
Preamble��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 3
I Introduction�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 8
1. General background����������������������������������������������������������������������������������������������������������������������������������������������������������������������� 8
2. Aims and content of the handbook����������������������������������������������������������������������������������������������������������������������������� 9
2.1.
2.2.
2.3.
2.4.
Aims of all handbooks���������������������������������������������������������������������������������������������������������������������������������������������������������� 9
Aims of this first handbook�������������������������������������������������������������������������������������������������������������������������������������������� 9
Content���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 10
Limits of the guide���������������������������������������������������������������������������������������������������������������������������������������������������������������� 10
3. History of boiler making and pipework������������������������������������������������������������������������������������������������������������� 10
3.1. Changes to equipment����������������������������������������������������������������������������������������������������������������������������������������������������� 10
3.2. Development of dimensioning methods�������������������������������������������������������������������������������������������������������� 11
4. References����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 11
4.1. Codes and standards���������������������������������������������������������������������������������������������������������������������������������������������������������� 11
4.2. Practices of manufacturers���������������������������������������������������������������������������������������������������������������������������������������� 12
4.3. Current research and needs for the future������������������������������������������������������������������������������������������������ 12
II Terminology���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 13
1. Aim���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 13
2. Types of vessels�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 13
2.1.
2.2.
2.3.
2.4.
General��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 13
Typical pressure vessels������������������������������������������������������������������������������������������������������������������������������������������������ 13
Process vessels����������������������������������������������������������������������������������������������������������������������������������������������������������������������� 15
Storage vessels������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 16
3. Parts of the vessels���������������������������������������������������������������������������������������������������������������������������������������������������������������������� 17
3.1.
3.2.
3.3.
3.4.
3.5.
Base����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 17
Supports������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 18
Heads�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 29
Body or shell������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 34
Roof for vertical tanks������������������������������������������������������������������������������������������������������������������������������������������������������� 35
4. Equipment and accessories���������������������������������������������������������������������������������������������������������������������������������������������� 36
4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
4.7.
Equipment on the shell���������������������������������������������������������������������������������������������������������������������������������������������������� 36
Auxiliary components�������������������������������������������������������������������������������������������������������������������������������������������������������� 37
Electrical and fire protection������������������������������������������������������������������������������������������������������������������������������������� 37
Inspection instruments���������������������������������������������������������������������������������������������������������������������������������������������������� 38
Flanges��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 38
Gaskets��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 44
Bolting����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 48
5. Definitions������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 51
5.1. Main terms������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 51
5.2. Tensile tests��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 52
6. SoM assumptions��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 54
6.1.
6.2.
6.3.
6.4.
Materials���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 54
Geometry��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 54
Forces������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 54
Contacts������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 55
7. Stresses and strains������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 55
7.1.
7.2.
7.3.
7.4.
Stress/Strain relation������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 55
Concept of stresses������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 55
Mohr’s circle������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 59
Hooke’s law�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 68
8. Elastic and plastic regions������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 71
8.1. Strain hardening coefficient�������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 71
9. Stress criteria������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 73
9.1. Tresca criterion����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 74
9.2. Von Mises criterion������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 74
III Calculation methods���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 76
1. Aim of the calculation�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 76
2. Starting the calculation��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 76
2.1. Membrane stress analysis������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 76
2.2. Shell theory��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 77
2.3. Boundary conditions and working assumptions���������������������������������������������������������������������������������������������������������������������� 77
3. Philosophy of the codes��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 78
3.1. General�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 78
3.2. Problems associated with designing based on codes�������������������������������������������������������������������������������������������������������� 79
4. Finite elements��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 80
4.1. General�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 80
4.2. Finite element problem-solving steps������������������������������������������������������������������������������������������������������������������������������������������������ 80
4.3. Drawbacks of finite element calculation������������������������������������������������������������������������������������������������������������������������������������������ 81
5. Method proposed in the guide�������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 82
5.1. Aim������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 82
5.2. Necessary information���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 82
6. Loadings����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 82
6.1. Categories of loadings����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 83
6.2. Types of loadings������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 83
7. Pressure����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 84
7.1. General�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 84
7.2. Different types of thicknesses��������������������������������������������������������������������������������������������������������������������������������������������������������������������� 84
8. Local loads (see handbook 5)���������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 85
9. Climatic loadings���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 85
9.1. Wind���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 85
9.2. Earthquakes������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 89
9.3. Snow and ice������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 90
10. Thermal loading��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 91
10.1. Types of temperatures������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 91
10.2. Temperature effect����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 91
10.3. Temperature gradient in the material��������������������������������������������������������������������������������������������������������������������������������������������� 91
11. Load combinations (handbook 5)�������������������������������������������������������������������������������������������������������������������������������������������������������������� 91
6
IV Failure or fracture modes��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
93
1. Fracture theory..................................................................................................................................................................................��������������������������������
93
Maximum stress theory����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
Maximum shear stress theory (Tresca)������������������������������������������������������������������������������������������������������������������������������������������
Distortion energy theory (Von Mises)������������������������������������������������������������������������������������������������������������������������������������������������
Comparison������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
93
93
94
95
2. Causes of failure��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
95
Materials (CCVL Orléans)������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
Design��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
Manufacturing�����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
Operation������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
95
96
96
96
3. Various failure modes of pressure vessels����������������������������������������������������������������������������������������������������������������������������������
97
1.1.
1.2.
1.3.
1.4.
2.1.
2.2.
2.3.
2.4.
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
3.7.
Failure modes������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 97
Elastic deformation��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 97
Plastic deformation��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 97
Brittle fracture and ductile fracture�������������������������������������������������������������������������������������������������������������������������������������������������� 98
Fatigue / fracture by progressive crack propagation under variable amplitude loading���������������� 101
Creep����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 103
Corrosion������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 104
V Practice and basic calculations on the vessels������������������������������������������������������������������������������������������������������ 111
1. Representation system�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 111
1.1.
1.2.
1.3.
1.4.
The basics of technical drawing������������������������������������������������������������������������������������������������������������������������������������������������������������� 111
Steel construction������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 116
Boiler making������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 117
Pipework������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 125
2. Location of the centre of gravity����������������������������������������������������������������������������������������������������������������������������������������������������������������� 126
3. Estimating the weight����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 127
3.1.
3.2.
3.3.
3.4.
3.5.
Different types of weights����������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 127
Vessel weight�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 128
Weight of equipment������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 130
Weight of contents������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 130
Total weight������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 130
4. Examples of optimum tank proportions������������������������������������������������������������������������������������������������������������������������������������������� 131
VI References / Bibliography������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 137
1. Standards and codes�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 137
2. Works����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� 137
VII Conclusion������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 138
7
I
Introduction
1.
General background
Since 2000, the Boiler Making and Pipework Professional Commission has been financing a
study and research programme to compile a Strength of Materials guide specifically geared towards
sector professionals. The aim is to put together a compendium officially documenting theoretical
knowledge, Cetim’s expertise and the know-how of manufacturers. It is intended to provide guidance
for the design of pressure equipment without using finite element and other complex calculations
for simple cases.
Continuous research and the use of powerful computational tools help to address complex
cases, specify the theory and upgrade design methods. Every year, the design codes for industrial
boiler making and pipework are enriched and cover more advanced topics such as earthquakes,
fatigue, frangibility and the behaviour of materials. Formulas are more accurate while calculation
rules and mandatory requirements are becoming increasingly complex. Equipment design and validation studies, often computer-aided, are more specific and more expensive. Calculation methods
have become more diverse and more refined and cover a wider array of parameters. The use of finite
element calculations for the design of simple cases is an easy but expensive and debatable solution.
The simple calculation methods that are currently being used in design offices of the sector
to quickly verify the validity of more complex calculations are not readily accessible to beginners.
In many cases, the training received by young technicians and engineers is often too general and
does not adequately prepare them for their future positions. They have not yet acquired the automatic reflexes allowing them to simply extrapolate and model a piece of equipment in order to
validate simple components.
Many books and articles have been written on the Strength of Materials or the design of equipment. Among these numerous works, it is difficult to pinpoint and choose the most relevant ones.
This guide stems from extensive work to consolidate information available in major overviews so
that engineers and designers can acquire “additional training”. It has been written in functional
and plain language. It sets out basic principles and provides detailed answers to many questions.
This instructional tool has been created to enable readers to easily acquire specific knowledge and
calculation methods and obtain a better understanding of the codes.
Pressure equipment and piping are important components which must be designed and manufactured in keeping with highly stringent regulations. This documents sets out mandatory requirements to be observed or verified in the new regulations or codes for each item of equipment,
depending on its function and conditions of use. It reviews the analytic SoM formulas, and offers
a comprehensive form with useful data for boiler makers. It outlines the calculation and service
conditions, the sizing of the vessels and their support as well as all the necessary information for
designing pressure equipment.
Our goal is to develop an instructive, functional and practical guide for the study and design
of boilers and industrial piping. Due to the many real life examples, it will be a model for many
manufacturers.
8
2.
Aims and content of the handbook
2.1. Aims of all handbooks
This guide seeks to summarise current engineering knowledge about the design and verification
of vertical pressure vessels. It can be used to size the various components of a vertical pressure
vessel and verify the resistance of the structure for different environmental or accidental conditions. It lays down the principles used to define all components of the vessel, from the support to
the access equipment. For each category of stresses, the guide provides detailed information about
the loading conditions to be factored in for vertical boiler structures.
The foundation and procedures for designing vessels have been extensively covered in the literature. The design principles and methods contained in this guide have mainly been drawn from
codes and standards (CODAP, NF EN 13445, Eurocodes and ASME). However, the procedures have
been analysed and simplified for the user. The document outlines the methods to be applied and
primarily uses Strength of Materials formulas. The application of the codes is guided step by step
throughout the handbooks and it is therefore easy to understand the fundamental principles of the
standards. This guide does not replace the design codes in force in the relevant countries.
A number of methods can be used to estimate a stress or load. Firstly, Strength of Materials
principles are used to establish a simple and basic method. The initial results are only estimations.
More complex methods are then introduced to best assess these stresses. The guide tries to make
the principles used in the French, European or international codes more accessible.
2.2. Aims of this first handbook
This guide is intended to summarise the fundamentals of engineering for pressure vessel
design. It looks at the terminology, the principles used to dimension the structure, and the loading
conditions to be taken into account.
Following the selection of the materials, it discusses the dimensioning of the vessel. As such,
it proposes methods to determine the stresses in the material that may lead to its failure if they
exceed a critical value. An overview of the standards and codes used to determine the critical values
and to verify that the stresses do not exceed these values is also provided.
Only the finite element method is able to calculate and estimate stresses in all points of the
material. Current codes lay down calculation rules to avoid detailed estimation of the stresses
undergone by the material. They take into account the principal and secondary stresses and apply
safety factors to consider all parameters which may affect the calculation.
Boiler makers need to be familiar with:
◗◗ Applicable codes and standards;
◗◗ The various types of stresses and loadings;
◗◗ The main failure modes of the vessels;
◗◗ And must be able to determine the maximum allowable stress.
9
2.3. Content
The content of this handbook is broken down into the following chapters:
∙ Terminology
This chapter covers the various types of vessels and the different components. Diagrams are
used for instructive purposes. The remainder of this chapter explains the basic principles of Strength
of Materials such as SoM assumptions, the concepts of stress, strain as well as the elasticity and
plasticity of a material.
∙ Calculation methods
This chapter discusses a number of concepts in Strength of Materials, such as shell theory.
It provides a quick overview of the calculation codes and standards; then explains why the finite
element method is not included in this guide. Lastly, the concepts of the method selected in this
guide are outlined. This chapter also reveals the types of loadings and their combinations.
∙ Failure or fracture modes
This section presents fracture theory, the various failure modes and causes of failure.
∙ Practical applications and basic calculations on the vessels:
representation, cog; weight calculation
Locating the centre of gravity and estimating the weight of an item of equipment are the main
themes addressed in this chapter. It also looks at how to use technical drawings to represent
these items.
∙ Bibliographic references
You can quickly find references for the codes and standards that are useful for dimensioning
pressure vessels, as well as the works on design methods.
2.4. Limits of the guide
This handbook is not intended to replace the codes and standards. It is rather a summary of the
sizing rules applied to boiler making. It can be used on a daily basis by the designer. Efforts have
also been made to make this guide as exhaustive as possible. However, in certain cases, it would
be useful to consult the codes.
In addition, this handbook provides an alternative to finite element calculation. Therefore, this
method is only touched on in the guide and will not be covered in detail.
3.
History of boiler making and pipework
3.1. Changes to equipment
There have been so many changes since the Middle Ages! Nowadays, boiler makers manufacture
equipment for the nuclear, oil, chemical and gas industries. Although some processes are mechanised, these items of equipment - that sometimes weigh several hundred tons - are still man-made.
This is probably what binds us to the past more so than other industrial trades where automation
has replaced manual labour. In the past, boiler makers only worked by hand; they made copper utensils reserved for domestic use as well as religious ornaments; a boiler maker was considered an artist.
10
Up to the XVIIth century, boiler makers made outstanding pieces which now adorn our museums
and churches. This industry was widespread across Europe, the city of Dinant located on the Meuse
River, today in Belgium, had a special reputation for these kinds of objects. Dinant had such a wellestablished reputation that boiler makers were often called “dinandiers”; they were also sometimes
called “maignans” which comes from an old French word “magnien”, which means boiler.
A lot has changed since then. The manufacture of heat exchangers, reactors, columns, boilers,
tanks or piping requires the use of all types of metals, obviously steel, but also stainless steel,
titanium, zirconium and many other exotic metals.
3.2. Development of dimensioning methods
The first record of dimensioning dates back to 1638 with Galileo who, in one of his publications,
studied the bending of a beam, even though he incorrectly assumed that stresses were uniformly
distributed over the cross-section of the beam. Forty years later, Robert Hooke discovered that the
stress on a body, in the elastic range, is proportional to the applied force.
In the XVIIIth century, Thomas Young recognised shear as an elastic deformation. He observed
that elastic resistance to shear and elastic resistance to tension-compression are different within
a given material. He introduced the idea of the elastic modulus of a material, from which arose the
currently used Young’s modulus.
On 14 May 1821, Henri Navier presented Mémoire sur les lois de l’équilibre et du mouvement
des corps solides élastiques to the French Academy of Sciences in which he researched the equilibrium equations of elastic solids by using a “theory of molecular mechanics”. By assuming that
the medium is isotropic, he obtained equilibrium equations for elastic solids. He only used a onematerial dependent constant similar to the Young’s modulus. Siméon Denis Poisson objected to
Navier’s theory between 1828 and 1829.
In 1822, in a paper to the French Academy of Sciences, Augustin Louis Cauchy introduced the
idea of stress and explained the concept of deformation described by its six components or by the
principal axes of deformation and the corresponding principal stretches. From the equilibrium
equations expressed in terms of stresses, Cauchy hoped to arrive at the displacement equations
governing the equilibrium of the elastic solid. He assumed that the materials were isotropic and,
from a stress-strain relation, that the principal axes of stresses and strains coincide. He introduced
two material constants to describe the equilibrium equations for an elastic solid expressed in terms
of displacement.
4.
References
4.1. Codes and standards
In France, vertical pressure vessels are designed and dimensioned in compliance with the CODAP
(this comprehensive code outlines all the main principles for the safe design of a column). This
guide, the Practical Guide for Strength of Materials applied to pressure equipment, supplements the
CODAP construction code and is fully consistent with the instructions laid down therein. However,
the committee in charge of this programme acknowledges that the CODAP does not cover all
structures or the stresses that may be experienced on an industrial fleet. Accordingly, the members
of the committee recommend other documents and resources which may be useful given the diverse
number of cases and the large number of vessels. These documents include:
◗◗ Eurocodes;
◗◗ ASME, ASCE, API…
11
It is worth noting that a vessel can be designed or dimensioned using many sources. Engineers
must exercise caution when selecting their references. They must check that the use of the formulas
of the various codes or regulations is compatible with their methodology.
4.2. Practices of manufacturers
This guide is largely based on the current practices of industrial manufacturers. It aims to
obtain a good understanding of the in-house procedures implemented by the companies to apply
the methods of the codes. It reflects the practice of an engineer in the sector.
This work seeks to answer questions asked by manufacturers. Our priority is to highlight the
issues of interest to companies and which are not comprehensively discussed in current literature.
This guide provides answers to key priorities and highlights issues faced.
4.3. Current research and needs for the future
A lot of research work and studies are currently underway, and their results and conclusions will
help to clarify certain calculation aspects or implement new methods. As time goes by, additional
information will be included in this guide. There are many areas to be refined; to this end, each
year the commission requests the performance of additional studies.
12
II Terminology
1.
Aim
The aim of this section is to learn to describe the general geometry of the vessels, particularly
their type, the main components such as the shell, the head, the supports and piping. It also provides details about specific equipment such as flanges, gaskets, shields, nozzles, manholes, etc.
In addition, it introduces a few SoM concepts (main terms, assumptions, criteria, etc.)
2.
Types of vessels
2.1. General
In most cases, vessels consist of a cylindrical body called a shell. Each end is closed by a head
which can have several shapes. The structure rests on the ground thanks to supports. Components
are added to the structure to allow the vessel to be functional: inlet and outlet of material, instrumentation and control, internal equipment to process the content, etc.
2.2. Typical pressure vessels
2.2.1. Vertical pressure vessels
Head
Possible uses
Storage of liquids or gases
Compressor
Characteristics
2 heads
Shell
Supports: Lugs (less expensive),
legs, rings, skirt
Additional
components
Nozzles
Manhole
Framework
Weak points
to be checked
Attachment points of supports,
framework
Pressure on the lower head
Nozzle
Shell
Head
Support
legs
13
2.2.2. Horizontal vessels
Nozzle
Head
Head
Saddle
support
(sliding)
Saddle
support
(fixed)
Shell
Possible uses
Storage of liquids
or gases
Compressor
Characteristics
2 heads
Shell
Supports: saddle
Additional
components
Nozzles
Manhole
Framework
support
Weak points
to be checked
Position and size
of saddles
Attachment points
of the framework
Radial pressure
Possible uses
Storage of liquids
or gases
Characteristics
2 poles
Legs
8 to 72 petals
Additional
components
Nozzle
Manhole
Framework
supports
Weak points
to be checked
Attachment points
of legs
Legs
Petal welds
2.2.3. Spherical pressure vessels
Nozzle
Upper
pole
Petal
Equator
Lower
pole
14
Legs
2.3. Process vessels
2.3.1. Processing or fractionation column
2:1 Ellipsoidal
head
Flange nozzle
Coupling
Nozzle
Tray downcomer
Head
Possible uses
Weir plate
Shell
Reinforcement pad
Inlet connection
Tray support ring
Tray support beam
Collector tray
Accumulator tray complete
with centre chimney
and drawoff box
Drawoff nozzle
Trays
Manhole
Shell
Nozzle
Handrail
Cone
Valve tray
Toe plate
Disc tray
Shell
Platform support
bracket
Skirt access opening
Bottom head
Base plate
Drain
Skirt vent opening
Skirt
Cage hoop
Cage
Ladder rung
Nozzle
Ladder
Ladder support
2 heads
Shell
Supports:
skirt
Connecting
Characteristics
cone with two
independent
capacities
Framework
Internal trays
Additional
equipment
Nozzles
Manhole
Framework
supports
Weak points
to be checked
Thickness
and design
of the skirt
Wind stresses
Nozzle
Head
Skirt
support
Anchor bolt chair
Storage
of liquids
or gases
Distillation
Processing
2.3.2. Reactor
Head
Upper catalyst
bed
Inlet
nozzle
Lower catalyst
bed
Support
skirt
Chemical reactor
Treater
Mixer filter
Characteristics
2 heads
Shell
Support: skirt
Additional
components
Nozzle
Manhole
Framework support
Weak points to
be checked
Support
Framework attachment
points
Shell
Catalyst bed support
grid
Head
Possible uses
Outlet
collector
Outlet
nozzle
15
2.4. Storage vessels
2.4.1. Storage tank
Conical roof
Central column
Possible uses
Product storage
Characteristics
–
Additional
components
Manhole
Weak points to
be checked
–
Possible uses
Product storage
Characteristics
2 poles
Legs
4 to 10 petals
Additional
components
Nozzle
Manhole
Weak points to
be checked
Legs
Petal welds
Possible uses
Storage of liquids
or gases
Characteristics
–
Additional
components
Nozzle
Manhole
Weak points to
be checked
–
2.4.2. Storage sphere
Nozzle
Pole
Petal
Equator
Legs
Pole
2.4.3. Tank
Nozzle
Head
Saddle
support
(sliding)
16
Head
Shell
Saddle
support
(fixed)
2.4.4. Silos
Apex ring
Roof belt
Possible uses
Product storage
Characteristics
Conical roof
Shell
Hopper
Support: short skirt
Support structure
Additional
components
Nozzle
Manhole
Weak points to
be checked
Corrosion of the legs
Thickness of the shell
Hopper
Explosion vent
panel
Shell
Lower belt
Skirt
Hopper
Support structure
2.4.5. Buried tank
Sand
3.
Internal reinforcements
Possible uses
Storage of
liquid or gases
Characteristics
2 heads
Shell
Support
Internal
reinforcements
Additional
components
Nozzle
Manhole
Weak points to
be checked
–
Earth
Parts of the vessels
3.1. Base
3.1.1. Foundations
The foundations are needed to transmit and redistribute the loads to the ground and thereby
stabilise the structure. The geotechnical design and the foundations are defined based on models
of acceptable foundations. The selected solution mainly depends on the nature of the ground (piles
underneath the seat for unstable grounds) and the region (seismic stresses, vicinity to the sea, etc.).
A geotechnical study is carried out in order to identify the risks associated with geological
hazards. Based on the geotechnical study of the selected location and an assessment of the load
(diameter, tank height, product density), it is possible to set / propose / discard technical solutions.)
17
There are a number of different types of foundations suited to the nature of the ground, as shown
in the following figure.
Solution 1
Concrete slab
Solution 2
Differential
settlement
Solution 3
Concrete ring
Solution 4
Concrete ring
and slab
3.1.2. Anchor bolts
Under the action of horizontal stresses on the vessel, the installation of anchor bolts may be
recommended. The anchoring must be installed if one of the following conditions can cause the
detachment of the supports:
◗◗ a) The action of the wind may lift the empty vessel.
◗◗ b) The action of the internal pressure is not counterbalanced by the weight of the empty vessel.
