Design of Steam Piping including Stress Analysis Muhammad Sardar Thesis submitted in partial fulfillment of requirements for the MS Degree in Mechanical Engineering Department of Mechanical Engineering, Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad, Pakistan. October, 2008.
Design of Steam Piping System Including Stress Analysis
Nov 23, 2014
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Design of Steam Piping including Stress Analysis
Muhammad Sardar
Thesis submitted in partial fulfillment of requirements for the MS Degree in Mechanical Engineering
Department of Mechanical Engineering, Pakistan Institute of Engineering & Applied Sciences,
Nilore, Islamabad, Pakistan. October, 2008.
Lap_corc
Text Box
Note. This is not a handbook, it is MS Thesis of a student in Pakistan Institute of Engineering & Applied Sciences, Pakistan (PIEAS).
ii
iii
Department of Mechanical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS)
Nilore, Islamabad, Pakistan
Declaration of Originality
I hereby declare that the work contained in this thesis and the intellectual content of
this thesis are the product of my own work. This thesis has not been previously
published in any form nor does it contain any verbatim of the published resources
which could be treated as infringement of the international copyright law.
I also declare that I do understand the terms ‘copyright’ and ‘plagiarism’ and
that in case of any copyright violation or plagiarism found in this work, I will be held
fully responsible of the consequences of any such violation.
Signature:
Name: Muhammad Sardar
Date:____________________
Place: PIEAS, Nilore Islamabad
iv
Certificate of Approval
This is to certify that the work contained in this thesis entitled
“Design of Steam Piping including Stress Analysis”
was carried out by
Muhammad Sardar
Under my supervision and that in my opinion, it is fully adequate, in
scope and quality, for the degree of M.S. Mechanical Engineering from
Pakistan Institute of Engineering and Applied Sciences (PIEAS).
Approved By:
Signature: ________________________
Supervisor: Mr. Basil Mehmood Shams, P.E. (DTD, Islamabad)
Signature: _______________________ Co-Supervisor: Muhammad Younas, S.E. (DTD, Islamabad)
Signature: ________________________ Co-Supervisor: Hafiz Laiq-ur-Rehman, J.E. (PIEAS, Islamabad)
Verified By:
Signature: ________________________
Head, Department of Mechanical Engineering
Stamp:
v
Dedication
Dedicated to my parents, brothers, sisters and my teachers
who always supported me and whose
prayers enabled me to
do my best in every
matter of my life
vi
Acknowledgement First of all I am humbly thankful to Allah Almighty, giving me the power to think and
enabling me to strengthen my ideas. I glorify ALMIGHTY ALLAH for HIS
unlimited blessings and capabilities that HE has bestowed upon me, without HIS
blessings, I would not be able to complete my work. I offer my thanks to Holy
Prophet (Peace Be Upon Him), “The mercy for all the worlds” and whose name has
given me special honor and identity in life.
I am very grateful to my project supervisor Mr. Basil Mehmood Sham, P.E. for his
guidance for the completion of this work. I am also grateful to my co-supervisors
Mr. Muhammad Younas, S.E. and Mr. Hafiz Laiq-ur-Rehman, J.E. for their
inspiring guidance, constant encouragement and fruitful suggestions. At the end I am
also thankful to Engr. Dr. Mohammad Javed Hyder for his keen interest in the
project and constructive criticism, which enabled me to complete my report.
Muhammad Sardar
vii
Table of Contents
1 INTRODUCTION................................................................................................1
1.1 Thesis Introduction ........................................................................................1
1.2 Basic aim of the thesis ...................................................................................1
1.3 Steam Piping Network ...................................................................................2
1.4 Thesis Organization .......................................................................................2
2 THEORETICAL BACKGROUND OF PIPING SYSTEM ............................5
2.1 Historical background of the piping system ..................................................5
2.2 Piping Terminologies.....................................................................................6
2.2.1 Pipe.......................................................................................................................6 2.2.2 Types of pipes and its uses...................................................................................6 2.2.3 Pipe Size...............................................................................................................6 2.2.4 Nominal Pipe Size (NPS).....................................................................................6 2.2.5 Piping ...................................................................................................................6 2.2.6 Piping System ......................................................................................................7 2.2.7 Process Piping ......................................................................................................7 2.2.8 Service Piping ......................................................................................................7
2.3 Pipe Fittings ...................................................................................................7
2.3.1 Valves...................................................................................................................7 2.3.2 Expansion Fittings................................................................................................8
2.4 Supports .........................................................................................................9
3 PIPING CODES AND STANDARDS..............................................................12
3.1 Piping Code Development ...........................................................................12
3.2 B31.1 Power Piping .....................................................................................13
3.3 ASME Code Requirements..........................................................................14
3.3.1 Stresses due to sustained loadings......................................................................14 3.3.2 Stress due to occasional loadings .......................................................................14 3.3.3 Stresses due to thermal loadings ........................................................................15
3.4 Stress analysis of piping system ..................................................................15
3.4.1 Stress and Strain.................................................................................................15 3.4.2 Failure Theories .................................................................................................15 3.4.3 Piping Design Criteria........................................................................................16
viii
4 PIPING DESIGN PROCEDURES...................................................................19
4.1 Process Design .............................................................................................19
4.2 Piping Structural Design ..............................................................................19
4.2.1 Pipe Thickness Calculations ..............................................................................20 4.2.2 Allowable Working Pressure .............................................................................20 4.2.3 Sustained Load Calculations ..............................................................................21 4.2.4 Wind Load Calculations.....................................................................................21 4.2.5 Thermal Loads Calculations ..............................................................................22 4.2.6 Occasional Loads ...............................................................................................22 4.2.7 Seismic Loads ....................................................................................................22
4.3 Pipe Span Calculations ................................................................................23
4.3.1 Span Limitations ................................................................................................23 4.3.2 Expansion Loop Calculations ............................................................................24
5 SUPPORT DESIGN...........................................................................................25
5.1 Beam Design................................................................................................25
5.1.1 Bending Stress....................................................................................................26 5.1.2 Shear Stress ........................................................................................................26 5.1.3 Deflection...........................................................................................................27
5.2 Column.........................................................................................................27
5.3 Base Plate.....................................................................................................29
5.4 Base Plate Bolts ...........................................................................................29
6 PIPE DESIGN CALCULATIONS...................................................................30
6.1 Design Parameters .......................................................................................30
6.2 Physical Properties.......................................................................................32
6.3 Design Calculations .....................................................................................32
6.3.1 Pipe Thickness Calculations ..............................................................................32 6.3.2 Allowable Working Pressure .............................................................................36 6.3.3 Wind load Calculations ......................................................................................38 6.3.4 Dead Loads Calculation .....................................................................................40 6.3.5 Pipe Span Calculations (based on limitation stress)...........................................42 6.3.6 Calculation for Supports based on Standard Spacing ........................................45 6.3.7 Thermal Expansion (deflection).........................................................................47 6.3.8 Expansion Loops Calculations ...........................................................................49 6.3.9 Impact Loading on Bends ..................................................................................53
ix
6.3.10 Normal Impact Load on elbow ..........................................................................54
7 THERMAL CALCULATIONS........................................................................56
7.1 Thermal Analysis .........................................................................................56
7.2 Verification from Code ................................................................................67
7.3 Static Loads Calculations.............................................................................68
7.3.1 Manual Calculations...........................................................................................68 7.3.2 Verification from Code ......................................................................................71
7.4 Piping Analysis on ANSYS.........................................................................72
7.4.1 Comparison of Analysis.....................................................................................74
7.5 Seismic Loads Calculations .........................................................................74
7.5.1 Seismic stress .....................................................................................................74 7.5.2 Seismic Lateral load...........................................................................................74 7.5.3 Verification from Code ......................................................................................75
8 SUPPORT DESIGN CALCULATION............................................................77
8.1 Design Parameters .......................................................................................77
8.2 Beam Design................................................................................................77
8.3 Beam Analysis .............................................................................................79
8.3.1 Manual Analysis.................................................................................................79 8.3.2 ANSYS Analysis................................................................................................80
8.4 Column Design ............................................................................................82
8.4.1 Verification for critical load...............................................................................84 8.4.2 Verification for stresses......................................................................................84 8.4.3 Manual Analysis.................................................................................................85 8.4.4 ANSYS Analysis................................................................................................87 8.4.5 Comparison of analysis ......................................................................................89
8.5 Base Plate Design ........................................................................................89
8.5.1 Base Plate Design Calculations..........................................................................90 8.5.2 Thickness of the plate due to concentric load ....................................................91 8.5.3 Thickness due to bending moment.....................................................................91 8.5.4 Specifications of base plate ................................................................................93 8.5.5 Bolt specifications..............................................................................................93
9 COMPLETE SYSTEM MODELING..............................................................94
9.1 Pro-E Modeling............................................................................................94
x
9.2 ANSYS 3-D Modeling and Analysis...........................................................95
9.2.1 Results and Discussion.......................................................................................98
10 CONCLUSIONS ................................................................................................99
11 FUTURE RECOMMENDATIONS ...............................................................100
REFERENCES.........................................................................................................101
APPENDIXE ............................................................................................................101
VITA..........................................................................................................................113
xi
List of Figures Figure 1-1 PFD of the complete piping net work ........................................................4
Figure 2-1 Full loop ....................................................................................................8
Figure 2-2 Z, L and U shaped loop .............................................................................9
Figure 2-3 Anchor support ........................................................................................10
Figure 2-4 Hanger support ........................................................................................10
Figure 2-5 Sliding support ........................................................................................10
Figure 2-6 Spring support .........................................................................................11
Figure 2-7 Snubber support .......................................................................................11
Figure 2-8 Roller support ..........................................................................................11
Figure 5-1 Effective length constants table ..............................................................28
Figure 6-1 Forces on the bend by the fluid ................................................................53
Figure 7-1 Header Pipe including an expansion loop................................................56
Figure 7-2 Header Pipe Sections................................................................................57
Figure 7-3 Symmetry of header pipe considering as a beam.....................................68
Figure 7-4 Segment A-B............................................................................................69
Figure 7-5 Segment A-B-C........................................................................................69
Figure 7-6 Shear Force Diagram................................................................................70
Figure 7-7 Bending Moment Diagram.......................................................................71
Figure 7-8 Loaded view of the meshed beam............................................................72
Figure 7-9 Deflection in Pipe....................................................................................73
Figure 7-10 Bending stress in Pipe .............................................................................73
Figure 8-1 Uniformly load distributed Cantilever Beam...........................................77
Figure 8-2 Double Cantilever beam...........................................................................79
Figure 8-3 Deformed Shape of the beam ..................................................................80
Figure 8-4 Bending Moment diagram of the beam ...................................................81
Figure 8-5 Max. Stress distribution Diagram ...........................................................81
Figure 8-6 Loads on column of the support...............................................................82
Figure 8-7 Meshed and loaded column......................................................................88
Figure 8-8 Deformation of the column .....................................................................88
Figure 8-9 Stress distribution in column ...................................................................89
Figure 8-10 Base Plate Dimensions.............................................................................90
Figure 8-11 Pressure diagram ......................................................................................91
xii
Figure 8-12 Bolt dimensions........................................................................................93
Figure 9-1 Anchor support along with a pipe ............................................................94
Figure 9-2 Convergence line b/w no. of elements and Von Mises Stresses ..............95
Figure 9-3 Meshed diagram of the support model.....................................................96
Figure 9-4 Deformed shape of the support model .....................................................96
Figure 9-5 First Principle Stress distribution in support...........................................97
Figure 9-6 Von Mises stress distribution in support..................................................97
xiii
List of Tables Table 3-1 Primary stresses of pipes ...........................................................................17
Table 3-2 Secondary stresses of pipes .......................................................................18
Table 5-1 Limitation of column slenderness ratio .....................................................28
Table 6-1 Characteristics of Fluid at inlet and out let of pipes and its sizing............30
Table 6-2 Material Properties ....................................................................................32
Table 6-3 Input Parameters used in pipe thickness calculation .................................33
Table 6-4 All pipes thickness along with standard thickness ....................................34
Table 6-5 Input data ...................................................................................................36
Table 6-6 Design and working Pressure ....................................................................36
Table 6-7 Wind loads for each pipe...........................................................................38
Table 6-8 Pipe, Fluid and insulation weights.............................................................40
Table 6-9 Pipe Span based on limitation of stress .....................................................43
Table 6-10 Spacing based on standard spacing ...........................................................45
Table 6-11 Thermal deflection for pipes complete segments......................................47
Table 6-12 Sizing of expansion loops..........................................................................50
Table 6-13 Input Data ..................................................................................................53
Table 6-14 Input data ...................................................................................................54
Table 7-1 Input Data ..................................................................................................56
Table 7-2 For main line magnitude of expansion and directions...............................58
Table 7-3 Vertical section magnitude of expansion and direction ............................58
Table 7-4 Summary of all Loads due to Thermal expansion.....................................66
Table 7-5 Input data ...................................................................................................67
Table 7-6 Input data ...................................................................................................71
Table 7-7 Comparison of analysis for beam..............................................................74
Table 7-8 Input data ...................................................................................................76
Table 8-1 Available loads for analysis of anchor support .........................................77
Table 8-2 Properties of the channel beam..................................................................78
Table 8-3 Comparison of analysis for beam..............................................................82
Table 8-4 Specifications of column ...........................................................................83
Table 8-5 Input data ...................................................................................................86
Table 8-6 Input data ...................................................................................................87
xiv
Table 8-7 Comparison of analysis of column.............................................................89
Table 8-8 Base plate specifications.............................................................................93
Table 8-9 Bolts standard dimensions..........................................................................93
xv
Abstract This report is about the design of steam piping and its stress analysis of a
given process flow diagram. The prime objective of this project is to design
the piping system and then to analyze its main components. Wall thicknesses
are calculated for all pipes which were found very safe for the operating
pressure. For header pipe the calculated wall thickness is 0.114 inch and the
standard minimum wall thickness is 0.282 inch which is greater than the
calculated one by more than 2.4 times. Different loads such as static loads,
occasional loads and thermal loads of all pipes were also calculated. After
load calculations, spacing of supports and designing of expansion loops were
carried out. Thermal, static and seismic analysis of main system pipe has
been done and results were compared with ASME Power Piping Code B31.1.
After calculation of all applied loads, anchor support components including
half channel beam C5 x 9 and standard circular column of 4 inch nominal size
were designed and analyzed both manually and on ANSYS software. Base
plate of size 15x15x1/4 inch and bolts of ¾ inch diameter and of length 20
inch were also designed. The results obtained from both methods were
compared and found safe under available applied loads.
1
1 Introduction 1.1 Thesis Introduction
Piping System design and analysis is a very important field in any process and power
industry. Piping system is analogous to blood circulating system in human body and is
necessary for the life of the plant. The steam piping system, mentioned in the thesis
will be used for supplying steam to different locations at designed temperature and
pressure. This piping system is one of the major requirements of the plant to be
installed.
This thesis includes the following tasks:
a) Process design of the complete piping system
b) Structural design of the pipes manually
c) Stress analysis of the pipes using ANSYS
d) Structural and thermal analysis of the expansion Loops
e) Structural design of supports manually
f) Modeling and stress analysis of support
1.2 Basic aim of the thesis
The aim of the thesis was to design and analyze piping system according to standard
piping Codes. The design should prevent failure of piping system against over stresses
due to:
I. Sustained loadings which act on the piping system during its operating time
e.g. static loads including dead loads, thermal expansion loads, effects of
supports and internal and external pressure loading.
II. Occasional loads which act percentages of the system’s total operating time
e.g. impact forces, wind loads, seismic loads and discharge loads etc.
While piping stress analysis is used to ensure:
1) Safety of piping and piping components
2) Safety of the supporting structures
3) Safe stress relieving of the expansion loops
2
1.3 Steam Piping Network
Basically the sizing of this steam piping has already done and contained nearly on
750x300m2 area, including 48 pipes and 52 junctions. The detail of the piping system
e.g. length of each pipe, Nominal Pipe Size (NPS) with pipe no. starting from 208 and
ending on pipe no. 256 are shown from the following Figure 1-1. The rest of the data
e.g. inlet and out let velocities of each pipe, inlet and out let pressure of each pipe and
inlet and out let temperature of each and every pipe are arranged in Table 6-1, which
will be used in further calculations.
1.4 Thesis Organization
Chapter 1
In this chapter introduction to the project, basic aim of the project and process flow
diagram of the complete piping system with information about sizing has been
discussed.
Chapter 2
Literature survey has been done in this chapter. Detail study about the pipes and
piping system along with the code development has been included. This chapter also
consists on some of the basic terminologies relating to pipes, explanation of the piping
components and supports.
Chapter 3
Explanation about piping codes and standards and stress analysis of the piping system
has been included in this chapter.
Chapter 4
In this chapter piping design procedure, pipe span and expansion loop calculations
and support design methodology has been discussed.
Chapter 5
This chapter included all the detail about Anchor support and its components.
Chapter 6
This chapter related to all calculations of pipe design. All loads applied on the pipes
during operation have been calculated.
Chapter 7
This chapter included on thermal, static and seismic loads on pipes and their analysis
along with verification from the code has been done.
3
Chapter 8
This chapter consists on the piping support design calculations, in which selection and
analysis of beam, column, base plate and bolts has been done.
Chapter 9
This chapter contained full modeling of anchor support in Pro-E and ANSYS and its
analysis in ANSYS.
4
Steam Piping Network
Figure 1-1 PFD of the complete piping network
5
2 Theoretical Background of Piping System
A piping system is generally considered to include the complete interconnection of
pipes, including in line components such as pipe fittings, valves, tanks and flanges
etc. The contributions of the piping systems are essential in industrialized society.
They provide drinking water to cities, irrigation water to farms, cooling water to
buildings and machinery. Piping system are the arteries of our industrial processes;
they transmit the steam to turn the turbines which drive generators, thus providing
electricity that illuminates the world and power machines [1].
2.1 Historical background of the piping system
Initially there were no basic concepts of the piping system engineering when wind,
water and muscle were the prime movers. The advent of the industrial revolution,
especially the practical use of steam in the seventeenth century required the design
and manufacturing of piping to withstand the rejoins of conveying pressurized and
heating fluids. The combination of very high pressures, thermal stresses and thermal
deformations required that fundamental design requirements and analytical technique
be developed. However, piping system design progressed with little or no design
standards or code limitations during the early years of industrial revolution [3].
In the 1920s, the introduction to meet the electrical demand of turbine plants
with super heated steam at temperature up to 600oF and gauge pressure of 300 psi
posed to the next major piping system design challenge. These design conditions
exceeded safe cast iron values, thus requiring the introduction of cast steel for critical
components. By 1924, the steam gauge pressure had increased to 600 psi, doubling in
just a few years. One year later, steam pressure and temperature of 1200 psi and
700oF were achieved, demonstrating the advances made in the development of steam
generator and attached piping. By 1957, some 900oF designs were in service with
1200oF designs projected, using austenitic stainless steel materials in the high
temperature zones, currently, the top gauge pressure is 2400 psi for most fossil fuel
plants. With new materials available, the boiler, turbine and piping have equal
strength capabilities [3].
6
2.2 Piping Terminologies
Detail of some of the basic terminologies like pipe, pipe sizes and pipe system are
given below.
2.2.1 Pipe
“A pipe is a closed conduit of circular cross section which is used for the
transportation of fluids”. If pipe is running full, then the flow is under pressure and if
the pipe is not running full, then the flow is under gravity.
2.2.2 Types of pipes and its uses
Standard Pipe: Mechanical service pipes, low pressure service e.g. refrigeration pipes
Pressure Pipe: It is used for liquid, gas or vapor for high pressure and temperature
application.
