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.
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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
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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:
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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
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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
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Table of Contents 1
2
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
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 2.3.1
Valves...................................................................................................................7
2.3.2
Expansion Fittings................................................................................................8
2.4 3
Pipe Fittings ...................................................................................................7
Supports .........................................................................................................9
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
5
4.3.1
Span Limitations ................................................................................................23
4.3.2
Expansion Loop Calculations ............................................................................24
SUPPORT DESIGN...........................................................................................25 5.1
6
Pipe Span Calculations ................................................................................23
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
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
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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 7.4.1
7.5
8
Comparison of Analysis.....................................................................................74
Seismic Loads Calculations .........................................................................74
7.5.1
Seismic stress .....................................................................................................74
7.5.2
Seismic Lateral load...........................................................................................74
7.5.3
Verification from Code ......................................................................................75
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
9
Piping Analysis on ANSYS .........................................................................72
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
COMPLETE SYSTEM MODELING..............................................................94 9.1
Pro-E Modeling............................................................................................94
x 9.2 9.2.1
ANSYS 3-D Modeling and Analysis...........................................................95 Results and Discussion.......................................................................................98
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CONCLUSIONS ................................................................................................99
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FUTURE RECOMMENDATIONS ...............................................................100
REFERENCES.........................................................................................................101 APPENDIXE ............................................................................................................101 VITA..........................................................................................................................113
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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
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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
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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.
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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
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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.
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Steam Piping Network
Figure 1-1 PFD of the complete piping network
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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].
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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.
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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]
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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 o
coolant piping for temperatures as low as 320 F. B31.8 governs most of the pipe lines in gas transmission and distribution system up to the outlet of the customer’s meter set o
assembly. Excluded from this code with metal temperature above 450 F or below o
20 F. 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 o
exceeding 160psig or temperatures exceeding 250 F. 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]. SL =
PDo 0.75i × M A + ≤ 1.0 S h Z 4t
(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]. PDo 0.75i ( M A + M B ) + ≤ KS h Z 4t
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.
(3.2)
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3.3.3 Stresses due to thermal loadings The effects of thermal expansion must meet the following equation [1].
iM C ≤ S A + f ( Sh − S L ) 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
τ max =
(σ 1 − σ 3 ) S y = 2 2
(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 Circumferential membrane stress Longitudinal membrane stress Primary bending stress
Due to type of sustained load Pressure Pressure, Dead weight 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 Bending and Torsional Bending and Torsional
Due to type of load Thermal loading (expansion or contraction) 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.
Piping System Design
Process Design 9 Lay outing 9
9 9
Structural Design Loads Calculations
Analysis of Pipes And Expansion Loops
Support Design and Analysis
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.
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]. tm =
P × Do +A 2 × ( S × Eq + P × Y )
(4.1)
Or
tm = 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]. P=
2( S × Eq ) × t ( Do − 2Yt )
(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 =
π 4
Fluid Weight =
ρ steel × ( Do 2 − Di 2 ) ×
π 4
× ρ fluid × ( Di ) 2 ×
g gc
g gc
Insulation wt. = Insulation factor x ρInsulationx g/gc
(4.4) (4.5) (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]:
P = 0.00256 × V 2 × CD
(4.7)
And to calculate the wind dynamic load (lb/ft), the following expression is used [1]:
F = 0.000213 × V 2 × CD × D Where P = Dynamic pressure, lb/ft 2 V = basic wind speed, miles/hr
(4.8)
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) = α × L × ∆T
(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 9 Operation Based Earthquake Load 9 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 9 The pipe is considering to be a straight beam 9 Simply supported at both ends
So based on limitation of stress [2] 0.33ZS h w
(4.10)
∆EI 22.5w
(4.11)
Ls =
Based on limitation of deflection [2] Ls =
4
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) = α × L × ∆T Based on thermal expansion calculated above, size of expansion loops can be calculated from equation below as [2] L=
3EDo ∆ 144 S A
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.
(4.12)
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].