◗◗ c) The action of the internal pressure is not counterbalanced by the weight of the vessel
and the product.
◗◗ d) Earthquakes.
Anchor bolts must be attached to the support of the vessels, however they can also be on the
shell. They must allow to be integrated into the foundations. There are different types of anchors,
as shown in the figure of the paragraph base rings and anchor bolts for skirts.
3.2. Supports
3.2.1. Skirts
General
The skirt is the most commonly used method of supporting vertical pressure vessels and
columns. A skirt is a cylindrical or conical shell that is placed underneath the vessel. This method
is regularly used as it minimises the local stresses and redistributes the loading over the entire
circumference. The critical area is the weld attaching the skirt to the structure. It must withstand
the weight of the vessel and the overturning moment. However, it must also resist the thermal and
bending stresses due to the temperature drop inside the skirt. In many cases, the outside diameter
of the skirt matches that of the vessel.
Types of skirts
a) Inset vessel, straight skirt b) Vessel set on straight skirt
18
c) Pedestal
d) Conical skirt
Base rings and anchor bolts for skirt
The skirt is welded to a base ring, that is to say an annular plate in contact with the concrete
foundations and the bottom of the skirt. This ring serves to distribute the loads to the entire
circumference. The base ring is secured to the concrete with anchor bolts (Figure A). Components
can be added to solidify the structure. Gussets, that is to say metal plates, can be distributed along
the skirt. They are welded to the skirt and the base ring (Figure B). It is possible to attach gussets
as well as an additional plate above the gussets. This configuration is called a chair (Figure C).
The most rigid solution is to add an additional ring that can be welded to the skirt. Gussets will be
used to support the ring (Figure D).
a) Simple base ring
b) Gusset
c) Chair
d) Ring
3.2.2. Support legs
General
Many types of vessels can be supported by legs. The design varies from a small vessel supported
by 3 to 4 legs or for a storage sphere of more than 25 meters in diameter supported by 16 to 20
legs. Any number of legs can be used; however the most common variations are 3, 4, 6, 8, 12, 16,
20. They must be evenly distributed over the circumference of the vessel.
Braced or unbraced legs
Legs can be braced or unbraced. Braced legs are reinforced with either cross bracing or sway
bracing. Sway bracing only operates in tension. Diagonal connecting bars are used to transfer the
horizontal loads to the next leg. Tensioners are used to adjust the braces. Cross bracing works in
tension and in compression, as the bars are directly welded to the legs or bolted to the wing plates.
Bracing is used to reduce the number or size of legs required by eliminating bending in the legs.
The disadvantage of bracing is that is complicates the installation of the nozzles and pipes to the
head of the vessel.
19
Vessel supported by cross braced legs (general view, bracing, wing plate)
Types of legs
The structure of legs can be made from circular pipe sections, rectangular pipes, angles or any
other type of profiled section. They may be welded directly to the vessel, bolted or welded to clips
directly attached to the shell. For very large vessels, a compression ring or a ring stiffener may be
welded to the vessel. The legs are welded locally to the ring and the localised loads induced by the
legs are redistributed along the ring.
Pipe
Legs on ring
20
Beam
Beam flange out
Angle
Pedestal-type leg
Base plates and anchor bolts for legs
Legs are anchored to the foundation by base plates. The base plates are secured to the concrete
by anchor bolts.
Example of base plates depending on the type of leg
The codes help to calculate the equivalent thicknesses of the support plate. It is possible to
reduce these thicknesses by adding components to the bottom of the leg. Cetim has developed
calculation methods to reduce the equivalent thickness provided by the conventional methods
such as those developed in D. Moss – Pressure vessel design manual, 4th Edition. Procedure 4‑12,
through the use of spacers or other components. This information has been validated by finite
element calculations.
Various reinforcement designs are presented in handbook 4 with the calculation methodology.
Example of solution proposed by Cetim:
IPN and IPE profile:
Height of the profile = H
Thickness of the wing = E
Width of the profile = b
Proposed dimensioning
Base plate
A=2×H
B=2×b
H
b
a=— c=—
2
2
Hp = 1.2 × H
Gussets x4
Plates x2
Plates and gussets emin = E
Base plate Es = 1.2 × E
Bd = 0.75 × B
Ab = 0.875 × A
3
—
e × Hp 6 > Ee3
Otherwise H = 1.3 × φ
21
3.2.3. Saddle support
General
Horizontal pressure vessels or storage tanks are usually supported by two vertical cradles called
saddles. The use of several saddles is not necessary and must be avoided. If the vessel is supported
by more than two saddles; this creates additional stresses (static indeterminacy).
The methodology for estimating the stresses in the shell and the heads of a horizontal pressure
vessel is called the Zick analysis (L.P. Zick was an American engineer). The assumption of this
method is that supports are rigid and not attached to the vessel. In fact, the supports are flexible
and generally welded. The analysis is not 100% accurate; however the correct results for 45 years
have proved its effectiveness.
The location of the saddle is very important. If the saddles are too far, bending can be produced
in the vessel. If the vessels are placed too close to the centre, the heads may collapse.
Types of saddles
Saddle supports can be made from concrete or metal. In the case of concrete saddles, attachment to the vessel is complicated and it is recommended to use a liner. In the case of metal
supports, the support may be vertical or slopped, and there may be two or more ribs.
The arrangement of the saddles varies depending on the type of vessel and its components, for
example manholes, nozzles, etc. There are three types of arrangements. The first is the simplest
and is intended for a symmetrical vessel with two saddles. The second corresponds to a symmetrical
vessel with several saddles. The last is reserved for non-symmetrical vessels.
• Make up
In most cases, the saddle has various parts: wear plate, ribs and base plate. The wear plate is
not mandatory; it is a metal part which serves to distribute the loads of the support on a band. Ribs
are vertical or sloped parts, there may be outer or inner ribs, often both are used.
22
During an earthquake, the ribs absorb longitudinal and horizontal loads. The saddle is normally
bolted to the foundation through the base plate.
Wear plate
Rib
Shell
Base plate
The minimum contact angle between the saddle and the vessel is 120°. The maximum efficient angle is 180°. The weight and splitting force go to zero above this angle. For saddles with
a wear plate, it is possible to reduce the angle by 6° on each side; the maximum angle therefore
becomes 168°.
Concrete saddles are often loose saddles; that is to say that the vessel is not attached to the
support. One end of the vessel is anchored and the other end rests freely on the saddle. A liner
between the support and the tank may avoid friction during expansion or contraction.
Stiffeners
The vessel is normally supported by two saddles; stiffeners may be used to solidify the structure.
Stiffeners may be inner or outer and may be located in the supports or on each side.
23
Shell with stiffener ring in the support plane
Shell with stiffener ring on each side of the support
Checking the dimensions of the saddle
The check of the saddles is covered in the various pressure equipment construction codes, the
most well-known method is the Zick method. It is used to check the level of stress at the connection
with the body of the vessel. A buckling check is required for the saddle.
Below is a table presenting various vessel diameters and the maximum allowable load for
the saddle.
Degassing hole
Equally-spaced gussets
24
25
mm
mm
440
480
530
570
620
660
710
740
770
840
890
930
1,070
1,190
1,320
1,460
1,590
1,730
1,850
1,980
2,120
2,250
2,370
2,530
2,640
2,780
2,910
3,050
510
560
610
660
710
760
810
860
910
970
1,020
1,070
1,220
1,370
1,520
1,680
1,830
1,980
2,130
2,290
2,440
2,590
2,740
2,900
3,050
3,200
3,350
3,510
1,980
1,910
1,830
1,750
1,680
1,600
1,520
1,450
1,370
1,300
1,220
1,140
1,070
990
910
760
690
660
640
610
580
560
530
510
480
460
430
410
B
A
Diameter of the
vessel (mm)
230
230
230
230
230
230
230
230
230
230
230
230
150
150
150
150
150
150
150
150
150
100
100
100
100
100
100
100
mm
C
610
610
610
610
610
460
460
460
460
460
460
460
280
280
280
280
280
280
280
280
280
150
150
150
150
150
150
100
mm
D
1170
1120
1070
1020
970
910
860
810
760
710
660
610
560
510
460
410
360
330
300
280
250
240
230
220
200
190
180
170
mm
E
30
30
30
30
30
30
30
30
30
30
20
20
20
20
20
20
20
20
20
20
10
10
10
10
10
10
10
10
mm
Bolts
3
2
2
2
2
2
2
2
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Number
of ribs
25.40
25.40
25.40
25.40
25.40
25.40
25.40
25.40
19.05
19.05
19.05
19.05
19.05
19.05
19.05
19.05
12.70
12.70
12.70
12.70
12.70
12.70
12.70
12.70
6.35
6.35
6.35
6.35
mm
Base plate
19.05
19.05
19.05
19.05
19.05
12.70
12.70
12.70
12.70
12.70
12.70
9.53
9.53
9.53
9.53
9.53
9.53
9.53
6.35
6.35
6.35
6.35
6.35
6.35
6.35
6.35
6.35
6.35
mm
Gusset
12.70
12.70
12.70
12.70
12.70
12.70
12.70
9.53
9.53
9.53
9.53
9.53
9.53
9.53
9.53
9.53
9.53
9.53
6.35
6.35
6.35
6.35
6.35
6.35
6.35
0.00
0.00
0.00
mm
Wear plate
467,208
447,250
426,384
406,426
386,467
365,602
344,736
243,130
227,707
213,192
197,770
182,347
156,038
141,523
127,915
114,307
99,792
95,256
65,318
60,782
58,061
50,803
47,174
44,453
40,824
38,102
34,474
31,752
kg
Max. weight
3.2.4. Lug support
Lugs are the simplest and least expensive ways of supporting pressure vessels. Lugs can readily
absorb diametral expansion by sliding over greased plates. They are easily attached to the vessel
by simple welding and allow easy levelling in the field.
Lugs are eccentric and as such they induce compressive stresses and shear forces in the shell
wall. These loads may cause excessive deformation which in turn can cause angular rotation of
the lugs.
Two-or four-lug systems are normally used. There is a wide variety of lugs which create different stress distributions in the shell. Gussets, a compression plate or other components can be
added: gussets stiffen the support, the compression plate serves to transmit the load uniformly
along the shell and reinforcing pads reduce the stresses in the shell. Several standards solutions
are regularly used:
◗◗ 2 lugs, single gussets;
◗◗ 2 lugs, double gussets;
◗◗ 2 lugs with compression plate;
◗◗ 2 lugs, compression plate and reinforcing pads;
◗◗ Increased size of lugs;
◗◗ 4 lugs, single gussets;
◗◗ 4 lugs, double gussets;
◗◗ 4 lugs with compression plate;
◗◗ 4 lugs with compression plate and a reinforcing pad added;
◗◗ Increased size of lugs;
◗◗ Addition of a ring support.
26
Various types of lugs
a) Single
gusset
b) Double
gusset
c) Single gusset
with compression
plate
d) Double gusset
with compression
plate
e) Single gusset
f) Double gusset
with compression with compression
plate and top plate plate and top plate
Example of lug with or without reinforcing pad
Unreinforced shell
Reinforced shell
3.2.5. Ring support
Ring supports are used when the stresses in the lugs are excessively high. This option is
much more expensive than the previous solution. Typically, vessels supported by rings or lugs are
contained within a larger structure which absorbs the loads on the ground. In the event of seismic
movements, it is the structure and not the vessel which is subjected to the stresses arising from
the earthquake.
27
Ring supports are only used for low or medium temperature vessels (below 400 or 500 °C).
Significant strains and stresses may appear in high temperature vessels due to differences in
expansion between the ring and the shell.
The analysis for the design of the rings and the stresses induced in the shell uses the same
principles as those for lug supports. The eccentric load points are translated into radial loads in
the rings by the gussets, and the composite section formed by the shell and the ring is analysed
for various loadings.
3.2.6. Combining supports
Depending on the type of vessel and its size, not to mention the environment, it is possible to
combine different types of supports to hold the structure.
If the system requires legs but legs are not sufficient, a lug or a ring may be added. However,
if the structure needs a skirt, it is possible to reinforce the skirt with legs or a ring. This gives the
following configurations: skirt + legs, ring + legs or lug + legs.
Skirt + legs
28
Ring + legs
Lug + legs
3.3. Heads
3.3.1. Terminology
It is worth defining certain terms used in the table below:
◗◗ Flange: connection between two cylinders.
◗◗ Straight flange.
◗◗ Flanged: which has a turned out edge where the height is noted “h” or “h1”.
◗◗ Dished: which is curved.
◗◗ 80‑10 Flanged & Dished: head where the crown radius (denoted R) is 80% of the outside
diameter and the knuckle radius (denoted r) is 10% of the outside diameter. This type of
head is often more appropriate and less expensive than the 2:1 elliptical head.
3.3.2. Types of vessel heads
Type
Standards
Relations
HEMISPHERICAL
HEAD
ASME VIII Division
1
Example
De
e
R
r
2000
10
990
h
H
V
Standards
1.9:1 ELLIPTICAL
HEAD
NF E 81‑103
Relations
2000
10
R
r
h
1716 366
50
H
V
Standards
2:1 ELLIPTICALL
HEAD
ASME VIII Div. 1
2000
10
R
r
1800 340
h
50
Di
3,8
=
Ri
1, 9
Relations
Example
e
h2 =
H = h1 + h2 + e
581 1069
V(h2) = (1,06Di)2 × 0,466h2
Type
De
Diagrams
R = 0,856De
r = 0,183De
h1 ≥ 3e
Example
e
R = 0,5Di
V = 0,2618Di3
1000 2032
Type
De
Diagrams
H
V
R = 0,9De
r = 0,17De
h2 =
Di
4
=
Diagrams
Ri
2
H = h1 + h2 + e
555 1009 V(h2) = (0,52 × Di)2 × h2
29
Type
Standards
FLAT HEAD
–
Relations
Example
De
e
2000
10
R
r
h
H
V
50
50
110
147
Type
Standards
SPHERICAL CAP
–
Relations
Example
e
R
H
(sine)
V
2000
10
2000
268
432
Type
Standards
FLAT EDGE CAP
–
e
R
h
0,085De
1,04De
1,08De
1,02De
V
Relations
0,085De
1,04De
+ 2h1
1,08De
+ 2h1
1,02De
+ 2h1
268
432
V
NF E 81‑100
R
r
h1
H
0,054De3 0,072De3 0,034De3
Relations
R = De
Example
e
h2
V
Dd
2000 10 3000 50 50 264 360
Type
Standards
INVERTED HEAD
–
R
r
2000 10 2000 50
30
h
H
Di
2
R = 2De
2
–r
1,03De + r 1,02De + r 1,01De + r
+ 1,7h1
+ 1,7h1
+ 1,7h1
V(h2) = (De + r)2 × 0,42h2
Relations
H = r + h1 + e
Example
e
Diagrams
R = 1,5De
R = (R – r)2 –
H = h1 + h2 + e
De
R = 0,8De R = 1,5De
0,175De
Dd
DISHED HEAD
(low pressure)
Diagrams
H(sin e) 0,134De
V
Standards
De
0,054De3 0,072De3 0,034De3
R = De
Type
R = 0,8De R = 1,5De
0,175De
H
(sine)
2000 10 2000 100
Diagrams
H(sin e) 0,134De
Dd
Example
De
h2 = r
H = r + h1 + e
Dd = De + r + 2h1
V (h2) = 0,75 × Di2 × h2
R = De
De
Diagrams
V
50 110 228
Hc = R + r – (R + r )2 – (0,5Di – r )2
Dd(R = D) = 1,02De + r + 1,7h1
Diagrams
Type
Standards
PRC HEAD
NF E 81‑101
(small knuckle radius)
Example
De
e
R
r
2000 10 2300 50
h
50
H
V
Standards
MRC HEAD
(medium knuckle
radius)
NF E 81‑104
R
r
2000 10 2000 66
h
50
H
GRC HEAD
(large knuckle
radius)
NF E 81‑102
R = De
V
r
2000 10 2000 200
h2 = R – (R – r )2 – (0,5Di – r )2
h
50
H
V
Standards
FLANGED
& DISHED
ASME
R
r
2000 10 2000 120
h1
50
H
Relations
Standards
80‑10 FLANGED
& DISHED
ASME
V
R
r
2000 10 1600 200
h2 = R – (R – r )2 – (0,5Di – r )2
H = h1 + h2 + e
Di
25,4
)3 × 0,0013
Relations
Diagrams
R = 0,80De
r = 0,1De
h2 = R – (R – r )2 – (0,5Di – r )2
Example
e
Diagrams
R = De
r = 0,006De
393 616 V (h2 ) = (
Type
De
H = h1 + h2 + e
V(h2) = (De + r)2 × 0,42h2
442 776
Type
e
Diagrams
R = De
Example
De
H = h1 + h2 + e
V(h2) = (De + r)2 × 0,42h2
Relations
Example
R
Diagrams
361 540
Standards
e
H = h1 + h2 + e
V (h2) = (Di + 0,2)2 × 0,455h2
h2 = R – (R – r )2 – (0,5Di – r )2
Type
De
h2 = R – (R – r )2 – (0,5Di – r )2
Relations
Example
e
Diagrams
316 457
Type
De
Relations
h1
50
H
V
H = h1 + h2 + e
504 900 V (h2 ) = (
Di
25,4
)3 × 0,0019
31
Type
Standards
HIGH CROWN
FLANGED &
DISHED
ASME
Relations
R = 0,80De
r = 0,006De
h2 = R – (R – r )2 – (0,5Di – r )2
Example
De
e
R
r
2000 10 1600 120
h1
50
H
Standards
KLÖPPER
(large knuckle
radius)
DIN 28011
Example
e
R
r
2000 10 2000 200
h1
50
Standards
KORBOGGEN (KBB)
(small knuckle
radius)
DIN 28013
De
e
R
r
2000 10 1600 308
h1
50
H = h1 + h2 + e
V (h2 ) = (
Di
25,4
)3 × 0,0016
Relations
Diagrams
R = De
r = 0,1De
h1 ≥ 3,5e
h2 = 0,1935De – 0,455e
H
V H = h1 + h2 + e
Dd = 1,1De + 1,85h1
442 776 V(h ) = 0,1 × D 3
2
i
Type
Example
V
463 758
Type
De
Diagrams
Relations
Diagrams
R = 0,8De
r = 0,154De
h1 ≥ 3e
h2 = 0,255De – 0,635e
H
V H = h1 + h2 + e
Dd = 1,16De + 2h1
564 1008 V(h ) = 0,1298 × D 3
2
i
3.3.3. Heads for tanks
The heads on storage tanks are flat and made up of several plates. They must be airtight and
be able to transfer loads into the foundations.
There are two types of heads for vertical tanks. The first is a series of rectangular plates welded
together to guarantee a flat surface below the shell. The second is made up of a ring plate on the
periphery. The outer section is circular and the inner section is a regular polygon.
The second type of heads is used for larger tanks as the loads are more evenly distributed.
Heads may be flat, sloped towards the centre of the vessel or towards the periphery. The slope
towards the centre is used to gather the deposits to the centre of the vessel. The slope towards the
periphery compensates the ground movements during compaction.
Head for vertical storage tanks
32
In some cases, it is possible to use dual heads to prevent the risk of leakage. It is also possible
to have heads supported by beams in the cases where the foundation is not continuous.
Double head with filling
Top head with plates
Double head separated by
a steel structure
Top head with striated plate
3.3.4. Head fabrication process
All heads are not manufactured in the same way. The selected process depends on the type
of head (dished, flat, cap, etc.) its size, the number (small or large series) and the manufacturer.
There are two ways of forming heads: stamping and spinning.
Stamping is a technique that is more geared towards large series of parts. It is carried out using
stamping presses equipped with special tools. A distinction is made between cold stamping and hot
stamping. Cold stamping is carried out at room temperature while in the case of hot stamping the
metal sheet is brought to a temperature of more than 800 °C. Hot stamping is recommended when
the thickness of the metal sheet used requires a more powerful action than that of the cold stamping
press in order to limit tool costs for small series.
Spinning is another method for forming dished heads that is used to obtain parts that are difficult
to fabricate with stamping.
It is the process of deforming a circular metal sheet. Spinning can be performed by hand on a
manual lathe or numerically on a CNC lathe.
When the metal sheet is deformed, either by stamping or spinning, then flanging is done to
round out the head. This is carried out according to specific standards. The edge is then machined
based on a well-defined profile. According to the requirements and fields of application, cut-outs
(openings) can be made in the head and polishing may be performed.
33
The processes that are generally used are as follows:
◗◗ Cold or hot forming (cutting, stamping, spinning, rolling, flanging, bending, hydroforming,
welding, etc.);
◗◗ Machining, particularly of the edge (reducing, plunging);
◗◗ Surface treatments, including polishing;
◗◗ Heat treatments.
Example from DVAI
FLANGED
DISHED HEADS
CUTTING
DISHING
FLANGING
EDGE MACHINING
POLISHING
SPUN DISHED
HEAD
CUTTING
SPINNING
FLANGING EDGE MACHINING POLISHING
3.4. Body or shell
The body or shell of the vessel must withstand the hydraulic pressure to which the equipment
is subjected. The body is made up of welded shells. Their thickness depends on the width of the
vessel and the position of the shell on the vessel. It is strongly recommended not to use a thinner
shell under a thicker one.
On some vessels, particularly tanks, a stiffener must be added at the top of the vessel to maintain
the roundness of the structure. Intermediate stiffeners may be required if the structure is large or
if the internal pressure is high. They guarantee stability against buckling. If the stiffeners are not
enough, the thickness of the shells must be increased.
34
Detail 1
Detail 2
Apex
angle
Tank
interior
Tank
interior
Stiffener
Shell
Shell
Gusset
Example of vertical tank with shells and stiffeners
3.5. Roof for vertical tanks
The roof of a vertical tank must be one of the following types:
◗◗ 1) Floating roof: The roof floats above the liquid inside the tank and is in contact with the
surface. It may be equipped with removable or fixed legs. The roof is only on legs during
the maintenance and inspection operations.
External floating roof
Floating roof
◗◗ 2) Fixed roof:
◗◗ a) A supported conical roof is one that is mainly supported by rafters, beams and a
framework on columns. The roof plates are welded to each other and to the top stiffener;
however they are never welded to the framework.
35
◗◗ b) A self-supported conical roof or dome has a surface that is similar to a cone or a
sphere, but is only supported on the periphery of the tank.