Line Pipe: Threaded or Plain ends used for gas, steam and as an oil pipe.
Water Well: Pump pipe, turbine pipe and driven well pipe etc [1].
2.2.3 Pipe Size
Initially a system known as iron pipe size (IPS) was established to designate the pipe
size. The size represented the approximate inside diameter of the pipe in inches e.g.
an IPS 6 pipe is one whose inside diameter is approximately 6 inches (in). With the
development of stronger and corrosion-resistant piping materials, the need for thinner
wall pipe resulted in a new method of specifying pipe size and wall thickness. The
designation known as nominal pipe size (NPS) replaced IPS, and the term schedule
(SCH) was invented to specify the nominal wall thickness of pipe.
2.2.4 Nominal Pipe Size (NPS)
NPS is a dimensionless designator of pipe size. It indicates standard pipe size when
followed by the specific size designation number without an inch symbol.
For example, NPS 2 indicates a pipe whose outside diameter is 2.375 in [2].
2.2.5 Piping
Pipe sections when joined with fittings, valves, and other mechanical equipment and
properly supported by hangers and supports, are called piping.
7
2.2.6 Piping System
The piping system means a complete network of pipes, valves, and other parts to do a
specific job in plant. There are two types of piping systems.
2.2.7 Process Piping
It is used to transport fluids b/w storage tanks and processing unites.
2.2.8 Service Piping
It is used to convey steam, air, water etc. for processing.
2.3 Pipe Fittings
Fittings permit a change in direction of piping, a change in diameter of pipe or a
branch to be made from the main run of pipe. Some of the fittings are elbows, long
radius and short radius elbow reducing elbow, reducer, bends and mitered bends etc.
2.3.1 Valves
A valve is a mechanical device that controls the flow of fluid and pressure within a
system. There are different types of valves some of them are discussed below [3].
a) ON/OFF Valves
These are the kind of valves which are used to stop of start the fluid flow e.g. Gate
valve, Globe valve, rotary ball valve, Plug valve and diaphragm valve etc.
b) Regulating Valve
These are the kind of valves which are used to start, stop and also to regulate the fluid
flow e.g. Needle valve, butterfly valve, Diaphragm and Gate valve etc.
c) Safety Valve
This valve reacts to excessive pressure in piping system. They provide a rapid means
of getting rid of that pressure before a serious accident occur. Safety valve is used
normally for gasses and steams. In safety valve the steam is discharge to the air
through a large pipe.
8
d) Pressure Regulating Valve
These valves regulate pressure in a fluid line keeping it very close to a pre-set level.
The valve is set to monitor the line, and make needed adjustments on signal from a
sensitive device.
2.3.2 Expansion Fittings
Expansion loops are used to release the stresses which produced due to thermal
gradients. All pipes will be installed at ambient temperature. Pipes carrying hot fluids
such as water or steam operate at higher temperatures. It follows that they expand,
especially in length, with an increase from ambient to working temperatures. This will
create stress upon certain areas within the distribution system, such as pipe joints,
which, in the extreme, could fracture. Therefore the piping system must be
sufficiently flexible to accommodate the movements of the components as they
expand [1].
The expansion fitting is one of method of accommodating expansion. These
fittings are placed with in a line, and are designed to accommodate the expansion,
with out the total length of the line changing. They are commonly called expansion
bellows, due to the bellows construction of the expansion sleeve. Different kinds of
expansion loops are used, some of which are given below.
2.3.2.1 Full loop
This is simply one complete turn of the pipe and, on steam pipe work, should
preferably be fitted in a horizontal rather than a vertical position to prevent
condensate accumulating on the upstream side as shown in Figure 2-1 below. When
space is available, it is best fitted horizontally so that the loop and the main are on the
same plane.
Figure 2-1 Full Loop [6]
9
2.3.2.2 Z, L, and U shaped loops
In majority of these loops guided cantilever method is used to find the deflection in
the loop. These loops are shown in the Figure 2-2 below.
Figure 2-2 Z, L and U shaped Loop [2]
2.4 Supports
Pipe support specifications for individual projects must be written in such a way as to
ensure proper support under all operating and environmental conditions and to
provide for slope, expansion, anchorage, and insulation protection. Familiarity with
standard practices, customs of the trade, and types and functions of commercial
component standard supports and an understanding of their individual advantages and
limitations, together with knowledge of existing standards, can be of great help in
achieving the desired results [1]. Good pipe support design begins with good piping
design and layout. For example, other considerations being equal, piping should be
routed to use the surrounding structure to provide logical and convenient points of
support, anchorage, guidance, or restraint, with space available at such points for use
of the proper component. Parallel lines, both vertical and horizontal, should be spaced
sufficiently apart to allow room for independent pipe attachments for each line. There
are different types of supports used in the piping system; some of them are discussed
below [2].
a) Anchor support
A rigid support providing substantially full fixity for three translations and
rotations about three reference axes. Figure 2-3 shows the model along with
10
the pipe and welding positions. Detail of this support will be discussed in
chapter 8.
Figure 2-3 Anchor Support [3]
b) Hanger support
A support for which piping is suspended from a structure, and so on, and
which functions by carrying the piping load in tension as shown below in
figure.
Figure 2-4 Hanger Support [3]
c) Sliding support
A device that providing support from beneath the piping but offering no
resisting other than frictional to horizontal motion as shown in Figure 2-5
below..
Figure 2-5 Sliding Support [3]
11
d) Spring support
Spring support is used when there is an appreciable difference b/w operating
and non operating conditions of the pipes. Constant load support is used when
loading condition change up to 6%.
Figure 2-6 Spring support [1]
e) Snubber support
These supports are used to restrain the dynamic load such as seismic loads,
water hammer and steam hammer etc. These supports are not capable of
supporting gravity loads. A simplified snubber support view is shown in
Figure 2-7 below.
Figure 2-7 Snubber support [3]
f) Roller support
A means of allowing a pipe to move along its length but not side ways. Roller
support is shown in Figure 2-8 below.
Figure 2-8 Roller support [3]
12
3 Piping Codes and Standards Before the selection of codes for the steam piping, a little detail about codes,
standards and its historical background is given below.
3.1 Piping Code Development
The increase in operating temperatures and pressures led to the development of the
ASA (now ANSI) B31 Code for pressure piping. During the 1950s, the code was
segmented to meet the individual requirements of the various developing piping
industries, with codes being published for the power, petrochemical and gas
transmission industries among others. The 1960s and 1970s encompassed a period of
development of standard concepts, requirements and methodologies. The
development and use of the computerized mathematical models of piping system have
brought analysis, design and drafting to new levels of sophistication. Codes and
standards were established to provide methods of manufacturing, listing and reporting
design data [3].
“A standard is a set of specifications for parts, materials or processes intended
to achieve uniformity, efficiency and a specified quality”. Basic purpose of the
standards is to place a limit on the number of items in the specifications, so as to
provide a reasonable inventory of tooling, sizes and shapes and verities [4]. Some of
the important document related to piping are:
I. American Society of Mechanical Engineers (ASME)
II. American National Standards Institute (ANSI)
III. American Society of Testing and Materials (ASTM)
IV. Pipe Fabrication Institute (PFI)
V. American Welding Institute (AWS)
VI. Nuclear Regulatory Commission (NRC)
On the other side “A code is a set of specifications for analysis, design,
manufacture and construction of something”. The basic purpose of code is to provide
design criterion such as permissible material of construction, allowable working
stresses and loads sets [4]. ASME Boiler and Pressure vessel codeB31, Sectiion-1 is
13
used for the design of commercial power and industrial piping system. This section
has the following sub section [1].
B31.1: For Power Piping.
B31.3: For Chemical plant and Petroleum Refinery Piping.
B31.4: Liquid transportation system for Hydrocarbons, liquid petroleum gas, and
Alcohols.
B31.5: Refrigeration Piping.
B31.8: Gas transportation and distribution piping system.
B31.1 Power piping code concerns mononuclear piping such as that found in
the turbine building of a nuclear plant or in a fossil-fueled power plant. Detail of this
code is given below in section 3.2. B31.3 code governs all piping within limits of
facilities engaged in the processing or handling of chemical, petroleum, or related
products. Examples are a chemical plant compounding plant, bulk plant, and tank
farm. B31.4 governs piping transporting liquids such as crude oil, condensate, natural
gasoline, natural gas liquids, liquefied petroleum gas, liquid alcohol, and liquid
anhydrous ammonia. These are auxiliary piping with an internal gauge pressure at or
below 15 psi regardless of temperature. B31.5 covers refrigerants and secondary
coolant piping for temperatures as low as 320oF. B31.8 governs most of the pipe lines
in gas transmission and distribution system up to the outlet of the customer’s meter set
assembly. Excluded from this code with metal temperature above 450oF or below -
20oF. As for as the steam piping is concerned, B31.1 Power piping is used because of
its temperature and pressure limitations which is discussed below in detail.
3.2 B31.1 Power Piping
This code covers the minimum requirements for the design, materials, fabrication,
erection, testing, and inspection of power and auxiliary service piping systems for
electric generation stations, industrial institutional plants, and central and district
heating plants. The code also covers external piping for power boilers and high
temperature, high-pressure water boilers in which steam or vapor is generated at a
pressure of more than 15psig and high-temperature water is generated at pressures
exceeding 160psig or temperatures exceeding 250oF. This code is typically used for
the transportation of steam or water under elevated temperatures and pressure as
14
mentioned above, so this is the reason that why this code is selected for the steam
piping system which is external to the boiler [5].
3.3 ASME Code Requirements
As it already mentioned in the previous section 3.2, Boiler outlet section of the steam
system comes under the category of ASME Code B31.1 Power. In order to ensure the
safety of the piping system, code requirements should be fully satisfied. For different
loads this code incorporates different relationships for stress level as given below.
3.3.1 Stresses due to sustained loadings
The effects of the pressure, weight, and other sustained loads must meet the
requirements of the following equation [1].
0.75
1.04
o AL h
PD i MS S
t Z×
= + ≤ (3.1)
Where
P = Internal Pressure, psi
Do = Out Side diameter of Pipe, in
t = nominal wall thickness, in
Z = Section modulus of pipe, in3
MA = Resultant moment due to loading on cross section due to weight and other
sustained loads, in-lb
Sh = Basic material allowable stress at design pressure, psi
3.3.2 Stress due to occasional loadings
The effects of pressure, weight, and occasional loads (earthquake) must meet the
requirements of the following equation [1].
0.75 ( )
4o A B
hPD i M M
KSt Z
++ ≤ (3.2)
Where
MB = Resultant moment loading on cross section due to occasional loads, psi
K= Constant factor depend on plant operation time
The rest of the terms are same to above equation.
15
3.3.3 Stresses due to thermal loadings
The effects of thermal expansion must meet the following equation [1].
( )CA h L
iMS f S S
Z≤ + − (3.3)
where
f = Stress range reduction factor
Mc =Range of resultant moment due to thermal expansion, in-lb
SA = Allowable stress range for expansion
The rest of the terms are same to above equation.
3.4 Stress analysis of piping system
Piping stress analysis is a discipline which is highly interreralated with piping layout
and support design. The layout of the piping should be performed with requirements
of piping stress and pipe support in mind. If necessary, layout solutions should be
iterated until a satisfactory balance b/w stress and layout efficiency is achieved [1].
3.4.1 Stress and Strain
Stress is defined as the reactive force per unit area which is developed when an
external force is being applied on the body. The stress is responsible for the
deformation and deterioration of the material.
There are two types of stresses, normal stress and shear stress. The normal
stresses are perpendicular stress on a body and they are directed normal of the surface
of the body. The tensile stresses are “those stress which produces tension in the
material whereas compressive stresses are those stresses which produce the
compression in the material”.
On the other side “shear stress is the force per unit area of shearing plane. The
shear stresses are those stresses which tend parallel plates of the material to slip past
each other”. The strain is the deformation in the dimension a material when it is under
stress. The strain is of two types shear strain and normal strain [3].
3.4.2 Failure Theories
The failure theories most commonly used in describing the strength of the piping
system are the:
16
1) Maximum principle stress theory
2) Maximum shear stress theory (Tresca theory)
3.4.3.1 Maximum principle stress theory
This theory states that failure will always occurs, whenever the greatest tensile stress
tends to exceed the uni-axial tensile strength or whenever the largest compressive
stress tends to exceed the uni-axial compressive strength. This theory has been found
to correlate reasonably well with test data for brittle fracture [3]. The maximum
principle stress theory form the basis for piping system governed by ANSI/ASME
B31 and subsection (class2 and class3) of section III of the ASME boiler and pressure
vessel codes [1].
3.4.3.2 Maximum shearing stress theory
Where on the other side the maximum shear stress theory states that failure of a
piping component occurs when the maximum shear stress exceed the shear stress at
the yield point in a tension test. In tensile test, at yield, σ1= Sy, where σ2 = σ3 = 0. So
yielding in the component occurs when
1 3max
( )2 2
ySσ στ −= =
(3.4)
This theory correlates reasonably well with the yielding of ductile materials [3]. This
maximum shear stress theory forms the basis for piping of subsection NB (calss1) of
ASME section III [1].
3.4.3 Piping Design Criteria
There are various failure modes which could affect a piping system. The piping
engineer can provide protection against some of these failure modes by performing
stress analysis according to the piping codes. Protection against other failure modes is
provided by methods other than stress analysis. For example, protection against brittle
fracture is provided by material selection. The piping codes address the following
failure modes, excessive plastic deformation, plastic instability or incremental
collapse, and high-strain–low-cycle fatigue. Each of these modes of failure is caused
by a different kind of stress and loading. It is necessary to place these stresses into
different categories and set limits to them. The major stress categories are primary,
17
secondary, and peak. The limits of these stresses are related to the various failure
modes as follows [3].
3.4.3.3 Primary Stress
The primary stress limits are intended to prevent plastic deformation and bursting.
Primary stresses which are developed by the imposed loading are necessary to satisfy
the equilibrium between external and internal forces and moments of the piping
system. Primary stresses are not self-limiting. Therefore, if a primary stress exceeds
the yield strength of the material through the entire cross section of the piping, then
failure can be prevented only by strain hardening in the material. Thermal stresses are
never classified as primary stresses. They are placed in both the secondary and peak
stress categories [1].
Primary stresses are the membrane, shear or bending stress resulting from imposed
loadings which satisfy the simple laws of equilibrium of internal and external forces
and moments as arranged in table below;
Table 3-1 Primary stresses of pipes
Type of primary stress Due to type of sustained load
Circumferential membrane stress Pressure
Longitudinal membrane stress Pressure, Dead weight
Primary bending stress Pressure, Dead weight, wind
Primary stresses which considerably exceed the yield strength of the piping material
will result in gross distortion or failure [5].
3.4.3.4 Secondary Stresses
The primary plus secondary stress limits are intended to prevent excessive plastic
deformation leading to incremental collapse. Secondary stresses are developed by the
constraint of displacements of a structure. These displacements can be caused either
by thermal expansion or by outwardly imposed restraint and anchor point movements.
Under this loading condition, the piping system must satisfy an imposed strain pattern
rather than be in equilibrium with imposed forces. Local yielding and minor
18
distortions of the piping system tend to relieve these stresses. Therefore, secondary
stresses are self-limiting [1].
Secondary stresses are self equilibrium stresses which are necessary to satisfy
the continuity of forces within a structure. As contrasted with stresses from sustained
loads, secondary stresses are not a source of direct failure in ductile with only a single
application of load. If the stresses exceed the material yield strength, they cause local
deformation which result in a redistribution of the loading and upper limit of the stress
in the operating condition. If the applied load is cyclic, however these stresses
constitute a potential source of fatigue failure e.g. the secondary stresses due to
different type of loads are given below in Table 3-2, [5].
Table 3-2 Secondary stresses of pipes
Type of secondary stresses Due to type of load
Bending and Torsional Thermal loading (expansion or contraction)
Bending and Torsional Non-uniform distribution of temperature
with in a body
19
4 Piping Design Procedures The following are the steps which need to be completed in mechanical design of any
piping system.
Flow chart: Complete stage designing of piping system
4.1 Process Design
This process is based on the requirement of the process variables. It defines the
required length & cross sectional area of pipe, the properties of fluid inside the pipe,
nature & rate of flow in it. These variables affect the positioning and placements of
equipments during lay outing and routing. The operating and design working
conditions are clearly defined. The end of Process Plan Design is the creation of a
Process Flow Diagram (PFD) and Process & Instrumental diagram (PID), which are
used in the designing & lay outing of the Pipe. The process design step in this project
is already been done and the data obtained from this step is arranged in Table 6-1.
4.2 Piping Structural Design
In piping structural design, according to pressure in pipelines, the design and
minimum allowable thicknesses are calculated; according to the required codes and
standards. ASME codes for various standards are available, for process fluid flow,
ASME B31.1 is used.
Process Design
Lay outing
Analysis of Pipes
And Expansion
Loops
SupportDesign
and Analysis
Structural Design Loads
Calculations
Piping System
Design
20
In the structural design of pipes, when all the loads are calculated then the required
span is also calculated for supporting the pipes.
4.2.1 Pipe Thickness Calculations
Piping codes ASME B31.1 Paragraph 104.1.2 require that the minimum thickness tm
including the allowance for mechanical strength, shall not be less than the thickness
calculated using Equation [2].
2 ( )m
P Dot AS Eq P Y
×= +
× × + × (4.1)
Or
mt t A= + (4.2)
where
tm = minimum required wall thickness, inches
t = pressure design thickness, inches
P = internal pressure, psig
Do = outside diameter of pipe, inches
S = allowable stress at design temperature (known as hot stress), psi
A = allowance, additional thickness to provide for material removed in threading,
corrosion, or erosion allowance; manufacturing tolerance (MT) should also
be considered.
Y = coefficient that takes material properties and design temperature into account.
For temperature below 900°F, 0.4 may be assumed.
E q = quality factor.
4.2.2 Allowable Working Pressure
The allowable working pressure of a pipe can be determined by Equation [2].
2( )( 2 )
S Eq tPDo Yt× ×
=−
(4.3)
where
t = specified wall thickness or actual wall thickness in inches.
For bends the minimum wall thickness after bending should not be less than the
minimum required for straight pipe.
21
4.2.3 Sustained Load Calculations
Sustained loads are those loads which are caused by mechanical forces and these
loads are present through out the normal operation of the piping system. These loads
include both weight and pressure loadings. The support must be capable of holding
the entire weight of the system, including that of that of the pipe, insulation, fluid
components, and the support themselves [2].
Pipe Weight 2 2( )4 steel
c
gDo Dig
π ρ= × − × (4.4)
Fluid Weight 2( )4 fluid
c
gDig
π ρ= × × × (4.5)
Insulation wt. = Insulation factor x ρInsulationx g/gc (4.6)
Where D0 = Out side diameter of pipe, in
Di = Inside diameter of pipe, in
t = Insulation Thickness depend on the NPS, in
g = Acceleration due to gravity, ft/sec2
gc = Gravitational constants, lbm-ft/ft-sec2
ρSteel = Density of steel, lb/in3
ρfluid = Density of water, lb/in3
ρinsul = Density of Insulation, lb/in3
Insulation factor depends on the thickness of the insulation of the pipe.
4.2.4 Wind Load Calculations
Wind load like dead weight, is a uniformly distributed load which act along the entire
length or portion of the piping system which is exposed to air.