σb =
Mc I
(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]:
τ=
VAy Ib
(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] ymax =
− wl 4 8 EI
(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 =
Kl r
(5.4)
Where K = a constant dependent on boundary conditions r = least radius of gyration of the member = I
A
, 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
0〈
Short column
60〈
Intermediate column
leff r leff
120〈
Long column
r leff r
〈 60 〈120 〈300
Critical load and critical stress can be find out from the following equations [7] Pcr =
σ cr =
π 2 EI
(5.5)
Leff 2
π 2E ⎛ Leff ⎞ ⎜ r ⎟⎠ ⎝
2
(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 f fa f + bx + by ≤ 1 0.6 Fy Fbx Fby
(5.7)
Also, when fa/Fa < 0.15, following equation can be used,
f a fbx f by + + ≤1 Fa Fbx Fby
(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
NPS
No.
D o, (in)
°
TIn, C
TOut,
VIn,
Vout
Pin
C
m/sec
m/sec
(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) Pipe S. No
Line
NPS
No.
D o, (in)
°
TIn, C
°
TOut, C
VIn,
Vout
m/sec
m/sec
Pin
POut
(static)
(static),
bar
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) S. No
Pipe Line
D o,
NPS
(in)
No.
°
TIn, C
VIn,
Vout
m/sec
m/sec
°
TOut, C
Pin
POut
(static)
(static),
bar
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
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 Carbon Steel Insulation
Parameter
Value
Modulus of Elasticity ‘E’
27.5 Mpsi
Allowable stress S all
14.4 ksi
Density, ‘ρ steel’
0.283 lb/in3
Density, ‘ρ Rock wool’
0.00343lb/in3
Density, ‘ρ water’
0.0361 lb/in3
Water
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.
33 Design thickness tm =
P × Do +A 2 × ( S × Eq + 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
±12.5%
Assuming maximum limit
3 mm = 0.03937 in
data provided
Tolerance limit A
Putting all these values in above equation of minimum thickness tm =
193.3 × 8.625 + 0.03937 2 × (144000 × 1 + 193.3 × 0.4)
tm = 0.09984 In 0.0998 0.85 tm = 0.12in tm =
tm = 2.9mm
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 Pipe Nominal Size,
Out side Diameter, D (in)
Design Pressure (stat.), P (lb/In2)
Velocity, Inlet (m/sec)
Total Head,(m) H=(P/W+V^2/2*g)
Pabs(Psi)= ρ*g*H
DesignPressure (gage.), P(lb/In2)= Psat-14.7
Allowable Stresss, S(psi)
D.T. Factor (y)
Min. Wall thickness,t(in)=P*D /2*(S+.4*P)
Corrosion allowance, A (in)
Total min. Wall thickt(t), (in)
t= (t/1-T) T=12.5% (in)
t(mm)
Min.Allowable thickness (in)
Pipe Line
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
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
S.No
P-208
2
No.
1
35
Table 6-4 All pipes thickness along with standard thickness (Continued) Pipe Nominal Size,
Out side Diameter, D (in)
Design Pressure (stat.), P (lb/In2)
Velocity, Inlet (m/sec)
Total Head,(m) H=(P/W+V^2/2* g)
Pabs(Psi)= ρ*g*H
DesignPressure (gage.), P(lb/In2)= Psat-14.7
Allowable Stresss, S(psi)
D.T. Factor (y)
Min. Wall thickness,t(in)=P *D/2*(S+.4*P)
Corrosion allowance (in)
Total min. Wall thickt(t) (in)
t= (t/1-T) T=12.5% (in)
t(mm)
No.
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
Min.Allowab
Pipe Line
P-237
le thickness (in)
S.No
26
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.
P=
2( S × Eq ) × t ( Do − 2Yt )
(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
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
Do
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 2
P-208 P-209
8 2
8.625 6.625
193.31 113.69
993.877 1955.074
3
P-210 P-211 P-212 P-213 P-214 P-215
8 8 8 4 8 6
8.625 8.625 8.625 4.5 8.625 6.625
189.93 192.17 149.94 146.28 124.09 111.40
993.877 993.877 993.877 1479.188 993.877 1156.616
4 5 6 7 8
37
Table 6-6 Design and working Pressure (Continued) S.No
Pipe Line No.