◗◗ c) A geodesic roof is formed by aluminium triangles covered with plates representing
the surface of a sphere.
Framework with legs
Self-supporting
frameworks
Types of roofs
4.
Equipment and accessories
4.1. Equipment on the shell
4.1.1. Nozzle
A nozzle is used to attach a tube to control the direction
and the characteristics of the liquid flow. It must be placed at
a certain distance from other equipment on the shell.
Nozzles are designed for various uses. They can serve to
drain the products from the vessel for maintenance or cleaning.
An alternative to this system is pumping the contaminated
product at the centre of the vessel. By adding a valve, the nozzle
can be used to take samples of the product.
The nozzle is normally made up of a flange and a pipe; in
some cases, it is preferable to add gussets or a reinforcement
sheet.
4.1.2. Internal diffuser
Internal diffusers enable the outlet or inlet of a product.
They increase the length of the pipe to allow better diffusion or
suction of the product. There are typical diffusers: Y-shaped,
with vortex breaker, or clarinet-type diffusers. Clarinets have
holes along the pipe for better dispersion.
4.1.3. Manhole
A manhole is a hole in the shell with a removable cover through which a person
can enter the vessel. It is an access way for maintenance and inspection inside
the vessel. The main manhole must be accessible from the ground.
36
4.1.4. Ventilation
On some vessels, in-breathing and out-breathing vents allow air to leave or enter the vessel.
They are dimensioned to ensure proper ventilation during filling or draining operations. They may
be supplemented by filters to retain odours or certain gases.
Vessels that are fitted with a roof may have goose necks to ventilate the structure. Vents may
also be combined with manholes on the roof.
An emergency vent is provided in addition to typical vents.
4.1.5. Identification plate
An identification plate must be affixed. It must state the different information of the vessel
including: manufacturer’s name, owner’s name, pressure of the equipment, temperature, etc.
In general, it is located above the main manhole.
4.2. Auxiliary components
4.2.1. Platform
A platform allows personnel to securely access the vessel. It may be placed at various altitudes
and must have a guard rail as well as a ramp.
4.2.2. Helical staircase
A helical staircase allows access to the top level of a vessel. It features a platform at the apex
and intermediate platforms depending on the height of the vessel. The platforms and walkways are
secured to supports welded onto the shell. The steps are removable and are not welded to the shell.
4.2.3. Safety ladder
A safety ladder is only used in case of emergency. It is a mandatory component on isolated vessels.
An intermediate platform may be added if the vessel is very high. The base platform is on a flat surface.
There may be one safety ladder for several vessels connected between them by walkways.
4.2.4. Walkways
Walkways allow access from one vessel to the other or make it possible to go across a storage
tank. They must be fitted with guard rails.
4.3. Electrical and fire protection
4.3.1. Grounding
Grounding is used to protect against lightning and sparks. Grounding
plates are welded to the vessel then connected to the ground. This safety
system is found on most vessels.
4.3.2. Lightning protection
It is mandatory to protect the vessels against lightning. The minimum
thickness of the plates is 5 mm to prevent the plate from being pierced
through upon impact from lightning.
37
4.3.3. Foam box
Foam boxes are used to prevent the risk of fire and can be accessed by the operators from a
platform. The number of boxes and their capacity depends on the size of the vessel.
4.3.4. Foam barrier
The foam barrier is designed to keep the foam on the periphery of the vessel.
4.3.5. Foam deflector
In the event of a fire, the foam deflector directly channels the foam to the entire periphery of
the vessel.
4.3.6. Cooling ring
In the event of a fire, the cooling ring is designed to discharge the foam immediately over the
entire periphery of the vessel.
4.4. Inspection instruments
All vessels are equipped with inspection instruments. They are more or less relevant depending
on the function of the vessel. The location of these instruments must not disturb the components
of the structure.
4.4.1. Phased array temperature probe
A phased-array temperature probe is installed on most vessels. It is easily accessible. It is used
to check the temperature of the product inside the vessel.
4.4.2. Level alarm
A level alarm is used to detect the quantity of product. Two alarms may be installed, the first
for a high level and the second for a very high level. They must be easily accessible by an operator.
Two technologies are often used: a sensor or a vibrating fork sensor.
4.4.3. Atmosphere controller
An atmosphere controller may be useful to check the nature or the pressure of gases above
the product.
4.4.4. Level gauge
A mechanical or automatic gauge is used to check the level of product in the vessel at any time.
It must be visible from the ground. A transmitter can transmit the level to a control room.
A remote gauge is one that is connected to a system to warn if the level is too high or too low.
4.5. Flanges
Connecting flanges are critical when designing the pressure resistance of the equipment or the
piping. The higher the service pressure, the thicker the flanges needed and the higher the number
of bolts. The pressure resistance decreases when the temperature increases. There are several
flange classes depending on their pressure resistance.
38
According to European designation, the name of a flange is composed of “PN” (nominal pressure)
followed by a number that approximately matches the maximum pressure of use in bar at ambient
temperature.
In English speaking countries, their name is composed of a pressure value in psi (Pound per
Square Inch). In the most recent versions of American standards, the pressure is no longer directly
referred to in their name. Therefore, the 150 lbs class has become the Class 150.
Connecting tubes were firstly standardised by the American industry in the 1920s by ASA
(American Standards Association). The first version of the B16.5 standard, which describes flange
connections, was published in 1953 by the ASA. In 1976, the ASA became ANSI (American National
Standards Institute) then, in 1982, the revision of this standard was entrusted to the ASME (American
Society of Mechanical Engineers). Since the first publication in 1953, the B16.5 standard has undergone many different revisions known under the names ASA B16.5, ANSI B16.5 or ASME B16.5.
In Europe, the most commonly used flanges were defined by German standards DIN 25xx and
British standard BS4504. A European transposition of American standards produced the EN 1759‑1
standard for “Class”-designated flanges. However, class 400 is absent from the standard. Standard
EN 1092‑1 describes PN-designated European flanges, which do not have an equivalent in the
American standards. Standard ISO 7005, transposed in France by NF E 29‑203, aims to provide an
overview by summarising the low pressure series of European flanges and high pressure classes
of American flanges.
The European classes that are equivalent to ASME classes are often designated by ISO PN xxx
to differentiate between PN classes that do not have an ASME equivalent. This is especially useful
to avoid any confusion for PN 100 and PN 250 series whose definitions, based on EN 1759‑1 and
EN 1092‑1, are different and not compatible.
There are a number of equivalences between European and American standards.
4.5.1. Types
Standard NF 1092‑1 is the first part of a set of four standards pertaining to PN-designated
flanges made from various materials. It specifies the requirements for circular steel flanges with
designations PN 2.5 to PN 400 and nominal diameters DN 10 to DN 4000. Standard NF 1092‑1 establishes the types of flanges and their facings, dimensions, tolerances, threads, bolt dimensions, the
surface conditions of the flange facings, marking, materials, pressure / temperature relationship
and the approximate weight of the flanges.
39
Types of flanges without collar (NF 1092‑1)
Types of flanges with collar (NF 1092‑1) (Welding neck flange)
40
Types of collars (EN 1092‑1) (Welding neck)
41
Types of flanges (EN 1759‑1)
Types 14 and 15 of standard EN 1759‑1 are not included in standard EN 1092‑1. The other types
of standard EN 1759‑1 are also included in standard EN 1092‑1.
Types 01 and 05 cover flanges which do not feature a collar or a weld neck.
Types 11 to 15 cover flanges which feature a collar or a weld neck and are manufactured by
forging or moulding.
Type 21 is integral to another item of equipment or component.
42
4.5.2. Flange face
Standard NF 1092‑1 also specifies the various flange faces that can be used depending on their
application.
Flange facing types (EN 1092‑1)
Jointing faces
– B1: Standard facing for all PN numbers.
– B2: only if agreed between the purchaser and the flange manufacturer (smoother surface finish
for jointing faces).
43
Standard EN 1759‑1 features the same types of faces. However, it also proposes type J, ring
joint face.
Type J, ring joint face
Flanges may be secured using bolts or directly welded onto the pipes. Most common flanges
are slip on type with a shoulder, while blind flanges are used to close piping systems. The class or
the PN and the nominal diameter are given on the outside diameter of the flange specifications.
Flanges can also be used to reduce the diameter of the piping.
Gasketed circular flange connections specified in EN 1092‑1 are dimensioned based on the
calculation method in standard EN 1591‑1.
4.5.3. Flanges for tanks
The flanges used for tanks stem from different standards:
◗◗ The first standard is based on ISO PN 20 flanges or class 150 flanges. It is based on ASME
B16.5 and B16.47.
◗◗ The second is based on PN 10 flanges defined in standards EN 1092 and is used for
manholes.
◗◗ The third is defined by construction codes for roof manholes.
4.6. Gaskets
“Class”-designated flanges, i.e. those specified in EN 1759 standard, which are the European
equivalent of ASME B16.5 and ASME B16.47 standards, feature the gaskets described in standard
NF EN 12560‑1 to 7. As for “PN”-designated flanges specified in NF EN 1092‑1, their gaskets are
described in standards EN 1514‑1 to 8.
The titles of the 7 parts of standard NF EN 12560‑1 to 7, for “Class”-designated flanges, provide
information about the materials and shapes of the gaskets:
◗◗ NF EN 12560‑1: Non-metallic flat gaskets with or without inserts.
◗◗ NF EN 12560‑2: Spiral wound gaskets for use with steel flanges.
◗◗ NF EN 12560‑3: Non-metallic PTFE envelope gaskets.
◗◗ NF EN 12560‑4: Corrugated, flat or grooved metallic and filled metallic gaskets for use
with steel flanges.
◗◗ NF EN 12560‑5: Metallic ring joint gaskets for use with steel flanges.
◗◗ NF EN 12560‑6: Covered serrated metal gaskets for use with steel flanges.
◗◗ NF EN 12560‑7: Covered metal jacketed gaskets for use with steel flanges.
44
Standard EN 1514‑1 to 8 uses almost the same titles but apply to “PN”-designated flanges.
◗◗ NF EN 1514‑1: Non-metallic flat gaskets with or without inserts.
◗◗ NF EN 1514‑2: Spiral wound gaskets for use with steel flanges.
◗◗ NF EN 1514‑3: Non-metallic PTFE envelope gaskets.
◗◗ NF EN 1514‑4: Corrugated, flat or grooved metallic and filled metallic gaskets for use
with steel flanges.
◗◗ NF EN 1514‑6: Covered serrated metal gaskets for use with steel flanges.
◗◗ NF EN 1514‑7: Covered metallic jacketed gaskets for use with steel flanges.
◗◗ NF EN 1514‑8: Polymeric O-ring gaskets for grooved flanges (types G and H).
Therefore, gaskets can be metallic, covered metallic, metal jacketed, non-metallic, non-metallic
PTFE envelope, polymeric, etc.
They may be flat, spiral wound, grooved, corrugated, ring, O-ring shaped, etc.
The following table proposes an overview of the various shapes of gaskets.
Types of gaskets covered by the rules
Types of gaskets covered by the rules
Non-metallic flat gaskets
– Without envelope
– With non-metallic envelope
Metal jacketed flat gaskets
– Non corrugated
– Corrugated
– Spiral wound
Metallic flat gaskets
– Smooth
– Grooved
– Corrugated with or without filling
Full-faced metallic ring joint gaskets
45
Standard 12560 covers all the gaskets required for constructing vessels and their piping, depending on the flange and its facing:
Types of flat gaskets depending on the flange facing (EN 12560‑1)
46
Types of spiral wound gaskets depending on the flange facing (EN 12560-2)
a) Type C/I
b) Type C/O
Designs with spiral wound gaskets
a. Sealing element with centring ring and inner ring (designation: C/I)
b. Sealing element with centring ring (designation: C/O)
The type C/I and C/O gaskets are for type A or B flanges as per standard EN 1759-1.
Types of ring joint gaskets for type J flanges (EN 12560-5)
a) Oval type
b) Octagonal type
Gasket with oval or octagonal core section
Covered serrated metal gasket types (EN 12560-6)
Type NR
Type IR
Type LR
Type NR: Sealing element without any location ring (only used with spigot faced or tongue and groove faced flanges).
Type IR: Sealing element with integral location ring.
Type LR: Sealing element with loose location ring.
Covered metal jacketed gasket types (EN 12560-7)
Type SC: Sealing element with self-centring (used with type C/D or E/F flange facings).
Type C/I: Sealing element with inner ring (used with type C/D or E/F flange facings).
Type C/O: Sealing element with centring ring (used with type A or B flange facings).
Type C/IO: Sealing element with centring ring and inner ring (used with type A or B flange facings).
47
4.7. Bolting
The bolting for flanges is codified for standard EN 1515 which consists of 4 parts:
◗◗ NF EN 1515‑1: Flanges and their joints – Bolting – Part 1: Selection of bolting.
◗◗ NF EN 1515‑2: Flanges and their joints – Bolting – Part 2: Classification of bolt materials
for steel flanges, PN-designated.
◗◗ NF EN 1515‑3: Flanges and their joints – Bolting – Part 3: Classification of bolt materials
for steel flanges, Class-designated.
◗◗ NF EN 1515‑4: Flanges and their joints – Bolting – Part 4: Selection of bolting for equip-
ment subject to the Pressure Equipment Directive 97/23/EC.
European standard EN 1515 is applicable to the selection of bolting for PN-designated flanges
in accordance with EN 1092 series and Class-designated flanges in accordance with EN 1759 1
series, but is not for general purpose use.
It specifies standards for dimensions, materials and technical conditions of delivery for bolts,
stud bolts and nuts.
The selection of materials is based on commonly used materials. It covers all pressure and
temperature ranges of the general service of standard flanges. For special application, other
materials may be selected by the user.
The bolting must be selected by the user depending on the pressure, temperature, flange
material and gasket material. For junctions comprising at least one grey cast iron flange, it is
recommended to use bolting whose yield strength does not exceed 240 N/mm2.
The selection of bolting types (bolts, nuts, stud bolts) given in the following table is based on
the material or the property class. It is necessary that all other service conditions, such as fluids,
are taken into account by the user of this standard EN 15145.
Types of bolting based on the material (EN 1515‑1)
Dimensional standard
Bolts, stud bolts
Nuts
Material
or property class
Remarks
EN 24016
EN 24034
4.6/5
5.6/5
6.8/5
Hexagon head bolt
EN 24014
EN 24032
EN 24033 1)
All
Hexagon head bolt
Annex A of this
standard
EN 24032
EN 24033 1)
All
Stud bolt,
Threaded full length
1) Nuts in accordance with EN 24033 are normally used for industrial plants.
For sizes greater than or equal to M39, nuts with m = d are recommended.
Type of bolting based on the type of gasket, material and temperature (EN 1515‑1)
48
49
– 10 to 120
– 10 to 300
– 10 to 300
– 10 to 300
– 10 to 450
– 10 to 450
– 60 to 400
– 100 to 450
– 40 to 300
– 10 to 500
– 10 to 500
– 10 to 540
– 10 to 600
PN 40 1)
Cl. 300
PN 40 1)
Cl. 300
PN 40 1)
Cl. 300
All
All
All
All
All
All
All
All
All
Temperature
range °C
PN 40
Cl. 300
PN or Class
up to
0.2C-1Cr-1Mo-V-Ti-B
0.21C-1.3Cr-0.7Mo-V
0.40C-1Cr-0.6Mo-V
0.42C-1.3Cr-0,6Mo
0.3C-2Cr-Ni-Mo
0.42C-1Cr-Mo
0.25C-1Cr-Mo
0.42C-1Cr-Mo
0.25C-1Cr-Mo
C-St
C-St
C-St
C-St
Bolts
A2‑50, A2‑70
EN ISO 3506‑2
42CrMo4 1.7225
EN 10269
42CrMo4 1.7225
EN 10269
42CrMo4 1.7225
EN 10269
42CrMo4 1.7225
EN 10269
21CrMoV5‑7 1.7709
EN 10269
20CrMoVTiB4‑10
EN 10269
25CrMo4 1.7218
EN 10269
42CrMo4 1.7225
EN 10269
30CrNiMo8 1.6580
EN 10269
42CrMo5‑6
EN 10269
40CrMoV4‑6 1.7711
EN 10269
21CrMoV5‑7 1.7709
EN 10269
20CrMoVTiB4‑10
EN 10269
0.2C-1Cr-1Mo-VTi-B
0.21C-1.3Cr-0.7Mo-V
0.42C-1Cr-Mo
0.42C-1Cr-Mo
0.42C-1Cr-Mo
0.42C-1Cr-Mo
18Cr-9Ni
C45E 1.1191
EN 10269
42CrMo4 1.7225
EN 10269
C-St
elev. temp.
C35E 1.1181
EN 10269
25CrMo4 1.7218
EN 10269
8 - EN 20898‑2
6 - EN 20898‑2
5 - EN 20898‑2
5 - EN 20898‑2
Nuts
C-St
elev. temp.
6.8 - EN 20898‑1
5.6 - EN 20898‑1
4.6 - EN 20898‑1
Bolts
8.8 - EN 20898‑1
Nuts
C-St
C-St
C-St
C-St
Type of material
Steel designation name or property class
Steel designation No.
Material standard
50
– 200 to 550
– 10 to 550
– 200 to 400
– 200 to 400
– 200 to 400
– 200 to 400
– 200 to 550
– 200 to 200 2)
– 200 to 550
– 200 to 200 2)
All
PN 40
Cl. 300
PN 100
Cl. 600
PN 40
Cl. 300
PN 100
Cl. 600
PN 40
Cl. 300
PN 100
Cl. 600
PN 40
Cl. 300
PN 100
Cl. 600
Temperature
range °C
All
PN or Class
up to
18Cr-10NiAT+C
18Cr-10Ni
17Cr-12Ni-2MoAT+C
17Cr-12Ni-2Mo
18Cr-9Ni
18Cr-9Ni
18Cr-9Ni-Mo
18Cr-9Ni-Mo
16Cr-16Ni-Mo-BNb
25Ni-15Cr-0.2TiMo-V-B
Bolts
Nuts
18Cr-10Ni
18Cr-10Ni
17Cr-12Ni-2Mo
17Cr-12Ni-2Mo
18Cr-9Ni
18Cr-9Ni
18Cr-9Ni-Mo
18Cr-9Ni-Mo
16Cr-16Ni-Mo-BNb
25Ni-15Cr-0.2TiMo-V-B
Type of material
X7CrNiMoBNb16‑16
1.4986
EN 10269
X7CrNiMoBNb16‑16
1.4986
EN 10269
A2‑70
EN ISO 3506‑2
X5CrNiMo17‑12‑2
1.4401
EN 10269
X5CrNiMo17‑12‑2
1.4401
EN 10269
X5CrNi18‑10
1.4301
EN 10269
X5CrNi18‑10
1.4301
EN 10269
X5CrNiMo17‑12‑2
1.4401
EN 10269
X5CrNiMo17‑12‑2
AT+C
1.4401
EN 10269
X5CrNi18‑10
1.4301
EN 10269
X5CrNi18‑10AT+C
1.4301
EN 10269
A2‑50
EN ISO 3506‑2
A4‑70
EN ISO 3506‑2
A2‑70
EN ISO 3506‑1
A2‑50
EN ISO 3506‑1
A4‑70
EN ISO 3506‑1
A4‑50
EN ISO 3506‑2
X6NiCrTiMoVB
25‑15‑2
1.4980
EN 10269
X6NiCrTiMoVB
25‑15‑2
1.4980
EN 10269
A4‑50
EN ISO 3506‑1
Nuts
Bolts
Steel designation name or property class
Steel designation No.
Material standard
Stud bolts shall be threaded full length. The points shall be chamfered or rounded at the manufacturer’s option. The height of point shall be a maximum one times the pitch of the thread.
The length of stud bolts has to be measured including points. The lengths are stepped by increments of 5 mm for lengths up to 80 mm, by increments of 10 mm for lengths above 80 mm and up
to 200 mm, and by increments of 20 mm for lengths above 200 mm.
Threads in accordance with ISO 261 and ISO 965‑2 are tolerance class 6 g. Type of thread is
either coarse thread or, above M39, fine thread with 4 mm pitch.
The type of thread shall be selected by the user.
Fine thread above M39 is normally used for industrial plants, coarse thread up to and including
M64 is normally used for water service.
5.
Definitions
In the previous chapter, all components of a vessel were outlined. When dimensioning a pressure
vessel, the goal is to calculate the state of stress in each point, then checking that the stress intensity does not exceed a critical value in any point. This process is often impossible if the calculations
are carried out manually. Therefore, finite element calculation makes it possible to determine the
stress state in each point.
This guide offers a simple solution. It helps to calculate the state of stress at different places
of the equipment using Strength of Materials. The basic principles are outlined in the following
chapters.
5.1. Main terms
Load
The physical meaning of load is similar to stress. The load may be mechanical (newton or
newton-metre), electrical (charge expressed in coulomb) or thermal (°C). It involves external actions
to the studied system which have an influence on this system.
Force applied to the component
The forces in newton or newton-metre applied to a component make up a part of what is called the
boundary conditions of the system. They therefore apply to the limits of the studied part or system.
Force
A force is expressed in newton or newton-metre. It can be the result of a weight (kg) under the
action of gravity (1 g = 9.81 m/s2). It may also stem from the action of one component on another,
at the boundary conditions.
Allowable load
The allowable load is the limit load that can be accepted by a system. The value of this limit is
often set by a standard. Beyond this threshold value, the system no longer conforms to the standard
and its integrity is no longer guaranteed. Often, in mechanical engineering, the term “allowable
stress” (N/mm2 or MPa) is used which is a percentage of the yield strength of the material “Re”.
Stress
Stress is similar to load; it is an action external to a system which influences the system. Stress
may be mechanical, electrical, chemical, thermal, frequential, etc.
51
5.2. Tensile tests
Uniaxial tension of a long bar
The tensile test usually highlights three main stages in the behavioural development of a metallic material:
◗◗ An elastic behaviour, whether linear or not, where there is no residual deformation after
unloading.
◗◗ A pure plastic deformation stage with strain hardening characterised by irreversible resi-
dual strain after unloading; the entire behaviour is fully independent of time, particularly
the rate of loading.
◗◗ A damaging step leading to failure. Damaging is demonstrated by the gradual alteration
of the mechanical properties which is usually combined with rather significant deformations
or the formation and growth of microcracks and micro-cavities; this alteration may extend
to failure.