For standard air, the expression for the wind dynamic pressure is given below [1]:
20.00256 DP V C= × × (4.7)
And to calculate the wind dynamic load (lb/ft), the following expression is used [1]:
20.000213 DF V C D= × × × (4.8)
Where
P = Dynamic pressure, lb/ft 2
V = basic wind speed, miles/hr
22
CD = Drag co-efficient, dimensionless
CD can be calculated using table and the following equation;
R = 780xVxD
R = Reynolds number
F = Linear dynamic pressure loading (lb/ft)
D = Pipe Diameter (in)
4.2.5 Thermal Loads Calculations
All pipes will be installed at ambient temperature. If pipes carrying hot fluids such
steam,
then they expand, especially in length, with an increase from ambient to working
temperatures. This will create stress upon certain areas within the distribution system,
such as pipe joints, which, in the extreme, could fracture. The amount of the
expansion is readily calculated using the following expression [6].
( )Expansion mm L Tα= × ×∆ (4.9)
Where
∆L = Length of pipe (m)
T = Temperature difference between ambient and operating Temperatures (°C)
α = Expansion coefficient (mm/m °C) x 10-3
4.2.6 Occasional Loads
Occasional load will subject a piping system to horizontal loads as well as vertical
loads, Where as sustained loads are normally only vertical (weight). There are
different types of occasional loads that act over a piping system but for our analysis
we will use wind loads and seismic loads.
4.2.7 Seismic Loads
Earthquake loads are of two major types
Operation Based Earthquake Load
Safe Shutdown Earthquake Load
Piping systems and components are designed to withstand two levels of site
dependent hypothetical earthquakes, the safe shut down earthquake and the
operational basis earthquake. Their magnitudes are expressed in terms of the
23
gravitational g. There motions are assumed to occur in three orthogonal directions,
one vertical and two horizontal directions.
Earthquake loads can either be calculated by dynamic Analysis or static
Analysis. In Dynamic analysis frequency response of the system is used to calculate
the Earthquake load whereas in Static Analysis, these loads are taken to be some
factor of the Pipe Dead load [3].
4.3 Pipe Span Calculations
The maximum allowable spans for horizontal piping systems are limited by three
main factors that are bending stress, vertical deflection and natural frequency. By
relating natural frequency and deflection limitation, the allowable span can be
determined as the lower of the calculated support spacing based on bending stress and
deflection [2].
4.3.1 Span Limitations
The formulation and equation obtained depend upon the end conditions assumed.
Assumptions
The pipe is considering to be a straight beam
Simply supported at both ends
So based on limitation of stress [2]
0.33 h
sZSL
w= (4.10)
Based on limitation of deflection [2]
4
22.5sEIL
w∆
= (4.11)
Where
Ls = Allowable pipe span, ft
Z = Modulus of pipe section, in3
Sh = Allowable tensile stress at design temperature, psi
w = Total weight of pipe, lb/ft
∆ = Allowable deflection/sag, in
I = Area moment of inertia of pipe, in4
24
E = Modulus of elasticity of pipe material at design temperature, psi.
4.3.2 Expansion Loop Calculations
Thermal expansion are calculated for all the pipes by using equation
Expansion (mm)
Based on thermal expansion calculated above, size of expansion loops can be
calculated from equation below as [2]
3144
o
A
EDLS∆
= (4.12)
Where
L = Length of expansion Loops, ft
E, Do, SA, same as in above calculations
Size of Expansion Loops assuming to be symmetrical U shaped. L = 2H + W Where H = 2W for U shaped loop.
L Tα= × ×∆
25
5 Support Design Pipe support specifications for individual projects must be written in such a way as to
ensure proper support under all operating and environmental conditions and to
provide for slope, expansion, anchorage, and insulation protection. Familiarity with
standard practices, customs of the trade, types and functions of commercial
component standard supports and an understanding of their individual advantages and
limitations, together with knowledge of existing standards, can be of great help in
achieving the desired results [3].
Good pipe support design begins with good piping design and layout. For
example, other considerations being equal, piping should be routed to use the
surrounding structure to provide logical and convenient points of support, anchorage,
guidance, or restraint, with space available at such points for use of the proper
component. Parallel lines, both vertical and horizontal, should be spaced sufficiently
apart to allow room for independent pipe attachments for each line. There are
different types of supports used in the piping system e.g. Anchor support, Guide,
hanger, sliding, snubber support etc. The type of support which we will design in this
project is anchor support. It is a rigid support providing substantially full fixity for
three translations and rotations about three reference axes.
This support mainly includes the beam, column, base plate and anchor bolts. So the
design of all these components will be discussed in this chapter [1].
5.1 Beam Design
Beams are the structural members resisting forces acting laterally to its axis. Either
forces or couples that lie in a plane containing the longitudinal axis of the beam may
act upon the member. The forces are understood to act perpendicular to the
longitudinal axis, and the plane containing the forces is assumed to be a plane of
symmetry of the beam. There are some limits states that must be considered when
designing a beam that are bending, shear and deflection [3].
26
5.1.1 Bending Stress
Bending stresses which caused by bending moments are internal member moments
which resist externally applied moments in order to maintain the member in
equilibrium. Bending stresses are usually far more significant than normal stresses
due to axial forces, therefore the flexural formula in its many form is one of the most
commonly used equations in structural analysis.
The flexural formula states that the value of the bending stress at any point on the
cross section of a member is [3].
bMcI
σ = (5.1)
where
M = Bending moment on the cross section, in-lb
c = Distance from neutral axis to point of interest, in
I = Moment of inertia of cross section, in4
The failure mode for bending is material yielding. For this reason the allowable stress
for bending is usually limited to the material stress reduced by a safety factor.
5.1.2 Shear Stress
Theses stresses resist the relative slippage of adjacent cross-sectional planes in the
members and can cause by shear forces. Shearing stress can be find out by using the
following formula [3]:
VAyIb
τ = (5.2)
where
V = shear force on cross section, lb
A = Cross sectional area, in2
y = Distance from the neutral axis to the centriod of the area, in
I = Moment of inertia of the beam cross section, in4
b = width of the beam, in
The horizontal shear stress is a maximum at the neutral axis of the beam.
This is opposite of the behavior of the bending stress which is maximum at the outer
edge of the beam and zero at the neutral axis.
27
5.1.3 Deflection
The lateral load acting on beam causes the beam to bend, deforming the axis of the
beam into a curve called the deflection of the beam. This deformation of a beam is
most easily expressed in terms of the deflection of the beam from its original
unloaded position. This deflection is measured from the original neutral surface to the
neutral surface of the deformed beam. The deflection in uniformly distributed
cantilever beam can be calculated by using the following equation [3]
4
max 8wlyEI
−= (5.3)
Where
y = deflection at point l, in
w = uniformly distributed load, lb/in
l = length at which deflection is to be calculated
E = Modulus of elasticity of the material being used in beam, Mpsi
I = Moment of inertia, in4
5.2 Column
A long slender bar subject to axial compression is called a column. The term column
is frequently used to describe a vertical member. Column may be divided into three
general types: Short columns, Intermediate columns and Long Column. The
compressive capacity of a column is dependent on its slenderness ratio, which is
defined as [3]
Slenderness ratio = Klr
(5.4)
Where
K = a constant dependent on boundary conditions
r = least radius of gyration of the member = IA , in
I = moment of inertia of cross section, in4
A = area of cross section, in2
Theoretical and recommended values of K for some typical column end conditions are
shown in Figure 5-1 below.
28
Figure 5-1 Effective length constants for different columns [7]
Combination of K and L is also called effective length, leff = Kl. A generally accepted
relationship between the slenderness ratio and type of column is as follows.
Table 5-1 Limitation of column slenderness ratio [7]
Type of Column Limits of slenderness Ratio
Short column 0 60efflr
⟨ ⟨
Intermediate column 60 120efflr
⟨ ⟨
Long column 120 300efflr
⟨ ⟨
Critical load and critical stress can be find out from the following equations [7]
2
2creff
EIPLπ
= (5.5)
2
2creff
EL
r
πσ =⎛ ⎞⎜ ⎟⎝ ⎠
(5.6)
For column subjected to both axial and bending stress, AISC subsection H1
specification requires that the following equations must be satisfied [7].
29
10.6
bya bx
y bx by
ff fF F F
+ + ≤ (5.7)
Also, when fa/Fa < 0.15, following equation can be used,
1bya bx
a bx by
ff fF F F
+ + ≤ (5.8)
Where
fa = axial stress in column = P/A
Fa = allowable axial stress
Fb, x/y = Bending stress in x or y direction = Mc/I
Fb, x/y = allowable bending stresses in x or y direction
5.3 Base Plate
Base plate is used to provide ground support to the column concentric and bending
load. Base plate may either be of the anchor bolted type or embedded type. Base
plates with anchor bolts are normally used in cases where the building concrete has
already been poured, while embedded plates are used when they can be specified prior
to pouring the concrete [3].
5.4 Base Plate Bolts
The strength of the bolts is a function of the embedment depth, the bolt or stud head
diameter, the concrete strength and the spacing between adjacent bolts. Anchor bolts
are installed by drilling a hole through the concrete into which the bolts are inserted.
Depending on the type of bolt the bolt expands to grip the concrete either by
hammering the bolt or by torquing the nut against the base plate [7].
30
6 Pipe Design Calculations In this chapter piping thickness as well as all the basic loads are calculated and the
characteristics are also given below.
6.1 Design Parameters
As already sizing of this piping system has been done and the available
information are;
Number of pipes = 48
Number of junctions = 49
Wind Velocity = 100 miles/hr
Pipe Nominal Size, Inlet-Out let velocities, Temperatures and Pressure of steam for
every pipe are given below in the following Table 6-1.
Table 6-1 Characteristics of Fluid at inlet and out let of pipes and its sizing
S. No
Pipe Line No.
NPS Do, (in)
TIn, °C TOut,
°C VIn,
m/sec Vout
m/sec Pin
(static)bar
POut (static)
bar
1 P-208 8.00 8.63 169.59 168.70 35.37 36.21 7.98 7.78
2 P-209 2.00 6.63 168.20 167.04 13.98 14.03 7.77 7.73
3 P-210 8.00 8.63 168.70 167.04 35.27 36.43 7.78 7.52
4 P-211 8.00 8.63 167.04 166.20 36.46 37.58 7.51 7.27
5 P-212 8.00 8.63 165.92 165.04 28.15 28.65 7.29 7.14
6 P-213 4.00 4.50 164.81 158.09 27.77 31.10 7.14 6.30
7 P-214 8.00 8.63 165.04 164.92 21.61 21.62 7.14 7.13
8 P-215 6.00 6.63 166.20 166.09 16.27 16.29 7.27 7.26
9 P-216 2.00 2.38 165.87 162.92 20.79 21.03 7.26 7.13
10 P-217 4.00 4.50 166.04 164.70 31.60 32.27 7.23 7.07
11 P-218 3.00 3.50 164.65 164.31 17.70 17.81 7.08 7.03
12 P-219 4.00 4.50 157.37 157.20 18.15 18.14 4.00 3.99
13 P-220 4.00 4.50 164.59 161.42 22.01 22.29 7.06 6.92
14 P-221 2.00 2.38 161.26 153.81 17.99 18.21 6.92 6.72
31
Table 6-1 Characteristics of Fluid at inlet and out let of pipes and its sizing (continued)
S. No
Pipe Line No.
NPS Do, (in)
TIn, °C TOut, °C
VIn, m/sec
Vout m/sec
Pin
(static) bar
POut (static),
bar
15 P-224 4.00 4.50 161.31 157.81 17.56 17.62 6.92 6.83
16 P-225 2.00 2.38 157.76 151.53 18.07 18.28 6.83 6.65
17 P-226 3.00 3.50 157.92 156.42 22.18 22.38 6.82 6.74
18 P-227 2.00 2.38 155.87 132.75 10.95 10.55 6.74 6.59
19 P-228 3.00 3.50 156.37 155.09 17.43 17.46 6.73 6.70
20 P-229 2.00 2.38 154.65 147.09 10.26 10.15 6.70 6.64
21 P-230 2.00 2.38 134.14 123.87 23.95 25.66 2.00 1.89
22 P-231 1.00 1.32 133.92 119.20 37.41 43.79 1.98 1.63
23 P-232 3.00 3.50 154.92 149.98 12.81 12.76 6.69 6.64
24 P-233 2.00 2.38 149.20 140.09 6.93 6.79 6.64 6.61
25 P-236 1.50 1.90 126.81 117.36 23.32 23.84 1.99 1.90
26 P-237 1.00 1.32 126.81 118.70 32.02 34.36 1.99 1.82
27 P-238 2.00 2.38 150.09 145.42 21.20 21.65 6.63 6.42
28 P-239 1.00 1.32 145.09 130.70 21.74 22.91 6.42 5.88
29 p-240 2.00 2.38 145.31 140.48 16.06 16.12 6.42 6.31
30 P-241 1.00 1.32 140.37 125.70 29.15 35.66 6.30 4.99
31 P-242 2.00 2.38 140.03 130.87 8.63 8.45 6.31 6.28
32 P-243 2.00 2.38 130.31 112.98 5.52 5.27 6.28 6.24
33 P-244 1.00 1.32 130.64 95.31 11.43 10.80 6.28 6.00
34 P-250 3.00 3.50 159.15 158.87 12.28 12.32 4.00 3.98
35 P-251 1.00 1.32 158.53 121.48 29.53 36.80 3.97 2.97
36 P-252 2.00 2.38 158.87 152.87 19.58 19.77 3.98 3.89
37 P-253 1.50 1.90 152.48 146.31 16.82 16.84 3.89 3.83
38 P-254 1.00 1.32 152.59 132.53 37.37 48.68 3.86 2.83
39 P-256 2.00 2.38 155.87 150.03 37.39 41.14 4.00 3.59
40 P-257 6.00 6.63 152.70 152.37 21.55 21.59 4.00 3.99
41 P-259 3.00 3.50 142.09 137.09 27.65 28.75 2.00 1.90
42 P-260 3.00 3.50 139.81 138.42 27.50 28.06 2.00 1.95
43 P-261 3.00 3.50 118.25 116.42 20.90 21.16 1.50 1.47
44 P-262 3.00 3.50 134.81 133.98 15.23 15.21 2.00 2.00
32
Table 6-1 Characteristics of Fluid at inlet and out let of pipes and its sizing (continued)
6.2 Physical Properties
Physical properties of pipe material, insulation and water are arranged in Table 6-2
below;
Table 6-2 Material Properties [Appendix Table A14]
Material Parameter Value
Modulus of Elasticity ‘E’ 27.5 Mpsi
Allowable stress S all 14.4 ksi Carbon Steel
Density, ‘ρ steel’ 0.283 lb/in3
Insulation Density, ‘ρ Rock wool’ 0.00343lb/in3
Water Density, ‘ρ water’ 0.0361 lb/in3
6.3 Design Calculations
Piping design calculation means to find out the pipe thickness for the available
size and operating pressure of the fluid. This thickness is then compared to the
allowable minimum standard thickness defined by the code. After thickness
calculations all loads applied on this pipe can be calculated, which will form the
basis for spacing of supports and sizing of expansion loops.
6.3.1 Pipe Thickness Calculations
Piping codes require that the minimum thickness tm including the allowance for
mechanical strength, shall not be less than the thickness calculated using Equation
(4.1) as follows.
S. No
Pipe Line No.
NPS Do, (in)
TIn, °C TOut, °C
VIn, m/sec
Vout m/sec
Pin
(static) bar
POut (static),
bar
45 P-263 2.00 2.38 127.87 126.70 22.37 22.36 2.00 1.99
46 P-264 2.00 2.38 119.20 115.70 17.26 17.35 2.00 1.97
47 P-270 3.00 3.50 157.31 152.37 28.44 29.92 3.99 3.75
48 P-271 1.00 1.32 156.48 151.48 24.31 24.67 4.00 3.89
33
Design thickness 2 ( )
om
q
P Dt AS E P Y
×= +
× × + × (4.1)
or
= t + A
Let take Pipe no. 208 and calculate its minimum thickness by using equation.
Where all the parameters are arranged in Table 6-3 below;
Table 6-3 Input Parameters used in pipe thickness calculation
Parameter Value Reference/Reason
Do 8.625 in Appendix Table A2
Pg 193.3 Psi Table 6.1
E 1 For seamless pipe
Y 0.4 b/c Temperature < 900oF
S 14400 Psi Appendix Table A1
Tolerance limit ±12.5% Assuming maximum limit
A 3 mm = 0.03937 in data provided
Putting all these values in above equation of minimum thickness
193.3 8.625 0.039372 (144000 1 193.3 0.4)mt
×= +
× × + ×
0.09984mt In=
0.09980.85
0.122.9
m
m
m
t
t int mm
=
==
Standard tm = 0.282 in
For all 48 pipes the thickness were calculated and arranged in the Table 6-4 below
along with the standard minimum wall thickness. From the table it is cleared that
nearly 2 to 3 times, so our calculated thickness is safe.
34
Table 6-4 All pipes thickness along with standard thickness
S.No
Pipe Line N
o.
Pipe Nom
inal Size,
Out side D
iameter,
D (in)
Design Pressure
(stat.), P (lb/In2)
Velocity, Inlet
(m/sec)
Total H
ead,(m)
H=(P/W
+V^2/2*g)
Pabs(Psi)= ρ*g*H
DesignPressure
(gage.), P(lb/In2)= Psat-14.7
Allow
able Stresss, S(psi)
D.T
. Factor (y)
Min. W
all thickness,t(in)=P*D/2*(S+.4*P)
Corrosion
allowance, A
(in)
Total m
in. Wall
thickt(t), (in)
t= (t/1-T)
T=12.5%
(in)
t(mm
)
Min.A
llowable
thickness (in)
1 P-208 8 8.625 117.23 35.37 146.274 208.01 193.31 14400 0.4 0.0605 0.0394 0.0999 0.114 2.903 0.282 2 P-209 2 6.625 114.22 13.98 90.283 128.39 113.69 14400 0.4 0.0274 0.0394 0.0668 0.076 1.940 0.135 3 P-210 8 8.625 114.37 35.27 143.894 204.63 189.93 14400 0.4 0.0595 0.0394 0.0988 0.113 2.872 0.282 4 P-211 8 8.625 110.44 36.46 145.470 206.87 192.17 14400 0.4 0.0602 0.0394 0.0995 0.114 2.892 0.282 5 P-212 8 8.625 107.15 28.15 115.774 164.64 149.94 14400 0.4 0.0470 0.0394 0.0864 0.099 2.510 0.282 6 P-213 4 4.5 105.00 27.78 113.203 160.98 146.28 14400 0.4 0.0239 0.0394 0.0633 0.072 1.839 0.207 7 P-214 8 8.625 104.90 21.61 97.598 138.79 124.09 14400 0.4 0.0389 0.0394 0.0783 0.090 2.275 0.282 8 P-215 6 6.625 106.88 16.28 88.676 126.10 111.40 14400 0.4 0.0268 0.0394 0.0662 0.076 1.924 0.245 9 P-216 2 2.375 106.69 20.79 97.079 138.05 123.35 14400 0.4 0.0107 0.0394 0.0500 0.057 1.454 0.178
10 P-217 4 4.5 106.34 31.60 125.735 178.80 164.10 14400 0.4 0.0268 0.0394 0.0662 0.076 1.924 0.207 11 P-218 3 3.5 104.05 17.70 89.148 126.77 112.07 14400 0.4 0.0143 0.0394 0.0536 0.061 1.559 0.189 12 P-219 4 4.5 58.80 18.15 58.155 82.70 68.00 14400 0.4 0.0111 0.0394 0.0505 0.058 1.468 0.207 13 P-220 4 4.5 103.78 22.01 97.703 138.94 124.24 14400 0.4 0.0203 0.0394 0.0597 0.068 1.735 0.207 14 P-221 2 2.375 101.77 17.99 88.072 125.24 110.54 14400 0.4 0.0096 0.0394 0.0489 0.056 1.422 0.178 15 P-224 4 4.5 101.67 17.56 87.227 124.04 109.34 14400 0.4 0.0179 0.0394 0.0573 0.066 1.664 0.207 16 P-225 2 2.375 100.45 18.07 87.298 124.14 109.44 14400 0.4 0.0095 0.0394 0.0488 0.056 1.419 0.178 17 P-226 3 3.5 100.28 22.18 95.626 135.99 121.29 14400 0.4 0.0154 0.0394 0.0548 0.063 1.593 0.189 18 P-227 2 2.375 99.12 10.95 75.822 107.82 93.12 14400 0.4 0.0081 0.0394 0.0474 0.054 1.378 0.178 19 P-228 3 3.5 98.96 17.43 85.080 120.99 106.29 14400 0.4 0.0135 0.0394 0.0529 0.061 1.538 0.189 20 P-229 2 2.375 98.43 10.26 74.589 106.07 91.37 14400 0.4 0.0079 0.0394 0.0473 0.054 1.374 0.178 21 P-230 2 2.375 29.34 23.95 49.908 70.97 56.27 14400 0.4 0.0049 0.0394 0.0442 0.051 1.286 0.178 22 P-231 1 1.315 29.16 37.41 91.916 130.71 116.01 14400 0.4 0.0055 0.0394 0.0449 0.051 1.305 0.116 23 P-232 3 3.5 98.39 12.81 77.563 110.30 95.60 14400 0.4 0.0122 0.0394 0.0515 0.059 1.498 0.189 24 P-233 2 2.375 97.59 6.94 71.081 101.08 86.38 14400 0.4 0.0075 0.0394 0.0468 0.054 1.361 0.178 25 P-236 1.5 1.9 29.27 23.32 48.327 68.72 54.02 14400 0.4 0.0037 0.0394 0.0431 0.049 1.253 0.127
35
Table 6-4 All pipes thickness along with standard thickness (Continued)
S.No
Pipe Line N
o.