9 P-216 10 P-217 11 P-218 12 P-219 13 P-220 14 P-221 15 P-224 16 P-225 17 P-226 18 P-227 19 P-228 20 P-229 21 P-230 22 P-231 23 P-232 24 P-233 25 P-236 26 P-237 27 P-238 28 P-239 29 p-240 30 P-241 31 P-242 32 P-243 33 P-244 34 P-250 35 P-251 36 P-252 37 P-253 38 P-254 39 P-256 40 P-257 41 P-259 42 P-260 43 P-261 44 P-262 45 P-263 46 P-264 47 P-270 48 P-271 NPS = Nominal Pipe Size
NPS, in 2 4 3 4 4 2 4 2 3 2 3 2 2 1 3 2 1.5 1 2 1 2 1 2 2 1 3 1 2 1.5 1 2 6 3 3 3 3 2 2 3 1
Do (in) 2.375 4.5 3.5 4.5 4.5 2.375 4.5 2.375 3.5 2.375 3.5 2.375 2.375 1.315 3.5 2.375 1.9 1.315 2.375 1.315 2.375 1.315 2.375 2.375 1.315 3.5 1.315 2.375 1.9 1.315 2.375 6.625 3.5 3.5 3.5 3.5 2.375 2.375 3.5 1.315
Pressure (gage.) psi 123.35 164.10 112.07 68.00 124.24 110.54 109.34 109.44 121.29 93.12 106.29 91.37 56.27 116.01 95.60 86.38 54.02 88.97 115.34 113.95 98.32 139.63 83.50 87.76 87.05 55.05 106.89 71.65 62.98 143.41 145.55 77.79 70.20 69.57 39.03 31.53 50.99 36.32 88.07 42.89
Allowable Pressure psi 2625.538 1479.188 1817.818 1479.188 1479.188 2625.538 1479.188 2625.538 1817.818 2625.538 1817.818 2625.538 2625.538 3503.527 1817.818 2625.538 2488.415 3503.527 2625.538 3503.527 2625.538 3503.527 2625.538 2625.538 3503.527 1817.818 3503.527 2625.538 2488.415 3503.527 2625.538 1156.616 1817.818 1817.818 1817.818 1817.818 2625.538 2625.538 1817.818 3503.527
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]. P = 0.00256 × V 2 × CD − Or To calculate the wind dynamic load (lb/ft), equation is used [1].
(4.7)
(4.8) F = 0.000213 × V 2 × CD × D 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 F = 0.000213 ×1002 × 0.6 ×11.77 = 15.05lb / 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 D o, (in)
Reynold's No. (Re)= 780*V*D
CD
Wind Load (lbs)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
P-208 P-209 P-210 P-211 P-212 P-213 P-214 P-215 P-216 P-217 P-218 P-219 P-220 P-221 P-224 P-225 P-226 P-227
262 16 394 341 361 787 16 16 98 164 16 9.8 279 230 262 197 115 525
8 2 8 8 8 4 8 6 2 4 3 4 4 2 4 2 3 2
8.625 6.625 8.625 8.625 8.625 4.5 8.625 6.625 2.375 4.5 3.5 4.5 4.5 2.375 4.5 2.375 3.5 2.375
80 50 80 80 80 65 80 80 50 65 50 65 65 50 65 50 50 50
11.77 8.59 11.77 11.77 11.77 7.06 11.77 9.77 4.34 7.06 5.47 7.06 7.06 4.34 7.06 4.34 5.47 4.34