Stress-strain relation - Elastic and plastic regions
52
PRINCIPLE
TENSILE TEST
A standard specimen is subjected to a gradual tensile force usually up to failure
to determine the toughness and elasticity of the material and to identify its properties
(yield stress, elongation at break).
Round specimen
SPECIMENS
SQ =
πd
4
2
Flat specimen
SO = a b where
where d > 4
b
<8
a
A gauge length l0 (mm) and cross-sectional area S0 (mm)
shall be determined between two grips.
DETERMINED PROPERTIES
BEHAVIOUR OF THE METAL
DURING THE TEST
l0 = 5,65 S0
Elongation (mm)
Yield stress Re
Re (MPa) =
Tensile
strength Rm
Rm (MPa) =
Longitudinal
modulus of
elasticity
SAFETY
FACTOR K
Elongation Δl
(Hooke’s law)
E (MPa) =
Fe
Elastic strain ➀; force Fe
◗ Elongation is proportional to the force Fe.
◗ If the applied load is removed, the
specimen returns to its original size.
Permanent set ➁; force Fm
◗ The elongation is no longer proportional
to the force Fm.
◗ If the applied load is removed, the
deformation remains.
Reduction of area to failure: force Fu
◗ The force decreases, as a reduction of
area occurs in a point of the gauge length.
◗ The initial length l0 become lu after fracture.
Elongation (A)
SO
Coefficient
of reduction
of area Σ
Fm
SO
Fe lO
SO
l
For steels:
E = 210,000 MPa
Δl = Δlu – Δl0
Proof strength
Rpe
A (%) =
Σ (%) =
lu – lO
lO
SO – Su
SO
× 100
× 100
Used for Strength of
Materials calculations,
this is an empirical value
such that Rpe (MPa) =
K = safety factor
1.5 < K < 15
Unit elongation
εx
x
=
Re
K
l
lO
The allowable tensile stress which a mechanical part can undergo must be less than
the yield strength.
The nature of the force to which the part is subjected is involved in the selection of K.
In conclusion, K depends on the material (elasticity) and the use of the part (stresses).
53
6.
SoM assumptions
Strength of Materials is the study of the strength and strain of solids. Its aim is to determine or
to check the transverse dimensions so that solids withstand the loads imposed under satisfactory
conditions of safety.
6.1. Materials
To simplify the calculations and the analysis, materials are considered as homogenous, that is
to say their mechanical properties are the same in all points.
In addition, it is assumed that the materials are isotropic. They have the same mechanical problems in a single point, in all directions. Isotropy is not verified for fibrous steel such as laminated
and forged steels.
6.2. Geometry
Ideal solids are beams with:
◗◗ Constant straight sections or sections which slowly vary in size and shape;
◗◗ Significant longitudinal dimensions with respect to the transverse dimensions.
Definition of a beam: it is generated by a flat cross-section (S) where the centre of gravity travels
on a curved line (C), with large bend radius, called the mean line. The cross-section (S) remains
perpendicular to (C).
6.3. Forces
The forces applied in a point, are pointers. They cannot be replaced with a “vectorially” equivalent
system of forces as the physical effects are different.
In the first example, if the two forces A and B slide from their support, the tension becomes
compression.
Tension
Compression
In the second example, the resultant of the force 2F causes a deflection (displacement) which
is more significant than the two forces F in D and E.
54
6.4. Contacts
Point contacts cause concentrated loads which are modelled by pointers (A, F ).
The linear (or surface) contacts cause distributed elementary loads that are modelled by ­pointers
(Mi , dfl ) and applied on the elementarys length dl (or on the elementary surfaces dS).
df
The following is defined: p =
where p is the linear load factor, df the elementary force applied
dl
to dl and dl the elementary length.
In SoM, it is prohibited to replace distributed loads with their resultant.
7.
Stresses and strains
7.1. Stress/Strain relation
Internal forces occur in all points of a body subjected to external forces. When this body is in
static equilibrium with the system of external forces, the distances between the points are altered.
To explain the concept of stress and strain, we will study the case of a tensile test on a round
specimen. During the tensile test, an axial force is applied to the ends of a cylinder of diameter
d. On a cross section of the specimen, each surface unit is subjected to an elementary stress
F 4F
equal to σ = = 2
S πd
All of these stresses, on the cross-section, balance out the external force F.
Under the action of the force F, the specimen is elongated. A basic distance l0 between two points
l
of the unloaded specimen becomes l0 + Δl after tensioning. The strain is defined by the ratio: =
lO
For materials such as steels, it can be noted that as long as the stress remains less than
a certain limit, referred to as the “proportional limit”, also called the “yield strength”, we obtain
the following relation:
σ=E·ε
It is Hooke’s law in uniaxial tension, where:
σ: The stress, in N/mm2 or MPa
E: Young’s modulus also called modulus of elasticity, in MPa
ε: The strain, which does not have any unit
7.2. Concept of stresses
In Strength of Materials, a mechanical stress is a force divided by a surface area; it is therefore
homogenous to a pressure. It is often expressed in N/mm2 or MPa. In the case of bending and torsion, the stress is a moment divided by the bending modulus or torsion modulus. In general, the
moment is expressed in N.m or N.mm, the bending or torsion moduli in mm3. The quotient of the
division is a pressure.
55
7.2.1. Normal and tangential stress
Normal stress (σ) results from a tensile-compressive force applied perpendicular to the crosssectional area of the object under tension. The stress is therefore perpendicular to this cross-section.
Normal stress (tension) (Source: Wikipedia)
Upon pure bending (bending torque in a beam), normal stress occurs.
Refer to the figure below:
Normal stress (bending) (Source: Wikipedia)
Tangential stress (τ), more commonly known as “shear stress”, results from a shear force.
It corresponds to a force on the surface tangential to the cross-sectional area of the object. The
stress is therefore parallel to this cross-section.
56
Upon torsion (torque on a beam), shear stress occurs.
Refer to the figure below:
Torsional deformation (Source: Wikipedia)
Torsional shear stress (Source: Wikipedia)
57
7.2.2. Principal stresses
To properly understand principal stresses, we firstly need to understand the notation of a stress
tensor.
In an object, let us take point M and around this point, a small cube of material with very small
side denoted by “a”. Let us place this cube in an orthonormal coordinate system (e1, e2, e3) or (x, y, z)
collinear to the faces of this cube. We obtain the following representation:
We will number the faces so that faces j and –j are normal (perpendicular) to the vector ej of the
coordinate system.
Let us take face j and any force “F” applied to this face. It is possible to break down this force in
the coordinate system (e1, e2, e3) so that:
F1j
Fj =
F2 j
F3 j
Fij is the component according to ei of the force vector being applied to face j. The surface area
of each face is a2, and therefore we can define nine components σij homogenous to the stresses:
ij
58
=
Fij
a2
T(M) =
11
12
13
21
22
23
31
32
33
Where σ11, σ22, σ33 are the normal stresses (perpendicular) on faces 1, 2 and respectively 3.
The others are shear stresses. In the coordinate system (x, y, z), we have the stress tensor:
xx
xy
xz
yx
yy
yz
zx
zy
zz
T(M) =
The eigenvalues of the matrix above are the principal stresses, and the eigenvectors are the
principal directions.
To determine the principal stresses, we can simplify the tensor seen above. Indeed, in statics,
to achieve the equilibrium of movements, we have σij = σji. The tensor is thus a symmetrical square
matrix. This matrix is therefore diagonalisable.
There is an orthonormal base (x1, x2, x3) for which this matrix is a diagonal matrix.
The directions x1, x2 and x3 are the principal directions. The tensor becomes:
I
T=
0
0
0
II
0
0
0
III
The principal stresses are σI, σII and σIII. In addition, the maximum shear is:
{
1
τmax = max | σI – σII|;| σII – σIII|;| σIII – σI
2
}
7.3. Mohr’s circle
Mohr’s circle is a graphical representation of the state of stress in a point of an object. In an
object, let us consider a point M, then let us cut the object, where the section passes through this
point M. Regardless of the stress running through this section, it can be broken down into a normal
stress (perpendicular) to the section and into 2 shear stresses tangential to the section. Let us
vary the angle of the section passing through point M, the normal stress and the shear stresses
therefore vary accordingly.
59
Case of uniaxial stress in pure tension:
The following figures show the Mohr’s circle for uniaxial stress (simple tension or pure bending):
Mohr’s circle for simple tension (uniaxial) in a plane problem (Source: Wikipedia)
60
The horizontal axis shows the variation in the normal stress and the vertical axis shows the
variation in the shear stress.
Let us reconstruct the Mohr’s circle for the simple tension in a cylindrical specimen with the
following data:
Fx (N)
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
Angle of the section Radius
Radius
with X (deg)
R0 (mm) R1 (mm)
0.1
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
179.9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
572.96
11.47
5.76
3.86
2.92
2.37
2.00
1.74
1.56
1.41
1.31
1.22
1.15
1.10
1.06
1.04
1.02
1.00
1.00
1.00
1.02
1.04
1.06
1.10
1.15
1.22
1.31
1.41
1.56
1.74
2.00
2.37
2.92
3.86
5.76
11.47
572.96
Sectional
area (mm2)
1,800.00
36.05
18.09
12.14
9.19
7.43
6.28
5.48
4.89
4.44
4.10
3.84
3.63
3.47
3.34
3.25
3.19
3.15
3.14
3.15
3.19
3.25
3.34
3.47
3.63
3.84
4.10
4.44
4.89
5.48
6.28
7.43
9.19
12.14
18.09
36.05
1,800.00
Normal
Shear
stress (MPa) stress (MPa)
0.00
2.42
9.60
21.32
37.24
56.85
79.58
104.72
131.52
159.15
186.79
213.59
238.73
261.46
281.07
296.99
308.71
315.89
318.31
315.89
308.71
296.99
281.07
261.46
238.73
213.59
186.79
159.15
131.52
104.72
79.58
56.85
37.24
21.32
9.60
2.42
0.00
0.56
27.64
54.43
79.58
102.30
121.92
137.83
149.56
156.74
159.15
156.74
149.56
137.83
121.92
102.30
79.58
54.43
27.64
0.00
– 27.64
– 54.43
– 79.58
– 102.30
– 121.92
– 137.83
– 149.56
– 156.74
– 159.15
– 156.74
– 149.56
– 137.83
– 121.92
– 102.30
– 79.58
– 54.43
– 27.64
– 0.56
61
We obtain the following plot:
Mohr’s circle
The intersections between the circle and the horizontal axis give the 2 principal stresses which
are σI = 0 MPa (angle of the section of 0°) and σII = 318 MPa (angle of 90°).
We also note that the shear stress (tangential stress) is maximum for a section at 45°, which
explains the fracture surface at a 45° angle of the tensile specimens. Indeed, ductile materials are
always subject to shear fracture: the force required to “tear” the atoms is much more significant
than that needed to slide the atoms one after the other.
Fracture at 45° of an aluminium specimen
62
Case of uniaxial stress in pure shear:
The following figures present the Mohr’s circle for uniaxial stress (torsion or pure shear):
The shear is maximum and the normal stress is zero for a section directed at 90°.
63
Biaxial case in the plane (tension in two directions):
This case can be illustrated by a small component on the surface of a pressure tank.
The following figure shows the Mohr’s circle in this case:
For a 90° angle with Ox:
◗◗ The normal stress is σx, the shear stress is zero.
For a 90° angle with Oy (0° or 180° with Ox):
◗◗ The normal stress is σy, the shear stress is zero.
64
General case for plane stresses:
The following figure shows the Mohr’s circle in the general case of a 2d stress tensor (plane
stresses):
x
=
xy
y
0
0
0
Where:
◗◗ σx: Normal stress on the face normal to the x axis
◗◗ σy: Normal stress on the face normal to the y axis
◗◗ τxy: Shear stress on the face normal to the z axis
The tensor shown above allows us to easily determine the points A and B on the circle. The centre
of the circle is the intersection of segment AB and the horizontal axis.
65
General case for triaxial stresses (in the 3 dimensions):
The stress tensor has the following shape:
x
xy
xz
y
yz
=
z
This matrix can be diagonalised. The three terms of the diagonal matrix are the eigenvalues
of the tensor above. These three terms are also the principal stresses. We therefore obtain the
following tensor:
I
=
0
0
0
II
III
We write this tensor of the principal stresses in a coordinate system x, y and z directed along
the principal directions. We obtain:
x
=
0
0
0
y
z

We pose σx ≥ σy ≥ σz. If we consider a surface of normal and unit vector n(nx , ny , nz ), then the
vector of the stresses is:
n
x x
Tn =
n=
y
ny
n
z z
The normal stress is:
The shear stress is:
σ (n) = n ⋅ Tn = n ⋅ σ ⋅ n = σ x nx2 + σ y n2y + σ z nz2
|| T(n)||2 = σ 2 (n) + τ 2 (n) soit σ 2x nx2 + σ 2y n2y + σ 2z nz2 = σ 2 + τ 2

In addition, the vector n(nx , ny , nz ) is a unit vector, we have a system of three equations with three
unknowns nx², ny², nz²:
nx2 + n2y + nz2 = 1
σ x nx2 + σ y n2y + σ z nz2 + σ z nz2 = σ
σ 2x nx2 + σ 2y n2y + σ 2z nz2 = σ 2 + τ2
66
The solution of the system is:
2
x
n =
2
y
τ2 + (σ – σ y )(σ – σ z )
(σ x – σ y )(σ x – σ z )
n =–
2
z
n =
τ2 + (σ – σ z )(σ – σ x )
(σ x – σ y (σ y – σ z )
τ2 + (σ – σ x )(σ – σ y )
(σ x – σ y )(σ z – σ y )

When the vector n(nx , ny , nz ) rotates, the values of n²i sweep the normal space width [0;1]. We infer
three inequations:
τ2 + (σ – Cx )2 ≥ R2x
τ2 + (σ – Cy )2 ≤ R2y
τ2 + (σ – Cz )2 ≥ R2z
Where
◗◗ Cx = (σy + σz)/2, Rx = (σy - σz)/2
◗◗ Cy = (σx + σz)/2, Ry = (σx - σz)/2
◗◗ Cz = (σx + σy)/2, Rz = (σx - σy)/2
In the plane (σ, τ), the solutions to the equation τ² + (σ - Ci )2 = R²i are represented by circles of
centre Ci and radius Ri. Therefore, all of the values (σ, τ) for all possible directions of the vector “n”
is a surface delineated by three circles.
Each of the circles is the circle that would be obtained if we were within a context of biaxial
stresses (σy, σz), (σx, σz) and (σx, σy). In order to plot the tri-circle, as σx, σy and σz are known,
we therefore refer to the previous cases.
67
We note that all the circles are tangent two by two, and that the largest circle is that of radius
Ry, therefore corresponding to the plane (x, z). The maximum shear is thus:
τmax = Ry = (σx - σz )/2.
7.4. Hooke’s law
An object becomes deformed under the effect of mechanical loading in the same way as a spring
is extended if it is pulled. This is called Hooke’s law, named after physicist Robert Hooke and his
work on springs and materials.
Robert Hooke highlighted the proportionality (linear relation) between the extension of the spring
and the applied force. This relation is true to some extent.
Consider the case of a spring, we obtain the following linear relation: F = K ΔL
Where:
◗◗ F: Force applied to the spring (N)
◗◗ K: Stiffness of the spring (N/mm)
◗◗ ΔL: Elongation of the spring so that ΔL = L-L0 (mm)
Consider the case of a slender object undergoing tension, we can apply the same relation:
F = K ΔL
Where:
◗◗ F: Force applied in the slender direction of the object
◗◗ K: Stiffness of the object
◗◗ ΔL: Elongation of the object
In addition, if the initial area of the section normal to the force is known, we have the law of
elasticity: σ = E ε
Where:
◗◗ σ: The stress normal to the section (N/mm2 or MPa) so that σ = F / S0
◗◗ E: The modulus of elasticity or Young’s modulus (N/mm2 or MPa). Young’s modulus is
specific to each material
◗◗ ε: The strain or relative elongation of the part so that ε = ΔL / L0 (without unit)
This law is therefore linear up to a certain force. Beyond this threshold, the behaviour of the
material is no longer linear. Consider an engineering stress-strain curve for better understanding.
68
This curve represents the stress σ (and therefore the force) in the object depending on the
strain ε of the object.
We note a threshold, denoted Re, from which the curve is no longer linear. This threshold is
called the yield strength. It is the stress from which the deformation of the part begins to become
permanent. The yield strength is specific to each material and is expressed in MPa.
Below the yield strength (curve in blue):
◗◗ The deformation of the object is not permanent. After unloading, the object returns to its
initial shape, the strain is referred to as elastic.
◗◗ The deformation of the part is linear, in other words, the stress and the strain are directly
proportional to the force applied to the object.
◗◗ The slope of this straight line is the Young’s modulus “E”.
Above the yield strength (curve in red):
◗◗ A portion of the deformation of the object is permanent. After unloading, the object does not
fully return to its original shape, but only the portion corresponding to the elastic deformation.
The residual strain is referred to as plastic.
◗◗ The deformation of the object is not linear, the stress and the strain are no longer pro-
portional to the applied load.
◗◗ Beyond a certain threshold, denoted Rm, the curve decreases, the deformation increases
although there is not more force applied to the object. This threshold is the ultimate stress,
denoted Rm and expressed in MPa. This quantity is specific to each material.
◗◗ On the horizontal axis, we can read the notation Ag. This notation refers to the strain at
failure of the object after unloading. It is therefore the plastic (or permanent) portion of the
strain.
◗◗ On the horizontal axis, we can read the notation Agt. This notation refers to the strain at
failure of the object under load. It is therefore the total deformation, elastic deformation
and plastic deformation.
69
7.4.1. Principal strains
As previously seen for stresses, it is possible to write the strains in a point of the material in the
form of a tensor, therefore a square and symmetrical matrix of 3 x 3 dimensions.
There is an orthonormal coordinate system (x1, x2, x3) in which the strain tensor can be diagonalised. It is the same coordinate system that is used to diagonalise the stress tensor. The eigenvectors
of the strain tensor and the eigenvectors of the stress tensor are therefore identical, as they form
the orthonormal coordinate system (x1, x2, x3).
The eigenvalues of the stress tensor give the 3 principal stresses. The eigenvalues of the strain
tensor give the 3 principal strains.
As for the principal stresses, after diagonalisation of the strain tensor, we obtain the principal
strains:
0
I
E=
0
0
0
0
II
0
III
7.4.2. Compatibility equations
Compatibility equations or compatibility conditions make it possible to switch from the stress
tensor to the strain tensor and the displacement field, and vice versa.
=
=
70
1+
E
1+
E
Where:
ν = Poisson’s ratio
I = unit matrix
δij = 1 if i = j; but δij = 0 if i ≠ j
E = Young’s modulus
tr (σ ) the trace of the matrix (σ)
–
+
E
tr( ) I
1– 2
tr( )I
ij
ij
8.
Elastic and plastic regions
Refer to Chapter II, paragraph 7.4: Hooke’s law.
8.1. Strain hardening coefficient
Strain hardening is intended to increase the yield strength Re of an object by subjecting it to
plastic deformation. Consider the following engineering stress-strain curve:
Where:
◗◗ σ = F / S0, here the variation of the section is not taken into account
◗◗ ε = (L – L0) / L0
This curve represents 3 steps:
◗◗ 1. The object is loaded beyond the yield strength Re, permanent deformation occurs.
◗◗ 2. The object is unloaded, we see on the horizontal axis that it does not return to its original
shape. Plastic deformation has occurred.
◗◗ 3. If the object is loaded again, a higher stress (σ = F / S0) is required to reach the yield
strength again.
Strain hardening is often used in the industry to form profile sections or sheets made from
ductile metals. The rolling of a sheet results in its strain hardening.
71
Strain hardening on a metal sheet by rolling
Strain hardening only works on ductile metals. Cast irons cannot be strain hardened. All objects
obtained through working, i.e. by plastic deformation (rolling, wire drawing, forging), are strain
hardened. Castings are thus not strain hardened.
The capacity of the metal to be strain hardened is estimated by the strain hardening coefficient n:
during a tensile test, we plot the true stress-strain curve, that is to say the curve: σ = ƒ(ε)
Where:
◗◗
=
F F
L
=
1+
: true stress, here, the variation of the section during the tensile test
S SO
LO
is taken into account.
◗◗
= ln
L
L
= ln 1+
: the true strain.
LO
LO
When there is no viscous behaviour, this curve can be approximated by different equations,
including the following equations where “n” is the strain hardening coefficient:
◗◗ Zener-Hollomon equation: σ = k⋅εn
◗◗ Ludwig equation: σ = σ0 + k⋅εn
72
Where:
◗◗ n: strain hardening coefficient
◗◗ K: strength coefficient (MPa)
The following table provides examples of these coefficients:
Strength coefficient
K [MPa]
Strain hardening
exponent, n
Austenitic steel
400 - 500
0.40 - 0.55
Low carbon steel
525 - 575
0.20 - 0.23
HSLA (high strength low-alloy) steel
650 - 900
0.15 - 0.18
Copper
420 - 480
0.35 - 0.35
Brass 70/30
525 - 750
0.45 - 0.60
Aluminium alloys
400 - 550
0.20 - 0.30
Material
K and n can be determined by making the equations previously examined linear (straight line)
so that:
◗◗ Zener-Hollomon equation: σ = k⋅εn → ln(σ) = ln(K) + n ln(ε)
◗◗ Ludwig equation: σ = σ0 + k⋅εn → ln(σ-σ0) = ln(K) + n ln(ε)
Where:
◗◗ n: Slope coefficient of the straight line
◗◗ ln(K): Intercept point of the straight line
9.
Stress criteria
In general, when dimensioning parts or structures, there is an allowable stress that is set by a
standard as being a percentage of the yield strength Re.
When the loading is simple and in a single direction (tension, pure bending, pure torsion, etc.),
it is easy to determine whether or not the stress exceeds the yield strength.
However, if the loading leads to stresses in multiple directions, it is difficult to determine whether
or not these combined stresses exceed the yield strength.
For example, a simply supported cantilever beam (fixed at one end and with a vertical force at
the other end) is subjected to a shear force, and thus a shear stress as well as a bending moment,
and consequently a tensile-compressive stress (normal).
