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

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


thicknesses for 3.5 in. diameter pipe.

39




40




41




42




43




44




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 4.9 Comparison of bolt tension for 12 in. diameter pipe and flange

thickness = pipe wall thickness

46


thickness = pipe wall thickness.

47



48



49


thickness = 2 × pipe wall thickness. 50



Figure 4.15 Comparison of bolt tension for 8 inch diameter pipe and flange


Figure 4.16 Comparison of bolt tension for 6 inch 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



56



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.


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


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


"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


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


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.


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.


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


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.


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.


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.


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


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.


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.


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


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


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.


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.


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


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


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.


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


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


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.


FIGURE 3.8 Finite elements mesh with load and boundary conditions.

FIGURE 3.9 Typical deflected shape of a flanged pipe joint.


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


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


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,


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




Flange thickness = 3 × Pipe thickness

Proposed equation:

cbnanpT +++= 2

Where,



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




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.


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.


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)


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.


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


thickness (kips)


thickness (kips)


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


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.


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


thickness (kips)


thickness (kips)


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 = 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)



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


thickness (kips)


thickness (kips)


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 = 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)



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


thickness) (kips)


thickness) (kips)


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 = 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)



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


thickness) (kips)


thickness) (kips)


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 = 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)




Bolts Bolt Tension


thickness (kips)


thickness) (kips)


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 = 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)




Bolts Bolt Tension


thickness (kips)


thickness (kips)


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=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)



Comparison of bolt tension with conventional method Flange thickness = Pipe thickness

Proposed equation: ( ) bnnapT −×+=

Where,



deb 3111.051.0 ×=


d = Pipe diameter, 12 in.


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


Flange thickness = Pipe thickness


Where,



deb 3111.051.0 ×=




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





Where,



deb 3111.051.0 ×=




0

50

100

150

200

250

4 6 8 10 12Number of bolts.

Bol

t ten

sion

(kip

s)






Where,



deb 3111.051.0 ×=




0

20

40

60

80

100

120

4 6 8 10Number of bolts.

Bol

t ten

sion

(kip

s)





( ) bnnapT +×+=

Where,



322

1 adadaa ++=

322

1 bdbdbb ++=

26.01 −=a 06.11 =b

1.02 −=a 2.02 =b

95.183 =a 1.413 −=b




0

100

200

300

400

500

600

700

4 6 8 10 12 14 16Number of bolts.

Bol

t ten

sion


FIGURE 4.13 Comparison of bolt tension for 12 in. diameter pipe.



( ) bnnapT +×+=

Where,



322

1 adadaa ++=

322

1 bdbdbb ++=

26.01 −=a 06.11 =b

1.02 −=a 2.02 =b

95.183 =a 1.413 −=b




0

50

100

150

200

250

300

350

400

450


Bol

t ten

sion

(kip

s)





( ) bnnapT +×+=

Where,



322

1 adadaa ++=

322

1 bdbdbb ++=

26.01 −=a 06.11 =b

1.02 −=a 2.02 =b

95.183 =a 1.413 −=b




0

50

100

150

200

250


Bol

t ten

sion





( ) bnnapT +×+=

Where,



322

1 adadaa ++=

322

1 bdbdbb ++=

26.01 −=a 06.11 =b

1.02 −=a 2.02 =b

95.183 =a 1.413 −=b




0

20

40

60

80

100

120

140


Bol

t ten

sion

(kip

s)





Proposed equation: cbnanpT +++= 2

Where,



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




0

100

200

300

400

500

600

700

4 6 8 10 12 14 16Bolt number

Bol

t ten

sion

(kip

s)






Where,



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




0

50

100

150

200

250

300

350

400

450


Bol

t ten

sion

(kip

s)






Where,



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




0

50

100

150

200

250


Bol

t ten

sion

(kip

s)






Where,



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




0

20

40

60

80

100

120


Bol

t ten

sion

(kip

s)



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

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

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