A Computational Investigation on Bolt
Tension of a Flanged Pipe Joint Subjected to
Bending
Submitted by
Md. Jahidul Islam
Student No. 9904095
Thesis
Submitted in Partial Fulfillment of the Requirements for the Degree of
BACHELOR OF SCIENCE IN CIVIL ENGINEERING
Department of Civil Engineering
BANGLADESH UNIVERSITY OF
ENGINEERING AND TECHNOLOGY, DHAKA
JUNE, 2005
i DECLARATION
Declared that except where specified by reference to other works, the studies embodied in
thesis is the result of investigation carried by the author. Neither the thesis nor any part
has been submitted to or is being submitted elsewhere for any other purposes.
Signature of the student
(Md. Jahidul Islam)
ii TABLE OF CONTENTS Declaration i Table of Contents ii List of Tables iv List of Figures v Acknowledgement viii Abstract ix
Chapter1. Introduction
1.1 Background 1 1.2 Objective 1 1.3 Methodology 1 1.4 Organization of the Thesis 2
Chapter 2. Literature Review
2.1 Introduction 3 2.2 Types of Pipe Joint 8
2.3 Types of Flange 9
2.4 Flanged Connection Subjected to Bending 11
2.5 Previous Works 11
2.5.1 Stress in Bolted Flanged Connection 11
2.5.2 Comparison of Performance of Bolts and Rivets 14
2.6 Conventional Analysis and Design 15
Chapter 3. Methodology for Finite Element Analysis
3.1 Introduction 18
3.2 The Finite Element Packages 18
3.3 Types of Analysis on Structures 19
3.4 Finite Element Modeling of Structure 20
3.4.1 Modeling of the Pipe and Flange 21
3.4.2 Modeling of the Bolt and the Surface Spring 23
3.4.3 Modeling of the Stiffening Ring 25
3.5 Finite Element Model Parameters 27
iii 3.6 Meshing 27
3.6.1 Meshing of the Pipe 27
3.6.2 Meshing of the Flange 28
3.6.3 Properties of the Contact Element 28
3.6.4 Properties of the Bolts 29
3.7 Boundary Conditions 29
3.7.1 Restraint 29
3.7.2 Load 30
CHAPTER 4 Computational Investigation
4.1 Introduction 33
4.2 Sample Problems 33
4.3 Results and Discussion 33
4.3.1 Effect of Mesh Density and Element Type 33
4.3.2 Effect of Number of Bolts 34
4.3.3 Effect of Flange Thicknesses 34
4.3.4 Proposed Empirical Equations 34
4.4 Remarks 36
4.5 Tables and Graphs 37
CHAPTER 5 Conclusion
5.1 General 58
5.2 Findings 58
5.3 Scope for Future Investigation 59
References 60
Appendixes
A ANSYS Script used in this Analysis 61
iv LIST OF TABLES
Table 3.1 SHELL93 Input Summary. 22
Table 3.2 COMBIN39 Input Summary. 24
Table 3.3 BEAM4 Input Summary. 26
Table 3.4 Various parameters. 27
Table 4.1 Study parameters for a flanged pipe joint. 33
Table 4.2 Various parameters for 3 in. diameter pipe. 38
Table 4.3 Bolt tension for various numbers of bolts according to various flange
thicknesses for 3 in. diameter pipe.
38
Table 4.4 Various parameters for 3.5 in. diameter pipe. 39
Table 4.5 Bolt tension for various numbers of bolts according to various flange
thicknesses for 3.5 in. diameter pipe.
39
Table 4.6 Various parameters for 4 in. diameter pipe. 40
Table 4.7 Bolt tension for various numbers of bolts according to various flange
thicknesses for 4 in. diameter pipe.
40
Table 4.8 Various parameters for 5 in. diameter pipe. 41
Table 4.9 Bolt tension for various numbers of bolts according to various flange
thicknesses for 5 in. diameter pipe.
41
Table 4.10 Various parameters for 6 in. diameter pipe. 42
Table 4.11 Bolt tension for various numbers of bolts according to various flange
thicknesses for 6 in. diameter pipe.
42
Table 4.12 Various parameters for 8 in. diameter pipe. 43
Table 4.13 Bolt tension for various numbers of bolts according to various flange
thicknesses for 8 in. diameter pipe.
43
Table 4.14 Various parameters for 10 in. diameter pipe. 44
Table 4.15 Bolt tension for various numbers of bolts according to various flange
thicknesses for 10 in. diameter pipe.
44
Table 4.16 Various parameters for 12 in. diameter pipe. 45
Table 4.17 Bolt tension for various numbers of bolts according to various flange
thicknesses for 12 in. diameter pipe.
45
v LIST OF FIGURES
Figure 2.1. Pipe column supported the industrial building of Abdul Monem Ltd,
near Shahbag, Dhaka.
5
Figure 2.2. Foot over bridge supported by pipe columns at BUET campus, Dhaka. 5
Figure 2.3. Circular pipe columns supported the track of the roller coaster at
Fantasy Kingdom Entertainment Park, Ashulia.
6
Figure 2.4. Water tank supported on nine tubular columns at Lalmatia, Dhaka. 6
Figure 2.5. A large advertisement bill board supported by a circular pipe column
at Shahbag, Dhaka.
7
Figure 2.6. Cylindrical column of a T.V. mast at Emley Moore, Yorkshire
(Appleby-Frodingham Steel Company).
7
Figure 2.7 3-legged circular pipe transmission tower of BTTB at Katabon,
Dhaka.
8
Figure 2.8 A flanged pipe joint with different components. 9
Figure 2.9 Different types of flanges. 10
Figure 2.10 Illustration of earlier methods of calculating stress in a bolted flange
connection.
11
Figure 2.11 3-D view of a typical flanged pipe joint with 12 bolts and 12 in.
diameter pipe.
16
Figure 2.12 Front view of a typical flanged pipe joint with 12 bolts and 12 in.
diameter pipe.
16
Figure 2.13 Plan and force distribution of a typical flanged pipe joint with 12 bolts
and 12 in. diameter pipe.
17
Figure 3.1 General sketch of the flanged pipe joint studied. 20
Figure 3.2 SHELL93 8-Node Structural Shell. 21
Figure 3.3 COMBIN39 Nonlinear Spring. 23
Figure 3.4 BEAM4 3-D Elastic Beam. 25
Figure 3.5 Force - deflection behavior of contact springs. 28
Figure 3.6 Force – deflection behavior of bolts. 29
Figure 3.7. Finite elements mesh of a flanged pipe joint. 30
vi Figure 3.8. Finite elements mesh with load and boundary condition. 31
Figure 3.9. Typical deflected shape of a flanged pipe joint. 31
Figure 3.10 Typical stress contour of a flanged pipe joint. 32
Figure 3.11 Typical stress contour of bolts. 32
Figure 4.1 Effect of number of bolts on bolt tension for 3 in. diameter pipe. 38
Figure 4.2 Effect of number of bolts on bolt tension for 3.5 in. diameter pipe. 39
Figure 4.3 Effect of number of bolts on bolt tension for 4 in. diameter pipe. 40
Figure 4.4 Effect of number of bolts on bolt tension for 5 in. diameter pipe. 41
Figure 4.5 Effect of number of bolts on bolt tension for 6 in. diameter pipe. 42
Figure 4.6 Effect of number of bolts on bolt tension for 8 in. diameter pipe. 43
Figure 4.7 Effect of number of bolts on bolt tension for 10 in. diameter pipe. 44
Figure 4.8 Effect of number of bolts on bolt tension for 12 in. diameter pipe. 45
Figure 4.9 Comparison of bolt tension for 12 in. diameter pipe and flange
thickness = pipe wall thickness
46
Figure 4.10 Comparison of bolt tension for 10 in. diameter pipe and flange
thickness = pipe wall thickness.
47
Figure 4.11 Comparison of bolt tension for 8 in. diameter pipe and flange
thickness = pipe wall thickness.
48
Figure 4.12 Comparison of bolt tension for 6 in. diameter pipe and flange
thickness = pipe wall thickness.
49
Figure 4.13 Comparison of bolt tension for 12 in. diameter pipe and flange
thickness = 2 × pipe wall thickness. 50
Figure 4.14 Comparison of bolt tension for 10 in. diameter pipe and flange
thickness = 2 × pipe wall thickness. 51
Figure 4.15 Comparison of bolt tension for 8 inch diameter pipe and flange
thickness = 2 × pipe wall thickness. 52
Figure 4.16 Comparison of bolt tension for 6 inch diameter pipe and flange
thickness = 2 × pipe wall thickness. 53
Figure 4.17 Comparison of bolt tension for 12 in. diameter pipe and flange
thickness = 3 × pipe wall thickness.
54
vii Figure 4.18 Comparison of bolt tension for 10 in. diameter pipe and flange
thickness = 3 × pipe wall thickness
55
Figure 4.19 Comparison of bolt tension for 8 in. diameter pipe and flange
thickness = 3 × pipe wall thickness.
56
Figure 4.20 Comparison of bolt tension for 6 in. diameter pipe and flange
thickness = 3 × pipe wall thickness.
57
viii ACKNOWLEDGEMENT
At first the author would like to express his wholehearted gratitude to the Almighty for
each and every achievement of his life. May Allah lead every individual to the way which
is best suited for that particular individual.
The author has the pleasure to state that, this study was supervised by Dr. Khan Mahmud
Amanat, Associate Professor, Department of Civil Engineering, Bangladesh University of
Engineering and Technology, Dhaka. The author has also greatly indebted to him for all
his affectionate assistance, proper guidance and enthusiastic encouragement. It would
have been impossible to carry out this study without his dynamic direction.