Pipe Nom
inal Size,
Out side
Diam
eter, D (in)
Design Pressure
(stat.), P (lb/In2)
Velocity, Inlet
(m/sec)
Total H
ead,(m)
H=(P/W
+V^2/2*
g)
Pabs(Psi)= ρ*g*H
DesignPressure
(gage.), P(lb/In2)= Psat-14.7
Allow
able Stresss, S(psi)
D.T
. Factor (y)
Min. W
all thickness,t(in)=P
*D/2*(S+.4*P)
Corrosion
allowance (in)
Total m
in. Wall
thickt(t) (in)
t= (t/1-T)
T=12.5%
(in)
t(mm
)
Min.A
llowab
le thickness (in)
26 P-237 1 1.315 29.27 32.02 72.901 103.67 88.97 14400 0.4 0.0043 0.0394 0.0436 0.050 1.268 0.116
27 P-238 2 2.375 97.40 21.21 91.441 130.04 115.34 14400 0.4 0.0100 0.0394 0.0493 0.056 1.434 0.178
28 P-239 1 1.315 94.34 21.74 90.466 128.65 113.95 14400 0.4 0.0055 0.0394 0.0448 0.051 1.303 0.116
29 p-240 2 2.375 94.30 16.06 79.478 113.02 98.32 14400 0.4 0.0085 0.0394 0.0479 0.055 1.391 0.178
30 P-241 1 1.315 92.67 29.15 108.524 154.33 139.63 14400 0.4 0.0067 0.0394 0.0460 0.053 1.338 0.116
31 P-242 2 2.375 92.80 8.63 69.054 98.20 83.50 14400 0.4 0.0072 0.0394 0.0466 0.053 1.354 0.178
32 P-243 2 2.375 100.25 5.52 72.050 102.46 87.76 14400 0.4 0.0076 0.0394 0.0470 0.054 1.365 0.178
33 P-244 1 1.315 92.27 11.43 71.549 101.75 87.05 14400 0.4 0.0042 0.0394 0.0435 0.050 1.265 0.116
34 P-250 3 3.5 58.80 12.28 49.046 69.75 55.05 14400 0.4 0.0070 0.0394 0.0464 0.053 1.348 0.189
35 P-251 1 1.315 58.33 29.53 85.499 121.59 106.89 14400 0.4 0.0051 0.0394 0.0445 0.051 1.293 0.116
36 P-252 2 2.375 58.54 19.58 60.724 86.35 71.65 14400 0.4 0.0062 0.0394 0.0456 0.052 1.324 0.178
37 P-253 1.5 1.9 57.15 16.82 54.626 77.68 62.98 14400 0.4 0.0044 0.0394 0.0437 0.050 1.271 0.127
38 P-254 1 1.315 56.77 37.37 111.180 158.11 143.41 14400 0.4 0.0069 0.0394 0.0462 0.053 1.343 0.116
39 P-256 2 2.375 58.80 37.39 112.691 160.25 145.55 14400 0.4 0.0126 0.0394 0.0519 0.059 1.509 0.178
40 P-257 6 6.625 58.80 21.55 65.042 92.49 77.79 14400 0.4 0.0188 0.0394 0.0581 0.067 1.690 0.245
41 P-259 3 3.5 29.40 27.66 59.703 84.90 70.20 14400 0.4 0.0089 0.0394 0.0483 0.055 1.404 0.189
42 P-260 3 3.5 29.40 27.50 59.258 84.27 69.57 14400 0.4 0.0089 0.0394 0.0482 0.055 1.402 0.189
43 P-261 3 3.5 22.05 20.90 37.781 53.73 39.03 14400 0.4 0.0050 0.0394 0.0443 0.051 1.289 0.189
44 P-262 3 3.5 29.40 15.23 32.510 46.23 31.53 14400 0.4 0.0040 0.0394 0.0434 0.050 1.261 0.189
45 P-263 2 2.375 29.40 22.37 46.194 65.69 50.99 14400 0.4 0.0044 0.0394 0.0438 0.050 1.272 0.178
46 P-264 2 2.375 29.40 17.26 35.877 51.02 36.32 14400 0.4 0.0031 0.0394 0.0425 0.049 1.236 0.178
47 P-270 3 3.5 44.10 28.44 72.267 102.77 88.07 14400 0.4 0.0112 0.0394 0.0506 0.058 1.470 0.189
48 P-271 1 1.315 14.70 24.31 40.496 57.59 42.89 14400 0.4 0.0021 0.0394 0.0414 0.047 1.204 0.116
36
6.3.2 Allowable Working Pressure
After calculating the design thickness, now checking the working pressure by using
the standard thickness to find the maximum pressure that the pipe material can
withstand. The allowable working pressure of a pipe can be determined by Equation
(4.3) given below.
2( )( 2 )o
S Eq tPD Yt× ×
=−
(4.3)
Let take Pipe no. 208 and calculate its minimum thickness by using Table 6-5.
Table 6-5 Input data
Parameter Value Reference/Reason
Do 8.625 in Appendix Table A2
E 1 For seamless pipe
Y 0.4 b/c Temperature < 900oF
S 14400 Psi Appendix Table A1
t 0.322 in Appendix Table A2
t = specified wall thickness or actual wall thickness in inches, in
So the allowable working pressure comes out to be P = 993.87 psi
Where as the designed working pressure =117.23 psi (From Table 6-1). For all the 48
pipes the working pressures are calculated and arranged in the following table.
Table 6-6 Design and working Pressure S.No
Pipe Line No. NPS, in Do (in) Pressure (gage)
psi Allowable Pressure psi
1 P-208 8 8.625 193.31 993.877 2 P-209 2 6.625 113.69 1955.074 3 P-210 8 8.625 189.93 993.877 4 P-211 8 8.625 192.17 993.877 5 P-212 8 8.625 149.94 993.877 6 P-213 4 4.5 146.28 1479.188 7 P-214 8 8.625 124.09 993.877 8 P-215 6 6.625 111.40 1156.616
37
Table 6-6 Design and working Pressure (Continued)
S.No Pipe Line No. NPS,in Do (in) Pressure (gage.)
psi Allowable Pressure psi
9 P-216 2 2.375 123.35 2625.538 10 P-217 4 4.5 164.10 1479.188 11 P-218 3 3.5 112.07 1817.818 12 P-219 4 4.5 68.00 1479.188 13 P-220 4 4.5 124.24 1479.188 14 P-221 2 2.375 110.54 2625.538 15 P-224 4 4.5 109.34 1479.188 16 P-225 2 2.375 109.44 2625.538 17 P-226 3 3.5 121.29 1817.818 18 P-227 2 2.375 93.12 2625.538 19 P-228 3 3.5 106.29 1817.818 20 P-229 2 2.375 91.37 2625.538 21 P-230 2 2.375 56.27 2625.538 22 P-231 1 1.315 116.01 3503.527 23 P-232 3 3.5 95.60 1817.818 24 P-233 2 2.375 86.38 2625.538 25 P-236 1.5 1.9 54.02 2488.415 26 P-237 1 1.315 88.97 3503.527 27 P-238 2 2.375 115.34 2625.538 28 P-239 1 1.315 113.95 3503.527 29 p-240 2 2.375 98.32 2625.538 30 P-241 1 1.315 139.63 3503.527 31 P-242 2 2.375 83.50 2625.538 32 P-243 2 2.375 87.76 2625.538 33 P-244 1 1.315 87.05 3503.527 34 P-250 3 3.5 55.05 1817.818 35 P-251 1 1.315 106.89 3503.527 36 P-252 2 2.375 71.65 2625.538 37 P-253 1.5 1.9 62.98 2488.415 38 P-254 1 1.315 143.41 3503.527 39 P-256 2 2.375 145.55 2625.538 40 P-257 6 6.625 77.79 1156.616 41 P-259 3 3.5 70.20 1817.818 42 P-260 3 3.5 69.57 1817.818 43 P-261 3 3.5 39.03 1817.818 44 P-262 3 3.5 31.53 1817.818 45 P-263 2 2.375 50.99 2625.538 46 P-264 2 2.375 36.32 2625.538 47 P-270 3 3.5 88.07 1817.818 48 P-271 1 1.315 42.89 3503.527
NPS = Nominal Pipe Size Discussion: From results obtained from Table 6-6, it is cleared that all the allowable
pressures are greater than the operating pressure by more than 4 times. So that it is
concluded from above table that all the pipes are safe under applied pressure.
38
6.3.3 Wind load Calculations
For standard air, the expression for the wind dynamic pressure is calculated by using
equation as given below [1].
20.00256 DP V C= × × − (4.7) Or
To calculate the wind dynamic load (lb/ft), equation is used [1].
20.000213 DF V C D= × × × (4.8) To find out the drag co-efficient CD, using (Appendix Figure A1) and Reynolds number. Re = 780 x V x D Where V = Wind velocity, 100 miles/hr D = Out side diameter of insulated pipe, in So, considering pipe no. 208 Re = 780 x100 x 11.77 = 9.18 x 105
20.000213 100 0.6 11.77 15.05 /F lb ft= × × × = So for all 48 pipes wind loads are calculated by using wind velocity 100 miles/hr and
pipe out side diameter including insulation thickness. These values are arranged in
Table 6-7 below.
Table 6-7 Wind loads for each pipe
S. No
Pipe Line No.
Pipe length
(ft) NPS Do (in) tinsul ,
mm Total Do, (in)
Reynold's No. (Re)= 780*V*D CD
Wind Load (lbs)
1 P-208 262 8 8.625 80 11.77 9.18E+05 0.6 3942.56 2 P-209 16 2 6.625 50 8.59 6.70E+05 0.8 234.29 3 P-210 394 8 8.625 80 11.77 9.18E+05 0.6 5928.89 4 P-211 341 8 8.625 80 11.77 9.18E+05 0.6 5131.35 5 P-212 361 8 8.625 80 11.77 9.18E+05 0.6 5432.31 6 P-213 787 4 4.5 65 7.06 5.51E+05 0.9 10649.857 P-214 16 8 8.625 80 11.77 9.18E+05 0.6 240.77 8 P-215 16 6 6.625 80 9.77 7.62E+05 0.67 223.19 9 P-216 98 2 2.375 50 4.34 3.39E+05 1.2 1088.00 10 P-217 164 4 4.5 65 7.06 5.51E+05 1 2465.87 11 P-218 16 3 3.5 50 5.47 4.27E+05 1.1 205.00 12 P-219 9.8 4 4.5 65 7.06 5.51E+05 1 147.35 13 P-220 279 4 4.5 65 7.06 5.51E+05 1 4194.98 14 P-221 230 2 2.375 50 4.34 3.39E+05 1.2 2553.46 15 P-224 262 4 4.5 65 7.06 5.51E+05 1 3939.38 16 P-225 197 2 2.375 50 4.34 3.39E+05 1.2 2187.09 17 P-226 115 3 3.5 50 5.47 4.27E+05 1.1 1473.46 18 P-227 525 2 2.375 50 4.34 3.39E+05 1.2 5828.55
39
Table 6-7 Wind loads for each pipe (Continued) S. No
Pipe Line No.
Pipe length
(ft) NPS Do (in) tinsul ,
mm Total Do, (in)
(Re)= 780*V*Do Cd
Wind Load (lbs)
19 P-228 82 3 3.5 50 5.47 4.27E+05 1.1 1050.64 20 P-229 164 2 2.375 50 4.34 3.39E+05 1.2 1820.73 21 P-230 164 2 2.375 50 4.34 3.39E+05 1.2 1820.73 22 P-231 115 1 1.315 40 2.89 2.25E+05 1.2 849.43 23 P-232 246 3 3.5 50 5.47 4.27E+05 1.1 3151.93 24 P-233 131 2 2.375 50 4.34 3.39E+05 1.2 1454.36 25 P-236 98 1.5 1.9 50 3.87 3.02E+05 1.2 969.01 26 P-237 66 1 1.315 40 2.89 2.25E+05 1.2 487.50 27 P-238 213 2 2.375 50 4.34 3.39E+05 1.2 2364.73 28 P-239 197 1 1.315 40 2.89 2.25E+05 1.2 1455.11 29 p-240 180 2 2.375 50 4.34 3.39E+05 1.2 1998.36 30 P-241 262 1 1.315 40 2.89 2.25E+05 1.2 1935.22 31 P-242 197 2 2.375 50 4.34 3.39E+05 1.2 2187.09 32 P-243 262 2 2.375 50 4.34 3.39E+05 1.2 2908.72 33 P-244 394 1 1.315 40 2.89 2.25E+05 1.2 2910.22 34 P-250 6.6 3 3.5 50 5.47 4.27E+05 1.2 92.25 35 P-251 328 1 1.315 40 2.89 2.25E+05 1.2 2422.72 36 P-252 115 2 2.375 40 3.95 3.08E+05 1.2 1161.01 37 P-253 66 1.5 1.9 50 3.87 3.02E+05 1.2 652.60 38 P-254 197 1 1.315 40 2.89 2.25E+05 1.2 1455.11 39 P-256 230 2 2.375 50 4.34 3.39E+05 1.2 2553.46 40 P-257 33 6 6.625 80 9.77 7.62E+05 0.8 549.65 41 P-259 164 3 3.5 50 5.47 4.27E+05 1.1 2101.28 42 P-260 39 3 3.5 50 5.47 4.27E+05 1.1 499.70 43 P-261 49 3 3.5 50 5.47 4.27E+05 1.1 627.82 44 P-262 16 3 3.5 50 5.47 4.27E+05 1.1 205.00 45 P-263 16 2 2.375 50 4.34 3.39E+05 1.2 177.63 46 P-264 49 2 2.375 50 4.34 3.39E+05 1.2 544.00 47 P-270 262 3 3.5 50 5.47 4.27E+05 1.1 3356.93 48 P-271 33 1 1.315 40 2.89 2.25E+05 1.2 243.75 NPS = Nominal Pipe Size Do = Out side Diameter of Pipe tinsul = Insulation Thickness Cd = Drag Coefficient
40
6.3.4 Dead Loads Calculation
For all pipes pipe thickness loads, fluid loads and insulation loads are calculated and
added together by using the equation (4.4) for pipe weight, Equation (4.5) for fluid
weight and Equation (4.6) for insulation weight [3].
Pipe weight 2 2( )4 steel
c
gDo Dig
π ρ= × − × (4.4)
Fluid weight 2( )4 fluid
c
gDig
π ρ= × × × (4.5)
Insulation wt. = Insulation factor x ρInsulationx g/gc (4.6)
Using Table 6-1 for properties of pipes and Appendix Table A14 for calculating
weights
Where
Do = Out side diameter of pipe
Di = Inside diameter of pipe
g = 32.17 ft/sec2 (acceleration due to gravity)
gc = 32.17 lbm-ft/lbf-sec2 (gravitational constant)
ρSteel = 0.283lb/in3
ρfluid = 0.0361 lb/in3
ρinsul = 0.00343lb/in3
Table 6-8 Pipe, Fluid and insulation weights
S. No
Pipe Line No.
L, (ft) NPS
Insul. Thick(In)
XInsul Insul.
wt. (lb)
Pipe wt., (lbs)
Fluid wt.(lbs)
Total static Loads (lbs)
1 P-208 262 8 3.15 0.97 10.369 7450.18 5680.53 13141.08 2 P-209 16 2 1.97 0.21 0.137 58.21 23.27 81.61 3 P-210 394 8 3.15 0.97 15.593 11203.71 8542.47 19761.78 4 P-211 341 8 3.15 0.97 13.495 9696.61 7393.36 17103.47 5 P-212 361 8 3.15 0.97 14.287 10265.33 7826.99 18106.60 6 P-213 787 4 2.56 0.39 12.523 8456.94 4342.05 12811.51 7 P-214 16 8 3.15 0.97 0.633 454.97 346.90 802.51 8 P-215 16 6 3.15 0.83 0.542 302.33 200.33 503.21 9 P-216 98 2 1.97 0.21 0.840 356.51 142.52 499.87 10 P-217 164 4 2.56 0.39 2.610 1762.31 904.82 2669.74 11 P-218 16 3 1.97 0.25 0.163 120.71 51.26 172.14 12 P-219 9.8 4 2.56 0.39 0.156 105.31 54.07 159.53 13 P-220 279 4 2.56 0.39 4.439 2998.08 1539.30 4541.82
41
Table 6-8 Pipe, Fluid and insulation weights (Continued)
S. No
Pipe Line No.