As discussed above, the stresses are expressed in the most general way in the form of the
following tensor, where the diagonal terms are normal stresses and the other terms are shear
stresses:
x
=
xy
xz
y
yz
z
73
We have also seen that there is a base of eigenvectors of this tensor (principal directions) which
makes it possible to diagonalise the tensor, so that the diagonal terms are the eigenvalues of the
above tensor (principal stresses):
I
=
0
II
0
0
III
The principal stresses can be combined using a number of criteria, particularly the Tresca criterion
and the Von Mises criterion.
9.1. Tresca criterion
We admit that plastic deformation occurs through shear: it is easier to slide atoms one on top
of the other. Shear stress is maximal for a plane sloped at a 45° angle with respect to the tensile
axis (see Chapter II, paragraph 7.3: Mohr’s circle).
Therefore, the Tresca criterion considers that the deformation remains elastic (not permanent)
for a stress, so that:
|σI - σII | ≤ Re and |σI - σIII | ≤ Re and |σII - σIII | ≤ Re
Or:
Max i ≠ j(|σi - σj |) ≤ Re
The plastic flow function can be written as:
ƒ(σI, σII, σIII) = Max i ≠ j(|σi - σj |) - Re
9.2. Von Mises criterion
The Von Mises criterion is an energy-based one: the elastic deformation energy is written as
follows in simple cases:
1
◗◗ Tension-compression: U = σ ε
2
1
◗◗ Shear: U = τ γ
2
1
◗◗ In general: U = σ ij εij
2
As a result, the Von Mises criterion considers that the deformation remains elastic (not permanent)
for a stress, so that:
(σI – σII)2 + (σII – σIII)2 + (σI – σIII)2 ≤ 2 R2e
Or:
1
2
(σI – σII)2 + (σII – σIII)2 + (σI – σIII)2 ≤ Re
The plastic flow function can be written as:
f (σI, σII, σIII) =
74
1
2
(σI – σII)2 + (σII – σIII)2 + (σI – σIII)2 – Re
In the case of beams that undergo bending (generating a maximum normal stress σmax) and
torsion loading (generating a maximum shear stress τmax), the criterion becomes (Huber shape):
2
2
σmax
+ 3τmax
≤ Re
Consider the case of a simply supported beam subjected to a bending load:
The maximum normal stress σmax is in B and is due to the bending moment F.L. The shear
stress τmax is the same over the entire length of the beam and is due to the force F on the section of
the beam S. In this case, we can use the Huber shape to determine the equivalent stress so that:
2
2
σ eq = σmax
+ 3τmax
The following diagram shows the limit between the elastic region and the plastic region, according to the Tresca criterion and the Von Mises criterion.
75
III Calculation methods
1.
Aim of the calculation
The aim of the calculation is to determine the size and thickness of the significant components
of the structure in order to withstand mechanical, thermal, combined or other stresses throughout
the intended service life of the system. We want to calculate the state of stress and strain at the
most critical points of the vessel.
Studying the effects of the external forces applied to the vessel in terms of stresses on the one
hand and strains on the other hand, will help to measure the strength and rigidity of the various
vessel components.
Therefore, the stress analysis will highlight the relationship between the external forces applied
and the stresses undergone as well as the relationship between the stresses and the generated
strains.
2.
Starting the calculation
2.1. Membrane stress analysis
Pressure vessels commonly have the form of spheres, cylinders, cones, or ellipsoids.
When the thickness is small in comparison to other dimensions (Rm /e ≥ 10), a simple membrane
analysis is sufficient. The stresses in the membrane are average tension or compression and possibly bending stresses.
The state of stress in a membrane is triaxial and the three principal stresses are:
◗◗ Longitudinal stress;
◗◗ Circumferential stress;
◗◗ Radial or normal stress.
Most codes are based on this type of analysis.
normal
direction
or
or
or
circumferential
direction
76
longitudinal
direction
Forces along the axis
Axial equilibrium
Membrane theory
2.2. Shell theory
A shell is a body in which one of dimensions (the thickness) is much smaller than the other two.
The middle surface of a shell is its surface at mid-thickness. This theory is also called the thin
plate theory or the Love-Kirchhoff theory.
Assumptions of the shell theory:
◗◗ The thickness is small with respect to the bend radius of the middle surface (Rm /t ≥ 10).
◗◗ The displacements are very small with respect to the thickness.
◗◗ As the thickness is very small, the normal stress is negligible, and therefore the state of
stress will be considered as biaxial.
◗◗ The sections or straight lines normal to the middle surface remain straight after loading,
we can therefore ignore the shear.
◗◗ The material is considered as homogenous, isotropic and linear elastic.
For structures with discontinuities (different diameters, sections, etc.), the state of stress is
represented by stresses on the simple forms + stresses at the discontinuities (calculation of the
stresses in a shell + calculation of the stresses at the discontinuities).
2.3. Boundary conditions and working assumptions
For any calculation method (analytical or numerical), simplifying assumptions are sometimes
made to take into account the way the outside will act on the boundaries of our system. These are
boundary conditions.
77
These conditions are primarily:
◗◗ The loadings. This may be the self-weight of the structure, internal or external pressure,
a point force, a temperature field, etc.
◗◗ The contacts or connections with the surrounding parts and structures. This may be
embedding in the ground, pivot link or ball joint connection with another structure, a
direct contact or friction with another part. These connections will induce loads in the
form of point forces or forces on a surface (pressure) at the boundaries of the system to
be studied.
The loadings external to the structure are generally expressed in Newton (N) for point forces,
N.m for moments, bar or N/m2 (pascal) for pressures. They can also be expressed using other units
such as pound of force (Lbf), foot pound force (Lbf.ft), pound force per square inch (PSI) or pound
force per square foot (Lbf.ft2).
The working assumptions also lie in the loads to be taken into account (snow, wind, lifted
or ­s upported load, etc.), the value to be considered, their occurrences and combinations or
­concomitance.
The application zone of these loads on the structure should also be factored into the a
­ ssumptions.
Some questions to be asked are: What are the principal loadings? What are the most stressed
areas?
In general, calculation codes provide answers to these points and help to determine these
assumptions.
3.
Philosophy of the codes
3.1. General
A number of codes are used in industrial boiler making - piping from design through to fabrication. These codes refer to the relevant standards of the industry (EN 12952, EN 13445, etc.) and
serve to clearly define the practices.
Amongst these, construction codes establish the design and calculation rules for each type of
vessel. These include the CODAP for pressure vessels, CODETI for industrial piping and COVAP for
steam generators.
The construction codes classify the criticality of the vessel, depending on its use, its risk of
explosion and the stresses to which it is subjected. They determine the surcharge coefficients
needed to avoid any risk. In addition, they provide formulas to determine the thicknesses of the
basic components of the vessels or to estimate the stresses. Using these codes, we can for example
determine the maximum allowable stress without carrying out complex calculations.
The main codes used for boiler making are:
◗◗ AISC: American code for the design of steel structures.
◗◗ API: American code for oil and gas equipment.
◗◗ ASME VIII: American code for pressure vessels.
◗◗ ASME X: Composite vessels and pipes.
◗◗ ASME/ANSI B16.5 and B16.47: Codes for flanges.
78
◗◗ ASME B31.3: American code - Design and manufacturing of process piping.
◗◗ CODAP 20015/CODAP 2010: French Construction Code for pressure vessels.
◗◗ CODETI Division 1: French Construction Code for industrial or factory piping.
◗◗ CODETI Division 2: French Construction Code for pipelines.
◗◗ CODETI Division 3: French Construction Code for penstocks (hydropower systems).
◗◗ CODRES Division 1: French Construction Code for cylindrical, vertical and flat-bottomed
storage tanks.
◗◗ CODRES Division 2: Maintenance recommendations for cylindrical, vertical and flat botto­
med storage tanks.
◗◗ COVAP Division 1: French Construction Code for steam generators or superheated water
boilers with smoke tubes.
◗◗ COVAP Division 2: French Construction Code for steam generators or superheated water
boilers with water tubes.
◗◗ DTU P06‑002, P06‑006: NV65, rules defining the effect on buildings of snow and wind.
◗◗ DTU P06‑013: PS92, EUROCODES 8: Earthquake design rules.
◗◗ EN 1090: Execution of steel structures and aluminium structures.
◗◗ EN 12952: Water tube boilers and auxiliary installations.
◗◗ EN 13121: Boiler making and composite piping.
◗◗ EN 13445: European standard for the construction of pressure vessels.
◗◗ EN 13480: European standard for metallic industrial piping.
◗◗ Eurocode 0: Basics of structural design (EN 1990).
◗◗ Eurocode 1: Actions on structures (EN 1991).
◗◗ Eurocode 3: Design of steel structures (EN 1993).
◗◗ Eurocode 8: Design of structures for earthquake resistance (EN 1998).
◗◗ Eurocode 9: Design of aluminium structures (EN 1999).
◗◗ GESIP: Safety, health, hygiene, environment.
◗◗ ISO 14692: GRP piping systems.
◗◗ NFT57‑900: GRP piping systems.
◗◗ RCCM: Construction Code for nuclear pressure equipment.
3.2. Problems associated with designing based on codes
Many codes cover the same topics. Therefore, it is not always easy to select the right code,
especially as this choice may depend on the company’s geographical location, business culture (oil
and gas, nuclear, etc.) or the customer’s requirements.
79
After selecting the right code, quite often, the procedure has to be followed through entirely.
This means classifying the vessel depending on its criticality in relation to its use, is risk of
explosion and the stresses to which the vessel is subjected. Then, the right safety factors and
allowable stresses will have to be set. Lastly, the right case of application must be found in the
forms, and then the company has to do everything included in this case of application, at the risk
of not finding its own specific case of application. Therefore, the options and freedoms in the
design are limited.
Furthermore, overall, the selected code may be too general thereby preventing easy day-to-day
use for specific aspects in the design and dimensioning of pressure vessels.
4.
Finite elements
4.1. General
An analytical study is needed to determine the stresses and strains in all points (an infinite number of points) of a structure. This is possible if the structure is simple and can be considered a beam,
a plate or a shell of simple shape, for instance. The loading must also be relatively simple, such as
forces that can be broken down over the principal directions (refer to Chapter II, paragraph 7.3:
Mohr’s circle). It is quite complicated to solve multi-physical problems analytically (thermal and
fluid coupling, dynamic and thermal coupling, etc.).
The finite element method can be used to solve the problems where there are no analytical
solutions. It provides an approximate solution.
As a matter of fact, the studied medium is discretised into several elements (a finite number)
that are connected by nodes. The elements can be any geometry, but remain characterised by a
finite number of nodes over their perimeter.
The solution to the problem will therefore involve finding the displacement of these nodes.
The field of displacement in any point is determined by interpolation between the values determined
at the nodes based on the shape functions.
This method provides approximate solutions for complex structures and for complex multiphysical loadings.
4.2. Finite element problem-solving steps
The following steps must be applied to solve a structural mechanic problem using finite
­elements:
1) Defining the geometry of the studied structure:
It is often necessary to simplify and “clean” the shapes, particularly for objects with many faces
due to successive chamfers.
2) Meshing the structure
The discretisation of the structure into a finite number of elements and nodes requires selecting
the right type of element based on the shape of the structure and the stress (bar element, beam,
shell, volume).
◗◗ 1D bar elements only work in tension-compression. The only sectional property allocated
to this element is its area (in mm2). They are used to represent slender structures such as
tubes or cables.
80
◗◗ 1D beam elements work in tension-compression, bending, shear and torsion. The sectional
properties to be entered are the quadratic moments and the area. They are used to represent
slender structures such as small beams.
◗◗ 2D elements are used to represent thin structures, such as plates, membranes, shells,
etc. A thickness value must be entered. They may be triangular or quadrilateral.
◗◗ 3D elements are used to represent thick objects. They may be tetrahedral or brick-shaped.
There are a number of rules governing how meshing should be carried out to avoid stress
concentrations or to obtain a credible approximated result in the fillet radii for example.
3) Defining the model associated to the structure (e.g. isotropic elastic material)
A material law must be defined (linear elastic, elastic-plastic, viscous, etc.).
4) Defining the boundary conditions
The boundary conditions are the restrictions at the boundary of the studied system. In general,
these restrictions relate to the possibilities of movement in an area (embedding, required displacement, etc.). They can also be mechanical or thermal loads for example.
5) Problem solving to obtain nodal displacement of the elements
The selection of the problem solving method (direct, indirect, etc.), the solver (implicit, explicit)
and the interpolation functions may significantly affect the rapidity, convergence and the results of
the calculation. The stresses and strains are calculated using the field of displacement.
4.3. Drawbacks of finite element calculation
Although the finite element method has the advantage of providing results in situations where
the analytical method is not possible, there are a few drawbacks:
One such drawback is the cost arising from the calculation time of finite element software.
As a matter of fact, some structure calculations require a rather long calculation solving time
(several days). The power of the computers and the way the calculation software is designed significantly affect this resolution time.
The financial cost of this finite element software can also be several thousands or several tens
of thousands of euros. Analytical resolution only requires purchasing standards and a spreadsheet
program for example.
Interpretation of the results is essential, as the finite element method only offers an approximate solution. To enable this interpretation, the user must always bear in mind the nature of the
physical phenomenon studied and the variables which influence this phenomenon. The user must
always bear in mind the SoM principles. However, paradoxically, the use of software for finite
element calculation may lead to omitting the link with physics and producing results that are out
of step with the studied phenomenon.
It is very important to properly select the type of element, the resolution method and the solver.
This requires experience as well as sound understanding of SoM. The wrong choice may significantly
slow down the calculation and produce results that are far from reality. The risk is giving too much
credit to the results which are nevertheless inaccurate.
81
5.
Method proposed in the guide
5.1. Aim
The aim of this guide is not to determine the stresses in all points of the vessel, but rather to
define the governing stresses and the parts of the vessel on which they act.
It is an analysis of the vessel and its components to arrive at an economical and safe design.
Stress analysis will be carried out when necessary, primarily in the most critical parts of the
vessel.
5.2. Necessary information
A structure is subjected to actions such as temperature, pressure, wind, etc. during service.
When these actions are reflected inside of the material, they are stresses. A situation is a state of
the vessel subjected to a simultaneous set of stresses. This set is called loading.
The structure is verified by two calculation methods which can be complementary, either
by analytical formula (SoM), or by numerical analysis, or both.
Therefore, the following must be performed:
◗◗ 1. Determine the operating pressure and temperature of the vessel.
◗◗ 2. Once these parameters are defined, take into account the damaging modes selected
during the check such as excessive or gradual plastic deformation, fatigue, creep, etc.
◗◗ 3. Then, determine the loadings which apply to the structure: internal or external pressure,
hydrostatic pressure, differential temperature, forces at the nozzles, wind, snow, earth­
quake, supports, lifting lugs, etc.
◗◗ 4. Additionally, you have to determine, as accurately as possible, the specific properties
of the studied material, which are not the same for all solids. For work on the elastic range
of a material, knowledge of its Poisson’s ratio (v), Young’s modulus (E) and its density are
required. For work in the plastic region of a material, its yield strength (Re) and its Young’s
modulus (E) are essential for the calculations. In addition to a significant stress associated
with temperature, the thermal conductivity (λ) must be known.
◗◗ 5. Eligibility conditions are fundamental to validate or reject a given situation. They are
generally explicitly defined in specifications or implicitly defined (through standards).
6.
Loadings
The forces applied to the vessel or to the structure stem from external loadings and the mechanical design. The first step during the design of the vessels is to determine the values of the forces
applied and the conditions under which the vessel will operate.
It is necessary to draw on experience, the knowledge laid down in the codes and the various
tools available to best assess the forces to which our structure is subjected. The main loadings to
be taken into account are outlined in this section. It is also important to consider load combinations
for an economical and safe design.
82
6.1. Categories of loadings
6.1.1. General loads
These loads are applied more or less continuously on a section of the vessel:
◗◗ Pressure: internal or external pressure (operating pressure, test pressure, hydro-static
pressure).
◗◗ Moment: wind, seismic, construction, lifting, transportation.
◗◗ Tension and compression: dead weight, installed equipment, ladders, platforms, nozzles
and contents.
6.1.2. Local loads
These loads are due to reactions from supports, internal components, piping, platforms, etc.
◗◗ Radial load.
◗◗ Compressive load.
◗◗ Longitudinal or circumferential shear load.
◗◗ Torsional load.
◗◗ Longitudinal or circumferential moment load.
◗◗ Thermal load.
6.2. Types of loadings
6.2.1. Steady loads
Their effects are continuous over a long term. These loads are the basis of the study, they make
up a loading for ideal conditions of use. They include:
◗◗ Internal or external pressure.
◗◗ Dead weight.
◗◗ Vessel contents (liquid, gas), static and filling.
◗◗ Loadings due to attached piping on the vessel.
◗◗ Loadings due to platforms.
◗◗ Loading due to vessel supports.
◗◗ Thermal loads.
◗◗ Wind loads.
83
6.2.2. Non-steady loads
Their effects are short term or variable. These loads are the principal limits of the study, they
take into account exceptional situations. These loads induce high stresses on rarely stressed
components. They include:
◗◗ Hydrostatic tests.
◗◗ Draining.
◗◗ Earthquake.
◗◗ Lifting.
◗◗ Transportation.
◗◗ Maximum or emergency conditions.
◗◗ Start-up or shutdown of the vessel.
◗◗ Ten-year/five-year climatic hazard.
◗◗ Maintenance.
7.
Pressure
7.1. General
The pressure of the equipment is the essential element for designing the vessel, it helps to
determine the minimum required thickness in each component. There are two types of pressure:
internal pressure and external pressure (in general, atmospheric pressure).
7.2. Different types of thicknesses
In the technical data of the vessels, different types of thicknesses can be noted.
These include:
◗◗ Required or allowable thickness: it can be calculated in accordance with standard EN 13445
and depends on the type of vessel and its general data (internal pressure, volume, operating fluid, temperature, etc.). This thickness can be directly calculated. Unless otherwise
specified, all design calculations must be done in the corroded state with a consistent set
of dimensions (thickness, diameter, etc.).
◗◗ Allowable corrosion thickness: this is the corrosion allowance taken into account in the
allowable thickness, it is calculated depending on the useful life of the vessel. If there
are any doubts about this item of data, it is recommended to carry out corrosion tests on
the metal actually used.
◗◗ Standardised tolerance values are provided in EN 13445‑4.
◗◗ Raw product order thickness: it must be more than the sum of the lower tolerance
limit and the previous thicknesses. This thickness can be found in manufacturer’s catalogues. The sum of the upper tolerance limit and the raw product order thickness gives
the maximum weight of the structure, this is an important item of data for the logistics
and dimensioning of the supports.
84
Possible reduction in thickness during manufacturing
Allowable thickness for
checking the strength of the
component
Minimum necessary
thickness of the component
Useful thickness of the
component (smallest possible
thickness after corrosion)
Corrosion allowance
Smallest possible actual
thickness of the component
on new equipment
Nominal raw product order thickness
Lower tolerance on the thickness of the raw product
Additional thickness resulting from
selection of the order thickness
A number of software applications can be used for the dimensioning calculation: NextGem,
Auxecap. CODAP can also help with the dimensioning of the vessel.
8.
Local loads (see handbook 5)
The principal load of the structure comes from the vessel itself, however all items of equipment
which can be added to the vessel and which will create additional loads must be taken into account.
These loads are primarily found at the pipes, attachments and supports and generally at the junction
between vessels and/or parts.
High stresses are concentrated at these local loads. They are the root cause of many equipment
failures: cracks, creep, premature wear, pitting corrosion, etc. As a result, this type of structure
must be avoided as much as possible and must be dimensioned as best possible when they are
unavoidable.
9.
Climatic loadings
9.1. Wind
9.1.1. Basic concept about wind
• Wind components
Wind can be described as a turbulent flow of air moving across the Earth’s surface at variable
speed. Wind components depend on the three dimensions of space. In general, the direction of wind
is horizontal. However, a vertical component may appear when the flow moves over an obstacle.
It remains minor for construction calculations, it is therefore assumed that the average overall
direction of the wind is horizontal.
85
• Wind speed: measurement and statistics
In terms of turbulent wind, it must be borne in mind that the concept of speed is relative in that
speed constantly varies based on the three dimensions. A distinction must be made between the wind
fluctuations based on different time scales. A long duration of about a day corresponds to meteorological variations. A shorter duration of about a minute is associated with atmospheric turbulence. In
general, the average wind speed is integrated over 10 minutes and varies along the vertical direction
depending on the friction of the ground caused by the different natures of the terrain.
It is important to differentiate between average speed and peak speed. The peak speed can
be used in certain methods, but in general, it is preferable to carry out calculations based on the
average speed. According to the standards, the wind is measured under very specific conditions.
The height of the wind speed measurement equipment is set to 10 metres (i.e. 30 feet) and the
duration is 10 minutes. The reference wind speed is set for a given geographical area. By convention,
it is measured in flat open country. The selection of the reference speed often causes controversies
due to its statistical nature.
The reference wind speed return period represents the average statistical duration during which
a wind of a given speed can be observed. The dimensioning of operational structures often uses
five-year wind, whereas the calculation of structures under construction uses ten-year wind.
• Factors influencing wind speed
The first factor that influences the wind speed is the region. There are regions where there is
little wind and others where there is a high amount of wind. Weather maps are used to determine
the wind speed for a given region. Some regions suffer specific meteorological influence, this is the
case of islands or mountains. In this type of case, careful reference should be made to the maps,
a more thorough study in the area of the construction can also be considered.
Wind speed is highly dependent on the roughness of the Earth’s surface, that is to say the number
and the height of the obstacles have a major influence. A smooth and flat land is more exposed than
a forest area or a residential area. It should be noted that there is more turbulence within the vicinity
of obstacles.
The topography also changes wind speed, particularly when the wind must move across a hill
or a cliff. Wind speed also increases due to the law of conservation of the air mass at the obstacle.
There are many possible configurations in this case, often specific studies must be used with a site
mock-up for example, to determine the relevant speed for designing the structure.
Wind speed also increases depending on the altitude. Wind velocity increases with the height
above ground, and it decreases when it gets closer to the ground. There is a formula to express
wind power: V α zn. The exponent n depends on the roughness of the terrain; z corresponds to
the altitude.
In short, wind speed depends on the geographical situation (regional effect), the nature of the
terrain (roughness effect), topographical conditions (site effect) and the altitude (height effect).
• Undesired effects of wind
Wind has many effects on a vertical structure. Firstly, there is the risk of overturning the
structure, then the considerable increase of the deflection of the vessel. Dynamic effects such as
wind-induced vibrations are also a possible risk.