I would like to immensely thank my parents, their undying love, encouragement and
support throughout my life and education. Without them and their blessings, achieving
this goal would not have been possible. I thank all my friends for their assistance and
motivation.
ix ABSTRACT
Apparently there is no analytical method for the analysis of bolt tension of a flanged pipe
joint, when pipes are subjected to both bending and axial load. Generally approximate
linear distribution method is used for this analysis, but it is often not suitable. In this
project, an investigation is made to find the effects of various parameters relating to
flanged pipe joint structures, so that a definite guideline, on determining the bolt tension
can developed, whilst other leading dimensions constant. Design formulas are developed
for the computation of forces that are likely to be critical. In addition results are
compared with the conventional analysis.
To carry out the investigation, a flanged pipe joint subjected to both bending and axial
force has been modeled using finite element method, which also includes contact
simulation. In this analysis process shell element has been used for the modeling of pipe
and flange. Non-linear spring has been used to model contact and bolt. Non-linear finite
element analysis method has been used to find out more accurate results. Joint has been
subjected to ultimate moment and under this moment; the maximum bolt tension has
been evaluated. Based on the study, an attempt has been made to present a guideline to
find out bolt tension that is structurally effective for a flanged pipe joint. The whole
process is carried out under various parametric conditions within certain range.
It has been found that some parameters like pipe length, longitudinal divisions and bolt
diameter do not have any appreciable effect upon bolt tension for a flanged pipe joint. On
the other hand, flange thickness and number of bolts have found to have significant effect
on effective bolt tension. Based on the results of the analysis, some empirical equations
are developed to determine the bolt tension for different number of bolts and flange
thickness for different pipe diameter. It has been shown that, the suggested empirical
equations are useful in structural analysis for calculating the effective bolt tension with
acceptable accuracy.
Introduction 1
CHAPTER 1
INTRODUCTION 1.1 GENERAL
Pipes are required for many structural constructions. But wide application of pipes for
structural purposes are not possible until reliable and economical methods of determining
bolt tension at a pipe joints are devised. Bolts connect two flanges in a pipe joints and are
subjected to both bending and axial force. It is difficult yet necessary to determine the
bolt tension for the design of a flanged pipe joint. Generally, the linear distribution
method is used for determining bolt tension. But this method is not always valid for
application and more regretfully no guidelines are available to assist the designer to make
a decision in case of flanged pipe joint design. Due to the complexity of the moment-
transfer mechanism between the flange and the bolt under loading and lacking of
assumptions that may lead to a correct prediction of the flange pipe joint response, there
are significant scopes to investigate this matter. This investigation is expected to provide
the design engineer some definite guidelines to estimate the effective bolt tension.
1.2 OBJECTIVE
The objective of this present study is to investigate a flanged pipe joint under loading and
to develop a decisive guideline to determine the effective bolt tension for a flanged pipe
joint structure under various parametric conditions. The pipe joint with bolted flange
connection, subjected to both bending moment and axial load will be considered. For this
purpose, a typical problem is going to be studied under various parametric conditions that
influence the bolt tension. A flanged pipe joint subjected to both bending and axial force
shall be modeled using Finite Element Method, which shall also include contact
simulation. Based on the study, an attempt shall be made to present a definite guideline to
find bolt tension that is structurally effective for a flanged pipe joint.
1.3 METHODOLOGY
To carry out the investigation, a flanged pipe joint would be studied under different
parametric conditions. Analysis would use shell Element for the modeling of pipe and
Introduction 2
flange. Nonlinear Spring would be used to model contact and bolt. In this analysis, pipe
shall be subjected to ultimate moment. Under this moment, the maximum bolt tension
shall be evaluated. The bolt tension shall be determined under some parametric
conditions. Based on the results found, some mathematical formula will be generated to
appropriately determine the bolt tension. The whole process is carried out under various
parametric conditions within certain range.
1.4 ORGANIZATION OF THIS REPORT
The report is organized to best represent and discuss the problem and findings that come
out from the studies performed. Chapter 1 introduces the problem, in which an overall
idea is presented before entering into the main studies and discussion. Chapter 2 is
Literature Review, which represents the work performed so far in connection with it
collected from different references. It also describes the strategy of advancement for the
present problem to a success. Chapter 3 is all about the finite element modeling
exclusively used in this problem and it also shows some figures associated with this study
for proper presentation and understandings. Chapter 4 is the heart of this thesis write up,
which describes the computational investigation made throughout the study in details
with presentation by many tables and figures followed by some definite remarks. The last
chapter is Chapter 5, which summarizes the whole work as well as points out some
further directions.
Literature Review 3
CHAPTER 2
LITERATURE REVIEW
2.1 INTRODUCTION
Pipe is one of the most widely used products among all steel products. It is found in
every modern home for plumbing and heating, in industrial building, in railroad cars
and engineers, into cross-country oil lines, in water and gas systems, in transmission
towers and in countless other places. It can be also used as a structural frame element.
This thesis paper focuses on the pipe element that uses as a structural element.
Steel pipes are used in different structures as a structural frame member. Some of the
most widely used examples where pipes are used as frame member with bolted joint
connections are shown below:
• Buildings
• Foot over bridge
• Structures in entertainment park
• Water tank
• Bill board column.
• TV mast.
• Transmission tower.
Buildings:
Tubular steel pipe column can be used in the building system. For rapid construction
and high salvage value in industrial building steel frame structures are widely used in
our country. Among various steel elements pipe element is one of the most popular
elements. In Paribagh the industrial building of Abdul Monem Ltd is build on steel
pipe columns (Figure 2.1).
Foot over bridge:
In Dhaka city several foot over bridges are constructed for the pedestrian at different
road crossing to facilitate uninterrupted and safe movement of the pedestrian. These
over bridges are supported by means of various types of column system, such as,
concrete, steel I-section, steel pipe columns, etc. The foot over bridge in BUET
campus, is supported by steel pipe columns (Figure 2.2).
Literature Review 4
Structures in Entertainment Park:
Appearance is the first criteria for the structures in an entertainment park and pipes
are the most lucrative structural elements by any means. It takes least space, can take
both static and dynamic forces, and above all it makes the structure attractive to the
tourists. Such an example can be observed in Fantasy Kingdom Entertainment Park,
where the track of the roller coaster is supported by steel pipe columns (Figure 2.3).
Water tank:
Overhead water reservoir can be built on pipe columns. 500,000 gallon ellipsoidal
tank was built at Kaduna in Nigeria for the Government of Northern Nigeria
(Appleby-Frodingham Steel Company). It is 43 feet high and 55 feet in diameter and
is supported on ten tubular columns each 32 inches in diameter. In Dhaka several
overhead water tanks are built on circular pipe columns. At Lalmatia, there is a huge
overhead water tank, supported on nine pipe columns (Figure 2.4).
Bill board column:
Different types of support systems are used for the advertisement bill boards. Among
them steel pipe column is the most current practice. In Dhaka city numbers of bill
board are observed where steel pipe columns are used to support the structure (Figure
2.5).
TV mast:
The 1,265 foot T.V. mast constructed by Appleby-Frodingham Steel Company, at
Emley Moor, Yorkshire, mainly consists of cylindrical steel columns of 9 feet in
diameter (Figure 2.6).
Transmission tower:
For different purposes transmission towers are used. Such as telecommunication
network coverage, electricity coverage, etc. And like many other elements, steel pipes
are used as frame element in transmission towers. Three legged BTTB transmission
tower at Katabon has been built using steel pipe elements (Figure 2.7).
Beside these there are several others examples where pipes are used as a structural
frame element. Pipes are usually connected through flanges using bolts. The joints are
the weakest element in most structures. This is where the product leaks, wears, slips
or tears apart. In spite of their importance, bolted joints are not well understood. There
are widely used design theories and equations for liquid transmission pipe joints, but
Literature Review 5
they are not involved in the design and construction of the pipe frame systems. When
the pipe is subjected to bending or a moment acts on the pipe, some tension produces
in the bolt. It is very important to determine the tension value of the bolt. Maximum
bolt tensions are required for the safe design. In this thesis some rationale guidelines
are evaluated along with some results and graphs to calculate the bolt tension with
respect to some parameters such as number of bolts, thickness of the pipe or flange
etc.
FIGURE 2.1 Pipe columns supported the industrial building of Abdul Monem Ltd,
near Shahbag, Dhaka.
FIGURE 2.2 Foot over bridge supported by pipe columns at BUET campus, Dhaka.
Literature Review 6
FIGURE 2.3 Circular pipe columns supported the track of the roller coaster at
Fantasy Kingdom Entertainment Park, Ashulia.
FIGURE 2.4 Water tank supported on nine tubular columns at Lalmatia, Dhaka.
Literature Review 7
FIGURE 2.5 A large advertisement bill board supported by a circular pipe column at
Shahbag, Dhaka.
FIGURE 2.6 Cylindrical column of a T.V. mast at Emley Moore, Yorkshire
(Appleby-Frodingham Steel Company).
Literature Review 8
FIGURE 2.7 3-legged circular pipe transmission tower of BTTB at Katabon, Dhaka.
2.2 TYPES OF PIPE JOINTS
There are different types of steel and alloy steel pipe joints. Among them few names
are given below:
• Butt weld joint
• Socket weld joint
• Threaded joint
• Flanged joint
• Compression sleeve coupling
• Grooved segment-ring coupling.
Literature Review 9
This thesis paper concentrate on steel pipe that connects using bolt joint.
FIGURE 2.8 A flanged pipe joint with different components.
2.3 TYPES OF FLANGE
Flanges are most often used to connect pipes that have a diameter greater than 2
inches. A flange joint consists of two matching disks of metal that are bolted together
to achieve a strong seal. The flange is attached to the pipe by welding, brazing, or
screwed fittings. A number of the most common types of flanges are listed below.