9.18E+05 6.70E+05 9.18E+05 9.18E+05 9.18E+05 5.51E+05 9.18E+05 7.62E+05 3.39E+05 5.51E+05 4.27E+05 5.51E+05 5.51E+05 3.39E+05 5.51E+05 3.39E+05 4.27E+05 3.39E+05
0.6 0.8 0.6 0.6 0.6 0.9 0.6 0.67 1.2 1 1.1 1 1 1.2 1 1.2 1.1 1.2
3942.56 234.29 5928.89 5131.35 5432.31 10649.85 240.77 223.19 1088.00 2465.87 205.00 147.35 4194.98 2553.46 3939.38 2187.09 1473.46 5828.55
39
Table 6-7 Wind loads for each pipe (Continued) Pipe Pipe Line length NPS No. (ft) 19 P-228 82 3 20 P-229 164 2 21 P-230 164 2 22 P-231 115 1 23 P-232 246 3 24 P-233 131 2 25 P-236 98 1.5 26 P-237 66 1 27 P-238 213 2 28 P-239 197 1 29 p-240 180 2 30 P-241 262 1 31 P-242 197 2 32 P-243 262 2 33 P-244 394 1 34 P-250 6.6 3 35 P-251 328 1 36 P-252 115 2 37 P-253 66 1.5 38 P-254 197 1 39 P-256 230 2 40 P-257 33 6 41 P-259 164 3 42 P-260 39 3 43 P-261 49 3 44 P-262 16 3 45 P-263 16 2 46 P-264 49 2 47 P-270 262 3 48 P-271 33 1 NPS = Nominal Pipe Size Do = Out side Diameter of Pipe tinsul = Insulation Thickness Cd = Drag Coefficient S. No
Do (in)
tinsul , mm
3.5 2.375 2.375 1.315 3.5 2.375 1.9 1.315 2.375 1.315 2.375 1.315 2.375 2.375 1.315 3.5 1.315 2.375 1.9 1.315 2.375 6.625 3.5 3.5 3.5 3.5 2.375 2.375 3.5 1.315
50 50 50 40 50 50 50 40 50 40 50 40 50 50 40 50 40 40 50 40 50 80 50 50 50 50 50 50 50 40
Total D o, (in) 5.47 4.34 4.34 2.89 5.47 4.34 3.87 2.89 4.34 2.89 4.34 2.89 4.34 4.34 2.89 5.47 2.89 3.95 3.87 2.89 4.34 9.77 5.47 5.47 5.47 5.47 4.34 4.34 5.47 2.89
(Re)= 780*V*Do
Cd
4.27E+05 3.39E+05 3.39E+05 2.25E+05 4.27E+05 3.39E+05 3.02E+05 2.25E+05 3.39E+05 2.25E+05 3.39E+05 2.25E+05 3.39E+05 3.39E+05 2.25E+05 4.27E+05 2.25E+05 3.08E+05 3.02E+05 2.25E+05 3.39E+05 7.62E+05 4.27E+05 4.27E+05 4.27E+05 4.27E+05 3.39E+05 3.39E+05 4.27E+05 2.25E+05
1.1 1.2 1.2 1.2 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 0.8 1.1 1.1 1.1 1.1 1.2 1.2 1.1 1.2
Wind Load (lbs) 1050.64 1820.73 1820.73 849.43 3151.93 1454.36 969.01 487.50 2364.73 1455.11 1998.36 1935.22 2187.09 2908.72 2910.22 92.25 2422.72 1161.01 652.60 1455.11 2553.46 549.65 2101.28 499.70 627.82 205.00 177.63 544.00 3356.93 243.75
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].
π
Pipe weight =
4
Fluid weight =
π 4
ρ steel × ( Do 2 − Di 2 ) × × ρ fluid × ( Di ) 2 ×
g gc
(4.4)
g gc
(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.