Many columns withstand episodes of very violent wind. For instance, industrial structures are
able to withstand hurricanes and other tropical storms. However, buildings which suffer significant
damage allow us to understand the errors made by the designers. It may be interesting to analyse
a few cases in order to highlight serious design inadequacies.
86
9.1.2. Aerodynamics of pressure vessels
This chapter is not a general presentation of aerodynamics. It is only aimed at outlining the main
concepts involved in studying the behaviour of structures subjected to the actions of wind.
• Overview of fluid mechanics
Fluid mechanics is governed on the macroscopic plane by equations established from the usual
laws of conservation of mechanical engineering: conservation of mass and momentum. When it
comes to the aerodynamics of low altitude wind, these equations become simpler, as the speeds
involved are markedly less than the speed of sound. In addition, the air density and temperature are
assumed to be constant. Air is a light gas and its self-weight is not taken into account in comparison
with the other forces. There is a linear relationship between shear stresses, speed gradient and
the effects of the friction within the fluid. The main equations considered are the Navier-Stokes
and Bernoulli equations.
• Aerodynamics of cylinders
Vertical vessels are essentially large circular cylinders or components with circular or poly­
gonal cross-sections. This shape is relatively basic, it is easy to determine the wind loading on this
type of structure. The force coefficient for cylinders is an important factor for estimating the wind
loads. It depends on the Reynolds number, the surface roughness of the cylinder, and the height/
diameter ratio.
The Reynolds number is the most decisive parameter for the scale effect. It physically represents the ratio of inertial forces to the viscous forces in a particle of the fluid. To measure the
force on a structure, applying the Reynolds analogy is equivalent to maintaining the proportion
between the shear forces associated with the viscosity and the pressure forces arising from the
fluid velocity.
For profiled structures such as aircraft wings, the airflow is not detached, that is to say the
velocity of the fluid close to the wall tends to remain parallel. In the case of structures where
the profile moves away from this ideal profile, strong disturbances close to the walls may cause
powerful vortices. The more the structure has sharp edges, the more the flows are disturbed.
Surface roughness influences aerodynamic loads, external equipment should also be taken into
account.
To reduce the aerodynamic force coefficient, the height/diameter ratio must be reduced. For an
infinitely long cylinder, the airflow may be considered as two dimensional. When the height is
defined, the wind flow may occur at the circumference of the vessel or above the roof.
87
Surface pressure lower than the
pressure of the surrounding flow
(min. complete vacuum)
Flow
velocity
Distribution of the pressure around
a cylinder for ideal fluids.
A and B are respectively the front
and rear stagnation points.
Wind is by nature a highly turbulent flow of air above the Earth surface whose speed and direction
constantly vary. The direction of the airflow is generally horizontal, it can have a vertical component
when the flow moves above an obstacle. Wind speed increases with altitude. From a certain height,
it can be considered as maximum and constant. The shape of the profile above the ground, on an
open flat countryside, can be expressed by an exponent.
– According to Eurocode 1 – Part 2‑4
The calculation of the wind action includes the following steps:
◗◗ 1. Reference wind speed: defined on a probabilistic basis by a weather map.
◗◗ 2. Exposure factor depending on the site (flat terrain, suburban area, urban area) and the
height above ground.
◗◗ 3. Selection of the calculation procedure: simple or detailed.
◗◗ 4. Wind pressure coefficient selected based on the shape of the structure subjected to
wind.
– For ASA ANSI‑A58.1‑1955 (American Standard Building Code Requirements for Minimum
Design Loads in Buildings and Other Structures), the influential factors are:
◗◗ 1. The geographical area of the structure can be located on a wind pressure map. The basic
pressure of the wind can be determined, it is based on the maximum velocity measured over
the region, the shape factor (1.3 for a flat surface) and the exposure factor (1.3 for heights
of more than 150 meters – 500 feet).
◗◗ 2. The wind pressure corresponds to the basic wind pressure but varies depending on the
altitude of the sections.
◗◗ 3. The shape factor for round objects: it is 0.6 and is applied to the wind pressure.
88
◗◗ 4. The exposure factor describes the variation in the wind force depending on the land­
scape of the area. As a matter of fact, the wind will not have the same impact in a flat plain
as in an urban area with large structures (building, etc.).
◗◗ 5. The projected area of the vessel normal to the wind (section upstream of the wind) is
also an influential factor of the wind.
– For ASA ANSI A58.1‑1972, the influential factors are:
The effective wind pressure is calculated from the wind velocity (depending on the type of terrain
and the altitude), the Gust factor of the structure, the Gust factor for the relevant section.
9.2. Earthquakes
An earthquake is a sudden violent shaking of the ground as a result of tectonic plates moving
against each other. These movements are approximately a few centimetres per year, however energy
accumulates in the plates until it is released, which causes the earthquake. The intensity and the
duration of the vibrations depend on the accumulated energy. The areas close to a contact between
two plates are a more conducive environment for earthquakes. Vibrations begin at a specific point
called the epicentre and are propagated in all directions.
9.2.1. General
If the vessel must withstand earthquakes, the earthquake stresses are commonly represented in
the calculation by a horizontal load. Vertical loads may be taken into account, however their effects
on the overall structure are generally insignificant.
The information associated with the earthquake is, in principle, specified in local building codes;
specific information to the region may also be used. This is expressed by the horizontal acceleration
and sometimes the vertical acceleration.
For large or horizontal tanks, oscillations of the liquid must be taken into account.
The consequences of the liquefaction of the subsoil, if necessary, are also to be considered.
9.2.2. Test and dimensioning
When a covered tank is entirely full, there is no relative movement of the fluid inside the tank
further to seismic excitation at the base. From a dynamic standpoint, everything occurs as if the
fluid-tank assembly was a single mass. This corresponds to a “frozen water” situation, an interesting option to be considered as a reference value, but which disregards the motion of the fluid. This
assumption, which largely simplifies the study, cannot replace a vibration study of the full tank, at
less than 98%, apart from exceptional cases.
When the surface of the fluid is free, the motion of the tank leads to oscillations, with various
implications: distribution of dissymmetrical dynamic pressures, formation of waves, bending and
shear moment at the base different from the “frozen water” case. As incomplete filling of approximately 2% of the total volume enables wave formation, we will consider the surface of the fluid as
free in the study of tanks in seismic areas.
Many types of damage affect tanks in seismic areas.
Water towers are “reverse pendulums”. They are highly stressed, low ductility structures. They
are in a position of unstable equilibrium. Height amplifies the vibrations and the eigenfrequency of
a building must be determined to avoid any resonance phenomenon.
Thin-walled tanks set on the ground are subjected to dissymmetrical stresses which may lead
to buckling of the side walls or of the roof, as the applied stresses are unfavourable.
89
Therefore, a cylindrical tank wherein the stresses in the walls are normally circumferential
membrane stresses (horizontal), will also be subjected to:
◗◗ Vertical membrane stresses due to the overall bending under the horizontal action, which
may cause tensile failure of the anchor bolts and overturning of the tank;
◗◗ Out-of-roundness of the tank and bending stresses under the horizontal action;
◗◗ Additional horizontal membrane stresses due to the vertical acceleration;
◗◗ Bending stresses at the base of the walls, as the transverse expansion of the tank is not
free there due to the connection of the walls with the base of the tank.
9.2.3. In short
Earthquake = violent vibrational shaking of the ground.
Main damage factors = intensity and duration of the tremors.
Earthquake = transient, complex and dynamic phenomenon.
Assumption: all vessels withstand the vertical force of the earthquake.
Method: find the equivalent static force to be applied to the base of the vessel.
Results: depend on the dynamic response of the structure (rigid or flexible).
9.3. Snow and ice
Snow loads do not need to be taken into account to design the body of the column.
However, for platforms, landings and staircases, we can consider snow loads by applying standard
TGL 32 274/05.
9.3.1. 3 general cases
◗◗ The characteristic values of the snow load on flat grounds are highly variable, ranging
from 450 N/m2 for a region at less than 200 m in altitude to 5,200 N/m2 for exceptional cases
at less than 2,000 m in altitude. These values are taken from Eurocode 1.
◗◗ For an angle between the structure and the horizontal of more than 30° and less than 60°,
we can multiply the value of the snow load on the ground by a coefficient. This coefficient µ,
60 – α
to taken into account the angle, can be calculated using the following formula =
30
where: α the angle formed by the structure with the horizontal.
◗◗ Snow load is no longer taken into account when the angle formed by the structure with
the horizontal is more than 60°.
These values are taken from Eurocode 1.
9.3.2. Special cases
In regions with possible rainfall on the snow and consecutive melting and freezing, snow loads
should be increased.
Snow and ice loading should be specifically studied depending on the geographic location;
further complementary guidance may be given in the national Annex.
90
10.
Thermal loading
10.1. Types of temperatures
Temperature is to be taken into account for the design of the vessel. These temperatures may be:
◗◗ The outside temperature which depends on the weather and environmental conditions
associated with the location of the vessel.
◗◗ The operating temperature of the vessel which depends on the type of tank and its content.
10.2. Temperature effect
Temperature effect may include the embrittlement phenomenon when the temperature is excessively low and a ductility of certain materials when it is excessively high.
10.3. Temperature gradient in the material
In the structure, two expansion phenomena may occur:
◗◗ Pure expansion: component or whole vessel subject to temperature variations;
◗◗ Differential expansion: temperature variations between two points of the vessel.
11.
Load combinations (handbook 5)
Several load combinations can be studied, however they are improbable in most cases. Nevertheless, it is the engineer’s responsibility to design as best as possible for the loads to which a
vessel is subjected.
For example, when the vessel is designed for the worst case of wind or seismic loading, the
combination of both is not addressed. Typically, the worst design case for wind is with the vessel
empty, the worst case for seismic design is with the vessel full. It is therefore unlikely that the two
cases will occur at the same time.
We can differentiate between four operating states of the vessel:
◗◗ Handling / lifting of the vessel: empty vessel and influence of the wind and earthquake.
◗◗ Operating conditions: vessel not empty and influence of the weight, wind, earthquake as
well as other effects: vibrations, shockwaves, thermal effects.
◗◗ Conditions of a hydrostatic or pneumatic test: vessel in horizontal position under the
pressure of a hydrostatic test. No wind and earthquake loads.
◗◗ Conditions of overpressure or negative pressure: short duration of overpressure, emer-
gency, commissioning. No wind and earthquake loads.
Resistance criteria: the structure must be able to withstand the various load combinations.
Therefore, the worst case must be found under the siting conditions of the structure and they must
then be thoroughly studied.
The study of the load combinations can be broken down into two sections: normal loadings and
exceptional loadings.
Normal load combinations are studied over the long term.
These load combination cases include: internal and external pressure, “normal” climatic conditions, the weight of the vessel, the fluid and accessories.
91
Examples of load combinations used (based on standard 13445‑3, standard ASCE 7, reproduced
in PVD Moss):
Normal load combinations (non-exhaustive)
Load combinations
Description
P + D + 0.75S + 0.75L
D+W
P+D+L
Pressure, weight, partial snow and
partial live load
Wind and weight
Pressure, weight and live load
D = dead weight (loading due to the weight of the
structure)
E = earthquake loads
F = local load due to the fluid
P = local load due to the pressure
L = live load (of the accessories and auxiliary equipment)
R = rain load
S = snow load
W = wind load
For all load combinations, a load
assessment with P = 0 must be
considered
The exceptional load combinations are studied over the short term.
Exceptional load combinations include: internal and external pressure, exceptional weather
conditions, the full and empty weight of the vessel.
Exceptional load combinations
92
1
1.2 D + 1.6W + L + 0.5 (S or R)
Influence of wind and snow
2
D + P + F + 0.75 (W or 0.7E) + 0.75 L + 0.75 (S or R)
4 exceptional cases
3
0.9 D + 1.6W + 1.6 P
Test conditions associated with wind
4
0.6 D + W
Partial weight and wind
IV Failure or fracture modes
1.
Fracture theory
1.1. Maximum stress theory
This is the simplest and most widely used method. According to this theory, the fracture occurs
when the principal maximum stress is equal to the yield strength. The stresses in the other directions
are disregarded. This theory is often used for biaxial states of stress. In addition, it is more accurate
in the case of brittle and non-ductile fractures.
If σ1 > σ2 then fracture occurs when σ = Fy where Fy is the yield strength.
Safety factor boundary
imposed by ASME Code
Failure surface (yield surface) boundary
1.2. Maximum shear stress theory (Tresca)
In this case, plasticity is assumed to occur when the maximum shear stress reaches a threshold
value. According to the Tresca criterion, fracture occurs when the largest difference of the shear
stress is equal to the shear yield strength (refer to criterion and equation below). This theory is similar to the experimental results for ductile materials, which is why it is still very widely used today.
σ – σ 3 Fy
If σ1 > σ2 > σ3 then fracture occurs when 1
where Fy is the yield strength.
=
2
2
93
Fracture surface (yield surface boundary)
Point B
1.3. Distortion energy theory (Von Mises)
The total strain energy may be broken down into two parts: the strain energy required for the
hydrostatic strain and the strain energy required for the distortion.
Fracture occurs when the distortion energy is equal to the uniaxial yield strength.
1
If σ1 > σ2 > σ3 then fracture occurs when [(σ 1 – σ 2 )2 + (σ 2 – σ 3 )2 + (σ 3 – σ 1)2 ] = Fy 2 where Fy is
2
the yield strength.
Fracture surface (yield surface boundary)
94
1.4. Comparison
Three points are obvious when the maximum principal stress theory and the maximum shear
stress theory are compared:
◗◗ 1- For thin-walled pressure vessels (Dm ≥ 5 t), both theories give approximately the
same results.
Dm = Average diameter; t = thickness
◗◗ 2- For thin-walled pressure vessels, the radial stress is so small in comparison to the
longitudinal and circumferential stress that it can be ignored and a state of biaxial stress
is assumed to exist.
◗◗ 3- For thin-walled pressure vessels, when the radial stress becomes significant in esti-
mating the fracture, the maximum principal stress theory is no longer conservative. For
this reason, this handbook has limited its application to the cases where the stress state
can be considered as a biaxial state of stress.
2.
Causes of failure
Failure can be caused by various factors which are omitted or have changed during the life of
the component. This failure is to be considered as a fortuitous test bench. Failure analysis will help
to identify the omitted parameter(s).
Through the life cycle of the component, from the design to use, it is possible to identify what
parameters caused the failure. Therefore, the causes of failure should be connected to the misunder­
standing of the materials and their behaviour.
2.1. Materials (CCVL Orléans)
The selection of a material is guided by the following diagram where all the stresses, that is to
say the sum of the operating and manufacturing stresses, will impact the selection of the material:
Manufacturing
Stresses
Operating
Properties
Structure
Chemical composition + treatment (heat
treatment, mechanical treatment, etc.)
As such, when the material is responsible for the failure, we can consider:
◗◗ A bad choice.
◗◗ Defects in the material.
◗◗ Inadequate material inspection.
◗◗ Inaccuracy regarding the material.
95
The selection of the material grade is not limited to a chemical composition. As illustrated in
the diagram on the previous page, it is the structure which affects the mechanical properties.
2.2. Design
Design may be a factor due to:
◗◗ Bad choice of the material or the treatment (heat, surface or anticorrosion treatment);
◗◗ Properties that are not suited to the stresses;
◗◗ Poor selection of the forming process;
◗◗ Undersizing of the components;
◗◗ Lack of knowledge regarding the material behaviour;
◗◗ Oversimplified assumptions;
◗◗ Careless preparation of the specifications and calculations;
◗◗ Inaccurate or incorrect design methods;
◗◗ Inadequate testing.
2.3. Manufacturing
The manufacturing may be at issue:
◗◗ Due to the surface treatments: for example, acid pickling before surface treatment may
release hydrogen that causes deferred failure, or in contrast, shot blasting will increase
internal stresses.
◗◗ Due to heat treatments: the holding temperature and the cooling mode are specific points
which may cause cracking or corrosion.
◗◗ Due to the welding technique: the selection of the process and the operating conditions
must be specified to limit the possibility of defects in the weld bead.
◗◗ Depending on the selection of the assembling process: on stainless steel, a bolt-nut or
rivet joint does not have the same corrosion resistance.
◗◗ Depending on the forming process: machining defects are potentially initiation sites for
fatigue cracking.
◗◗ Poor quality control.
2.4. Operation
During the use of the equipment, failures can be caused by manufacturing operations: prior
storage, assembly or maintenance.
Some other factors include sudden overload, temporary change in the environment or external
vibrations to the system.
Even if the previous divisions have properly designed and manufactured the equipment, improper
operation can lead to its failure:
◗◗ Excessively severe operating conditions;
◗◗ Inexperienced maintenance personnel and poorly performed operations;
96
◗◗ Conditions pushed to the limit;
◗◗ Details not taken into account: fatigue, brittle fracture due to low temperature, distortion
due to high temperature, vibrations or shock, vessel content (hydrogen, ammonia, etc.);
◗◗ Use that is not compliant with the specifications;
◗◗ Lack of servicing.
3.
Various failure modes of pressure vessels
3.1. Failure modes
During the design of a vessel, the various possible failure modes must be studied. The designer
must check that, for each foreseeable loading, no significant damage can jeopardise the strength
of the vessel. The concept of failure does not only relate to the existence of a fracture or a crack;
it also relates to any deformation, even elastic, which prevents the vessel or the component from
fulfilling its function. Generally, there are three failure modes:
◗◗ Failures due to deformation of the components: elastic deformation, plastic deformation,
creep, buckling;
◗◗ Failures due to fracture: sudden fracture, fracture by progressive crack propagation,
creep;
◗◗ Failures due to surface damage: abrasion, corrosion, adhesion, cavitation, etc.
3.2. Elastic deformation
3.2.1. Excessive elastic deformation
This failure mode is often ignored. The elastic deformation, when it occurs, prevents the compo­
nent from fulfilling its function. There may, for example, be a lack of sealing or misalignment.
3.2.2. Elastic instability / Elastic buckling
This phenomenon is well-known, it is also called buckling. It is a failure mode which occurs
especially on thin-walled vessels subjected to compressive stresses. A critical pressure can be
defined below which no risk of buckling occurs. This critical pressure generally depends on round­
ness defects.
3.3. Plastic deformation
3.3.1. Excessive plastic deformation
An overload can lead to hazardous deformation given the
slope of the load-deformation curve. In fact, on this curve, a
low variation in the loading can cause significant deformation
once the plastic deformation zone is exceeded.
A maximum deformation value can be set in certain areas
of the vessel. It can be used as a limit for the entire vessel.
Based on the codes and regulations, there are several definitions of this maximum deformation. This limit serves to
protect against plastic instability which can occur upon an
accidental increase in pressure.
97
3.3.2. Plastic instability
If we continue to plot the previous curve, we note, after the strain hardening consolidation
period, that a fracture appears thereby making the vessel unusable. In fact, before fracture, there
is a reduction in area phenomenon, the section is reduced and the stress increases. This type of
failure is prevented by limiting the stress in the membrane.
3.3.3. Gradual plastic deformation
The plastic deformation areas are small in size. This is often the case with areas of discontinuity
such as the head-shell junctions, nozzles, etc.
After several loading application cycles, three possibilities may occur:
◗◗ If the pressure is low and less than Pa1, the residual stresses which appear during the
first unloading reduce the stresses due to application of the following loading. There is
plastic adjustment of the structure which will have an elastic behaviour for the subsequent
cycles.
◗◗ For a pressure of more than Pa, the vessel, after a few cycles, no longer undergoes defor-
mation in certain localised areas, there is no overall deformation.
◗◗ For an even higher pressure greater than Ps2, plastic deformation occurs at each cycle
and the vessel suffers damage by gradual deformation.
The pressure Ps marks the threshold for occurrence of damage by gradual deformation.
3.4. Brittle fracture and ductile fracture
3.4.1. Fracture mechanisms
Studies carried out on materials have revealed that the fracture propagation phenomenon is
primarily due to existing defects in the material. Operating conditions, particularly temperature
and stress rate, play a decisive role.
The fracture destroys the cohesion of the material by creating discontinuities at the scale of
existing microcracks or cavities, or cracks in the mechanical structures.
1. Pa: Atmospheric pressure.
2. Ps: Service pressure as defined by the directive, but in our case, this is the maximum allowable pressure.
98
Fracture modes
Mode I
Opening
Mode II
Shear
Mode III
Screwing
Location and geometry of defects
3.4.2. Types of fractures
There are two types of fractures:
◗◗ Fracture by rapid crack propagation: ductile, semi-brittle, brittle.
◗◗ Fracture by progressive crack propagation:
◗◗ Under static stresses: stress corrosion, creep, etc.;
◗◗ Under cyclic stresses: mechanical fatigue, thermal fatigue, etc.;
◗◗ Under complex stresses: corrosion fatigue, creep fatigue.
3.4.3. Brittle fracture
Definition
Brittle fracture occurs at the intra-atomic bonds without macroscopic plastic deformation, when
the local deformation energy arising from external stresses is equal to the energy required for
atomic decohesion.
The crack propagation for a brittle fracture is very rapid, and energy consumption is very low.
In this case, geometrical defects and accidents are central to the initiation of the fracture.
Transgranular brittle fracture (cleavage fracture)
Transgranular brittle fracture follows the crystallographic planes (cleavage plane). A crystalline
fracture surface, with a glossy appearance, is noted.
At the macroscopic scale, the fracture surface is perpendicular to the stress direction. At the
mesoscopic scale, for a transgranular fracture, the fracture follows crystallographic planes and
directions in each grain. At the microscopic scale, the fracture of the inter-atomic bonds occurs in
a direction perpendicular to the fracture plane.
99
The interaction of the crack with the microstructural defects and heterogeneities of the metal
leads to very typical microreliefs: cleavage surface in the form of marks and steps called river line
patterns and tongues.
Intergranular brittle fracture
The intergranular brittle fracture is characterised by intergranular decohesion. The fracture
follows the grain facets by deterioration of the
grain boundary.
3.4.4. Ductile fracture
Ductile fracture is mainly revealed by the
presence of inclusions or precipitates. The
fracture results from the emergence of cavities
and from their extension in the deformation
direction (reduction of area or shear). Ductile
fractures initiate from inclusions, precipitates,
grain boundaries. At the microscopic scale, we
see microreliefs called dimples.