1. Blind Or Blank Flange
2. Lap Joint Flange
3. Slip-On Flange
4. Socket Welding Flange
5. Threaded Flange
6. Welding Neck Flange
Literature Review 10
(a) Blind or Blank Flange (b) Lap Joint Flange
(c) Slip-On Flange
(d) Socket Welding Flange
(e) Threaded Flange (f) Welding Neck Flange
FIGURE 2.9 Different types of flange.
Literature Review 11
2.4 FLANGED CONNECTION SUBJECTED TO BENDING
Connections must be designed to resists moment because the pipes are the parts of a
rigid frame. For example, pipes, which are parts of the wind-bracing system of a tier
building, must resist end moments resulting from both wind forces and gravity loads.
In the usual case, moment resistance of bolted or riveted connections in such
frameworks depends upon tension in the fasteners.
2.5 PREVIOUS WORKS
2.5.1 Stress in Bolted Flanged Connection:
FIGURE 2.10 Illustration of earlier methods of calculating stress in a bolted flange
connection.
B
B
W
R R
C
C W
A A
X X’ X” a
b c
g
f e
d
h k j m
Literature Review 12
The earliest method of calculation to receive wide attention was the so-called
"Locomotive" method, (The Locomotive) generally credited to the late Dr. A.D.
Risteen (1905). The section abcdefg in Fig 1 is assumed to rotate counterclockwise,
but without distortion. The final equation is in effect the conventional flexure formula,
the external moment being the total bolt moment per radian angle and the section
modulus being that taken about the axis X-X' through the center of gravity. For ring
flanges this gives the tangential stress on either face, and for hubbed flanges it gives
the tangential stress at the free end of the hub.
Crocker and Sanford developed a method (Taylor-Waters, 1927; Discussion of paper
by Waters and Taylor, 1927) whereby the flange is analyzed as a beam, in which
bending about the neutral axis X-X " takes place on the section A-A, and the external
loads are one half the bolt load W and one half the reaction R, each concentrated at
the center of gravity of their respective half-circles (The location of the bolt-load
circle, however was assumed tangent to the inner edge of the bolt holes, and not along
the bolt circle in Fig 1) This method likewise gives the tangential stress on either face
of a ring, or at the end of the hub.
Den Hartog (Discussion of paper by Waters and Taylor, 1927) showed by vector
analysis that although the Locomotive and Crocker-Sanford methods are derived in
different ways, they are fundamentally identical.
A method devised by Tanner for ring flanges, and discussed by Waters and Taylor
(Taylor-Waters, 1927), is to assume the ring to be fixed at the section B-B around the
bolt circle and to be equivalent to a cantilever beam of length L I with the
"concentrated" load R uniformly distributed across a width equal to the circumference
of the ring. This method gives the radial stress assumed to be present at section B-B.
In the application of the method, Tanner took account of the tangential stresses by
using suitable factors derived from experiments on rings of the proportions in which
he was interested. The Tanner method was modified by Crocker (Taylor-Waters,
1927; Discussion of paper by Waters and Taylor, 1927) for application to hubbed
flanges (and presumably adaptable to ring flanges also) by assuming the fixed section
to be the weakest section C-C in the ring at the base of the hub, with the load W
Literature Review 13
"concentrated" at the distance L2 at the free end and distributed along the bolt-
loading circle. This likewise results in a calculation of the radial stress assumed to
exist, in this case at section C-C.
None of the foregoing methods took into account all the conditions present in the
flange under load, and so the Waters and Taylor paper in 1927 (Taylor-Waters, 1927)
based on a combination of the flat plate and the elastically supported beam theories,
was probably the first instance in which the stress conditions in a flange III the three
principal directions - tangential, radial, and axial - were explored with the object of
determining the location and magnitude of the maximum stress. Formulas were
included for the deflection of the ring, and the calculated deflections were compared
with those actually obtained in several series of tests, the data of which were also
reported. Because in flange proportions considered at that time the tangential stress in
the ring at the inside diameter was the controlling factor, the formulas for stresses
elsewhere in the flange were generally over-looked by designers.
The Waters-Taylor evoked extensive discussion (Discussion of paper by Waters and
Taylor, 1927) in the course of which Timoshenko presented an analysis for both ring
flanges and hubbed flanges, including a method of dealing with hubs shorter than the
so called "critical" length. Most of these formulas can be found also in his work on
"Strength of Materials"(S. Timoshenko, 1930).
In 1931 Holm berg and Axelson wrote a paper (Analysis of Stresses in Circular Plates
and Rings) in which they used the flat-plate theory in developing formulas for stresses
in loose-ring flanges and in flanges made integral with the wall of a pressure vessel or
pipe.
In a series of articles published in 1936 (Strength and Design of Covers and Flanges
for Pressure Vessels and Piping, 1936), Jasper, Gregersen, and Zoellner discussed
further the formulas of Timoshenko, and Holmberg and Axelson. They also made an
outstanding contribution to the subject by presenting the results of an extensive series
of tests on plaster-of-paris models. Some of the data obtained were used in developing
Literature Review 14
an analysis of the stresses in hubbed flanges having a large circular fillet at the
junction of hub and ring.
When the rules for flanges in the A.S.M.E. and the A.P.1-A.S.M.E. Unified Pressure
Vessel Codes were first published in 1934, the wide range of their application made it
necessary to use formulas based on a rational and complete theory, and because the
Waters-Taylor equations met this requirement and had been checked by experiment,
they were adopted, with auxiliary charts to simplify the calculations. The radial-stress
formula was omitted, however, because it was not believed that it would be the
critical factor in any practical design.
In 1937, Waters ET. Al. published a paper which outlines a revised analysis based on
the ring, tapered hub, and shell being considered as three elastically coupled units
loaded by a bolting moment, a hydrostatic pressure, or a combination of the two.
Design formulas and charts were developed for the computation of stresses that are
likely to be critical.
2.5.2 Comparison of Performance of Bolts and Rivets
The use of a bolted joint became more practical with the contributions of Withworth
and Sellers in England during the 18th century. The general design philosophy of the
bolted joint was based on the experience with the rivet applications until the work of
Rotscher in 1927, who began to question the relation of the preload to the external
load applied to the joint. In essence, the contribution of the external load to the actual
bolt load was examined in terms of the spring constants of the various components
comprising a particular joint. Since the time, fully engineered fasteners have been
recognized as the basic and fundamental components of assembled metal products
and a number of useful rules have been developed to guide future designs.
As far back as 70 years, considerable interest was shown in the feasibility of
employing high-preload bolts in frame construction with special regard to developing
an adequate margin of safety against the slip of the joined component parts. Based on
the laboratory tests at that time, it was determined that the minimum yield strength of
a bolt should not be less than about 50 ksi. It was also concluded that the fatigue
Literature Review 15
strength of a high-strength bolt should be as good as that of a well-driven rivet
provided high-preload could be assured. The Research Council of American Society
of Civil Engineers and the American Railway Engineering Association, faced with a
number of fatigue failures in the area of floor beam hangers and similar parts, were in
the forefront of high-strength joint developments. The immediate indication was that
the excessive rivet bearing loads, found in certain structural applications, could be
controlled by means of a high-clamping force provided by bolting. The pioneering
work of the foregoing societies culminated eventually in specifications for the
materials for high-strength bolt applications--and for the first time it was officially
recognized that the rivet could be replaced by the bolt on a one-to-one basis. This
recognition by the Research Council of the American Society of Civil Engineers
became known in 1951. It is, no doubt, a rather late development when viewed in the
context of the overall history of a bolted joint.
2.6 CONVENTIONAL ANALYSIS AND DESIGN
Bolt tension of a flanged pipe joint can be calculated by using the conventional linear
distribution method.
Sample Calculation:
Assume,
The pipe radius = ri in.
The outer radius of flange = ro in.
The distance from the center of the pipe to the center of the bolt = r in.
Literature Review 16
FIGURE 2.11 3-D view of a typical flanged pipe joint with 12 bolts and 12 in.
diameter pipe.
FIGURE 2.12 Front view of a typical flanged pipe joint with 12 bolts and 12 in.
diameter pipe.
Literature Review 17
FIGURE 2.13 Plan and force distribution of a typical flanged pipe joint with 12 bolts
and 12 in. diameter pipe.
Here,
°×=°×=
30sinTT60sinTT
13
12
Taking moment at the center of the pipe,
( )°+°+=
=°××+°××+××
=°××+°××+××
30sinr460sinr4r2MT,or
M30sinrT460sinrT4rT2,or
M30sinrT460sinrT4rT2
221
21
211
321
By using this method, the maximum tension of a bolt can be determined which is
farthest from the centre of the pipe for various pipe diameter and for different number
of bolts.
T1
T1 T2
T2
T3
T3 ri r ro
Methodology for Finite Element Analysis 18
CHAPTER 3
METHODOLOGY FOR FINITE ELEMENT ANALYSIS
3.1 INTRODUCTION
Finite-Element calculations more and more replace analytical methods especially if
problems have to be solved which are adjusted to specific tasks. In many countries a
lot of efforts are carried out to get new code standards for the calculation of flange
joints under various loadings. All these calculation methods are based on a linear
description of the material behavior. Concerning the non-linear and time dependent
characteristics of materials standard linear elastic finite element calculations in
addition to code methods are often not suitable.
Therefore a new finite element model was developed to describe the real (elastic-
plastic) behavior of the joint. Besides an exact geometric modeling the description of
the material behavior of all components is very important for the quality of performed
analyses. This applies to analytical as well as to numerical methods. For components
made of steel elastic or elastic-plastic material laws are able to simulate the real
behavior of those parts in sufficient accuracy.
The actual work regarding the finite element modeling of a flanged pipe joint has
been described in detail in this chapter. Representation of various physical elements
with the FEM (finite element modeling) elements, properties assigned to them,
boundary condition, material behavior, and analysis types have also been discussed.
The various obstacles faced during modeling, material behavior used and details of
finite element meshing were also discussed in detail.