1 2 3 4 5 6 7 8 9 10 11 12 13
P-208 P-209 P-210 P-211 P-212 P-213 P-214 P-215 P-216 P-217 P-218 P-219 P-220
L, (ft)
N P S
Insul. Thick (In)
262 16 394 341 361 787 16 16 98 164 16 9.8 279
8 2 8 8 8 4 8 6 2 4 3 4 4
3.15 1.97 3.15 3.15 3.15 2.56 3.15 3.15 1.97 2.56 1.97 2.56 2.56
XInsul
Insul. wt. (lb)
Pipe wt., (lbs)
Fluid wt.(lbs)
Total static Loads (lbs)
0.97 0.21 0.97 0.97 0.97 0.39 0.97 0.83 0.21 0.39 0.25 0.39 0.39
10.369 0.137 15.593 13.495 14.287 12.523 0.633 0.542 0.840 2.610 0.163 0.156 4.439
7450.18 58.21 11203.71 9696.61 10265.33 8456.94 454.97 302.33 356.51 1762.31 120.71 105.31 2998.08
5680.53 23.27 8542.47 7393.36 7826.99 4342.05 346.90 200.33 142.52 904.82 51.26 54.07 1539.30
13141.08 81.61 19761.78 17103.47 18106.60 12811.51 802.51 503.21 499.87 2669.74 172.14 159.53 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
14 P-221 230 2 1.97 0.21 15 P-224 262 4 2.56 0.39 16 P-225 197 2 1.97 0.21 17 P-226 115 3 1.97 0.25 18 P-227 525 2 1.97 0.21 19 P-228 82 3 1.97 0.25 20 P-229 164 2 1.97 0.21 21 P-230 164 2 1.97 0.21 22 P-231 115 1 1.57 0.1 23 P-232 246 3 1.97 0.25 24 P-233 131 2 1.97 0.21 25 P-236 98 1.5 1.97 0.21 26 P-237 66 1 1.57 0.1 27 P-238 213 2 1.97 0.21 28 P-239 197 1 1.57 0.1 29 p-240 180 2 1.97 0.21 30 P-241 262 1 1.57 0.1 31 P-242 197 2 1.97 0.21 32 P-243 262 2 1.97 0.21 33 P-244 394 1 1.57 0.1 34 P-250 6.6 3 1.97 0.25 35 P-251 328 1 1.57 0.1 36 P-252 115 2 1.57 0.21 37 P-253 66 1.5 1.97 0.21 38 P-254 197 1 1.57 0.1 39 P-256 230 2 1.97 0.21 40 P-257 33 6 3.15 0.83 41 P-259 164 3 1.97 0.25 42 P-260 39 3 1.97 0.25 43 P-261 49 3 1.97 0.25 44 P-262 16 3 1.97 0.25 45 P-263 16 2 1.97 0.21 46 P-264 49 2 1.97 0.21 47 P-270 262 3 1.97 0.25 48 P-271 33 1 1.57 0.1 NPS = Nominal Pipe Size XInsul = Insulation Factor [Appendix table A15]
Insul. wt. (lb)
Pipe wt., (lbs)
Fluid wt(lbs)
Total static Loads (lbs)
1.971 4.169 1.688 1.173 4.498 0.836 1.405 1.405 0.469 2.509 1.122 0.840 0.269 1.825 0.804 1.542 1.069 1.688 2.245 1.608 0.067 1.338 0.985 0.565 0.804 1.971 1.118 1.673 0.398 0.500 0.163 0.137 0.420 2.672 0.135
836.70 2815.40 716.66 867.62 1909.87 618.65 596.61 596.61 192.28 1855.95 476.56 265.24 110.35 774.86 329.39 619.04 438.07 716.66 953.12 658.78 49.79 548.43 418.35 178.63 329.39 836.70 623.56 1237.30 294.24 369.68 120.71 58.21 178.25 1976.66 55.18
334.49 1445.51 286.50 368.45 763.51 262.72 238.51 238.51 43.07 788.17 190.51 86.47 24.72 309.77 73.79 266.35 98.14 286.50 381.03 147.58 21.15 122.86 167.24 58.23 73.79 334.49 413.19 525.45 124.95 156.99 51.26 23.27 71.26 839.43 12.36
1173.16 4265.08 1004.84 1237.25 2677.87 882.21 836.52 836.52 235.83 2646.63 668.19 352.55 135.34 1086.45 403.98 886.94 537.28 1004.84 1336.39 807.96 71.01 672.62 586.58 237.43 403.98 1173.16 1037.87 1764.42 419.59 527.17 172.14 81.61 249.93 2818.77 67.67
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]. Ls =
0.33Z × S h w
(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 50.15 Ls = 40.72 ft Ls =
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,
Z,
w,
(ft)
In3
lb/ft
Rounded Ls, ft
N.O.S
No. of Support
Revised
max.