100
3.5. Fatigue / fracture by progressive crack propagation under
variable amplitude loading
3.5.1. Definition
Normally, fatigue phenomenon is presented as a process by which damage accumulates in the
material upon application of variable loads. This damage can ultimately cause fracture, even if the
maximum load is much less than that required to reach the yield strength of the material. In short,
fatigue is a phenomenon which locally produces a decrease in the material strength, mainly due to
the formation of microcracks or damage. It is a progressive phenomenon through which damage
develops slowly then increases very rapidly before fracture.
Such repeated stresses may stem from the start-up and shutdown phases of an engine, variations in speed, wind gusts on a structure, swell on floating structures (ships, offshore oil rigs), the
effects of expansion of a vessel which heats and cools (for example a boiler), repeated contacts
(gears, balls on the raceway of a ball bearing), bumps on the road for a vehicle, take-off and landing
phases for the landing gear of an aircraft and vibrations for small parts (attachment lugs, wire of
an electronic circuit), etc.
3.5.2. Characterisation of material endurance
During a fatigue test, the specimens are subjected to cycles with a set maximum amplitude and
constant frequency. The number of cycles to fracture is noted. By varying the maximum stress, it
is possible to plot the Wöhler curve or the S-N curve.
101
Fatigue zone
Limited endurance region
Low-cycle
fatigue region
Limited
endurance
region
Fatigue limit
Wöhler curve or S-N curve.
There are three regions:
◗◗ The low-cycle fatigue region is where there are highest stresses. These stresses exceed
the yield strength of the material. In general, the number of cycles is less than 104 and
the specimen reaches a state of plastic accommodation (periodic plastic deformation) or
an elastic-plastic ratcheting (plastic deformation which continuously increases). Plastic
deformation is predominant in this region.
◗◗ In the fatigue region or limited endurance region, fracture takes place after a number of
cycles ranging between 104 and 107. The fracture is not accompanied by any overall plastic
deformation (only in the first cycles). It is an elastic accommodation mechanism.
◗◗ The unlimited endurance region or safety region is reached as of 106‑107 cycles.
Below the fatigue limit or endurance limit, fatigue fracture never occurs, regardless of the
number of applied cycles.
Note: experience has shown that there may be significant scatter in the obtaining of a material
curve. It is important to consider this curve with caution.
3.5.3. Parameters influencing fatigue
• Metallurgical parameters
Fine grain structures exhibit better fatigue strength than coarse grain structures.
The general direction of the grains affects fatigue strength. The static properties and fatigue
strength are better in the longitudinal direction of the fibre structure. The strain hardening which
is achieved through the forming operations consolidates the material and improves its fatigue
strength. Depending on the heat treatment, the strength may be improved or decreased. Defects
in the components may cause fatigue damage.
102
• Nature of loading
As regards monotonic loadings, the predominant parameters are:
◗◗ A square type signal is more unfavourable than a sinusoidal type signal.
◗◗ At constant maximum stress, if the ratio between the maximum and minimum value of
the loading increases, the fatigue life increases.
◗◗ If the average stress increases for a constant loading amplitude, the fatigue life decreases.
◗◗ The period of the signal has little significance in the cases of pure fatigue.
As regards variable loadings, the predominant parameters are:
◗◗ The periodic repetition of an overload may delay crack propagation.
◗◗ The order in which the cycles appear may affect fatigue fracture.
• Geometry of the object
The discontinuities in the object may locally increase the stress level. The more the dimensions
of an object increase, the more the fatigue resistance decreases; this means that for two similar
components, the general dimensions are important.
3.5.4. Fracture surface
The mains stages of fatigue are: crack initiation (if defects are not already present in the material), fatigue crack propagation and final fracture.
The fracture surface is therefore very distinctive, it exhibits:
◗◗ A fatigue crack area: smooth;
◗◗ A final fracture area.
3.6. Creep
The progressive deformation of a material at high temperature under the influence of persistent
stresses is called creep. It depends on the applied stress, as well as the load application time and
occurs for temperatures of more than 0.5 Tf where Tf is the melting temperature of the material.
A creep test involves maintaining a specimen at high temperature under a constant load (and
not constant stress). Measurements of deformation are recorded over a period of time. The strain
curve as a function of time occurs in three stages described below.
103
During the primary creep stage, the specimen is placed under load, the elongation is elastic or
plastic depending on whether the applied stress is more than or less than the yield strength at the
test temperature. The strain is generally low.
The secondary creep stage is where the strain rate is constant. This stage has more significance
for manufacturers.
The tertiary creep stage is characterised by an increase in strain, the onset of necking and
fracture of the specimen.
Primary
I
Secondary
II
Tertiary
III
Strain ε
Fracture
Time t
The theoretical models showing the behaviour of creep strain and creep fracture are not reliable
enough to draw accurate predictions to be used during design.
3.7. Corrosion
3.7.1. Definition
Corrosion is the deterioration of a material due to its environment thereby making a component
or structure unfit for use.
Corrosion is the primary means by which materials deteriorate worldwide, ahead of phenomena
like wear and fractures. It affects all materials, whether metals, polymers or ceramics.
Corrosion is a chemical or electrochemical reaction between a material, usually a metal, and
its environment. It results in the deterioration or transformation of the material and its properties.
It therefore reflects the interaction between the surface of a material and its environment.
Corrosion damage is exhibited in various ways, either through perforation, leaks, cracks, fractures, or the swelling or disappearance of material.
104
Corrosion affects all industrial sectors. The cost of corrosion is not only limited to the replacement of an item of equipment. More specifically, 10 elements directly associated with the cost of
corrosion can be identified:
◗◗ Replacement of equipment;
◗◗ Loss of production;
◗◗ Maintenance and repair;
◗◗ Excess capacity of a parallel unit;
◗◗ Redundant equipment;
◗◗ Corrosion control;
◗◗ Technical support;
◗◗ Design;
◗◗ Insurance;
◗◗ Parts and equipment inventory.
The direct costs are the replacement of corroded materials, repair and maintenance of the means
of protection. The indirect costs are shutdown of the facilities, loss of products, inspections, etc.
Applied current
techology
Deferred
maintenance
Increased
performance
requirements
Technology
transfer
More hostile
environments
Corrosion
costs
Extensions
of useful life
Environmental
regulations
Research and
development
3.7.2. Influential factors
Corrosion is therefore an imbalance between a material and its environment. For each of these
factors, each criteria will affect the corrosion resistance of the equipment.
Secondly, the design and durability criteria will have to be studied to limit corrosion problems.
105
THE ENVIRONMENT
Chemical nature
Concentration
Impurity
pH (acidity)
Temperature
Pressure
Viscosity
Solid deposits
Agitation
Composition
Preparation
Metallurgical state
Heat and mechanical
treatments
Additions
Impurities
DESIGN
Surface condition
Shape
Assembling
Mechanical stresses
Vicinity to one or more metals
Contact with the environment
Means of protection
Aging
Change in tension
Variable temperature
Changes to the coating
Frequency of maintenance
MATERIAL
CORROSION
FACTORS
TIME
3.7.3. Possible states of the metal
A metal can behave in one of three ways to its ambient environment.
Immunity, the metal is immune to corrosion. The metal and the environment are in a state of
stability, there is no reaction. The absence of corrosion is not due to the formation of a material
“barrier” between the metal and the environment, but to the absence of reactivity. In practice, the
metals which display this immunity are noble metals (gold, platinum, etc.).
Passivity, the metal and the environment are not in a state of stability, however a protective
film is naturally formed on the metal which “insulates” the metal from the external environment.
This film, referred to as a passive film or passivation, must be stable with respect to the outer
environment and must not exhibit any local (or complete) weakness. Otherwise, the metal corrodes
locally. The corrosion resistance of aluminium, titanium, stainless steel, copper, etc. is due to their
passive behaviour.
Activity is when the metal corrodes. The metal is not stable and is not covered with a protective
film; it reacts with the surrounding environment by corroding. Corrosion is usually generalised
meaning that it is almost uniformly distributed over the entire surface of the metal.
3.7.4. Main forms of general corrosion
General corrosion is the simplest and most widely known corrosion phenomenon. General or
uniform corrosion occurs in a homogenous environment. It is uniformly distributed over the surface
of the metal in contact with the corrosive environment. It occurs at the same rate in all areas of the
metal thereby decreasing the thickness.
106
Original surface
Corrosion
products
Corrosion front
Different metallic
phases
Inclusions
Metal
The corrosion rate is generally expressed in terms of weight loss per unit of surface and per
unit of time or by the thickness of the corroded metal as a function of time. In most cases, it can
be simply determined (weight loss, loss of thickness, etc.) and serves to estimate the service life
of the object in question.
The general corrosion of buried materials can also be increased by the presence of bacteria,
including when the environment (soil) has a high content of sulphides or sulphates. This phenomenon is referred to as bio-corrosion.
Atmospheric corrosion is the most common form of general corrosion. It is the reaction of the
oxygen in the air at ambient temperature with a metal when humidity and contaminants form a
corrosive film at the surface of the metal and/or when the anticorrosion protection is defective.
Example of general corrosion
3.7.5. Main forms of localised corrosion
Localised corrosion is the most dangerous form of corrosion as it is difficult to predict. It occurs
when the material is in contact with an environment that behaves selectively towards the material.
This selective behaviour may be caused by a variety of sources both in terms of the material (twophased alloy, inclusions, defective surface protection, etc.) and the environment (local change in
composition, pH or temperature).
107
Pitting corrosion: In some circumstances, metals protected by a passive film may undergo
pitting corrosion, that is to say localised penetration of the film. Corrosion develops and spreads in
the created pit. The quantity of corroded metal is very low, however this form of attack may sometimes lead to complete and rapid perforation of the parts.
Outer surface
Metal of the sheet
Example of pitting corrosion
Micrographic section of a sheet: profile of a pit
Crevice corrosion: Crevice corrosion primarily affects passivatable alloys. It occurs in small
confined spaces where the medium is stagnant. It stems from the difference in accessibility of the
oxygen between two areas of a metal structure. The parts with less access to oxygen are therefore
attacked as these areas are difficult to repassivate.
Example of crevice corrosion underneath an O-ring
Intergranular corrosion: This localised attack occurs at the grain boundaries of the material.
The grain boundaries are disorganised areas compared with the more even crystallographic lattice
of the grains. It is a selective attack due to local heterogeneities. This corrosion may cause the
failure of the facility with a relatively low loss of material.
Galvanic corrosion: This is an attack in which one metal corrodes preferentially when placed in
the same environment with another metal or, in which the less noble phase of a two-phase alloy
corrodes preferentially. Galvanic corrosion can simply be defined as the effect resulting from the
contact of two dissimilar metals or alloys in a corrosive conductive environment.
108
Galvanic corrosion cannot occur:
Without a conductive
connection
Metal 1
Metal 2
Without connection by an electrolyte
Insulator
Metal 1
Metal 2
Metal 1
Metal 2
Metal 1
Metal 2
Insulator
Fretting corrosion: This is the deterioration of material that occurs at the interface of two surfaces in contact due to the combination of corrosion and low reciprocal sliding of the two faces.
3.7.6. Special cases of stress cracking
Cracking corrosion of materials under the combined action of a mechanical stress and the environment incorporates the following phenomena: stress corrosion, fatigue corrosion and hydrogen
embrittlement.
Stress corrosion results from the combined action of mechanical stress (residual or applied)
and an aggressive environment for the material. The dangers of this corrosion lies in the fact that
a fairly inoffensive medium can trigger the phenomenon due to the presence of high stresses or
that low stresses can cause fractures due to a highly aggressive medium.
This type of corrosion, which is insidious and dangerous for facilities, is characterised by sudden
major cracking or by many branched cracks. They propagate in the material in an inter­granular
and/or transgranular manner and the general direction of propagation is perpendicular to the
highest stress. The fracture surfaces exhibit a brittle appearance and the loss of material is generally very low.
Example of stress corrosion under a mechanically-welded shell
Hydrogen embrittlement is a specific case of stress corrosion. It stems from the capacity of
hydrogen to diffuse into metals, thereby changing their intrinsic properties. There are three possible
sources of hydrogen: the presence of gaseous hydrogen in the facility, the formation of hydrogen
by cathodic polarisation and the formation of hydrogen by corrosion reaction. In general, hydrogen
embrittlement affects alloys with high mechanical properties and is demonstrated through rapid
crack propagation.
109
Its intergranular surface is typical: the grain faces also exhibit wormholes and microporosities
denoting the release of the gas.
Example of stress corrosion combined with hydrogen embrittlement
Fatigue corrosion is highly similar to stress corrosion. This phenomenon occurs under the
combined action of the environment and cyclic stresses. It is indicated through a decrease in the
material’s fatigue resistance.
110
V Practice and basic calculations
on the vessels
1.
Representation system
1.1. The basics of technical drawing
1.1.1. Aim
A technical drawing, also referred to as an engineering drawing, is a universal means of expression. It follows specific rules and standards that must be observed in order to obtain an efficient
and stringent drawing. Any professional must be able to decode a technical drawing and know how
to easily use it.
Only the views that are relevant for understanding are represented on a technical drawing. Each
item of information is coded and has its importance on the drawing.
1.1.2. Terminology
General layout drawing: Relatively detailed drawing of a mechanism, building or vessel that is
represented on a certain scale. The components all appear assembled on the drawing.
Definition drawing: This is complementary to the general layout drawing. It represents one
component of the mechanism, which is fully drawn and defined.
Diagram: This is a drawing that is plotted based on symbols. It is used to give a simplified representation of a facility and its operation.
Exploded view: The vessel or the mechanism is represented in perspective and disassembled.
This highlights the assembly of the various components.
1.1.3. Essential elements
• Paper size
Engineering drawings or technical drawings are done on paper sheets that are cut out according
to standardised formats: A0, A1, A2, A3, A4. For digital formats, the computer aided design (CAD)
software provides a 3D view of the mechanisms.
• Scale (magnification or reduction)
Where possible, it is advisable to use a scale of 1, i.e. the drawing corresponds to the actual object.
In most cases, this is not possible for a vessel. Therefore, the scale of the drawing must be reduced or
magnified. In any case, the scale selected must be specified and applied to all elements of the drawing.
Recommended values
Actual size
1:1
Reduction
1:2 - 1:5 - 1:10 - 1:20 - 1:50 - 1:100 - 1:200, etc.
Magnification
2:1 - 5:1 - 10:1 - 20:1 - 50:1, etc.
• Title block
The title block is a box consisting of several items of information related to the drawing. It is used
for identification and analysis of the documents. The following information is generally supplied: title
of the drawing, scale, format, index of the drawing, date, classification markers, name of the company
and name of the author. It is usually located at the bottom right-hand corner of the drawing.
111
Quantity of parts to be
manufactured
Facility
Company logo
General tolerance
Miscellaneous
comments
Format
Revision
Revision number
Projection method: American or European
• Bill of materials
The bill of materials is a list of all the parts of the vessel. It is represented in the form of a table
on the drawing or is on a separate sheet.
Drawing No.: used by the
database for the precise
name of the drawing and
its change index.
Item No.: number which
is different for each part
and which is used to
easily identify it on the
drawing
The designation column
gives the description of
each part and its function
The material making
up the part
The number of
components with
the same item number,
this is used to
determine the
total number
of each identical
The weight may be added in the bill of materials or in the title block, as it is used at all stages in
the creation of the mechanism, from its design to its assembly. The total weight of the mechanism or
sub-assemblies is also used to estimate the weight of the welds (refer to Chapter V, paragraph 3.4.)
• Thickness and meaning of the lines
Depending on the represented view, certain sections of the part may be visible or invisible. Accordingly, the format of the lines in the drawing provides us with information. On engineering drawings,
we can also find information about the axes of symmetry, the dimensions, the cutting planes, etc.
Thick full lines represent the visible contours, shapes and edges of the object. Thin dotted lines
represent invisible or hidden shapes, contours or edges of the object. So as not to overload the
drawings, hidden edges are only represented if they improve the understanding of the drawing. Lastly,
broken and mixed lines represent the axes, the planes of symmetry and the cutting planes. Thin full
lines represent interrupted views, threads, hatches and dimensions of the object. For easy under­
standing of the drawing, a 3D view (CAD) of the mechanism supplements the technical drawing.
112
Thick full
line
Thin mixed
line
Thin broken
line
• GPS specification, ISO language
The mechanism or the part observed on the technical drawing is noted and surrounded by
various symbols, this is ISO language.
There are 2 types of dimensions:
◗◗ Functional (assembleability, sealing, resistance, operation, etc.) which are always included
on the drawings;
◗◗ Other dimensions (overall dimensions, etc.) included on the drawing on option.
ISO language is a developed language used to express the functional dimension as best possible.
It introduces:
◗◗ Reference concepts (context / environment of the product or the part during operation);
◗◗ Geometrical tolerances (tolerancing of the functional dimensions).
Aim:
◗◗ Avoid ambiguities when reading the drawing;
◗◗ Simplify interactions between departments (or multiple sites);
◗◗ Facilitate subcontracting;
◗◗ Standardise the dimensioning of the drawings.
This language consists of standardised symbols used to tolerance the functional dimensions
(reminder: there is no perfect dimension!).
Compliance with these functional dimensions will guarantee the quality of the assembly and
proper operation of the system or the vessel.
113
On a technical drawing, all the dimensions mentioned (or not) shall comply with a tolerance
included on the drawing in accordance with ISO language or outlined in a specified general tolerancing standard based on the manufacturing method of the part (ISO 2768, ISO 9013, NFE 02‑352, etc.).
Geometrical
Surface condition
Dimensional
• Various types of cuts and sections
In relation to general layout drawings or drawings of complex parts, it is preferable to provide
cross-sectional views in order to see inside the parts. The cross-sectional view is a projection of
the part via a sectional line in a given direction.
The section is therefore located in the material which is represented by hatching or symbols
specific to each material. This representation is no longer used today; for the most part, the sections
made in the CAD do not feature hatching specific to the material used. Therefore, it is necessary
to specifically state the material in the title block of the part, or in a special material specification
with a reminder in the bill of materials.
For convenience, the rules of representation of the materials are provided below:
Steels, cast irons and all
metals except aluminium
and copper
Wood cut in a longitudinal
direction
Aluminium alloys and light
alloys
Wood cut in a transverse
direction
Plastic and insulating
materials
Glass and optical
components
Copper alloy
Concrete
Winding and
electromagnet
Note: For parts with low
thickness, hatching can be
replaced with a solid background
Half sections
On some parts, a full section is not necessary; in this case, it is preferable to make a half section.
This section only goes through a portion of the part and shows not only the outside of the part but
also the inside, making it possible to reduce the number of views and simplify the drawing.
114
Partial section
The partial section is useful to show details without adding a view. It helps to define the cut out
area as well as the depth.
Blind tapped hole
Key groove
Broken section
The broken section is a full section of the part, however the section line goes through the typical
geometries of the part.
115
Removed section
This view is only used to show the section of the part in a given location, it does not show the
edges in the background or the hidden edges.
Flat
Drilled hole
Groove
Revolved section
The revolved section will also be used to show the sections of the part, however for space requirement reasons, the sections are added directly on the view.
1.2. Steel construction
1.2.1. Architect
There are various types of drawings used in architecture. These include the site plan, the block
plan and the plan of the façades, each having a well-defined function.
◗◗ The site plan locates the plot to be built in the municipality. In general, it is a land
register map.
116
◗◗ The block plan gives the position of the building on the plot of land. It shows the deve-
lopment of the site.
◗◗ The plan of the façades show the outside appearance of the various façades of the buil-
ding. A perspective can supplement this plan.
1.2.2. Design office
Other types of drawings can be done in the design office: layout plan, general layout drawing,
subassembly drawing, detail drawing, definition drawing.
The layout plan is intended for the civil engineering department to calculate and manufacture
the foundation blocks. It consists of an outline sketch, vertical load distribution and details regarding
the column bases with reservations.
The general layout drawing for a building consists of an elevation of the characteristic lines, an
outline sketch of the roof and possibly detail drawings.
The subassembly drawing of a building consists of views of one or more areas of the general
layout drawing and possibly detail drawings.
The detail drawings represent all the details of the assemblies marked on the general layout
drawing or the subassembly drawing with as many views as necessary for proper understanding.
It is also possible to represent the details on the general layout drawings or subassembly drawings.
The definition drawing provides a view of an isolated element with its full dimensioning thereby
completely defining the element.
1.2.3. Planning office
Various types of drawings are used in the planning office: location drawings of the elements,
production drawings, setting-out drawings.
The location drawing of the various elements is prepared using the general layout drawing and
the subassembly drawing. It is used for the assembly of the structure, to prepare the bills of materials of the elements in order to order the raw materials, and to prepare the production drawings.
The production drawing represents an isolated element with all the dimensions. It is used to
produce the element in the workshop.
The setting-out drawing represents the arrangement of the basic surfaces with information
regarding the number, dimensions and type of plates or sheets.
1.3. Boiler making
1.3.1. Types of drawings
The most commonly used type of drawing for boiler making is the general layout drawing of a
vessel.
117
118
The general layout drawing is relatively detailed and has a certain scale depending on the
dimensions of the vessel.
It must specify the dimensions, the main details, the layout of the pipes, partitions, manholes,
trays, internals, etc.
It also includes the conditions of study, the materials and a list of drawings in the event detail
drawings are necessary.
The dimensions are in millimetres.
1.3.2. Various elements of the drawing
The general layout drawing normally consists of:
◗◗ A main view of the assembled vessel;
◗◗ One or more directional views depending on the number of pipes, north will be indicated;
◗◗ A bill of materials;
◗◗ A list of the nozzles with the identification, diameter, series, type of flange, type of flange
facing, reinforcement or self-reinforced. The type and the nature of the gaskets may also
be included as necessary;
◗◗ A title block;
◗◗ Detail drawings depending on the size of the vessel (for small vessels, a drawing with all
the details is very common);
119
◗◗ One or more tables with the construction code, design data, weight (empty, test, operating),
materials and standards, non-destructive tests;
◗◗ A table with the symbols for the welds, possibly with the reference standard indicated.
Example of elevation and directions:
This is a special case as the directions are anticlockwise while clockwise direction is preferentially used.
120
Example of a list of nozzles with details about the chamfers:
DETAIL 1
(CIRCULAR WELD)
DETAIL 2
(LONGITUDINAL WELD OF THE SHELL)
121
Example of summary tables:
122
1.3.3. Conventions of representation
Conventions of representation for the general layout drawings:
◗◗ The pipes are brought into the plane of the drawing and positioned on an elevation dimension.