3.2 THE FINITE ELEMENT PACKAGES
A large number of finite element analysis computer packages are available now. They
vary in degree of complexity and versatility. The names of few such packages are
ANSYS AMaze Catalog PROKON STARDYN
DIANA ROBOTICS FEMSKI ALGOR
MICROFEAP STRAND 6 MARC LUSAS
Methodology for Finite Element Analysis 19
SAP2000 ABAQUS NASTRAN FELIPE
STADD PRO ETABS ADINA SAMTECH
AxisVM CADRE GT STRUDL
Of these packages ANSYS 5.6 has been chosen for its versatility and relative ease of
use. ANSYS is a general purpose finite element modeling package for numerically
solving a wide variety of structural as well as mechanical problems. These problems
include: static/dynamic structural analysis (both linear and non-linear), heat transfer
and fluid problems, as well as acoustic and electromagnetic problems. ANSYS finite
element analysis software enables engineers to perform the following the tasks.
• Build computer models or CAD models of structures, products, components
and systems.
• Apply operating loads and other design performance conditions.
• Study the physical responses, such as stress levels, temperature distributions,
or the impact of electromagnetic fields.
• Optimize a design early in the development process to reduce production
costs.
• Do prototype testing in environments where it otherwise would be
undesirable or impossible (for example, biomedical applications)
The ANSYS program has a comprehensive graphical user interface (GUI) that gives
user easy, interactive access to program functions, commands, and documentation and
reference material. An intuitive menu system helps users navigate through the
ANSYS program. Users can input data using a mouse, a keyboard, or a combination
of both.
3.3 TYPES OF ANALYSIS ON STRUCTURES
Structures can be analyzed for small deflection and elastic material properties (linear
analysis), small deflection and plastic material properties (material nonlinearity), large
deflection and elastic material properties (geometric nonlinearity), and for
simultaneous large deflection and plastic material properties.
Methodology for Finite Element Analysis 20
By plastic material properties, we mean that the structure is deformed beyond yield of
the material, and the structure will not return to its initial shape when the applied
loads are removed. The amount of permanent deformation may be slight and
inconsequential, or substantial and disastrous.
By large deflection, we mean that the shape of the structure has changed enough that
the relationship between applied load and deflection is no longer a simple straight-line
relationship. This means that doubling the loading will not double the deflection. The
material properties can still be elastic.
To analyze a flanged pipe joint, small deflection and plastic material properties
(material nonlinearity) are used. Though it costs more time, it gives a more realistic
result.
3.4 FINITE ELEMENT MODELLING OF STRUCTURE
FIGURE 3.1 General sketch of the flanged pipe joint studied.
Methodology for Finite Element Analysis 21
Figure 3.1 shows a general sketch of the flanged pipe joint. Due to symmetry, only
one side of the joint is modeled with appropriate boundary conditions. For the
analysis, a model of a flanged pipe joint has been created. For the modeling of pipe,
flange, contact surface, bolts and stiffening ring, separate elements have been used.
For the pipe and the flange SHELL93 8-Node Structural Shell, for the bolts and the
contact surface COMBIN39 Nonlinear Spring and for the stiffening ring BEAM4 3-D
Elastic Beam has been used.
3.4.1 Modeling of the pipe and flange
Since the whole modeling was done in three-dimension, the element used here is 3D in
nature. For representing the pipe and flange, SHELL93 8-Node Structural Shell element has
been used. Details discussion about the element is shown below:
SHELL93 — 8-Node Structural Shell
SHELL93 is particularly well suited to model curved shells. The element has six
degrees of freedom at each node: translations in the nodal x, y, and z directions and
rotations about the nodal x, y, and z-axes. The deformation shapes are quadratic in
both in-plane directions. The element has plasticity, stress stiffening, large deflection,
and large strain capabilities.
FIGURE 3.2 SHELL93 8-Node Structural Shell.
Methodology for Finite Element Analysis 22
Input Data
The geometry, node locations, and the coordinate system for this element are shown
in SHELL93. The element is defined by eight nodes, four thicknesses, and the
orthotropic material properties. Mid side nodes may not be removed from this
element. A triangular-shaped element may be formed by defining the same node
number for nodes K, L and O.
A summary of the element input is given in Table 3.1.
TABLE 3.1 SHELL93 Input Summary
Element Name SHELL93
Nodes I, J, K, L, M, N, O, P
Degrees of Freedom UX, UY, UZ, ROTX, ROTY, ROTZ
Real Constants TK(I), TK(J), TK(K), TK(L), THETA, ADMSUA
Material Properties EX, EY, EZ, ALPX, ALPY, ALPZ, (PRXY, PRYZ,
PRXZ or NUXY, NUYZ, NUXZ), DENS, GXY, GYZ,
GXZ, DAMP
Surface Loads Pressures -
face 1 (I-J-K-L) (bottom, in +Z direction),
face 2 (I-J-K-L) (top, in -Z direction), face 3 (J-I), face
4 (K-J), face 5 (L-K), face 6 (I-L)
Body Loads Temperature -T1, T2, T3, T4, T5, T6, T7, T8
Special Features Plasticity, Stress stiffening, Large deflection, Large
strain, Birth and death, Adaptive descent
Assumptions and Restrictions
Zero area elements are not allowed. This occurs most often whenever the elements are
not numbered properly. Zero thickness elements or elements tapering down to a zero
thickness at any corner are not allowed. The applied transverse thermal gradient is
assumed to vary linearly through the thickness. Shear deflections are included in this
element. The out-of-plane (normal) stress for this element varies linearly through the
thickness. The transverse shear stresses (SYZ and SXZ) are assumed to be constant
through the thickness. The transverse shear strains are assumed to be small in a large
Methodology for Finite Element Analysis 23
strain analysis. This element may produce inaccurate stress under thermal loads for
doubly curved or warped domains.
3.4.2 Modeling of the bolt and the surface spring
For the modeling of the bolt and the contact surface COMBIN 39 Nonlinear Spring
has been used, the details of which has been described below.
COMBIN39 — Nonlinear Spring
COMBIN39 is a unidirectional element with nonlinear generalized force-deflection
capability that can be used in any analysis. The element has longitudinal or torsional
capability in one, two, or three dimensional applications. The longitudinal option is a
uniaxial tension-compression element with up to three degrees of freedom at each
node: translations in the nodal x, y, and z directions. No bending or torsion is
considered. The torsional option is a purely rotational element with three degrees of
freedom at each node: rotations about the nodal x, y, and z axes. No bending or axial
loads are considered.
The element has large displacement capability for which there can be two or three
degrees of freedom at each node.
FIGURE 3.3 COMBIN39 Nonlinear Spring.
Methodology for Finite Element Analysis 24
Input Data
The geometry, node locations, and the coordinate system for this element are shown
in fig.3.2. The element is defined by two node points and a generalized force-
deflection curve. The points on this curve (D1, F1, etc.) represent force (or moment)
versus relative translation (or rotation) for structural analyses. The loading curve
should be defined on a full 360° basis for an axis-symmetric analysis. The force-
deflection curve should be input such that deflections are increasing from the third
(compression) to the first (tension) quadrants. The last input deflection must be
positive.
A summary of the element input is given in Table 3.2.
TABLE 3.2 COMBIN39 Input Summary
Element Name COMBIN39
Nodes I, J
Degrees of
freedom
UX, UY, UZ, ROTX, ROTY, ROTZ, PRES, or TEMP. Make
1-D choices with KEYOPT (3). Make limited 2- or 3-D
choices with KEYOPT (4).
Real Constants D1, F1, D2, F2, D3, F3, D4, F4, ...D20, F20
Material Properties None
Surface Loads None
Body Loads None
Special Features Nonlinear, Stress stiffening, Large displacement
Assumptions and Restrictions
For KEYOPT (4) =0, the element has only one degree of freedom per node. This
degree of freedom is defined by KEYOPT (3), is specified in the nodal coordinate
system and is the same for both nodes. KEYOPT (3) also defines the direction of the
force. The element is defined such that a positive displacement of node J relative to
node I tends to put the element in tension. For KEYOPT (4) 0, the element has two
or three displacement degrees of freedom per node. Nodes I and J should not be
coincident, since the line joining the nodes defines the direction of the force. The
element is nonlinear and requires an iterative solution. The nonlinear behavior of the
element operates only in the static and nonlinear transient dynamic analyses. As with
Methodology for Finite Element Analysis 25
most nonlinear elements, loading and unloading should occur gradually. If KEYOPT
(2) =1 and the force tends to become negative, the element "breaks" and no force is
transmitted until the force tends to become positive again. When KEYOPT (1) =1, the
element is both nonlinear and non-conservative. In a thermal analysis, the temperature
or pressure degree of freedom acts in a manner analogous to the displacement.
3.4.3 Modeling of the stiffening ring
For the modeling of the stiffening ring BEAM4 3D Elastic Beam has been used, the
details of which has been described below.
BEAM4 — 3-D Elastic Beam
BEAM4 is a uniaxial element with tension, compression, torsion, and bending
capabilities. The element has six degrees of freedom at each node: translations in the
nodal x, y, and z directions and rotations about the nodal x, y, and z axes. Stress
stiffening and large deflection capabilities are included. A consistent tangent stiffness
matrix option is available for use in large deflection (finite rotation) analyses.
FIGURE 3.4 BEAM4 3-D Elastic Beam.
Methodology for Finite Element Analysis 26
Input Data
The geometry, node locations, and coordinate systems for this element are shown in
BEAM4. The element is defined by two or three nodes, the cross-sectional area, two
area moments of inertia (IZZ and IYY), two thicknesses (TKY and TKZ), an angle of
orientation ( ) about the element x-axis, the torsional moment of inertia (IXX), and
the material properties.
A summary of the element input is given in Table 3.3.