L, (ft) N P S
Insul. Thick. (In)
XInsul Insul.
wt. (lb)Pipe wt.,
(lbs) Fluid
wt(lbs)
Total static Loads (lbs)
14 P-221 230 2 1.97 0.21 1.971 836.70 334.49 1173.16 15 P-224 262 4 2.56 0.39 4.169 2815.40 1445.51 4265.08 16 P-225 197 2 1.97 0.21 1.688 716.66 286.50 1004.84 17 P-226 115 3 1.97 0.25 1.173 867.62 368.45 1237.25 18 P-227 525 2 1.97 0.21 4.498 1909.87 763.51 2677.87 19 P-228 82 3 1.97 0.25 0.836 618.65 262.72 882.21 20 P-229 164 2 1.97 0.21 1.405 596.61 238.51 836.52 21 P-230 164 2 1.97 0.21 1.405 596.61 238.51 836.52 22 P-231 115 1 1.57 0.1 0.469 192.28 43.07 235.83 23 P-232 246 3 1.97 0.25 2.509 1855.95 788.17 2646.63 24 P-233 131 2 1.97 0.21 1.122 476.56 190.51 668.19 25 P-236 98 1.5 1.97 0.21 0.840 265.24 86.47 352.55 26 P-237 66 1 1.57 0.1 0.269 110.35 24.72 135.34 27 P-238 213 2 1.97 0.21 1.825 774.86 309.77 1086.45 28 P-239 197 1 1.57 0.1 0.804 329.39 73.79 403.98 29 p-240 180 2 1.97 0.21 1.542 619.04 266.35 886.94 30 P-241 262 1 1.57 0.1 1.069 438.07 98.14 537.28 31 P-242 197 2 1.97 0.21 1.688 716.66 286.50 1004.84 32 P-243 262 2 1.97 0.21 2.245 953.12 381.03 1336.39 33 P-244 394 1 1.57 0.1 1.608 658.78 147.58 807.96 34 P-250 6.6 3 1.97 0.25 0.067 49.79 21.15 71.01 35 P-251 328 1 1.57 0.1 1.338 548.43 122.86 672.62 36 P-252 115 2 1.57 0.21 0.985 418.35 167.24 586.58 37 P-253 66 1.5 1.97 0.21 0.565 178.63 58.23 237.43 38 P-254 197 1 1.57 0.1 0.804 329.39 73.79 403.98 39 P-256 230 2 1.97 0.21 1.971 836.70 334.49 1173.16 40 P-257 33 6 3.15 0.83 1.118 623.56 413.19 1037.87 41 P-259 164 3 1.97 0.25 1.673 1237.30 525.45 1764.42 42 P-260 39 3 1.97 0.25 0.398 294.24 124.95 419.59 43 P-261 49 3 1.97 0.25 0.500 369.68 156.99 527.17 44 P-262 16 3 1.97 0.25 0.163 120.71 51.26 172.14 45 P-263 16 2 1.97 0.21 0.137 58.21 23.27 81.61 46 P-264 49 2 1.97 0.21 0.420 178.25 71.26 249.93 47 P-270 262 3 1.97 0.25 2.672 1976.66 839.43 2818.77 48 P-271 33 1 1.57 0.1 0.135 55.18 12.36 67.67
NPS = Nominal Pipe Size XInsul = Insulation Factor [Appendix table A15]
42
6.3.5 Pipe Span Calculations (based on limitation stress)
The pipe span means that how much distance should be provided in between the two
adjacent piping supports for straight pipe. Using Equation (4.10), to calculate the pipe
span [2].
0.33 hs
Z SLw×
= (4.10)
Where,
Ls= Allowable Pipe Span, ft
L = Length of pipe, ft
Z = section Modulus, In3
Sh= Allowable tensile stress for the pipe at high temp, psi
w = Weight of the pipe (metal weight of pipe + fluid wt. + Insulation
wt.), lb/ft
Now to find the number of supports for every pipe, using the following equation [2],
Number of supports = (L/Ls) +1 (6.1)
Let take Pipe no. 208 and calculate span limitation for it by using the data from Table
6-1 and 6-8.
L = 262 ft (From Table 6-1)
Z = 16.8 in3 (Appendix Table A2)
Sh = 14400 ksi (Appendix Table A1)
w = 50.15 lb/ft (From Table 6.8)
0.33 16.8 14400
50.1540.72
s
s
L
L ft
× ×=
=
No. of Support (N.O.S) = (L/Ls) +1
= 7.43 ≈ 8
Revised Ls = 37.43 ft
But the max. Span limit according to Code B31.1 for NPS = 8 inch
Ls = 24 ft (Appendix Table A8)
Safety margin Span = 37.43 -24
= 13.43 ft
43
Table 6-9 Pipe Span based on limitation of stress
S. No
Pipe Line No.
L, (ft)
Z, In3
w, lb/ft
Ls, ft N.O.SRounded
No. of Support
Revised Ls, ft
max. Span
Safety Margin (ft)
1 P-208 262 16.8 50.15 40.72 7.43 8 37.43 24 13.43
2 P-209 16 0.561 5.07 23.41 1.68 2 16.00 13 3.00
3 P-210 394 16.8 50.15 40.72 9.68 11 39.40 24 15.40
4 P-211 341 16.8 50.15 40.72 9.37 10 37.89 24 13.89
5 P-212 361 16.8 50.15 40.72 9.87 10 40.11 24 16.11
6 P-213 787 3.21 16.28 31.24 26.19 27 30.27 17 13.27
7 P-214 16 16.8 50.15 40.72 1.39 2 16.00 24 -8.00
8 P-215 16 8.5 31.44 36.58 1.44 2 16.00 21 -5.00
9 P-216 98 0.561 5.10 23.34 5.20 6 19.60 13 6.60
10 P-217 164 3.21 16.28 31.24 6.25 7 27.33 17 10.33
11 P-218 16 2.23 10.76 32.03 1.50 2 16.00 15 1.00
12 P-219 9.8 3.21 16.28 31.24 1.31 2 9.80 17 -7.20
13 P-220 279 3.21 16.28 31.24 9.93 10 31.00 17 14.00
14 P-221 230 0.561 5.10 23.34 10.86 11 23.00 13 10.00
15 P-224 262 3.21 16.28 31.24 9.39 10 29.11 17 12.11
16 P-225 197 0.561 5.10 23.34 9.44 10 21.89 13 8.89
17 P-226 115 2.23 10.76 32.03 4.59 5 28.75 15 13.75
18 P-227 525 0.561 5.10 23.34 23.50 24 22.83 13 9.83
19 P-228 82 2.23 10.76 32.03 3.56 4 27.33 15 12.33
20 P-229 164 0.561 5.10 23.34 8.03 9 20.50 13 7.50
21 P-230 164 0.561 5.10 23.34 8.03 9 20.50 13 7.50
22 P-231 115 0.133 2.05 17.92 7.42 8 16.43 9 7.43
23 P-232 246 2.23 10.76 32.03 8.68 9 30.75 15 15.75
24 P-233 131 0.561 5.10 23.34 6.61 7 21.83 13 8.83
25 P-236 98 0.326 3.60 21.18 5.63 6 19.60 11 8.60
26 P-237 66 0.133 2.05 17.92 4.68 5 16.50 9 7.50
27 P-238 213 0.561 5.10 23.34 10.13 11 21.30 3 18.30
28 P-239 197 0.133 2.05 17.92 11.99 12 17.91 9 8.91
44
Table 6-9 Pipe Span based on limitation of stress (Continued)
S. No
Pipe Line No.
L, (ft)
Z, In3
w, lb/ft
Ls, ft N.O.SRounded
No. Revised Ls, ft
max. Span
Safety Margin (ft)
29 P-240 180 0.561 4.93 23.74 8.58 9 22.50 13 9.50
30 P-241 262 0.133 2.05 17.92 15.62 16 17.47 9 8.47
31 P-242 197 0.561 5.10 23.34 9.44 10 21.89 13 8.89
32 P-243 262 0.561 5.10 23.34 12.23 13 21.83 13 8.83
33 P-244 394 0.133 2.05 17.92 22.99 23 17.91 9 8.91
34 P-250 6.6 2.23 10.76 32.03 1.21 2 6.60 15 -8.40
35 P-251 328 0.133 2.05 17.92 19.31 20 17.26 9 8.26
36 P-252 115 0.561 5.10 23.34 5.93 6 23.00 13 10.00
37 P-253 66 0.326 3.60 21.18 4.12 5 16.50 11 5.50
38 P-254 197 0.133 2.05 17.92 11.99 12 17.91 9 8.91
39 P-256 230 0.561 5.10 23.34 10.86 11 23.00 13 10.00
40 P-257 33 8.5 31.44 36.58 1.90 2 33.00 21 12.00
41 P-259 164 2.23 10.76 32.03 6.12 7 27.33 15 12.33
42 P-260 39 2.23 10.76 32.03 2.22 3 19.50 15 4.50
43 P-261 49 2.23 10.76 32.03 2.53 3 24.50 15 9.50
44 P-262 16 2.23 10.76 32.03 1.50 2 16.00 15 1.00
45 P-263 16 0.561 5.10 23.34 1.69 2 16.00 13 3.00
46 P-264 49 0.561 5.10 23.34 3.10 4 16.33 13 3.33
47 P-270 262 2.23 10.76 32.03 9.18 10 29.11 15 14.11
48 P-271 33 0.133 2.05 17.92 2.84 3 16.50 9 7.50
N.O.S = Number of support
L = Length of pipe, ft
Ls = Span length, ft
Z = Section modulus, in3
In Table 6-9 last column, negative sign shows that the pipe length is less than that of
the standard spacing. So that in this case pipe length will be used as a span limit.
45
6.3.6 Calculation for Supports based on Standard Spacing
Now to calculate number of supports required based on the standard spacing using
Equation (6.1). Considering the case for pipe no. 208 [2],
No. of Supports = (L/Ls) +1 (6.1)
Where,
Ls (standard) = 24 ft (Appendix Table A8)
Pipe length, L = 262 ft (Table 6-1)
No. of supports = 11.9 ≈ 12
The numbers of supports for all 48 pipes are arranged in Table 6-10 below.
Table 6-10 Spacing based on standard spacing
Pipe Line No.
Pipe length
(ft) NPS
Section Modulus Z,( In3)
w, lb/ft
Ls, ft Stand. max. Span
No.of Support
Complete No. of
Support
P-208 262 8 16.8 50.15 40.72 24.00 11.9 12
P-209 16 2 0.561 5.07 23.41 13.00 2.2 3
P-210 394 8 16.8 50.15 40.72 24.00 17.4 18
P-211 341 8 16.8 50.15 40.72 24.00 15.2 16
P-212 361 8 16.8 50.15 40.72 24.00 16.0 16
P-213 787 4 3.21 16.28 31.24 17.00 47.3 48
P-214 16 8 16.8 50.15 40.72 24.00 1.7 2
P-215 16 6 8.5 31.44 36.58 21.00 1.8 2
P-216 98 2 0.561 5.10 23.34 13.00 8.5 9
P-217 164 4 3.21 16.28 31.24 17.00 10.6 11
P-218 16 3 2.23 10.76 32.03 15.00 2.1 3
P-219 9.8 4 3.21 16.28 31.24 17.00 1.6 2
P-220 279 4 3.21 16.28 31.24 17.00 17.4 18
P-221 230 2 0.561 5.10 23.34 13.00 18.7 19
P-224 262 4 3.21 16.28 31.24 17.00 16.4 17
P-225 197 2 0.561 5.10 23.34 13.00 16.2 17
P-226 115 3 2.23 10.76 32.03 15.00 8.7 9
P-227 525 2 0.561 5.10 23.34 13.00 41.4 42
P-228 82 3 2.23 10.76 32.03 15.00 6.5 7
P-229 164 2 0.561 5.10 23.34 13.00 13.6 14
46
Table 6-10 Spacing based on standard spacing (Continued)
Pipe Line No.
Pipe length
(ft) NPS
Section modulus Z( In3)
w, lb/ft
Ls, ft Stand. max. Span
No.of Supports
Complete No. of
Support
P-230 164 2 0.561 5.10 23.34 13.00 13.6 14
P-231 115 1 0.133 2.05 17.92 9.00 13.8 14
P-232 246 3 2.23 10.76 32.03 15.00 17.4 18
P-233 131 2 0.561 5.10 23.34 13.00 11.1 12
P-236 98 1.5 0.326 3.60 21.18 11.00 9.9 10
P-237 66 1 0.133 2.05 17.92 9.00 8.3 9
P-238 213 2 0.561 5.10 23.34 13.00 17.4 18
P-239 197 1 0.133 2.05 17.92 9.00 22.9 23
p-240 180 2 0.561 4.93 23.74 13.00 14.8 15
P-241 262 1 0.133 2.05 17.92 9.00 30.1 31
P-242 197 2 0.561 5.10 23.34 13.00 16.2 17
P-243 262 2 0.561 5.10 23.34 13.00 21.2 22
P-244 394 1 0.133 2.05 17.92 9.00 44.8 45
P-250 6.6 3 2.23 10.76 32.03 15.00 1.4 2
P-251 328 1 0.133 2.05 17.92 9.00 37.4 38
P-252 115 2 0.561 5.10 23.34 13.00 9.8 10
P-253 66 1.5 0.326 3.60 21.18 11.00 7.0 7
P-254 197 1 0.133 2.05 17.92 9.00 22.9 23
P-256 230 2 0.561 5.10 23.34 13.00 18.7 19
P-257 33 6 8.5 31.44 36.58 21.00 2.6 3
P-259 164 3 2.23 10.76 32.03 15.00 11.9 12
P-260 39 3 2.23 10.76 32.03 15.00 3.6 4
P-261 49 3 2.23 10.76 32.03 15.00 4.3 5
P-262 16 3 2.23 10.76 32.03 15.00 2.1 3
P-263 16 2 0.561 5.10 23.34 13.00 2.2 3
P-264 49 2 0.561 5.10 23.34 13.00 4.8 5
P-270 262 3 2.23 10.76 32.03 15.00 18.5 19
P-271 33 1 0.133 2.05 17.92 9.00 4.7 5
47
6.3.7 Thermal Expansion (deflection)
Thermal deflections are calculated for all the pipes by using Equation (4.9) as given
below [6],
Expansion (mm) L Tα= × ×∆ (4.9)
For Pipe No.208
L = 262 ft (From Table 6-1)
∆T = 169.7 oC (From Table 6-1)
α = 14.9 x 10-3 mm/m oC (Appendix Table A6)
In actual case the temperature difference is 0.9 oC, but for the verse condition the
temperature difference is to be taken b/w operating and non-operating conditions and
the non-operating condition is assume to be at 0 oC. Further every pipe has been
divided into segments of 200 ft, b/c the pipe length for an expansion loop is consider
to be 200 ft.
-3 262 12Expansion(mm)=14.9×10 × ×169.7=204.16mm39.37
×
These calculations are arranged for all 48 pipes in the Table 6-11 below.
Table 6-11 Thermal deflection for pipes complete segments
S. No
Pipe Line No. L, ft TIn,
oC Tout , oC
∆T (oC)
(α) = (mm*10-3/moC)
Deflection ∆(mm)
Deflection ∆(m)
1 P-208 262 169.70 168.80 169.70 14.9 204.16 0.20 P-208-1 200 169.70 169.20 169.70 14.9 154.18 0.15 P-208-2 65 169.00 168.80 169.00 14.9 49.90 0.05 2 P-209 16 169.00 168.30 169.00 14.9 12.28 0.01 3 P-210 394 168.80 167.50 168.80 14.9 302.12 0.30 P-210-1 200 168.80 168.10 168.80 14.9 153.36 0.15 P-210-2 194 168.10 168.00 168.10 14.9 148.14 0.15 4 P-211 341 167.50 166.30 167.50 14.9 259.47 0.26 P-211-1 200 167.50 166.90 167.50 14.9 152.18 0.15 P-211-2 141 166.90 166.50 166.90 14.9 106.90 0.11 5 P-212 361 166.40 165.20 166.40 14.9 272.88 0.27 P-212-1 200 166.40 165.80 166.40 14.9 151.18 0.15 P-212-2 161 165.80 165.50 165.80 14.9 121.26 0.12 6 P-213 787 165.20 158.30 165.20 14.9 590.61 0.59 P-213-1 200 165.20 165.00 165.20 14.9 150.09 0.15 P-213-2 200 165.00 164.00 165.00 14.9 149.91 0.15 P-213-3 200 164.00 163.00 164.00 14.9 149.00 0.15
48
Table 6-11 Thermal deflection for pipes complete segments (Continued)
S. No
Pipe Line No. L, ft TIn,
oC Tout , oC
∆T (oC)
(α) = (mm*10-3/moC)
Deflection ∆(mm)
Deflection ∆(m)
P-213-4 187 163.00 162.00 163.00 14.9 138.47 0.14 7 P-214 16 165.30 165.20 165.30 14.9 12.01 0.01 8 P-215 16 166.50 166.40 166.50 14.9 12.10 0.01 9 P-216 98 166.40 163.40 166.40 14.9 74.08 0.07 10 P-217 164 166.20 164.90 166.20 14.9 123.82 0.12 11 P-218 16 165.10 164.70 165.10 14.9 12.00 0.01 12 P-219 9.8 158.00 157.90 158.00 14.9 7.03 0.01 13 P-220 279 165.00 161.80 165.00 14.9 209.12 0.21 P-220-1 200 165.00 163.40 165.00 14.9 149.91 0.15 P-220-2 79 162.00 161.80 162.00 14.9 58.14 0.06 14 P-221 230 161.80 154.40 161.80 14.9 169.05 0.17 P-221-1 200 161.80 160.00 161.80 14.9 147.00 0.15 P-221-2 30 160.00 154.40 160.00 14.9 21.80 0.02 15 P-224 262 161.80 158.30 161.80 14.9 192.57 0.19 P-224-1 200 161.30 160.00 161.30 14.9 146.55 0.15 P-224-2 62 160.00 159.00 160.00 14.9 45.06 0.05 16 P-225 197 158.30 152.10 158.30 14.9 141.66 0.14 17 P-226 115 158.20 156.70 158.20 14.9 82.65 0.08 18 P-227 525 156.80 133.50 156.80 14.9 373.95 0.37 P-227-1 200 156.80 156.50 156.80 14.9 142.46 0.14 P-227-2 200 150.00 147.80 150.00 14.9 136.28 0.14 P-227-3 125 135.00 133.50 135.00 14.9 76.66 0.08 19 P-228 82 156.70 155.50 156.70 14.9 58.37 0.06 20 P-229 164 155.50 147.90 155.50 14.9 115.85 0.12 21 P-230 164 135.20 124.80 135.20 14.9 100.72 0.10 P-230-1 100 135.20 129.20 135.20 14.9 61.42 0.06 P-230-2 64 129.20 124.80 129.20 14.9 37.56 0.04 22 P-231 115 135.00 120.10 135.00 14.9 70.53 0.07 23 P-232 246 155.50 150.50 155.50 14.9 173.77 0.17 P-232-1 200 154.30 153.00 154.30 14.9 140.19 0.14 24 P-233 131 150.50 141.30 150.50 14.9 89.56 0.09 25 P-236 98 127.90 118.50 127.90 14.9 56.94 0.06 26 P-237 66 127.70 119.50 127.70 14.9 38.29 0.04 27 P-238 213 150.40 145.70 150.40 14.9 145.53 0.15 P-238-1 200 148.00 147.30 148.00 14.9 134.46 0.13 P-238-2 13 147.30 145.70 147.30 14.9 8.70 0.01 28 P-239 197 145.70 131.30 145.70 14.9 130.39 0.13 29 p-240 180 145.80 140.90 145.80 14.9 119.22 0.12 P-240-1 100 145.80 143.30 145.80 14.9 66.23 0.07 P-240-2 80 143.30 140.90 143.30 14.9 52.08 0.05 30 P-241 262 140.70 126.00 140.70 14.9 167.46 0.17 P-240-1 200 140.70 136.00 140.70 14.9 127.83 0.13
49
Table 6-11 Thermal deflection for pipes complete segments (Continued)
S. No
Pipe Line No. L, ft TIn,
oC Tout , (oC)
∆T (oC)
(α) = (mm*10-3/moC)
Deflection ∆(mm)
Deflection ∆(m)
31 P-242 197 140.90 131.60 140.90 14.9 126.09 0.13 32 P-243 262 131.70 114.10 131.70 14.9 156.75 0.16 P-243-1 200 131.70 122.40 131.70 14.9 119.65 0.12 P-243-2 62 117.50 114.10 117.50 14.9 33.09 0.03 33 P-244 394 131.62 95.90 131.62 14.9 235.58 0.24 P-244-1 200 131.62 120.62 131.62 14.9 119.58 0.12 P-244-2 94 100.30 95.90 100.30 14.9 42.83 0.04 34 P-250 6.6 160.20 159.90 160.20 14.9 4.80 0.00 35 P-251 328 159.70 122.20 159.70 14.9 237.95 0.24 P-251-1 200 159.70 145.70 159.70 14.9 145.09 0.15 P-251-2 128 139.40 122.20 139.40 14.9 81.06 0.08 36 P-252 115 159.90 153.80 159.90 14.9 83.53 0.08 37 P-253 66 153.80 147.60 153.80 14.9 46.11 0.05 38 P-254 197 153.50 133.30 153.50 14.9 137.37 0.14 39 P-256 230 156.20 150.40 156.20 14.9 163.20 0.16 P-256-1 200 156.20 153.30 156.20 14.9 141.91 0.14 P-256-2 30 153.30 150.40 153.30 14.9 20.89 0.02 40 P-257 33 153.10 152.80 153.10 14.9 22.95 0.02 41 P-259 164 142.80 137.80 142.80 14.9 106.39 0.11 42 P-260 39 140.50 139.10 140.50 14.9 24.89 0.02 43 P-261 49 119.20 117.30 119.20 14.9 26.53 0.03 44 P-262 16 136.10 135.30 136.10 14.9 9.89 0.01 45 P-263 16 129.10 127.90 129.10 14.9 9.38 0.01 46 P-264 49 120.40 116.80 120.40 14.9 26.80 0.03 47 P-270 262 157.70 152.70 157.70 14.9 187.69 0.19 P-270-1 200 157.70 155.20 157.70 14.9 143.28 0.14 P-270-2 62 153.40 152.20 153.40 14.9 43.20 0.04 48 P-271 33 157.80 152.70 157.80 14.9 23.66 0.02
6.3.8 Expansion Loops Calculations
Based on thermal expansion calculated above, size of expansion loops was calculated
below as [2].