◗◗ The frame of reference is generally the lower line of tangency for vertical vessels and the
straight line of tangency for horizontal vessels.
◗◗ One or more directional views in order to locate the various elements (longitudinal joints,
pipes, manholes, ladders, walkways, etc.).
◗◗ The position is given by the angle with respect to a main axis or by the angle plus an arc;
the arc is calculated on the outside of the element.
123
◗◗ The views of the vessel are dimensioned with an identification of the various elements.
◗◗ The thickness of the metal sheet is represented by a relatively thick line without any
relation to scale. If the thickness is significant with regard to the diameter, it may be represented for greater clarity.
◗◗ The bolts are represented by their axis.
◗◗ The holes of tube plates are not all represented.
◗◗ The weld lines are represented and identified in order to show the relationship with the
welding specifications.
◗◗ The quantity and location diameter of the anchor bolts are stated to show the relationship
with civil engineering.
Conventions of representation for the detail drawing:
◗◗ The thicknesses of the metal sheets are represented via a sectional view with two lines
between which no hatching is necessary.
◗◗ The drilling of standardised flanges is never dimensioned.
◗◗ In certain cases, the detail drawings may be done on a separate plan called a detailed
plan. These are done where necessary in order to clarify important points (saddles,
internals, tray supports, etc.).
◗◗ The welds are detailed and symbolically represented in accordance with the standard.
◗◗ The sections, details and views must be clearly identified for easy reading.
◗◗ The trays are numbered from the bottom upwards.
IMPORTANT: When creating drawings, the designer must bear in mind that the reader should
be able to find all information needed to build the vessel.
Question to ask: Do I have all information to fabricate the vessel?
Conversely, the designer must also check that there is not an excessive amount of information,
which would overload the drawing.
124
1.3.4. Advice for reading
The general layout drawing provides all information, the first reference is the construction code,
it will be the guide for all rules to be followed for the calculation, fabrication, inspections and test.
The general layout drawing is the reference with respect to the detail drawings, it must always
be consulted at the same time as the detail drawings.
1.4. Pipework
The types of drawings used for pipework are: general layout drawing of the installation, definition drawings of the flowlines. These drawings may be represented in various ways. For example:
Orthogonal or isometric, double-line or single-line mode of representation.
The general layout drawing of the installation is normally orthogonal, single-line or double-line.
It consists of:
◗◗ A front view (elevation);
◗◗ A top view (plan view);
◗◗ Possibly additional views;
◗◗ The flowlines of the installation with their markings, their relative positions and their
positions with respect to the vessels, the position of accessories.
125
The single-line isometric representation (two-line for large diameters) is used for the flowline
definition drawings. The drawing includes:
◗◗ The isometric representation of the flowline with the symbolised and dimensioned
changes in direction;
◗◗ The position and dimensions of the accessories;
◗◗ The identification of the various elements.
2.
Location of the centre of gravity
FIND or REVISE THE CENTRE OF GRAVITY OF A VESSEL
Notation
C = distance to the centre of gravity, m or mm
D’ = revised distance to the centre of gravity,
m or mm
Dn = distance from original centre of gravity
to width to add (+) or remove (-) as shown,
m or mm
Ln = distance from reference line to the
centre of gravity of a component, m or mm
Mn = weight of vessel component, contents
or attachments, kg
M’ = new overall weight, kg
W +/- Σ Mn
Wn = revised weight, kg
(+) to add weight (-) to remove weight
To find the centre of gravity, we use the formula:
C=
ΣLnMn
M
This means that the position of the centre of gravity of the structure is equal to the sum of the
average locations of the centre of gravity, weighted by their weight. We can therefore divide the
structure into various components to study their centres of gravity independently. By breaking
down the structure into simple components, we can easily determine the centre of gravity of any
structure. However, depending on the filling rate of a storage vessel, its centre of gravity varies.
126
To revise the centre of gravity, we use the formula:
D =C±
Σ dnWn
M
This formula serves to translate, with respect to a reference plane, the centre of gravity depending on the filling of the vessel.
The weight calculation and estimations for the components are given in the following chapter.
3.
Estimating the weight
Estimating the weight of the structure is an important aspect of vessel design. The more the
calculation of the weight is representative of actual conditions, the more accurate the determination
of the forces and moments will be. Weight can be determined for various operating conditions of
the vessel:
◗◗ The vessel before or during lifting;
◗◗ The empty vessel;
◗◗ The vessel in operation;
◗◗ The vessel during hydrostatic testing.
There are a number of ways to estimate the total weight. The methods that will be used here
starts with determining the volume of metal for the shells, heads and supports. Next, the weight
of the product is assessed as this represents a substantial portion of the total weight for operating
conditions. Lastly, the weights of the various accessories and items of equipment are taken into
account.
Many uncertainties must be considered during the calculation. For example, the exact thickness
of the metal sheets is not known. A difference of a few tens of millimetres over such a large surface could significantly increase the total weight of the structure. A percentage is added to enable
the best estimation possible of the weight of the structure. This depends on the total weight of the
vessel. It takes into account the weight of the welds and variations in thickness of the metal sheets
and the heads.
3.1. Different types of weights
Six types of weights of the vessel are calculated:
◗◗ 1 - Fabricated weight: The weight of the vessel without the equipment and accessories
when it leaves the workshop.
◗◗ 2 - Shipping weight: Fabrication weight plus the weight of the necessary equipment for
shipping such as saddles.
◗◗ 3 - Lifted weight: Fabricated weight plus the weight of the equipment installed during
lifting such as insulation, fire protection, piping and access equipment.
◗◗ 4 - Empty weight: Weight of the vessel with all equipment ready for operation.
◗◗ 5 - Operating weight: Empty vessel weight + liquid weight.
◗◗ 6 - Test weight: Empty vessel weight + the weight of water.
127
3.2. Vessel weight
Firstly, the general weight of the structure is estimated. Accordingly, the weight of the shells,
heads, support and openings must be taken into consideration. The considered thickness for calculating the volume is the nominal ordering thickness of the metal sheets.
It is recommended to methodically fill out a table. Firstly, the weight of all cylindrical shells of
the vessel, the conical and other transitions, is estimated. For specific heads, reference should be
made to the standards or characteristics of the manufacturer. Next, the support consists of several components whose weight must be estimated. Lastly, the nozzles and manholes are pipework
additions with flanges and reinforcements that should not be ignored.
Once this estimation is complete, the weight of the general structure or the simple vessel is
estimated.
The weight of the vessel is obtained by multiplying the volume by the theoretical density of the
material.
M=ρ*V
Cylindrical shell
D (mm)
th (mm)
h (mm)
V (m3)
M (kg)
V = π(R 2 – r 2 )H
Shell
V=
Conical transition
Heads
D (mm)
th (mm)
-
V (m3)
M (kg)
Elliptical head
eπh
3
(e + 2R + 2r )
Formulas or comments
Standard NF E 81‑103
V=
Spherical head
4
6
π(R 3 – r 3 )
V = e * L* l
Flat head
Support
Formulas or comments
D (mm)
th (mm)
-
V (m3)
M (kg)
Formulas or comments
Skirt - Leg Lug - Ring
Provide details about
all support components
Base ring
Bolts
Gussets
Openings
D (mm)
th (mm)
Qty
Wunit (kg)
M (kg)
Formulas or comments
Flanges
Valves and fittings
Manhole
See table below
(Figure 3.2‑1)
Nozzles
See table below
(Figure 3.2‑1)
Total
For the nozzles, the values are taken from the Pressure Vessel Design manual written by Dennis
Moss. For conventional nozzles, they take into account the flange and the pipe. For the manholes,
the value takes into account piping, open end flange, blind flange and bolting.
128
The values taken from the Pressure Vessel Design Manual by Moss were compared with those
of Piping Equipment (2001) by Trouvay & Cauvin. The difference between the weight of the nozzle
and the weight of the flange corresponds on average to the weight of the piping. For example, for
a 600 diameter nozzle, Trouvay & Cauvin gives a flange weight of 247 kg. For Moss, the full nozzle
weight is estimated at 266 kg.
TABLE SHOWING WEIGHT ESTIMATIONS OF NOZZLES AND MANHOLES
Rating (PN/Class)
Size
20/
150
50/
300
100/
600
150/
900
Rating
Size
250/ 420/
1500 2500
DN
NPS
(in.)
25
1ʺ
2
2
3
5
6
40
11/2 ʺ
3
4
5
7
50
2ʺ
4
5
6
80
3ʺ
7
10
100
4ʺ
10
150
6ʺ
200
20/
150
50/
300
DN
NPS
(in.)
Weight in kg
8
650
26 ʺ
104
222
10
15
700
28 ʺ
118
249
12
19
21
750
30 ʺ
127
511
311
1306
10
15
35
50
800
32 ʺ
138
365
14
19
27
50
73
850
34 ʺ
156
399
17
25
37
58
98
172
900
36 ʺ
175
783
445
1671
8ʺ
24
37
60
94
152
236
950
38 ʺ
200
474
250
10 ʺ
33
53
98
141
295
454
1000
40 ʺ
211
510
300
12 ʺ
49
72
118
190
426
612
1050
42 ʺ
231
1083
478
2177
350
14 ʺ
60
105
185
278
431
1100
44 ʺ
204
628
400
16 ʺ
74
181
130
320
249
572
341
730
533
1474
1150
46 ʺ
277
735
450
18 ʺ
91
217
154
397
381
694
473
1030
669
2359
1200
48 ʺ
299
1347
533
2502
500
20 ʺ
107
269
191
483
355
873
582
1270
782
2463
1250
50 ʺ
320
869
600
24 ʺ
141
374
266
726
500
1218
1037
2474
1202
4082
1300
52 ʺ
336
919
1350
54 ʺ
363
984
1400
56 ʺ
379
1266
1450
58 ʺ
440
1347
1500
60 ʺ
476
2622
1397
3935
Weight in kg
Notes:
1. Weights include pipe and flange weld.
2. Low weight in bold is weight of manhole including: bolts, flange
and nozzle.
3. Class 1500 manholes are based on LWN (Long Weld Neck).
FIGURE 3.2‑1: Taken from Pressure Vessel Design Manual – Weights of nozzles and manholes
129
3.3. Weight of equipment
The vessel is fitted with three internal trays with support that must be taken into account when
calculating the weight. Ladders and platforms have a significant weight that can be estimated
by calculating the total surface area of the platforms and the total length of ladders. Lastly, the
vessel is insulated with 150 mm thick rock wool. This insulation is covered with a thin steel plate,
0.5 mm thick.
Equipment
Qty
D
th
(mm) (mm)
V
(m3)
W
(kg)
Formulas or comments
Internal trays
Tray support
Coatings
According to Moss, 50 kg per support
th
D
h
(mm) (mm) (mm)
V
(m3)
W
(kg)
Formulas or comments
Rock wool density
ρ = 50 kg/m3
Insulator
Steel density
P = 7850 kg/m3
Plate
Access
l (m)
S
(m2)
-
-
W
(kg)
Rectangular
platform
Formulas or comments
Surface density: 100 kg/m2
Circular
platforms
Average surface density for a circular
platform: 150 kg/m2
Linear density of a caged ladder:
35 kg/m
Ladders
Total
12,993.05
3.4. Weight of contents
The volume of the fluid contained in the vessel is not equal to the total volume inside the vessel.
This is stated in the technical specification of the vessel. It is easy to determine the weight of
contents using this information.
Weight of contents
V (dm3)
ρ(kg/m3)
W (kg)
Process product
Dual shell liquid (heating, cooling)
Hydrostatic testing water
1,000
3.5. Total weight
The total weight of the structure can be determined using the previous estimations. An additional
percentage represents the weight of the welds or variations in the shell thickness. This additional
percentage depends on the total weight of the vessel.
130
Additional percentage
< 25,000 kg
10%
25,000 kg - 35,000 kg
8%
35,000 kg - 45,000 kg
6%
> 45,000 kg
5%
Total weight (kg)
Empty vessel weight
Additional weight
Total empty vessel weight
Operating weight (+ fluid contents)
Hydrostatic testing weight (+ water)
4.
Examples of optimum tank proportions
This procedure specifically addresses drums3, but can be made applicable to any type of tank.
The basic question is: what are the proportions of the tank? Usually expressed as an L/D (length/
diameter) ratio, they will give the lowest weight for a given volume. The maximum volume for the
least surface area and the lowest weight is of course a sphere. Unfortunately, spheres are generally
more expensive to build. Thus, spheres are not the most economical option until you get to very
large volumes and for some process applications where that shape is required.
For tanks without pressure such as atmospheric vertical storage tanks, the optimum length/
diameter ratio is 1, again using the criteria for the maximum volume for the minimum surface area.
The optimum L/D ratio varies with the following parameters:
◗◗ Pressure;
◗◗ Allowable stress;
◗◗ Corrosion allowance;
◗◗ Joint coefficient (coefficient of the welded joint).
In Process Equipment Design, Brownell and Young suggest that for vessels with thickness less
than 2 inches (i.e. 50 mm), the optimum L/D ratio is 6, and for greater thicknesses is 8. However,
this does not account for the parameters just shown. Others have suggested a further breakdown
by pressure categories:
Pressure (MPa)
L/D ratio
0 – 1.7
3
1.7 – 3.4
4
> 3.4
5
3. Drum = boiler drum
131
Although this refinement is an improvement, it still does not factor in all of the variables. But
before describing the actual procedure, a brief description of the sizing of drums in general is
warranted. Here are some typical types of drums:
◗◗ Knock-out drums;
◗◗ Accumulator drums;
◗◗ Suction drums;
◗◗ Liquid-vapour separators;
◗◗ Liquid-liquid separators;
◗◗ Storage vessels;
◗◗ Surge drums.
Typically, the dimensioning of drums is related to the nature of the process such as liquid
hold­up (surge), storage volume, or velocity considerations for separation. The volume collected in
the process units relates to the response time required for the alarms and operators to respond to
upstream or downstream conditions.
For small liquid holdup, tanks tend to be vertical, whereas for large surge volumes they tend to
be horizontal. For small volumes, it may be necessary to increase the L/D ratio beyond the optimum
proportions to allow for control suited to the systems. Thus, there may be an economic L/D ratio
for determining the least amount of metal for the given process conditions as well as an L/D ratio
suited to the process.
For liquid-vapour separators, the diameter of the vessel is determined by the velocity of the
product and the time it takes for the separation to occur. Baffles and demister pads can speed
up the process. In addition, liquid-vapour separators must provide for minimum vapour spaces.
The sizing of the vessel is of course beyond this discussion and is the subject of numerous articles.
An economic L/D ratio is between 1 to 10. L/D ratios greater than 10 may produce the lowest
surface-area-to-volume ratio. However, this should be considered as impractical for most applications. Plot space is also a consideration in ultimate cost. In general, the higher the pressure the
larger the ratio, and the lower the pressure the lower the ratio. As previously stated, the optimum
L/D ratio for an atmospheric drum is 1. Average pressure vessels will range between 3 and 5.
Two procedures are described here and are called “Method 1” and “Method 2” respectively. The
two procedures, though similar in execution, give different results.
Both methods take into account pressure, corrosion, joint efficiency and allowable stress. Even
with this much detail, it is impossible to determine exactly what proportions will yield the lowest
overall cost, since there are many more variables that enter into the ultimate cost of a vessel.
However, determining the lowest weight is probably the best parameter in achieving the lowest cost.
The procedure for determining optimum L/D ratios for the two methods is as follows:
Data:
V: Volume
P: Pressure
C: Corrosion allowance
S: Allowable stress
E: Joint efficiency
132
Method 1
◗◗ 1. Calculate F1 (see Figure A below).
◗◗ 2. From Figure B provided below, using F1 and vessel volume V, determine the vessel
diameter, D.
◗◗ 3. Use D and V to determine the required length L.
Method 2
◗◗ 1. Calculate F2 (see Figure A).
◗◗ 2. From Figure C given below, using F2, determine the L/D ratio.
◗◗ 3. From the L/D ratio, calculate diameter D.
◗◗ 4. Use D and V to calculate the required length L.
CALCULATION OF F1 AND F2
Optimum vessel proportions for vessels with elliptical heads
Notation
Equations
V = vessel volume (m )
P = internal pressure (Pa)
L = length, head to head (m)
t = shell thickness (m)
W = vessel weight (kg)
D = diameter (m)
C = corrosion allowance
A = surface area (m2)
Fn = vessel ratios
S = allowable stress
E = joint efficiency
W = unit weight of plate (kg.m–2)
Le = equivalent length of a cylinder equal to the volume of a vessel
with 2:1 (m) elliptical head
H = Height of cone
R = radius (m)
C1, K1 = constant for ellipsoidal head
3
Diameter for different L/D ratios
L/D
3
D
Le = L + 0.332D
πD3
V=
12
3 12V / 13π
5
3 3V / 4π
6
3 12V / 19π
7
3 6V / 11π
8
3 12V / 25π
πD2L
4
4V
3
D=
π(0,3333 +
L
D
W = Aw
A = 2.18D2 + πDL
t=
PR
SE – 0,6P
L=
4V
2
πD
3 6V / 13π
4
+
F1 =
–
+C
D
3
P
CSE
F2 = C
SE
P
– 0,6
FIGURE A
133
1mmH20 = 9.80665 Pa = 9.80665 kg.m-2
METHOD 1
Vessel volume (m3)
Chart for determining optimum diameter
Vessel diameter (m)
FIGURE B
METHOD 2
Chart for determining the optimum L/D ratio
Optimum L/D ratio
7
Vessel volume (m3)
FIGURE C
134
Optimum vessel proportion - Comparison of the two methods
V (m3)
P (MPa)
1
42.5
2
1
56.6
2
1
85
2
1
141.6
2
Method
D(m)
L(m)
t (mm)
W(kg)
L/D
1
2.3
10.3
14.3
9.2
4.5
2
2.6
7.2
15.9
9.1
2.8
1
1.8
16.1
20.6
16.2
8.8
2
2.3
9.6
20.6
13
4.2
1
2.1
15.8
12.7
11.6
7.4
2
2.7
8.6
15.9
11.3
3.2
1
1.9
18.6
22.2
23.2
9.4
2
2.6
9.9
28.6
18
3.8
1
2.6
16.1
15.9
18.2
6.3
2
3.2
9.5
17.5
16.1
3
1
2.3
20.7
23.8
29.9
9.1
2
2.3
11.9
31.8
31.6
4.1
1
3
19.5
17.5
28.4
6.4
2
3.5
13.5
28.6
39.4
3.9
1
2.6
26.8
28.6
48.9
10.4
2
3.5
13.5
35
48.1
3.9
Atmospheric tank proportions
2d
K1 =
R
K2 =
C1 = 2 +
Ellipsoidal head
Flat elliptical head
K12
1– K12
b
a
ln
1+ 1– K12
1– 1– K12
Note: For 2:1 elliptical head,
C1 = 2.76 and K1 = 0.5
135
Case
Optimum proportions
Volume
L=D
2πR3
Cylinder with flat heads
Cylinder with ellipsoidal heads
L = R(C1 + 4K1)
πR
3
3C1 – 8K1
3
3C1 + 8K1
Cylinder with internal ellipsoidal heads
L = R(C1 + 4K1)
πR
3
3
Cylinder with internal hemi-heads
Cylinder with conical heads
Cylinder with internal conical heads
L = 8R
6.66πR3
h = 0.9R
L = 0.9R
1.5πR3
H = 0.9R
L = 3.28R
2.68πR3
Elliptical tank with flat heads
L = 2K 2a
136
2
1+ K
2
2
2K 22 πa3
2
1 + K 22
VI References / Bibliography
1.
Standards and codes
langes: ASME B16.5, ASME B16.47, EN 1092, EN 1759‑1, EN 1092‑1, ISO 7005, NF E 29‑203,
F
SAE 3000/6000.
eads: ASME VIII Div. 1, NF E 81‑100, NF E 81‑101, NF E 81‑102, NF E 81‑103, NF E 81‑104,
H
DIN 28011, DIN 28013.
Loadings: NF 13445, ASCE 7‑10, NF 1991 1 3 2007, NF 1993 4 1 2007.
2.
Works
Stresses_in_Large_Horizontal_Cylindrical_Pressure_Vessels_on_Two_Saddle_Supports_-_
Zick_(1951)_Original
Vocabulaire trilingue de la profession CECT/SNCT (Trilingual vocabulary of the profession).
Pressure Vessel Design Manual (Dennis R. Moss & Michel Basic).
Rappels sur la fatigue H. Karaouni.
Mécanique de la rupture.
Wind Loads for Petrochemical and Other Industrial Facilities.
ASME training course Overview of Pressure Vessel Design.
www.metiers-avenir.com
https://www.plakagroup.com/
vis-express.fr
137
VII Conclusion
This document is a basic handbook of the SoM guide. It lays the necessary foundation for under­
standing the following works. Its aim is to outline a number of terms used in the profession.
Lastly, this handbook incorporates a few simple and useful methods for dimensioning components, and provides weights and other useful information for preliminary calculations and checks.
138
Practical guide for boiler making and pipework
General pressure vessel design principles
For several years now, the Boiler Making and Pipework Professional Commission
has been financing a study and research programme in order to compile a
Strength of Materials guide consisting of several handbooks. The aim is to
merge theoretical knowledge, Cetim’s expertise and the know-how of industrial
manufacturers in order to provide simple and clear guidelines for the design
of their equipment. This first instructive, functional and practical handbook
summarises the basics of engineering for the design of pressure vessels, via
many concrete examples in order to be used as a model for sector players.
It presents the principles used to design all components of the vessel, from
support to access equipment and outlines for each category of stresses, the
loading conditions to be taken into account. As the boiler maker has to be familiar
with the applicable codes and standards, the various stresses and loadings,
the main failure modes of the vessels and has to be able to determine the
maximum allowable stress, the writers of this work were careful to meticulously
address the information provided in the many chapters - terminology; calculation
method; failure and fracture mode; basic practice and calculations in relation
to the vessels. The guide also includes bibliographical references which cite
applicable codes and standards.
cetim.fr
2022 - AP code 023770
Centre technique des industries mécaniques
52, avenue Félix-Louat • C.S. 80067
60304 Senlis Cedex, France
Telephone: +33 (0)3 44 67 36 82
CETIM No.: 9Q429
ISSN: 1767‑2546
ISBN: 978‑2-36894‑244‑4
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