TABLE 3.3 BEAM4 Input Summary
Element Name BEAM4
Nodes I, J, K (K orientation node is optional)
Degrees of Freedom UX, UY, UZ, ROTX, ROTY, ROTZ
Real Constants AREA, IZZ, IYY, TKZ, TKY, THETA, ISTRN, IXX,
SHEARZ, SHEARY, SPIN, ADDMAS
Material Properties EX, ALPX, DENS, GXY, DAMP
Surface Loads Pressures –
face 1 (I-J) (-Z normal direction),
face 2 (I-J) (-Y normal direction),
face 3 (I-J) (+X tangential direction),
face 4 (I) (+X axial direction),
face 5 (J) (-X axial direction)
(use negative value for opposite loading)
Body Loads Temperatures –
T1, T2, T3, T4, T5, T6, T7, T8
Special Features Stress stiffening, Large deflection, Birth and death
Assumptions and Restrictions
The beam must not have a zero length or area. The moments of inertia, however, may
be zero if large deflections are not used. The beam can have any cross-sectional shape
for which the moments of inertia can be computed. The stresses, however, will be
determined as if the distance between the neutral axis and the extreme fiber is one-
half of the corresponding thickness. The element thicknesses are used only in the
Methodology for Finite Element Analysis 27
bending and thermal stress calculations. The applied thermal gradients are assumed to
be linear across the thickness in both directions and along the length of the element.
3.5 FINITE ELEMENT MODEL PARAMETERS
In this analysis small deflection and plastic material properties (material nonlinearity)
are considered. The following properties are used in the modeling.
TABLE 3.4 Various Parameters
Parameter Reference Value
Pipe length 10 in.
Pipe radius 1.75 in. to 6 in.
Outer radius of flange Pipe radius + 2 in.
Number of bolts 4 to 16
Division along pipe length 6
Division in radial direction 8
Divisions between two bolts in circumferential direction 8
Bolt diameter 1 in.
Pipe wall thickness 0.28 in.
Flange thickness 1 to 3 times of the pipe
wall thickness
Poisson’s ratio 0.25
Yield strength of steel 40 ksi
Applied Moment Ultimate Moment
3.6 MESHING
3.6.1 Meshing of the pipe
Pipe is divided along length and along periphery. Individual division is rectangular.
Number of division is chosen in such a way that the aspect ratio of the element is
reasonable.
Methodology for Finite Element Analysis 28
3.6.2 Meshing of the flange
Number of circumferential division and the number of radial division is the same to
match the nodes. Number of radial division is even, so that the centerline of the bolt
falls at the centerline of the flange. Number of circumferential division depends on the
number of the bolt. The number of circumferential division and the number of radial
division is same.
3.6.3 Properties of the contact element
In the flanged bolted connection, the flanges are in contact with each other.
COMBIN39 element has developed similar type of contact in this model. Each node
of the flange was extruded along the axis of the pipe, to generate COMBIN39 contact
element. Here the properties of the COMBIN39 link element were such that they can
resist compression and very much weak in tension. This element develops
compression normal to the plane of the flange.
FIGURE 3.5 Force - deflection behavior of contact springs.
Figure 3.5 shows the force - deflection behavior of contact springs. The value of Kc. is
high and the value of Kt is very low.
D
Fc
Ft
Kt
Kc
1
1
Methodology for Finite Element Analysis 29
3.6.4 Properties of the bolts
Same COMBIN39 link elements are used to simulate the behavior of bolts. In this
model, these link elements in position of bolts were assigned bolt properties. That is,
these elements, representing the bolts, can resist both tension and compression.
FIGURE 3.6 Force – deflection behavior of bolts.
Figure 3.6 shows the force-deflection behavior of bolts. The value of both Kc and Kt
are equal here.
3.7 BOUNDARY CONDITIONS
3.7.1 Restraint:
The free ends of the COMB1N39 link element, which simulate the contact, were
restrained in all directions. This element does not have any bending capability.
Therefore, to protect against sliding, the peripheral nodes of the flange were also
restrained in horizontal direction.
D
Kc
Kt
1
1
Fc
Ft
Methodology for Finite Element Analysis 30
3.7.2 Load:
The joint is subjected to moment. In this model, the moment is applied by a pair of
parallel and opposite forces representing a couple.
WXWYWZ
X
Y
Z
K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 K0 K0
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
FIGURE 3.7 Finite elements mesh of a flanged pipe joint.
Methodology for Finite Element Analysis 31
FIGURE 3.8 Finite elements mesh with load and boundary conditions.
FIGURE 3.9 Typical deflected shape of a flanged pipe joint.
Methodology for Finite Element Analysis 32
FIGURE 3.10 Typical stress contour of a flanged pipe joint.
X
Y
Z
FIGURE 3.11 Typical stress contours of bolts.
Computational Investigation 33
CHAPTER 4
COMPUTATIONAL INVESTIGATION
4.1 INTRODUCTION
Detailed modeling procedure of a flanged pipe with bolt joint is described in the
previous chapter. In this chapter, detail investigation procedure, to determine the
controlling parameters for ultimate bolt tension for a flanged pipe joint is described
with supported data and graphs.
4.2 SAMPLE PROBLEMS
The sample problems under investigation with the variable data within certain range
are described in the following Table 4.1. While one of the parameters is varied, the
other values of parameters are maintained equal to the reference values as mentioned
below. Bolt tensions are determined for different flange thickness and number of bolt
for different diameter of pipes. For each analysis, the tension of the bolt located
farthest from center is considered. Ultimate moment is applied in the analysis.
TABLE 4.1 Study parameters for a flanged pipe joint
Parameter Variable Data
No of bolt 4, 6, 8, 10, 12, 14, 16
Flange thickness 1 x Pipe thickness, 2 x Pipe thickness, 3
x Pipe thickness
Diameter of pipe 3, 3.5, 4, 5, 6, 8, 10, 12 in
4.3 RESULTS AND DISCUSSION
The results obtained from finite element analysis have been described in the following
articles according to the parameters involved:
4.3.1 Effect of Mesh Density and Element Type
It is evident that SHELL93 (8-Node Structural Shell) elements converge better than
SHELL63 (4-Node Elastic Shell) Elements. For this reason, SHELL93 elements have
been selected for the finite element analysis. The number of radials and
Computational Investigation 34
circumferential divisions are selected as eight divisions, at which the SHELL93
elements converge first.
4.3.2 Effect of Number of Bolts
For a flanged pipe joint, the effective bolt tensions obtained for different number of
bolts, pipe diameters ( i.e. 3, 3.5, 4, 5, 6, 8, 10 and 12 in) and flange thickness (i.e.
flange thickness = pipe wall thickness, flange thickness = 2 × pipe wall thickness and
flange thickness = 3 × pipe wall thickness) are shown in Table 4.2 through Table
4.17. The curves are generated with the help of bolt tensions against different number
of bolts from the respective finite element analysis results and conventional
calculations are presented in Figure 4.1 through Figure 4.8. The trend lines of the
curves are demonstrated a downtrend with a parabolic nature for increasing number of
bolt under the study parameters. It is evident from the figures that bolt tension
decreases with the increasing number of bolts. This implies that, increasing number of
bolts results in decreasing bolt tension.
4.3.3 Effect of Flange thickness
With reference to Figure 4.1 through Figure 4.8, it may be concluded that, flange
thickness has significant effect on bolt tension. There is an upward shift in the Bolt
tension against the number of bolts curves with the increase in flange thickness. That
is the bolt tension increases with the increase in flange thickness.
4.3.4 Proposed Empirical Equations
Conventional method of determining bolt tension in a flanged pipe joint, discussed in
Chapter 2. Since this a linear distribution method it does not reflect the non linearity
of the materials appropriately. Besides, for higher number of bolts, the bolt tension
from the conventional analysis differs from the more accurate non linear analysis.
Hence, to simplify the problem three empirical equations have been proposed for
three different flange thicknesses to pipe wall thickness relationships (i.e. flange
thickness = pipe wall thickness, flange thickness = 2 × pipe wall thickness and flange
thickness = 3 × pipe wall thickness), using the finite element analysis results. The
first two equations are logarithmic equation with constant values related to the
diameter of the pipe. The third equation is the second order polynomial equation with
all the constant values, depended on the diameter of the pipe. Computational results of
Computational Investigation 35
the bolt tension using conventional, proposed equations and finite element analysis
method are compared using the bar chart diagram are shown in Figure 4.9 through
Figure 4.20. To compare the bolt tension in different methods four different diameter
of pipes (i.e. 6, 8, 10 and 12 in) are used. From the bar charts it is evident that, for
flange thickness equal to pipe wall thickness, the bolt tensions using conventional
method are more close to the proposed equation and the finite element analysis
results. However, with the increase in number of bolts the bolt tensions differ.
Moreover, with the increase in flange thickness with respect to pipe wall thickness the
magnitude of bolt tension varies from the conventional method to the proposed
equation.
The three proposed empirical equations are shown below with the limiting values.
Flange thickness = Pipe thickness Proposed equation:
( ) bnnapT −×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip. dea 2018.0352.1 ×=
deb 3111.051.0 ×=
n = Number of bolts ( )164 ≤≤ n .
d = Pipe diameter ( )126 ≤≤ d , in.
Fy = Yield strength of pipe, 40 ksi.
Flange thickness = 2×Pipe thickness Proposed equation:
( ) bnnapT +×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
Computational Investigation 36
322
1 bdbdbb ++=
26.01 −=a 06.11 =b
1.02 −=a 2.02 =b
95.183 =a 1.413 −=b
n = Number of bolts ( )164 ≤≤ n .
d = Pipe diameter ( )126 ≤≤ d , in.
Fy = Yield strength of pipe, 40 ksi.