3144
o
A
EDLS∆
= (6.2)
Take Pipe no. 208 and calculating thermal expansion in it by using Equation (4.9).
L = 200 ft = 60.98 m (section of length 262 ft)
∆T = 169°C (operating temp - non operating temp)
α = 14.9 x 10-3 (mm/m C°) (Appendix Table A6)
50
Expansion (mm)
And expansion loop size by using Equation (6.2)
Where
E = 27.5 Mpsi (Appendix Table A3)
Do = 8.625 in (Appendix Table A2)
For allowable stress using Equation (6.3) below [2]:
SA = f x (1.25 Sc + 0.25 Sh) (6.3)
Where
f = stress reduction factor = 1 (Appendix Table A7)
Sc = Cold allowable stress = 14.4 psi (Appendix Table A1)
Sh = Hot allowable stress = 14.4 psi (Appendix Table A1)
SA = 21.4 ksi (Using Equation 6.3)
Equation (6.2) becomes:
Size of Expansion Loops
L = 39.47 ft
L = 2H + W
Where
H = 2W
L = 5W = 39.47 ft
W = 8 ft
H = 16 ft
Similarly the expansion loops sizes for all 48 pipes by considering full length, 200
feet length and the remaining length of each pipe are arranged in the following table.
Table 6-12 Sizing of expansion loops
Pipe Line No.
NPS, D in
Do,(in)
L, ft
Deflection (in)
Size of expansion
loop, ft
Width of expansion Loop (ft)
Height of expansion
loop(ft)
P-208 8 8.625 265 8.04 45.44 9 18 P-208-1 8 8.625 200 6.07 39.47 8 16 P-208-2 8 8.625 65 1.96 22.46 4 9 P-209 2 2 16 0.48 5.85 1 2
314.9 10 60.98 169153.556.04
mmin
−= × × ×==
63 27.5 10 8.625 6.07144 21400
39.47
L
L ft
× × × ×=
×=
51
Table 6-12 Sizing of expansion loops (Continued)
Pipe Line No.
NPS, D in
Do,(in)
L, ft
Deflection (in)
Size of expansion
loop, ft
Width of expansion Loop (ft)
Height of expansion
loop(ft)
P-210 8 8.625 394 11.89 55.26 11 22 P-210-1 8 8.625 200 6.04 39.37 8 16 P-210-2 8 8.625 194 5.83 38.69 8 15 P-211 8 8.625 341 10.22 51.21 10 20 P-211-1 8 8.625 200 5.99 39.22 8 16 P-211-2 8 8.625 141 4.21 32.87 7 13 P-212 8 8.625 361 10.74 52.51 11 21 P-212-1 8 8.625 200 5.95 39.09 8 16 P-212-2 8 8.625 161 4.77 35.01 7 14 P-213 4 4.5 787 23.25 55.80 11 22 P-213-1 4 4.5 200 5.91 28.13 6 11 P-213-2 4 4.5 200 5.90 28.11 6 11 P-213-3 4 4.5 200 5.87 28.03 6 11 P-213-4 4 4.5 187 5.45 27.02 5 11 P-214 8 8.625 16 0.47 11.02 2 4 P-215 6 6.63 16 0.48 9.70 2 4 P-216 2 2.38 98 2.92 14.37 3 6 P-217 4 4.5 164 4.87 25.55 5 10 P-218 3 3.5 16 0.47 7.02 1 3 P-219 4 4.5 9.8 0.28 6.09 1 2 P-220 4 4.5 279 8.23 33.21 7 13 P-220-1 4 4.5 200 5.90 28.11 6 11 P-220-2 4 4.5 79 2.29 17.51 4 7 P-221 2 2.375 230 6.66 21.69 4 9 P-221-1 2 2.375 200 5.79 20.23 4 8 P-221-2 2 2.375 30 0.86 7.79 2 3 P-224 4 4.5 262 7.58 31.87 6 13 P-224-1 4 4.5 200 5.77 27.80 6 11 P-224-2 4 4.5 62 1.77 15.41 3 6 P-225 2 2.375 197 5.58 19.86 4 8 P-226 3 3.5 115 3.25 18.41 4 7 P-227 2 2.375 525 14.72 32.26 6 13 P-227-1 2 2.375 200 5.61 19.91 4 8 P-227-2 2 2.375 200 5.37 19.47 4 8 P-227-3 2 2.375 125 3.02 14.61 3 6 P-228 3 3.5 82 2.30 15.47 3 6 P-229 2 2.375 164 4.56 17.96 4 7 P-230 2 2.375 164 3.97 16.74 3 7 P-230-1 2 2.375 100 2.42 13.07 3 5 P-230-2 2 2.375 64 1.48 10.22 2 4 P-231 1 1.32 115 2.78 10.44 2 4 P-232 3 3.5 246 6.84 26.70 5 11 P-232-1 3 3.5 200 5.52 23.98 5 10 P-233 2 2.375 131 3.53 15.79 3 6
53
6.3.9 Impact Loading on Bends
Impact loads on the first elbow of an expansion loop of pipe no.208 due to hammering
of steam can be calculated by using the following equations.
Figure 6-1 Forces on the bend by the fluid
Taking θ = 900 (b/c at lower and upper ends of expansion loops the bends are at 90o)
For the first time considering the fluid is flowing at its highest speed V1 and highest
pressure P1, so that for shock loading assuming V2 = 0. To find the force in horizontal
direction, using the impulse momentum equation given below [8].
1 1 2 2 2 1cos ( ) ( )x B xF
F P A P A F m V Vθ= − − = × −∑ (6.4)
All the in put data are arranged for above equation in Table 6-13. Table 6-13 Input Data
Parameter Value Reference/Reason
Pressure at inlet, P1 193.3 psi Table 6-1
Velocity at inlet, V1 116 ft/sec Table 6-1
Pressure at outlet, P2 14.7 psi Assuming Atmospheric
Loop bend at angle, θ 900 For 90o Loop
Mass flow rate, m 9.33 lbf/sec Provided
Diameter of pipie, D1 = D2 7.981 in Table 6-1
Density of Water, ρwater 0.0361 lb/in3 Appendix Table A-14
54
A1 = A2 = π/4 x 7.9812 = 50 in2
mV2 = 0, as V2 = 0 and P2A2cosθ = 0 as θ = 900, above Equation (6.4) becomes:
1 1 1( )
( ) 193.3 50 9.33 116 12
( ) 12.994
B xF
B xF
B xF
F P A m V
F
F kips
= + ×
= × + × ×
=
Similarly finding the force in x- direction, using impulse momentum equation below
[8],
1 1 2 2 2 1sin ( ) ( sin )y B yF
F P A P A F m V Vθ θ= − + = × −∑ (6.5)
As V1 = V2 and P1A1 sin (θ) = 0, therefore the above equation become:
2 2( )
( ) 14.7 50.03
( ) 735.44
B yF
B yF
B yF
F P A
F
F lb
=
= ×
=
Resultant force
2 2
2 2
( ) ( ) ( )
( ) (12994) (735.44)
( ) 13.014
B B x B yF F F
BF
BF
F F F
F
F kips
= +
= +
=
With direction θ < 10 along with X-axis
6.3.10 Normal Impact Load on elbow
For normal impact load the rest of parameters are same, except one condition that
To find P2 using Bernoulli’s equation as given below [8], and using Table 6-14 for its
different parameters;
2 1 1 2( )c
gP P Z Zg
ρ= − − × (6.6)
Table 6-14 Input data
Parameter Value Reference/ Reason V1 = V2 = V 116 ft/sec From Table 6-1 g 32.17 ft/sec2 Acceleration due to gravity gc 32.17 lbm-ft/lbf-sec2 Gravitational constant Z1 – Z2 12 ft Height of an expansion loop for the first bendP1 193.3 psi From Table 6-1
55
Using Equation (6.6) and obtaining the value of pressure at outlet of the expansion
loop.
2
2
32.17193.3 12 0.036132.17
192.868
P
P psi
= − × ×
=
Using Equation (6.4) for force in x-direction,
1 1 2 2 2 1cos ( ) ( )x B xF
F P A P A F m V Vθ= − − = × −∑ (6.4)
As V1 = V2, and P2A2cosθ = 0 as θ = 900, so the above equation becomes
1 1( )
( ) 9.67
B xF
B xF
F P A
F lb
= ×
=
Using Equation (6.5) for force in y- direction
1 1 2 2 2 1sin ( ) ( sin )y B yF
F P A P A F m V Vθ θ= − + = × −∑ (6.5)
As V1 = V2 and P1A1 sin (θ) = 0, for θ = 0o therefore the above equation becomes:
2 2( )
( ) 9.643
B yF
B yF
F P A
F lb
= ×
=
The resultant force comes out be
2 2
2 2
( ) ( ) ( )
( ) (9.67) (9.643)
B B x B yF F F
BF
F F F
F
= +
= +
0
( ) 13.65
45
BF
F lb
θ
=
=
For shock loading the value of load is greater than that of the value of the load at
normal operation, therefore for the verse condition shock load will be consider to
analyze the support.
56
7 Thermal Calculations Based on spacing calculated above considering header pipe P-208 of length segment
200ft. At both side of this expansion loop there are anchor supports and eight guided
supports equally spaced at length 22.22 ft. This expansion loop will be further
analyzed for thermal and static loads.
Figure 7-1 Header Pipe including an expansion loop
7.1 Thermal Analysis
For thermal analysis, using the data from Table 6-1, 6-11, Appendix A-2 and A-3,
and arranging it in Table 7-1 given below.
Table 7-1 Input Data
Type of Input Value
Modulus of Elasticity(E) 27.5 x 106 psi
Expansion rate (co-efficient)( α) 0.0226 in/ft
Moment of Inertia(I) 72.5 in4
Section modulus(Z) 16.8 in3
Note : (using appendix Table A3, A6 and A2)
Methodology
For thermal analysis in pipes we will use method of guided “cantilever method”, in
which thermal load and moments will be calculated as given below [3];
Thermal Load
3
12 E IF L
× × ×∆= (7.1)
57
Moment: 2
6 E IM L
× × ×∆= (7.2)
Where
∆ = Thermal Expansion, in
L = Length of segment under observation, in
E = Modulus of Elasticity, psi
I = Section modulus, in3
Total Displacement absorbed by a section of pipe [3]:
3
n Tn 3
i
L L∆
∆ =Σ
(7.3)
Where
∆n = Displacement absorbed by leg n, in
Ln = length of leg n, ft
Li = length of each leg resisting specified displacement, ft
∆T = Total displacement to be absorbed, in
Analysis
Considering 200 feet segment of pipe no. 208 and then taking its half symmetry for
analysis by assuming the pipe segments to be straight and acts just a cantilever beam.
As shown in figure the header pipe no. 208 has been divided into different sections.
As this pipe has two main sections, one is the main line and the other is vertical leg
which is perpendicular to the main line, so the nomenclature of the piping section as
given below:
Main line including the segments A-B, B-C, C-D, D-E = 22.22 ft, E-F= 7.1 ft
Figure 7-2 Header Pipe Sections
Segments perpendicular to the main line
F-G = 16 ft
58
For Main Line
Magnitude of expansion of each section = Expansion rate (0.0226in/ft) x Section
length, these magnitudes and resisting segments are arranged in Table 7-2 and 7-3
below.
Table 7-2 For main line magnitude of expansion and directions
Segment Length of
section (ft)
Direction of
expansion
Magnitude of
expansion
Resisting
segments
A-F 22.22 X 2.17 in F-G
A-B 22.22 X 0.50 in F-G
B-C 22.22 X 0.50 in F-G
C-D 22.22 X 0.50 in F-G
D-E 22.22 X 0.50 in F-G
E-F 7.11 X 0.16 in F-G
For Vertical Section of pipe
Table 7-3 Vertical section magnitude of expansion and direction
Segment Length of
section (ft)
Direction of
expansion
Magnitude of
expansion
Resisting
segments
F-G 16 Y 0.361in A-F
Thermal stress developed at on Anchor support A [2]
t E Tσ α= × ×∆ (7. 4)
Where
∆T = Temperature variation = 169-0 = 1690 C (From Table 6-1)
α = Thermal expansion co-efficient = 14.4 x 10-6mm/mm.0C (Appendix Table A6)
σt = Thermal stress, psi
6 627.5 10 14.4 10 169
69.25T
T Ksiσσ
−= × × × ×=
∆x absorbed by leg F-G, using Equation (7.3)
∆n = Ln3∆T/ΣLi
3 (7.3)
Ln = LFG = 16 ft (From Table 7.2)
59
Li = 16 ft, ∆T = 2.17 in (From Table 7-2)
3
3
16 2.1716
2.17
x
x in
×∆ =
∆ =
Fx across F-G by using Equation (7.1)
3
12EI∆Fx=L
(7.1)
Modulus of Elasticity (E) = 27.5 x 106 psi (Appendix Table A3)
Moment of Inertia (I) = 72.5 in4 (Appendix Table A2)
Length of pipe segment F-G, L = 16 ft (From Table 7-2)
∆ = 2.17 in
6
3
12×27.5×10 ×72.5×2.17Fx=(16×12)
Fx=7335lb
∆y absorbed by leg A-F using equation (7.3)
Ln = LAF = 96 ft
Li = 96 ft,
∆T = 0.3616 in
3
3
96 0.361696
0.3616
y
y in
×∆ =
∆ =
Fy across A-F
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
Length of pipe segment F-G, L = 96 ft,
∆y = 0.3616 in
For force in Y-direction across A-F, using Equation (7.1)
60
3
12 E IF L
× × ×∆= (7.1)
6
3
12×27.5×10 ×72.5×.3616Fy=(96×12)
Fy=5.65lb
Moment about Z-axis by using Equation (7.2)
2
6EI∆Mz=L
(7.2)
6
2
6×27.5×10 ×72.5×0.3616Mz=(96×12)
Mz=3259.5lb-in
Loads on Supports in Y-direction
For section A-B
Thermal expansion produced in section AB using Equation (7.3)
∆y, (A-B) = (∆y,total x LAB )/LAF (7.3)
(∆y,total ) = 0.3616 in
LAB = 22.22 ft = 266.64 in
LAF = 96 ft
0.3616 22.22,
96, 0.0837
A B
A B
y
y in
−
−
×∆ =
∆ =
Force and thermal moment in section AB using Equation (7.1) and (7.2)
6
A-B 3
A-B3
A-B
12×27.5×10 ×72.5×0.0837Fy, =266.64
Fy, =105.633lb
Mz, =14.083×10 lb-in
Similarly for the rest of sections, B-C, C-D, D-E and E-F by using Equations (7.1),
(7.2) and (7.3) in the same way as above,
For section B-C
Thermal expansion produced in section B-C using Equation (7.3)
∆y, (B-C) = (∆y,totalxLAC )/LAF (7.3)
(∆y,total ) = 0.3616 in
LAC = 44.44 ft
61
LAF = 96 ft
0.36166 44.44,
96, 0.167
B C
B C
y
y in
−
−
×∆ =
∆ =
For force in section B-C using Equation (7.1)
3
12 E IF L
× × ×∆= (7.1)
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
L = 22.22 ft = 266.64 in
6
B-C 3
B-C
12×27.5×10 ×72.5×0.167Fy, =266.64
Fy, =210.76lb
For thermal moment in section B-C using Equation (7.2)
2
6 E IM L
× × ×∆= (7.2)
3B-CMz, =28.098×10 lb-in
For section C-D
Thermal expansion produced in section C-D using Equation (7.3)
∆y, (C-D) = (∆y,total x LAD )/LAF
(∆y,total ) = 0.3616 in
LAD = 66.66 ft
LAF = 96 ft
0.36166 66.66,96
, 0.251
C D
C D
y
y in
−
−
×∆ =
∆ =
For force in section C-D using Equation (7.1)
3
12 E IF L
× × ×∆= (7.1)
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
62
L = 22.22 ft = 266.64 in
6
C-D 3
C-D
12×27.5×10 ×72.5×0.251Fy, =266.64
Fy, =316.78lb
For thermal moment in section C-D using Equation (7.2)
2
6 E IM L
× × ×∆= (7.2)
3C-DMz, =42.232×10 lb-in
For section D-E
Thermal expansion produced in section D-E using Equation (7.3)
∆y, (D-E) = (∆y,total x LAE )/LAF (7.3)
(∆y,total ) = 0.3616 in
LAE = 88.88ft
LAF = 96 ft
D-E
D-E
0.3616×88.88∆y, =96
∆y, =0.3348in
For force in section C-D using Equation (7.1)
3
12 E IF L
× × ×∆=
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
L = 22.22 ft = 266.64 in
6
D-E 3
D-E
12×27.5×10 ×72.5×0.3348Fy, =266.64
Fy, =421.71lb
For thermal moment in section C-D using Equation (7.2)
2
6 E IM L
× × ×∆= (7.2)
3D-EMz, =56.2×10 lb-in
For section E-F
63
Thermal expansion produced in section E-F using Equation (7.3)
∆y, (E-F) = (∆y,total x LA-F )/LA-F (7.3)
(∆y,total ) = 0.3616 in
LAE = 96ft
LAF = 96 ft
0.3616 96,96
, 0.3616
E F
E F
y
y in
−
−
×∆ =
∆ =
And similarly using Equation (7.1) for force in section E-F and Equation (7.2) for
thermal moment
6
E-F 3
E-F3
E-F
12×27.5×10 ×72.5×0.3616Fy, =266.64
Fy, =455.6lb
Mz, =60.74×10 lb-in
Vertical force on support A, B, C, D and E
AFy, =105.633lb
BCABB A
AB BC
MzMzFy, =Fy, + +
L L (7.5)
B
B
14082 28098Fy, =105.633+ +266.64 266.64
Fy, =264.62lb
Similarly using Equation (7.5) for supports C, D, and E in the same way as above,
C
C
28098 42232Fy, =210.76+ +266.64 266.64
Fy, =474.52lb
D
D
42232 56200Fy, =421.52+ +266.64 266.64
Fy, =792.26lb
E
E
56200 60740Fy, =455.6+ +266.64 266.64
Fy, =895.78lb
64
Loads on Supports in x-direction
Using Equation (7.3) for deflection across AF
∆x, (A-F) = (∆x,total x LFG )/LFG (7.3)
(∆x, total ) = 2.17 in
LAE = 16ft
LAF = 16 ft
∆x across AF3
3
16 2.1716
2.17
in
in
×=
=
For Section A-B
Thermal expansion produced in section A-B using Equation (7.3)
∆x, (A-B) = (∆y,total x LAB )/LAF
(∆y,total ) = 0.3616 in
LAB = 22.22 ft
LAF = 96 ft
2.17 22.22,
96, 0.50
A B
A B
x
x in
−
−
×∆ =
∆ =
For force in section A-B using Equation (7.1)
3
12 E IF L
× × ×∆= (7.1)
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
L = 22.22 ft = 266.64 in
6
A-B 3
A-B
12×27.5×10 ×72.5×2.17Fx, =266.64
Fx, =631lb.
