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
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A Computational Investigation on Bolt Tension of a Flanged Pipe Joint Subjected to Bending - Md. Jahidul Islam
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.
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Transcript
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
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
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
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
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
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
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
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