Flange thickness = 3 × Pipe thickness
Proposed equation:
cbnanpT +++= 2
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
322
1 cdcdcc ++=
0137.01 =a 38.01 −=b 71.21 =c
1677.02 −=a 99.42 =b 22.252 −=c
0481.03 =a 93.73 −=b 52.323 =c
n = Number of bolts ( )164 ≤≤ n .
d = Pipe diameter ( )126 ≤≤ d , in.
Fy = Yield strength of pipe, 40 ksi.
4.4 REMARKS
Number of bolts has significant effect upon bolt tension incase of a flanged pipe joints
and it is observed that bolt tension decreases with increasing number of bolts.
Computational Investigation 37
With increasing pipe diameter bolt tension varies randomly. For pipe diameter of 5 in.
or less, the conventional analysis method gives adequate results, while calculating the
bolt tension. For bolt diameter of 6 in. or above, bolt tension calculated by non-linear
finite element analysis varies from the linear conventional analysis results. Bolt
tension calculated from the non-linear finite element analysis gives higher values than
the conventional method.
Flange thickness has significant influence on bolt tension and it is noticed that bolt
tension increases with increasing flange thickness. From the study result it is clear that
bolt tension increases with increasing flange thickness for the pipe diameter of 5 in.
and above.
Difference in bolt tension, calculated from non-linear finite element analysis and
conventional analysis method, for pipe thickness equal to flange thickness, is nearly
ignorable for different pipe diameters. With increase in flange thickness compare to
pipe thickness, bolt tension calculated from the conventional analysis method is less
than the actual bolt tension. Hence, for higher flange thickness compare to pipe
thickness, the proposed equation can be used without significant effects, for more
accurate results.
Summing up the study results, it is conclusive that, numbers of bolts and flange
thickness are the two parameters, which influence the bolt tension significantly for a
flanged pipe joint. In view of the above, it is required to study further the two
parameters, i.e. number of bolts and flange thickness for different pipe diameter to
establish their effect conclusively on bolt tension for a flanged pipe joint. Other
parameters exhibit negligible effect on bolt tension.
4.5 TABLES AND GRAPHS
All the tables and figures mentioned earlier in article 4.3 are provided in the following
pages one after another cases, so as to best express the phenomena they are found to
relate with the bolt tension.
Computational Investigation 38
TABLE 4.2 Various parameters for 3 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 1.5 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.3 Bolt tension for various numbers of bolts according to various flange thicknesses for 3 in. diameter pipe. Number
of Bolts
Bolt Tension
Flange thickness=Pipe
thickness (kips)
Flange thickness=2×Pipe
thickness (kips)
Flange thickness=3×Pipe
thickness (kips)
Conventional method
(kips)
4 20.6 16.3 18.8 21.2 5 17.4 13.6 16.0 17.0
tf = Flange thicknesstp = Pipe wall thickness
tf = tp
tf = 2tp
tf = 3tp
Conventional
0
5
10
15
20
25
0 1 2 3 4 5 6
Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.1 Effect of number of bolts on bolt tension for 3 in. diameter pipe.
Computational Investigation 39
TABLE 4.4 Various parameters for 3.5 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 1.75 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.5 Bolt tension for various numbers of bolts according to various flange thicknesses for 3.5 in. diameter pipe. Number of Bolts
Bolt Tension
Flange thickness=Pipe
thickness (kips)
Flange thickness=2×Pipe
thickness (kips)
Flange thickness=3×Pipe
thickness (kips)
Conventional method (kips)
4 30.0 23.6 24.3 30.6 5 25.3 19.1 20.3 24.5 6 22.3 16.5 17.7 20.4
tf = Flange thicknesstp = Pipe wall thickness
Conventionaltf=tp
tf=2tp
tf=3tp
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.2 Effect of number of bolts on bolt tension for 3.5 in. diameter pipe.
Computational Investigation 40
TABLE 4.6 Various parameters for 4 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 2 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.7 Bolt tension for various numbers of bolts according to various flange thicknesses for 4 in. diameter pipe. Number of Bolts
Bolt Tension
Flange thickness=Pipe
thickness (kips)
Flange thickness=2×Pipe
thickness (kips)
Flange thickness=3×Pipe
thickness (kips)
Conventional method
(kips)
4 42.0 39.3 31.9 41.9 5 34.6 32.3 25.9 33.5 6 30.3 28.0 22.1 27.9
tf = Flange thicknesstp = Pipe wall thickness
tf = tptf = 2tp
tf = 3tp
Conventional
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7
Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.3 Effect of number of bolts on bolt tension for 4 in. diameter pipe.
Computational Investigation 41
TABLE 4.8 Various parameters for 5 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 2.5 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment
TABLE 4.9 Bolt tension for various numbers of bolts according to various flange thicknesses for 5 in. diameter pipe. Number of Bolts
Bolt Tension
Flange thickness=Pipe
thickness (kips)
Flange thickness=2×Pipe
thickness (kips)
Flange thickness=3×Pipe
thickness (kips)
Conventional method
(kips)
4 72.0 73.6 65.2 70.1 6 50.0 55.6 46.4 46.7 8 40.0 45.6 37.6 35.1
tf = Flange thicknesstp = Pipe wall thickness
tf = tp
tf = 2tp
tf = 3tpConventional
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6 7 8 9Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.4 Effect of number of bolts on bolt tension for 5 in. diameter pipe.
Computational Investigation 42
TABLE 4.10 Various parameters for 6 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 3 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.11 Bolt tension for various numbers of bolts according to various flange thicknesses for 6 in. diameter pipe. Number of Bolts
Bolt Tension
Flange thickness=Pipe
thickness) (kips)
Flange thickness=2×Pipe
thickness) (kips)
Flange thickness=3×Pipe
thickness) (kips)
Conventional method
(kips)
4 108.8 115.9 110.5 106.0 6 75.5 86.4 83.0 70.7 8 59.0 71.2 67.8 53.0 10 49.3 60.2 57.8 42.4
tf = Flange thicknesstp = Pipe wall thickness
tf = tp
tf = 2tptf = 3tp
Conventional
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.5 Effect of number of bolts on bolt tension for 6 in. diameter pipe.
Computational Investigation 43
TABLE 4.12 Various parameters for 8 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 4 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.13 Bolt tension for various numbers of bolts according to various flange thicknesses for 8 in. diameter pipe. Number of
Bolts Bolt Tension
Flange thickness=Pipe
thickness) (kips)
Flange thickness=2×Pipe
thickness) (kips)
Flange thickness=3×Pipe
thickness) (kips)
Conventional method
(kips)
4 205.1 231.0 228.4 201.1 6 139.8 164.8 170.1 134.0 8 109.0 133.6 139.8 100.5
10 90.8 113.4 119.1 80.4 12 78.0 98.2 103.5 67.0
tf = Flange thicknesstp = Pipe wall thickness
tf = tp
tf = 2tp
tp = 3tf
Conventional
0
50
100
150
200
250
0 2 4 6 8 10 12 14
Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.6 Effect of number of bolts on bolt tension for 8 in. diameter pipe.
Computational Investigation 44
TABLE 4.14 Various parameters for 10 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 5 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.15 Bolt tension for various numbers of bolts according to various flange thicknesses for 10 in. diameter pipe. Number of
Bolts Bolt Tension
Flange thickness=Pipe
thickness (kips)
Flange thickness=2×Pipe
thickness) (kips)
Flange thickness=3×Pipe
thickness (kips)
Conventional method
(kips)
4 330.1 383.1 390.7 327.2 6 224.2 270.4 282.4 218.2 8 173.1 213.6 229.7 163.6
10 143.3 181.1 195.3 130.9 12 123.5 157.1 169.6 109.1 14 108.6 138.3 149.7 93.5
tf = Flange thicknesstp = Pipe wall thickness
tf = tp
tf = 2tp
tf = 3tp
Conventional
0
50
100
150
200
250
300
350
400
450
0 2 4 6 8 10 12 14 16Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.7 Effect of number of bolts on bolt tension for 10 in. diameter pipe.
Computational Investigation 45
TABLE 4.16 Various parameters for 12 in. diameter pipe. Parameter Reference Value Pipe length 10 in. Pipe radius 6 in. Outer radius of flange Pipe radius + 2 in. Division along pipe length 6 Division in radial direction 8 Divisions between two bolts in circumferential direction 8 Bolt diameter 1 in. Pipe wall thickness 0.28 in. Applied Moment Ultimate Moment TABLE 4.17 Bolt tension for various numbers of bolts according to various flange thicknesses for 12 in. diameter pipe. Number of
Bolts Bolt Tension
Flange thickness=Pipe
thickness (kips)
Flange thickness=2×Pipe
thickness (kips)
Flange thickness=3×Pipe
thickness (kips)
Conventional method
(kips)
4 483.6 572.4 593.9 484.7 6 329.5 400.6 426.1 323.1 8 252.6 314.5 338.7 242.4
10 207.3 263.2 287.7 193.9 12 178.4 228.8 249.6 161.6 14 157.2 201.9 220.4 138.5 16 140.4 180.6 197.1 121.2
tf = Flange thicknesstp = Pipe wall thickness
tf=tp
tf=2tp
tf=3tp
Conventional
0
100
200
300
400
500
600
700
0 2 4 6 8 10 12 14 16 18
Number of Bolts
Bol
t Ten
sion
(kip
s)
FIGURE 4.8 Effect of number of bolts on bolt tension for 12 in. diameter pipe.
Computational Investigation 46
Comparison of bolt tension with conventional method Flange thickness = Pipe thickness
Proposed equation: ( ) bnnapT −×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip. dea 2018.0352.1 ×=
deb 3111.051.0 ×=
n = Number of bolts ( )164 ≤≤ n .
d = Pipe diameter, 12 in.
Fy = Yield strength of pipe, 40 ksi.
0
100
200
300
400
500
600
4 6 8 10 12 14 16
Number of bolts.