Thermal expansion produced in section B-C using Equation (7.3)
∆x, (B-C) = (∆y,total x LAC )/LAF (7.3)
(∆y,total ) = 0.3616 in
LAC = 44.44 ft
65
LAF = 96 ft
For Section B-C 2.17 44.44,
96, 1.004
B C
B C
x
x in
−
−
×∆ =
∆ =
For force in section B-C using Equation (7.1)
3
12 E IF L
× × ×∆= (7.1)
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
L = 22.22 ft = 266.64 in
6
B-C 3
B-C
12×27.5×10 ×72.5×1.004Fx, =266.64
Fx, =1267lb
Thermal expansion produced in section C-D using Equation (7.3)
∆x, (C-D) = (∆y,total x LAD )/LAF (7.3)
(∆y,total ) = 0.3616 in
LAD = 66.66 ft
LAF = 96 ft
For section C-D 2.17 66.66,
96, 1.5
C D
C D
x
x in
−
−
×∆ =
∆ =
For force in section C-D using equation given below
3
12 E IF L
× × ×∆= (7.1)
Modulus of Elasticity (E) = 27.5 x 106 psi
Moment of Inertia (I) = 72.5 in4
L = 22.22 ft = 266.64 in
6
C-D 3
C-D
12×27.5×10 ×72.5×1.5Fx, =266.64
Fx, =1893lb
And similarly for section D-E and E-F using Equation (7.1) for force and Equation
(7.3) for thermal expansion
66
For section D-E
D-E
D-E6
D-E 3
D-E
2.17×88.88∆x, =96
∆x, =2.00in
12×27.5×10 ×72.5×2Fx, =266.64
Fx, =2524.1lb
For section D-E
E-F
E-F6
E-F 3
E-F
2.17×96∆x, =96
∆x, =2.17in
12×27.5×10 ×72.5×2.17Fx, =266.64
Fx, =2738.645lb
Axial forces on every support A, B, C, D, and E separately are: , 631AFx lb= (From above calculation)
For every support in the middle of other support following equation is used [3].
( )A-B B-CB
F +FFx, = 2 (7.6)
BFx, =(631+1267)/2=949lb
And similarly for support C, D and E using Equation (7.6)
C
D
E
Fx, =(1267+1893)/2=1580lbFx, =(1893+2524.1)/2=2208.5lbFx, =(2524.1+2738.643)/2=2631.4lb
All the resultants loads are arranged in Table 7-4 below,
Table 7-4 Summary of all Loads due to Thermal expansion
Support Fx, lb Fy, lb Mz, lb-in
Anchor A 631 105.63 14.08x103
Support B 949 264.62 28.08x103
Support C 1580 474.96 42.23x103
Support D 2208.1 792.26 56.20x103
Support E 2631.l4 895.78 60.74x103
67
7.2 Verification from Code
The effects of thermal expansion must meet the following equation [1].
( )CA h L
iM S f S SZ
≤ + − (7.7)
Where f = Stress range reduction factor
Mc =Range of resultant moment due to thermal expansion, in-lb
SA = Allowable stress range for expansion, psi
Z = Section modulus of pipe, in3
Sh =Basic material allowable stress at design pressure, psi
i = stress intensification factor
These all values are arranged in Table 7-5 below,
Table 7-5 Input data
Parameter Value Reference
f 1 Appendix Table A7
Mc 60740in.lb Table 7-4
SA 21400psi From Equation 6.3
Z 16.8in3 Appendix Table A2
Sh 14.4psi Appendix Table A1
i 1 Appendix Table A13
Equation (7.7), after putting values from above table gives the following comparison;
3 3
1 60740 21400 1 (14400 1297.098)16.8
4.032 10 34.502 10
×≤ + × −
× ≤ ×
The value obtained from the above equation show that that the maximum moment due
to thermal expansion will produce no disturbance, if an expansion loop is used for 200
ft length of pipe.
68
7.3 Static Loads Calculations
For Static loads calculation, considering again pipe no. 208 and taking its section up
to first vertical leg of the expansion loop. This pipe is to be considering as a straight
beam with uniformly distributed load.
7.3.1 Manual Calculations
Considering again pipe no. 208 by assuming it to be a straight uniformly distributed
beam and taking its specification from Appendix Table (A-2).
Design Specifications
NPS (Nominal Pipe Size) = 8 in =200 mm
Pipe outer Diameter = 8.625 in
Pipe thickness = 0.322 in
Total (metal +Insulation +Fluid) distributed weight of pipe = 50lb/ft = 4.167 lb/in
Section Modulus, Z= 16.8 in3
Moment of Inertia, I = 72.5 in4
Modulus of Elasticity, E = 27.5 Mpsi (Appendix Table A1)
Figure 7-3 Symmetry of header pipe considering as a beam
Static analysis of pipe section A-B
As it is already mention that a straight main pipe section has been selected for
analysis, which is divided into the following sections A-B, B-C, C-D, D-E, and E-F.
As this pipe section is considered as straight beam with one anchor support and four
vertical restraints, so there are five unknowns in this problem. For this purpose to
solve this problem singularity method has been followed.
69
Solving Segment A-B
For segment A-B as shown in Figure 7-4 below, taking the weight, shear force and
moment equation and then solving for length L1 = 22.22 ft.
Figure 7-4 Segment A-B
2 1 0 1 20 0 1 1
1 0 1 0 10 0 1 1
0 1 2 1 00 0 1 1
( )
( )
( )
w x M x R x w x R x a M x L
V x M x R x w x R x a M x L
M x M x R x w x R x a M x L
− − − −
− −
= − ⟨ ⟩ + ⟨ ⟩ − ⟨ ⟩ − ⟨ − ⟩ − ⟨ − ⟩
= − ⟨ ⟩ + ⟨ ⟩ − ⟨ ⟩ − ⟨ − ⟩ − ⟨ − ⟩
= − ⟨ ⟩ + ⟨ ⟩ − ⟨ ⟩ − ⟨ − ⟩ − ⟨ − ⟩
(7.8)
Integrating the moment equation twice and putting boundary conditions we get
2 3 4
0 0( ) 02 6 24
M x R x w xEIy x ⟨ ⟩ ⟨ ⟩ ⟨ ⟩= − + − = (7.9)
As for segment AB, x = L1 = 266.64 in
2 3 4
0 1 0 1 1 02 6 24
M l R l w l⟨ ⟩ ⟨ ⟩ ⟨ ⟩− + − =
0 035548.44 3159545.774 877634043.8 0M R− + − = (7.10)
For Segment B-C
Figure 7-5 Segment A-B-C
3 3 4
2 0 2 1 2 1 22 0 2( ) 0
6 6 24R l R l l w lEIy l M l ⟨ ⟩ ⟨ − ⟩ ⟨ ⟩
= − ⟨ ⟩ + + − =
100 0 1142193.78 252766366.2 3159545.78 1.404 0M R R e− + + − = (7.11)
70
Similarly for segment C-D
3 3 3 42 0 3 1 3 1 2 3 2 3
3 0 3( ) 06 6 6 24
R l R l l R l l w lEIy l M l ⟨ ⟩ ⟨ − ⟩ ⟨ − ⟩ ⟨ ⟩= − ⟨ ⟩ + + − =
110 0 1 2320000 85333333.33 25287743.4 3159545.78 7.11 0M R R R e− + + + − = (7.12)
For segment D-E
3 33 3 42 0 4 3 4 31 4 1 2 4 2 4
4 0 4( ) 06 6 6 6 24
R l R L lR l l R l l w lEIy l M l ⟨ ⟩ ⟨ − ⟩⟨ − ⟩ ⟨ − ⟩ ⟨ ⟩= − ⟨ ⟩ + + + − =
0 0 1 211
3
568775.12 202210929.5 85307735.9 252776366.2
3156702.75 2.246 0
M R R R
R e
− + + + +
− = (7.13)
Now taking summation of moment at left end of right end support
0 0 4 1 4 1 2 4 2 3 4 3 1 4 2 1 4
2
3 2 4 4 3 4
( ) ( ) ( ) ( ) ( )( )
( )( ) ( )( ) 02
M R l R l l R l l R l l wl l a w l l l b
xw l l l c w l l l d w P x
+ + − + − + − − − − − −
− − − − − − − − × =
0 0 1 2 31066.56 800 533.28 266.64 2369952.574 0M R R R R+ + + + − = (7.14)
Solving all of the above five equations, we get
Mo = -24401 lb.in, Ro = 552 lb, R1 = 1123 lb R2 = 1067 lb, R3 = 1266 lb
For R4, taking
0 1 2 3 4 800R R R R R wL+ + + + = + (7.15)
R4 = 1591 lb
Plotting shear force and bending moment diagram for the beam solved above
Shear Force Diagram
-800-600-400-2000200400600800
0 267 507 747 987 1118
Pipe Length
She
ar F
orce
Figure 7-6 Shear Force Diagram
71
Bending Moment Daigram
-40000
-30000
-20000
-10000
0
10000
20000
0 267 507 747 987 1118
Pipe length
Ben
ding
Mom
ent
Figure 7-7 Bending Moment Diagram
Maximum Bending Moment = Mmax = -32741.44533 lb-in at x = 799.92 in
7.3.2 Verification from Code
The effects of the pressure, weight, and other sustained loads must meet the
requirements of the following equation [1].
0.75 1.0
4o A
L hPD i MS S
t Z×
= + ≤ (7.16)
These all inputs are arranged in Table 7-6 below, where the different parameters are,
P = Internal Pressure, psi
Do = Out Side diameter of Pipe, in
t = nominal wall thickness, in
Z = Section modulus of pipe, in3
MA = Resultant moment due to weight and other sustained loads, lb-in
Sh = Allowable stress at design hot pressure, psi
i = stress intensification factor
Table 7-6 Input data
Parameter Value Reference
P 193.7psi Appendix Table A2
Do 8.625 in Appendix Table A2
t 0.322in Appendix Table A2
Z 16.8in3 Appendix Table A2
MA 32700in.lb Mmax at x = 800 in (above calculation)
Sh 14400ps Appendix Table A1
i 1 Appendix Table A13
72
Equation (7.16) become; 3 3
193.7 8.625 0.75 1 32700 1.0 144004 0.322 16.8
2756.92 144002.75 10 14.4 10
× × ×+ ≤ ×
×≤
× ≤ ×
7.4 Piping Analysis on ANSYS
Analysis was performed for the pipe in ANSYS for using the following data.
Element type = Beam 3
Material properties
Modulus of Elasticity = 27.5 Mpsi
Poison’s Ratio = 0.283
Density = 0.283 lb/in3
Type of Loads
Four Vertical constraints in the middle and one all degree of Freedom
constrained at the start.
Gravity = 9.81(386.22 in/sec2)
Final Meshing = 96 elements for total length of the beam (22 elements for first
four each sections and 8 elements for the last section. Refining the mesh from
24 elements up to 96 elements but there is no change found in
deformation values and bending moment values).
Figure 7-8 Loaded view of the meshed beam
73
Figure 7-9 Deflection (inch) in Pipe
Figure 7-10 Bending stress (psi) in Pipe
74
7.4.1 Comparison of Analysis The maximum deflections and bending moment values obtained from both methods are arranged in Table 7-7 below,
Table 7-7 Comparison of analysis for beam
Method Max. Deflection(in) Max. Bending(lb-in)
Manual 0.064 32741.445
ANSYS Results 0.0596 32921.00
From the results obtained both manually and on ANSYS, the difference in
maximum deflection is 6.4% where on the other hand the difference in the max.
Bending moment is 1.35%. Deformation is less than 0.1 inch and also the
maximum bending stress is 1947.55 psi which is quite less than the allowable
stress of the pipe.
7.5 Seismic Loads Calculations
For a system seismic supports designed in the rigid range, the designed load for a
system decreases. For such a system the seismic stress and load are given below;
7.5.1 Seismic stress
A simplified seismic analysis can be done by assuming the simple beam formulas and
the load is to be most often considering in the lateral directions of the pipe. Seismic
stress based on seismic acceleration is calculated as follows [3].
2
0.75 12 ( (1.5 )8WLS i G
Z= × × × ×
× (7.17)
Where
Z = Section modulus of pipe, in3 = 16.8 in3 (Appendix Table A2)
G = seismic acceleration in gs = 0.15 (Data provided)
I = stress Intensification factor for straight pipe = 1.00 (Appendix Table A15)
7.5.2 Seismic Lateral load
For seismic lateral load based on static analysis is to be used to evaluate power piping.
It is performed by analyzing a piping system for the statically applied uniform load
75
equivalent to the site dependent earth-quake acceleration in each of the three
orthogonal directions .For seismic lateral load considering only in horizontal direction
using equation below [1]:
V Z I K C S W= × × × × × (7.18)
V = Seismic lateral load, lb
Z = constant depend upon earth quake zone 0.5 up to 1.0 = 1( Assuming
maximum)
K = Occupancy factor b/w 1.00 and 1.5 = 1 (Low occupancy region)
115
CT
= =0.12
T =Fundamental period of structure, s = 0.3 sec
S = soil factor b/w 1 and 1.5 = 1.5 (Data provided)
W = Total dead weight of the structure = 10,000lb (For 200 feet of pipe length)
1 1 1.5 0.12 1.5 100002700
VV lb= × × × × ×=
7.5.3 Verification from Code
To verify that the applied seismic loads are with in the limits as defined by the code,
following equation is used [1].
0.75 ( )
4o A B
hPD i M M KS
t Z+
+ ≤ (7.19)
Where
P = Internal Pressure, psi
Do = Out Side diameter of Pipe, in
t = nominal wall thickness, in
MA = Resultant moment due to loading on cross section due to weight and other
sustained loads = in-lb
MB = Resultant moment loading on cross section due to occasional loads, psi
MB = σ x Z = 108.482 x 16.8 = 1822.5 psi
K= Constant factor depend on plant operation time
76
Using the values given in Table 7-8, below for obtaining the comparative results
of seismic load,
Table 7-8 input data
Parameter value Reference/Reason
P 193.7psi Appendix Table A2
Do 8.625 in Appendix Table A2
t 0.322in Appendix Table A2
Z 16.8in3 Appendix Table A2
MA 32700in.lb Mmax at x = 800 in (above calculation)
Sh 14400ps Appendix Table A1
K 1.2 Appendix Table A13
Equation (7.19) becomes;
3 3
193.7 8.625 0.75 1 (32700 108.482 16.8) 1.2 144004 0.322 16.8
2.838 10 17.280 10
× × × + ×+ ≤ ×
×× ≤ ×
It means that the pipe is safe by more 7 times than allowable limits under the seismic
loads.
77
8 Support Design Calculations Anchor support will be loaded by the pipe load, wind load, seismic load. As already
loads were obtained from calculation already done. The major load on the support will
be that of the impact load on the first bend of expansion loop and most of our
calculation will be perform based on this load. The support beam will be chosen from
half channel beam and then it will be used in the Y- direction, just to provide an extra
support to the pipe and the support column will be of standard steel pipe.
8.1 Design Parameters
All the loads obtained from previous calculations are arranged in Table 8-1 below;
Table 8-1 Available loads for analysis of anchor support [From previous calculations]
Type of load Value, lb
Vertical static load 552
Supporting plate load 10.52
Wind load 334.14
Seismic load 300
Thermal load in X-direction 631
Thermal load in Y-direction 5.65
Impact load in X-direction 12.994x103
8.2 Beam Design
In beam design considering only the load in vertical direction along with the load of
the plate. Assuming that the beam is supported only in the middle, thus this beam
acting as double cantilever beam. Neglecting weight of the beam and finding moment
for one side of the beam in order to calculate the section modulus of the beam [4].
Figure 8-1 Uniformly load distributed Cantilever Beam
78
Finding the reaction in the middle of the beam, maximum moment and section
modulus of this beam using the following equations [4].
R = w x L (8.1)
Where
w = 73 lb/in
L = 8 in
= 568.14 lb
Mmax = w/2 x L2 (8.2)
Using same as in above Equation (8.2)
= 2.28in-kips
Z = M/σallowable (8.3)
Using the value of M from Equation (8.2) and for allowable stress = 27 ksi
= 2.28/27
= 0.10 in3
Looking values from Appendix Table A9:
For Z=>0.1
Required section comes out to be C5 x 9
Section modulus = Zy = 0.45 in3
Zx = 3.5 in4
The other properties of this beam are arranged in Table 8-2 below;
Table 8-2 Properties of the channel beam [7]
Beam parameters Values
Beam weight 9 lb/ft
Depth, d 5.0 in
Area ‘A’ 2.64 in2
Width, bf 1.885in
Thickness, tf 0.320 in
Inertia, Iy 0.632 in4
79
8.3 Beam Analysis
Now the beam will be analyzed for maximum stress and deflection, to check whether
it is in the desired limit or not. The analysis will be done through manual calculations
as well as through ANSYS.
8.3.1 Manual Analysis
First of all finding the reaction at the middle using Equation (8.2),
Figure 8-2 Double Cantilever beam
R = Vertical load + Beam Load = 585.44 lb
Mmax = w x L2/2 (8.2)
Total distributed load of the beam at one end of the support = w x L
= 73 x 8= 585.44 lb
The maximum moment at the center of the beam at L/2 distance of the beam is,
Mmax = w x L x (L/2) = 585.44 x 8/2
= 2.342 in-kips
For maximum bending stress using the following equation [4].
σ = M/Z ( 8.4)
= 2.342/0.45
= 5.204Kips
5.20 < 27 = σ all Now to find the maximum deflection, equation (8.5) is used [4].
y max = wL4/(8EI) (8.5)
Where
I = 0.632 in4
w = 73 lb/in
L = 8 in
E = 29 x 106psi
From Equation (8.5) the deflection comes out to be: y max = 0.00204 in
80
As the working stress and the deflection are well with in the limits so the beam used is
quite safe with working conditions.
8.3.2 ANSYS Analysis
Analyses were performed for beam in ANSYS for the following data.
Element type = Beam 3
Material properties
Modulus of Elasticity = 29.0 Mpsi
Poison’s Ratio = 0.283
Density = 0.286 lb/in3
Type of Loads
One Vertical constraint in middle
Gravity = 9.81(386.22 in/sec2)
Final Meshing = 100 divisions for each section of beam. The two sections of
the beam is meshed by refining it from 10 divisions up to 100 divisions at
increment of 10 divisions but there is no change found either in maximum
deflection or maximum stress.
Figure 8-3 Deformed Shape of the beam (inch)
81
Figure 8-4 Bending Moment diagram of the beam (lb-in)
Figure 8-5 Max. Stress distribution diagram (psi)
82
Table 8-3 Comparison of analysis for beam
Method Max. Deflection, in Max. B. Moment, in- Kips Max. Stress, kips
Manual 0.00204 2.342 5.20
ANSYS 0.00222 2.560 5.063
From table 8-3 above it is cleared that the difference in deformation b/w the two
methods is 8%, for bending moment the difference is 8.5% while in maximum
stress the difference is 2.8 %. Comparing these values to the allowable limits for
deflection and stress, the beam is found to be safe for the available loads.