Bol
t ten
sion
(kip
s)
Conventional
Proposed Equation
FE Analysis
FIGURE 4.9 Comparison of bolt tension for 12 in. diameter pipe
Computational Investigation 47
Flange thickness = Pipe thickness
Proposed equation: ( ) bnnapT −×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip. dea 2018.0352.1 ×=
deb 3111.051.0 ×=
n = Number of bolts ( )144 ≤≤ n .
d = Pipe diameter, 10 in.
Fy = Yield strength of pipe, 40 ksi.
0
50
100
150
200
250
300
350
4 6 8 10 12 14Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.10 Comparison of bolt tension for 10 in. diameter pipe
Computational Investigation 48
Flange thickness = Pipe thickness
Proposed equation: ( ) bnnapT −×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip. dea 2018.0352.1 ×=
deb 3111.051.0 ×=
n = Number of bolts ( )124 ≤≤ n .
d = Pipe diameter, 8 in.
Fy = Yield strength of pipe, 40 ksi.
0
50
100
150
200
250
4 6 8 10 12Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.11 Comparison of bolt tension for 8 in. diameter pipe
Computational Investigation 49
Flange thickness = Pipe thickness
Proposed equation: ( ) bnnapT −×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip. dea 2018.0352.1 ×=
deb 3111.051.0 ×=
n = Number of bolts ( )104 ≤≤ n .
d = Pipe diameter, 6 in.
Fy = Yield strength of pipe, 40 ksi.
0
20
40
60
80
100
120
4 6 8 10Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.12 Comparison of bolt tension for 6 in. diameter pipe
Computational Investigation 50
Flange thickness = 2×Pipe thickness Proposed equation:
( ) bnnapT +×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
26.01 −=a 06.11 =b
1.02 −=a 2.02 =b
95.183 =a 1.413 −=b
n = Number of bolts ( )164 ≤≤ n .
d = Pipe diameter, 12 in.
Fy = Yield strength of pipe, 40 ksi.
0
100
200
300
400
500
600
700
4 6 8 10 12 14 16Number of bolts.
Bol
t ten
sion
ConventionalProposed EquationFE Analysis
FIGURE 4.13 Comparison of bolt tension for 12 in. diameter pipe.
Computational Investigation 51
Flange thickness = 2×Pipe thickness Proposed equation:
( ) bnnapT +×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
26.01 −=a 06.11 =b
1.02 −=a 2.02 =b
95.183 =a 1.413 −=b
n = Number of bolts ( )144 ≤≤ n .
d = Pipe diameter, 10 in.
Fy = Yield strength of pipe, 40 ksi.
0
50
100
150
200
250
300
350
400
450
4 6 8 10 12 14Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.14 Comparison of bolt tension for 10 in. diameter pipe.
Computational Investigation 52
Flange thickness = 2×Pipe thickness Proposed equation:
( ) bnnapT +×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
26.01 −=a 06.11 =b
1.02 −=a 2.02 =b
95.183 =a 1.413 −=b
n = Number of bolts ( )124 ≤≤ n .
d = Pipe diameter, 8 in.
Fy = Yield strength of pipe, 40 ksi.
0
50
100
150
200
250
4 6 8 10 12Number of bolts.
Bol
t ten
sion
ConventionalProposed EquationFE Analysis
FIGURE 4.15 Comparison of bolt tension for 8 in. diameter pipe.
Computational Investigation 53
Flange thickness = 2×Pipe thickness Proposed equation:
( ) bnnapT +×+=
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
26.01 −=a 06.11 =b
1.02 −=a 2.02 =b
95.183 =a 1.413 −=b
n = Number of bolts ( )104 ≤≤ n .
d = Pipe diameter, 6 in.
Fy = Yield strength of pipe, 40 ksi.
0
20
40
60
80
100
120
140
4 6 8 10Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.16 Comparison of bolt tension for 6 in. diameter pipe.
Computational Investigation 54
Flange thickness = 3 × Pipe thickness
Proposed equation: cbnanpT +++= 2
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
322
1 cdcdcc ++=
0137.01 =a 38.01 −=b 71.21 =c
1677.02 −=a 99.42 =b 22.252 −=c
0481.03 =a 93.73 −=b 52.323 =c
n = Number of bolts ( )164 ≤≤ n .
d = Pipe diameter, 12 in.
Fy = Yield strength of pipe, 40 ksi.
0
100
200
300
400
500
600
700
4 6 8 10 12 14 16Bolt number
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.17 Comparison of bolt tension for 12 in. diameter pipe.
Computational Investigation 55
Flange thickness = 3 × Pipe thickness
Proposed equation: cbnanpT +++= 2
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
322
1 cdcdcc ++=
0137.01 =a 38.01 −=b 71.21 =c
1677.02 −=a 99.42 =b 22.252 −=c
0481.03 =a 93.73 −=b 52.323 =c
n = Number of bolts ( )144 ≤≤ n .
d = Pipe diameter, 10 in.
Fy = Yield strength of pipe, 40 ksi.
0
50
100
150
200
250
300
350
400
450
4 6 8 10 12 14Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.18 Comparison of bolt tension for 10 in. diameter pipe.
Computational Investigation 56
Flange thickness = 3 × Pipe thickness
Proposed equation: cbnanpT +++= 2
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
322
1 cdcdcc ++=
0137.01 =a 38.01 −=b 71.21 =c
1677.02 −=a 99.42 =b 22.252 −=c
0481.03 =a 93.73 −=b 52.323 =c
n = Number of bolts ( )124 ≤≤ n .
d = Pipe diameter, 8 in.
Fy = Yield strength of pipe, 40 ksi.
0
50
100
150
200
250
4 6 8 10 12Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.19 Comparison of bolt tension for 8 in. diameter pipe.
Computational Investigation 57
Flange thickness = 3 × Pipe thickness
Proposed equation: cbnanpT +++= 2
Where,
T = Bolt tension in kip.
p = Bolt tension by conventional analysis in kip.
322
1 adadaa ++=
322
1 bdbdbb ++=
322
1 cdcdcc ++=
0137.01 =a 38.01 −=b 71.21 =c
1677.02 −=a 99.42 =b 22.252 −=c
0481.03 =a 93.73 −=b 52.323 =c
n = Number of bolts ( )104 ≤≤ n .
d = Pipe diameter, 6 in.
Fy = Yield strength of pipe, 40 ksi.
0
20
40
60
80
100
120
4 6 8 10Number of bolts.
Bol
t ten
sion
(kip
s)
ConventionalProposed EquationFE Analysis
FIGURE 4.20 Comparison of bolt tension for 6 in. diameter pipe.
Conclusion 58
CHAPTER 5
CONCLUSION
5.1 GENERAL
The project emanated with an aim to find out the bolt tension for a flanged pipe joint.
The project is expected to generate a reasonable solution of the focused problem
defined under some parametric conditions. Initially some variable parameters are
chosen for a flanged pipe joint followed by an analysis with finite element method.
The bolt tension is then determined for different pipe diameter by considering
different flange thickness and number of bolts. After completing the analysis, curves
are drawn for different bolt diameter representing bolt tension against number of
bolts, to find out precisely the effect of various parameters (i.e., pipe diameter,
number of bolts and flange thickness) on bolt tension. These curves demonstrated
that, flange thickness and number of bolts, have significant effect on bolt tension for a
flanged pipe joint. From the analysis values three mathematical empirical equations
are developed from which, one can easily obtain the bolt tension with the relevant
values of flange thickness and number of bolts for different pipe diameter, under
certain range of parametric conditions. Thus, the objective of this project comes out
successfully with validation.
5.2 FINDINGS
The outcomes of the work are summarized as follows:
• Number of bolt has significant effect upon bolt tension incase of a flanged pipe
joint and it is observed that bolt tension decreases with increasing number of bolts.
• Flange thickness has also significant influence on bolt tension and it is noticed that
bolt tension increases with increasing flange thickness.
• To easily determine the bolt tension, three empirical equations are developed,
based on finite element analysis results and the validities of the equations are
established by comparison with several examples.
• Difference in bolt tension, calculated from non-linear finite element analysis and
conventional analysis method, for pipe thickness equal to flange thickness, is
nearly ignorable for different pipe diameters. With increase in flange thickness
compare to pipe thickness, bolt tension calculated from the conventional analysis
Conclusion 59
method is less than the actual bolt tension. Hence, for higher flange thickness
compare to pipe thickness, the proposed equation can be used without significant
effects, for more accurate results.
5.3 SCOPE FOR FUTURE INVESTIGATION
Equations are developed for bolt tension for a flanged pipe joint under certain range
of parametric condition. In future, investigation can be performed to develop a more
general equation involving pipe diameter, number of bolts, pipe wall thickness and
flange thickness, so that bolt tension can be determined for a flanged pipe joint for
different variable parameters. Also, pipe length, longitudinal, radial and
circumferential division are maintained constant for a flanged pipe joint throughout
this study, which can also be varied and further studied to generate solution
considering the effects of these parameters.
Reference 60
References
1. Alexander Blake, “Design of Mechanical Joints”.
2. A.S.M.E. Unified Pressure Vessel Code, Pars. UA-16 to UA-22, inclusive,
1935. Also: API-ASME Code for Unfired Pressure Vessels for Petroleum
Liquids and Gases, Pars. W-317 and R-317.
3. D. Y. Hwang and J. M. Stallings, “Finite Element Analysis of Bolted Flange
Connections”, Computer & Structures, Vol. 51, No. 5, pp. 521-533, 1994.
4. E. O. Waters and J. H. Taylor. “The Strength of Pipe Flanges”. Mechanical
Engineering, Vol. 49, Mid – May, 1927, pp. 531-542.
5. E. O. Waters, D. B. Wesstrom, D. B. Rossheim, and F. S. G. Williams.
“Formulas for stresses in bolted flanged connections”. Trans ASME 1937;
59:161-7.