8.4 Column Design
Column is necessary to maintain a required height for the supported pipe. Parameters
used in column design are given below.
Height of column ‘l’ = 3.28 ft = 39.37 in
Figure 8-6 Loads on column of the support
Type of column = Standard Circular pipe
Constraints = Fixed for all movements at the ground,
Free from top
Effective length constant = k = 2
Effective length ‘leff’ = Kl = 6.56 ft
83
Column effective design load by using the following equation [7]:
= P + MH x m (8.6)
Where
P = Compressive load on column, lb
MH = Horizontal equivalent moment, lb-in
m = Design factor for column
Equivalent Horizontal Load ‘FH’= (wind load + earth quick load + Impact load -
thermal load)/3.5
= 3714 lb
MH = FH x leff
= 24.36 ft-kips
Taking value of m = 2 (Appendix Table A10)
Column effective Design load = 585.47 + 24360 x 2
= 49.29 kips
Starting trial iteration from NPS 3 in, 3.5 in up to 4 in
Selecting NPS = 4 in with design load of 82 kips
From column design using Appendix Table A-12 for circular standard pipe, and
taking the parameters are arranged in Table 8-4 below;
Table 8-4 Specifications of column [7]
Column Parameters Value
Diameter(D), in 4
Area(A), in2 3.17
Moment of Inertia(I), in4 7.23
Radius of gyration(r), in 1.51
Thickness(t), in 0.237
Design factor of safety(Φ) 0.85
Yield strength(Fy), Kips 36
To check that column is safe under the applied loads critical load factor Equation
(8.7) is used, if this factor is less than 1.15, and then Equation (8.8) will be used for
load verification.
84
8.4.1 Verification for Critical Load
To find the critical load factor, using the following equation [7].
yc
Fklr E
λ = × (8.7)
Where
λc = critical load factor
(kl)/r = slenderness ratio
Fy = yield strength of the column material, ksi
E = modulus of elasticity, Mpsi
Using Table 8-4, and putting the values in above equation,
3
6
2 3.28 36 101.51 29 10cλ× ×
= ××
0.487 1.15cλ = ≤
If the critical load factor is less than 1.15, then Equation (8.8) can be used to calculate
the critical force [7].
( )2
0.658 ccr yF Fλ= × (8.8)
35.598crF kips=
allowable n crP P F Aφ φ= × = × × (8.9)
Where Φ = Design factor of safety (Using Table 8-4)
Fcr = Critical force, kips (From above calculation)
A = Cross sectional area of column (Using Table 8-4)
0.85 32.598 3.1787.835
allowable
allowable
PP kips
= × ×=
87.835 > 49.29
Pallowable > Column effective design load
As the allowable load is greater than the design load by factor of 1.8. So that it is safe.
8.4.2 Verification for Stresses
For axial and bending stress ratio verification using equation [7].
(Axial Stress ratio) + (Bending Stress ratio) < 1.0
85
1.0a b
ba
f fF F
⎛ ⎞ ⎛ ⎞+ ⟨⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ (8.10)
For axial stress
fa = P/A (Using Table 8-4)
= 585.74/3.17
= 0.185 ksi
At slenderness ratio = kl/r = 52.3132, looking value of Fa from Appendix Table A11,
Fa = 26.39 ksi
fa/Fa = 0.00701
For Bending Stress
bMCf
I= (8.11)
Where M = Bending moment = 24.36 kips-in (From above calculations)
C = D/2 = 4.5/2 = 2.25 in
I = 7.32 in4 (From Table 8.4)
24.36 2.25
7.327.48
b
b
f
f ksi
×=
=
Allowable bending stress by using equation below [7]:
Fb = 0.85 x Fy
Fb = 30.6 ksi
fb/Fb = 0.238
Putting these values in above equation
( ) ( )0.007 0.238 1.00.2459 1.0
+ ⟨
⟨
The result shows that the selected column for the calculated loads is quite safe.
8.4.3 Manual Analysis
To find the reaction at the bottom, taking summation of forces along y-direction,
0yF =∑ (8.12)
86
585.74
y y
y
R F
R
=
= (Compressive load from Table 8-1)
For deflection of the column, considering it is a cantilever beam and solving it for the
equivalent effective load by using the following equation [4].
3
3FlyEI
= (8.13)
Where
F = equivalent horizontal force, lb
L = Length of the column, ft
I = Moment of inertia, in4
E = Modulus of Elasticity, Mpsi
These all values are arranged in Table 8-5 below;
Table 8-5 Input data
Parameter Value Reference
F 3714 lb Calculated above
L 3.28 ft Length required
I 7.32 in4 From Table 8.4
E 29 x 106 psi Appendix Table A2
Using Equation (8.13), deflection in column comes out to be;
3
6
3714 (3.28 12)3 29 10 7.230.306
y
y in
× ×=
× × ×=
For combined axial and bending stress [7]:
max ( )eqP LC FA I
σ = + (8.14)
Where P = Compressive axial load, lb
A = Cross sectional area of column, in2
L = Length of the column, ft
I = Moment of inertia, in4
F = equivalent horizontal force, lb
C = D/2 = 4.5/2 = 2.25 in
87
All the input data are arranged in Table 8-6 below for combined stress.
Table 8-6 Input data
Parameter Value Reference
F 3714 lb Calculated above
L 3.28 ft Length required
I 7.32 in4 From Table 8-4
P 585.7 lb From Table 8-1
A 3.17 in2 From Table 8-2
Equation (8.14), gives the maximum stress due combined axial and bending load.
max
max
184.7 11492.64711.677kips
σσ
= +=
8.4.4 ANSYS Analysis
Analyses were performed for column in ANSYS for the following data.
Element type = Beam 3
Material properties
Modulus of Elasticity = 29.0 Mpsi
Poison’s Ratio = 0.283
Density = 0.286 lb/in3
Type of Loads
Vertical compressive and horizontal load at top end
All degree of freedom constrained at lower end
Gravity = 9.81(386.22 in/sec2)
Final Meshing = 100 divisions for the whole length of column
Figure 8-8 given below showing deflection in the column model. From this figure it
is clear that the maximum deflection is at the top of the end of the column. Where on
the other hand Figure 8-9 show that the maximum bending stress is at the bottom of
the column.
88
Figure 8-7 Meshed and loaded column
Figure 8-8 Deformation of the column (inch)
89
Figure 8-9 Stress distribution in column (psi)
8.4.5 Comparison of Analysis
Table 8-7 Comparison of analysis of column
Method Max. Deflection, in Max. Stress, kips
Manual 0.306 11.67
ANSYS 0.291 12.140
Difference b/w both methods for deformation 4.9%, while for maximum stress, the
difference is 3.8%. The deformation value comes out to be slightly greater than
the normal value, this is because at the same time shock load of more than 12 kips,
high seismic load, high thermal load were present and also if the wind has speed of
100 mile/hour, then under such conditions above deflection value is possible.
8.5 Base Plate Design
Base plate design means to find the feasible sides dimension for column support
and safe value of thickness both for concentric load and for bending moment.
Compressive strength of foundation concrete = 3000 psi
Type of material used = A-36 steel
90
Design factor of safety for concrete is, Φ = 0.35
Allowable bearing pressure of support on base plate, Fp = 0.35 x 3000 = 1050 psi
8.5.1 Base Plate Design Calculations
Selecting base plate dimension based on iteration starting from 10 inch side to 15 in
square side. For 15 in square base plate calculations are given below;
Bearing pressure due to concentric load, fp = Concentric load/Area(column)
= 622.8/225 = 2.768 psi
Figure 8-10 Base Plate Dimensions
Maximum bearing pressure due to moment [7],
( )2
6
MBearing pressureBN
− = ± (8.15)
Where
M = Bending moment = 24.36 kips-in (From above calculations)
B = N = Sided of the plate = 15 inch
( ) ( )2 2
24.38 12 0.51915 15
6 6
M kipsBN
×± = ± = ±
×
{Bearing pressure due to + {Bearing pressure < {Allowable bearing
Concentric load} due to moment} pressure of concrete}
2.768 + 519.0 < 1050
522.3 < 1050
2.768 - 519.0 < 1050
-517.07 < 1050
Thus the plate area is satisfactory
91
8.5.2 Thickness of the plate due to concentric load
Thickness of the plate can be calculated by using the following equation [7].
2 pp
y
ft l F= × × (8.16)
where
l = max (m, n), in
fp = Bearing pressure due to concentric load = 2.61 psi (Calculated above)
Fy = Yield strength of base plate, 36 ksi (Appendix Table A-10)
Distances from the column to edge of the plate are:
15 4.5 5.252 2
15 4.5 5.252 2
o
o
N Dm in
B Dn in
− −= = =
− −= = =
Therefore l = 5.25 in and putting all the values in the above Equation (8.16):
2.612 5.25 36000
0.09p
p
t
t in
= × ×
=
8.5.3 Thickness due to bending moment
The bearing pressure at a distance m = 5.25 in
)
)
5.25 522.315
182.8
m
m
p
p
f
f psi
×=
=
Now the pressure from the edge to the pipe edge is fp)m1= 522.3 – 182.8 = 339.5 Psi
Figure 8-11 Pressure diagram
And moment in this area between column edge and plate edge can be calculated as;
92
M = σ x Z (8.17)
Taking the section modulus and bearing pressure of the two sections, Equation (8.17) becomes,
1)2
2
6 3
339.5 522.315 5.256 3
39.37
mp pf fM B m
M
M in kips
⎡ ⎤= × +⎢ ⎥
⎣ ⎦⎡ ⎤= × +⎢ ⎥⎣ ⎦
= −
The thickness required to resist this moment [7]:
6
pall
MtB σ×
=×
(8.18)
where M = 39.37in-kips
σall = 27 kips (using design factor of 0.85 from Appendix Table A-11)
Side of the base plate, B = 15 in
6 39.3715 27
1.18
p
p
t
t in
×=
×=
Selecting the thickness to resist the bending moment b/c of its greater value, using
standard thickness for plate 1.25 in, base plate dimensions come out to be
115 15 14
in× ×
The total force on base plate and then force per bolt;
24.36 29.989.7512
29.98 7.54
MF kipsd
Force kipsBolt
= = =
= =
Allowable stress for bolts = 21ksi
Nominal area of bolt = 7.5/21 = 0.357 in2
Diameter of bolt 4 0.357 0.68
0.75
D in
D inπ
×= =
≈
And Bolt length by using bearing stress equation [7].
F
boltLD π σ
=× ×
(8.19)
using value of force and diameter of bolts as calculated
93
37.5 10
0.75 16019.89
boltL
L inπ
×=
× ×=
Bolt length = 20 in
Bolt length comes out to be 19.89 in which rounded up to 20 inch. The bolt length for
such base plate and column is quite reasonable. The calculated load in tension from
the load conditions 7.5 kips for each bolt which is less than the allowable tension by
factor of 3.7 as bolt minimum allowable tension is 28 kips.
8.5.4 Specifications of base plate
Specifications of base plate are arranged in Table 8-8.
Table 8-8 Base plate specifications [7] & [based on Calculation]
Parameter Value/Size
Base plate size 115 15 14
in× ×
Distances of column from edges, m = n 5.25 in
Bolt diameter of anchor rod, D 0.75 in = 3/4 in
Hole diameter 51 1 .6 2 58
i n=
Minimum edge distance for ¾ in bolt 1.25 in
Edge distance used in calculated case 1.8125 in
8.5.5 Bolt specifications
Table 8-9 shows the standard dimensions for 0.75 inch diameter and of length 20 inch.
Table 8-9 Bolts standard dimensions [7]
Nominal Bolt Size, in
(D)
Width across plate, in
(F)
Height, in
(H)
Thread length,
in
3/4 1 ¼ 15/32 1.375
Figure 8-12 Bolt dimensions
94
9 Complete System Modeling 9.1 Pro-E Modeling
The designed Anchor support is modeled in Pro-E Wildfire and the figure of
the complete system including supporting plate, beam, column, base plate along with
concrete base is shown below. The main header pipe passing on this support is of
nominal pipe size of 8 inch and out side diameter of 8.625 inch.
Figure 9-1 Anchor support along with a pipe
95
9.2 ANSYS 3-D Modeling and Analysis
The designed Anchor support is modeled in ANSYS and analyzed for
deformation and stress distribution. This model is analyzed by taking element Solid45
with vertical compressive and axial horizontal load at the top constrained fully at the
bottom and holes of the base plate.
Element type = Solid 45
Material properties
Modulus of Elasticity = 29.0 Mpsi
Poison’s Ratio = 0.283
Density = 0.286 lb/in3
Type of Loads
Vertical compressive and horizontal load at top end
All degree of freedom constrained at the bottom of the base plate &
holes.
Final Meshing
Following diagrams were obtained after refining the free mesh up to 7
iterations, starting from elements 5152 with stress value of 8023 psi
up to 36049 elements with stress value 9090 psi. In last three trials
there is no significant change in value of stress.
7800
80008200
8400
8600
88009000
9200
0 10000 20000 30000 40000Number of Elements
Von
Mis
es S
tres
ses
Figure 9-2 Convergence line b/w no. of elements and Von Mises Stresses (psi)
96
Figure 9-3 Meshed diagram of the support model
Figure 9-4 Deformed shape of the support model (inch)
97
Figure 9-5 First Principle Stress distribution in support (psi)
Figure 9-6 Von Mises stress distribution in support (psi)
98
9.2.1 Results and Discussion
Figure 9-4 shows the meshed model of the complete anchor support, while Figure 9-5
shows the deformed shape of the model. This diagram shows that the maximum
deformation is in the beam due to uniformly distributed pressure on the beam and in
the upper end of the column due to axial load and also the maximum deflection is
0.075 inch which is reasonable. Figures 9-5 and Figure 9-6 show the stress
distribution and the maximum stress occurred at the lower end of the column which is
less than the material strength by a factor more than 2.5. Looking all the above value
of principal stress, the maximum value of maximum principle stress is 9.78 ksi and
Von Mises at the bottom of the column is 9.09 ksi which is less than that of the
material allowable stress 15 ksi, so as a whole this anchor support is quite safe for the
available loads.
99
10 Conclusions Following conclusions are made from the analysis of the designed system.
1) The designed pipe verified all the conditions defined by the ASME Boiler and
Pressure Vessel code B31.1. Thickness and working pressure calculated are in
the safe limit. Thermal, Seismic and Sustained analysis results obtained are in
the safe limits defined by the Code.
2) Supporting Assembly confirms to the safety requirements of AISC standards.
3) The analysis shows that the complete system is safe and the results are verified
by manual calculations and ANSYS software.
4) On the positive side of the manual calculations lays the fact that it gives fully
basic concept of the piping system. While the assumptions made during
manual calculations make the results slightly differ from the software results.
5) As for thermal analysis is concerned, guided cantilever method was used and
this proved to be a useful tool for thermal stress loads calculations.
6) To do seismic analysis by manual calculations is really a tough job but static
analysis method was a handy tool to deal it.
100
11 Future Recommendations After completing the design of main header pipe and anchor support of the steam
piping system, following suggestions are recommended.
1) For future work more stress should be given on the proper use of the piping
software so that complex piping networks can be analyzed with it.
2) Although manual calculations method is a valuable tool for the understanding
and analysis of the simple piping network but for complex piping systems it
can lead no where. So therefore the best option we have is more and more
using of piping software.
3) Further optimization of Anchor support column is suggested.
4) To complete the analysis of Anchor support, analysis of base plate and bolts
are also suggested.
101
References [1]. Mohinder L. Nayyar, Piping Hand Book, 7th Edition, McGraw-Hill, Inc.
Singapore, 2000.
[2]. Sam Kannappan, Introduction To Pipe Stress Analysis, John Wiley & Sons,
USA, 1986.
[3]. Paul R. Smith, P.E, Piping and Piping Supports Systems, McGraw-Hill Book
Co., 1979.
[4]. J.E Shigley and C.R. Mischke,Mechanical engineering Design,5th edition,
McGraw-Hill Book Co. ,1989.
[5]. The American Society of Mechanical engineers, ASME B31.1-2001Power
piping, Revised edition 1998 ASME, USA.
[6]. Spirax Sarco Company Ltd, “Supports and Expansion Loops”, International
Site for Spirax Sarco.2008.
URL: http://www.spiraxsarco.com/resources/steam-engineering-tutorials/
[7]. The American Institute of Steel Construction, load & Resistance factor
Design, 2nd edition, USA, 1994.
[8]. L. Daugherty, B. Franzini, John Finnemore, Fluid Mechanics, Si Metric
edition.
[9]. Arthur H. Nilson, Design of Concrete Structures, 12th edition,Mc Graw Hill,
Inc., Singapore, 1982.
[10]. TPC Training System, Piping System, A Dun & Brad Street Comp, 1974.
[11]. David R. Sherwood, The Piping Guide, 2nd Edition, Syentek books.Inc., 1991.
[12]. A. Keith Escoe, Pipe Line Assessment Guide, Elseveir Book Aid Int. 2006.
102
APPENDIXE
103
Table A-1 Allowable stresses and yield stress for seamless Piping, KSI [2].
104
Table A-2 Properties and specification of pipe [2]
105
Table A-3 Modulus of elasticity at different temperatures [2]
106
Table A-4 Values of y Coefficient used in Pipe thickness calculations [5]
Table A-5 Value of casting quality factor used in pipe thickness calculations[2]
Table A-6 Expansion co-efficient at different temperatures [6]
107
Table A-7 Table Stress reduction factor used in allowable stresses [5]
Table A-8 Maximum standard spacing of pipes [5]
108
Table A-9 Properties of half channel beam [7]
109
Table A-10 Value of m as a design factor of column [7]
Table A-11 Column design stress [7]
110
Table A-12 Column Design axial Strength [7]
111
Table A-13 Stress Intensification factor and flexibility factors for various sections of pipe [5]
112
Table A-15 Material Properties [7]
Type of material
Parameters Value
Modulus of Elasticity 29 Mpsi Yield strength 36 ksi
Allowable Stress 21 ksi A36
Density 0.284 lb/in3 Yield strength 92 ksi
Bearing Strength 160 psi Design Factor 0.75 A325
Tensile Strength 120 ksi Rock Wool Density 0.003434 lb/in3 Carbon Steel Density 0.284 lb/in3 Water Density 0.0361 lb/in3
Table A-15 Insulation factor (inch)
NPS, (in)/ Insul. Thickness(in)
1 1-1/2 2 3 4 5 6 8
1 0.057 0.066 0.08 0.1 0.21 0.15 0.3 -- 2 0.16 0.21 0.21 0.25 0.3 0.34 0.38 -- 3 0.23 0.29 0.37 0.44 0.51 0.58 0.64 0.8
Figure A-1 Drag co-efficient v/s Reynolds no. used in wind loadings [1]
113
Vita
Muhammad Sardar was born on April 02, 1982 in a small village Kotigram of
Distt. Dir. He did his matriculation from Government High School Kotigram
Distt. Dir (lower). After matriculation, he got admission in Islamia College
Peshawar and passed his F.Sc (Pre-Engineering) in 2001 and did B.Sc.
Mechanical Engineering from N-W.F.P. UET Peshawar in 2006. After serving
Ghandhara Industires Limited (ISUZU), Karachi for six months, he joined
Pakistan Institute of Engineering and Applied Sciences, Islamabad as MS
Mechanical Engineering fellow on 13th of November, 2006.
Related Documents