6. Holm berg and Axelson, “Analysis of Stresses in Circular Plates and Rings”,
Trans. A.S.M.E., Vol. 54, 1932, paper APM-54-2, pp. 13-28.
7. Jasper, Gregersen, and Zoellner, “Strength and Design of Covers and Flanges
for Pressure Vessels and Piping”, Heating, Piping, and Air Conditioning, Vol.
8, 1936, pp. 605-608 and pp. 672-674.
8. John H. Bickford, “An Introduction to the Design and Behavior of Bolted
Joints”.
9. M. Abid and D.H. Nash, “A parametric study of metal-to-metal contact
flanges with optimized geometry for safe stress and no-leak conditions”,
International Journal of Pressure Vessels and Piping, 2004, pp. 67-74.
10. S. Timoshenko, D. Van Nostrand Company, Inc., “Strength of Materials”, part
2, article 29, 1930.
11. Tanjina Nur, “A Computational Investigation on Effective Bolt Tension of a
Flanged Pipe Joint Subjected to Bending.”, October, 2004.
12. Waters and Taylor, “Methods of Determining the Strength of Pipe Flanges”,
Mechanical Engineering, vol. 49, December, 1927, pp. 1340-1347.
13. “The Flanged Mouth – Piece Rings of Vulcanizers and Similar Vessels”. The
locomotive, Vol. 25, July, 1905, pp. 177-203.
ANSYS Script 61
APPENDIX
A ANSYS Script used in this Analysis
The ANSYS script used in this analysis is describer below:
finish
/clear
/title, Flanged Pipe Joint
/prep7
hp=10 !Pipe length
ri=3 !Pipe radius
ro=ri+2 !Outer radius of flange
nhdiv=6 !Division along pipe length
nrdiv=8 !Division in radial direction
nbolt=8 !number of bolts
ntheta=8 !divisions between two bolts in theta direction
dh=1 !Length of combine39
pi=3.141592654 !Define constant
Fy=40 !Ultimate strength of steel
II=pi*(ri**4)/4 !Moment of inertia of pipe
CC=ri !Distance from the neutral axis to the pipe surface
My=Fy*II/CC !Maximum applied moment
force=My/(2*ri) !Applied force
Eyys=30000 !Young's Modulus of steel(ksi)
!For Steel
ANSYS Script 62
SIGMAY=60 !Yield stress of steel (force/area)(ksi)
ETAN=0.01*Eyys !Tangent modulus (Force/Area)
!To make the division in radial direction an even number
rr=mod(nrdiv,2)
*if,rr,gt,0,then
nrdiv=nrdiv+1
*endif
Por=0.25 !Poissons ratio
thkp=0.28 !Pipe wall thickness
thkf=3*thkp !Flange thickness
bdia=1 !Bolt dia
!Stiffening beam
sbh=3 !Height
sbw=1 !Width
sbarea=sbh*sbw !Area
sizz=sbh*sbw**3/12 !Moment inertia along z-axis
siyy=sbw*sbh**3/12 !Moment inertia along y-axis
barea=pi/4*(bdia**2) !bolt area
!Spring constant or stiffness
bk=barea*Eyys/dh !k=A*E/L [lb/in] or [N/m]
TB,BISO,1 !Activates a data table for nonlinear material properties.
TBDATA,1,SIGMAY,ETAN !Defines data for the data table.
et,1,shell93 !Define shell93 element type
et,2,combin39 !Define combin39 element type
keyopt,2,4,1 !Sets combin39 element key options(4)
ANSYS Script 63
et,3,beam4 !Define beam4 element type
!Define Material Properties
mp,EX,1,Eyys !Elastic modulus
mp,nuxy,1,Por !Minor Poisson's ratio
!Define element real constants
r,1,thkp !For pipe
r,2,thkf !For falnge
r,3,-1,-bk*100,0,0,1,0.01 !For surface spring( Non linear Combin39 element)
!(D1,F1)=(-1,-bk*100);(D2,F2)=(0,0);(D3,F3)=(1,0.01)
r,4,-1,-bk,0,0,1,bk !For bolt( Linear Combin39 element)
!(D1,F1)=(-1,-bk);(D2,F2)=(0,0);(D3,F3)=(1,bk)
r,5,sbarea,sizz,siyy,sbw/2,sbh/2 !Stiffening beam
*DO,i,1,nhdiv+1,1 !Define keypoints for pipe
K,i,ri,(hp/nhdiv)*(i-1),0 !Define keypoints along y-axis
*ENDDO
*DO,i,1,nrdiv,1 !Define keypoints for flange
K,i+(nhdiv+1),ri+((ro-ri)/nrdiv)*i,0,0 !Define keypionts along x-axis
*ENDDO
klast=nhdiv+nrdiv+1 !Define last keypiont as klast
k,klast+1,ri,-dh,0 !Define keypoints for spring bottom
klast=klast+1 !Define last keypiont as klast
*DO,i,1,nrdiv,1
k,klast+i,ri+((ro-ri)/nrdiv)*i,-dh,0
*ENDDO
klast=klast+nrdiv !Define last keypiont as klast
k,klast+1,0,0,0 !define keypionts along y-axis
k,klast+2,0,hp,0
klast=klast+2 !Define last keypiont as klast
ANSYS Script 64
*DO,i,1,nhdiv,1 !Define lines for pipe
L,i,i+1
*ENDDO
llast=nhdiv !Define last line as llast
l,1,nhdiv+2 !Define first line for flange
*DO,i,1,nrdiv-1,1 !Define rest lines for flange
L,nhdiv+2+i-1,nhdiv+2+i
*ENDDO
l,1,nhdiv+nrdiv+2 !Define first line for surface springs
*DO,i,1,nrdiv,1 !Define rest lines for surface springs
L,nhdiv+1+i,nhdiv+1+i+nrdiv+1
*ENDDO
!For pipe
!Select a new set of line from range 1 to nhdiv with increment 1
lsel,S,line,,1,nhdiv,1
!Generates cylindrical pipe areas by rotating the above selected lines
arotat,all, , , , , ,klast-1,klast,360,nbolt*ntheta
!Specifies the number of element divisions per line=1 for all the selected lines
lesize,all, , ,1
type,1 !Assign pipe elements
mat,1
real,1
asel,all !Select all areas
amesh,all !Mesh all selected areas
!For flange
!Select a new set of line from range nhdiv+1 to nhdiv+nrdiv with increment 1
lsel,s,line, ,nhdiv+1,nhdiv+nrdiv,1
!Generates cylindrical flange areas by rotating the above selected lines
ANSYS Script 65
arotat,all, , , , , ,klast-1,klast,360,nbolt*ntheta
!Specifies the number of element divisions per line=1 for all the selected lines
lesize,all, , ,1
type,1 !Assign flange elements
mat,1
real,2
asel,s,loc,y,0,0 !Select a new set of lines in y direction in between 0 to 0
amesh,all !Mesh all selected areas
k, ,0,0,ri !Define keypoints on x-z plane for working plane
!Define a keypoint at lowest available number
korig=kp(0,0,0) !Define new keypoints from the previously generated keypoints
!For defining the origin of the working plane coordinate system
kx=kp(ri,0,0) !For defining the x-axis orientation
kpl=kp(0,0,ri) !For defining the working plane
wpstyl , , , , , ,1 !Select the working plane system to Polar wp system
kwplan , 1, korig, kx, kpl !Create new working plane using three coordinates
csys,WP !Activate Working Plane coordinate system
lsel,all !Select all lines
*get, lastline, line , 0 , num, max
!Generates additional lines radially for suface springs from prevously generated lines
lgen ,nbolt*ntheta,nhdiv+nrdiv+1,nhdiv+nrdiv+nrdiv+1,1 , ,360/(nbolt*ntheta),0
csys,0 !Activate Cartesian coordinate system
!Select a new set of lines from generated surface spring lines
lsel,s,loc,y,-dh/2,-dh/2
boltline=lastline+1+nrdiv/2 !To find the bolt spot
boincr=(nrdiv+1)*ntheta !To find the bolt line increment
*do,i,1,nbolt,1 !Unselect the bolt lines from the all selected lines
ANSYS Script 66
lsel,u,line, ,(i-1)*boincr+boltline
*enddo
type,2 !Define material properties for the surface spring
real,3
lesize,all, , ,1
lmesh,all
lsel,none !Unselect all lines
*do,i,1,nbolt,1 !Select lines for the bolts
lsel,a,line, ,(i-1)*boincr+boltline
*enddo
type,2 !Define maerial properties for the bolts
real,4
lesize,all, , ,1
lmesh,all
lsel,s,loc,y,hp,hp !Select lines for the stiffening beam
type,3 !Define material properties for stiffening beam
real,5
lesize,all, , ,1
lmesh,all
nsel,all
nsel,s,loc,y,-dh,-dh !Select nodes for defining degree of freedom
d,all,all,0 !Defining DOF
!Define DOF at the contact surface of pipe joint
nsel,all
csys,wp !Define WP coordinate system
*do,i,1,nbolt*ntheta,1
thetaa=360/(nbolt*ntheta)*(i-1)
ANSYS Script 67
d,node(ro,thetaa,0),ux,0
d,node(ro,thetaa,0),uz,0
*enddo
nsel,all
nummrg,node
csys,0
ang=360/(nbolt*ntheta)
xloc=ri*cos(ang*pi/180)
zloc=ri*sin(ang*pi/180)
F,node(xloc,hp,zloc),FY,force
F,node(-xloc,hp,-zloc),FY,-force
!finish
/solu
ANTYPE,0 !Perform a static analysis
OUTRES,BASIC,all !All solution data written to the database for every subset
autots,OFF !Do not use automatic time stepping
nsubst,50 !Specifies 100 number of substeps to be taken this load step.
!Specifies the maximum number(100) of equilibrium iterations for nonlinear analysis.
neqit,100
time,1 !Sets the time for a load step
solve
gplot
/POST1
finish