Ls, ft
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,
Z,
w,
(ft)
In3
lb/ft
Ls, ft
N.O.S
Rounded No.
Revised
max.
Ls, ft
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
Section NPS Modulus
(ft)
w,
3)
lb/ft
Z,( In
Stand. Ls, ft
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
Pipe
Line
length
Section NPS
modulus Z( In
3)
w, lb/ft
Stand. Ls, ft
max. Span
No.of Supports
Complete No. of
No.
(ft)
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) = α × L × ∆T
(4.9)
For Pipe No.208 L = 262 ft (From Table 6-1) o
∆T = 169.7 C (From Table 6-1) o
α = 14.9 x 10-3 mm/m C (Appendix Table A6) o
In actual case the temperature difference is 0.9 C, but for the verse condition the temperature difference is to be taken b/w operating and non-operating conditions and o
the non-operating condition is assume to be at 0 C. 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. Expansion(mm)=14.9×10-3 ×
262 × 12 ×169.7=204.16mm 39.37
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, o C
1
P-208 P-208-1 P-208-2 P-209 P-210 P-210-1 P-210-2 P-211 P-211-1 P-211-2 P-212 P-212-1 P-212-2 P-213 P-213-1 P-213-2 P-213-3
262 200 65 16 394 200 194 341 200 141 361 200 161 787 200 200 200
169.70 169.70 169.00 169.00 168.80 168.80 168.10 167.50 167.50 166.90 166.40 166.40 165.80 165.20 165.20 165.00 164.00
2 3
4
5
6
Tout , C
∆T o ( C)
(α) = (mm*10 o -3 /m C)
Deflection ∆(mm)
Deflection ∆(m)
168.80 169.20 168.80 168.30 167.50 168.10 168.00 166.30 166.90 166.50 165.20 165.80 165.50 158.30 165.00 164.00 163.00
169.70 169.70 169.00 169.00 168.80 168.80 168.10 167.50 167.50 166.90 166.40 166.40 165.80 165.20 165.20 165.00 164.00
14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9
204.16 154.18 49.90 12.28 302.12 153.36 148.14 259.47 152.18 106.90 272.88 151.18 121.26 590.61 150.09 149.91 149.00
0.20 0.15 0.05 0.01 0.30 0.15 0.15 0.26 0.15 0.11 0.27 0.15 0.12 0.59 0.15 0.15 0.15
o
48 Table 6-11 Thermal deflection for pipes complete segments (Continued) S. No
7 8 9 10 11 12 13
14
15
16 17 18
19 20 21
22 23 24 25 26 27
28 29
30
Pipe Line No.
L, ft
TIn, o C
Tout , C
∆T o ( C)
(α) = (mm*10 o -3 /m C)
Deflection ∆(mm)
Deflection ∆(m)
P-213-4 P-214 P-215 P-216 P-217 P-218 P-219 P-220 P-220-1 P-220-2 P-221 P-221-1 P-221-2 P-224 P-224-1 P-224-2 P-225 P-226 P-227 P-227-1 P-227-2 P-227-3 P-228 P-229 P-230 P-230-1 P-230-2 P-231 P-232 P-232-1 P-233 P-236 P-237 P-238 P-238-1 P-238-2 P-239 p-240 P-240-1 P-240-2 P-241 P-240-1
187 16 16 98 164 16 9.8 279 200 79 230 200 30 262 200 62 197 115 525 200 200 125 82 164 164 100 64 115 246 200 131 98 66 213 200 13 197 180 100 80 262 200
163.00 165.30 166.50 166.40 166.20 165.10 158.00 165.00 165.00 162.00 161.80 161.80 160.00 161.80 161.30 160.00 158.30 158.20 156.80 156.80 150.00 135.00 156.70 155.50 135.20 135.20 129.20 135.00 155.50 154.30 150.50 127.90 127.70 150.40 148.00 147.30 145.70 145.80 145.80 143.30 140.70 140.70
162.00 165.20 166.40 163.40 164.90 164.70 157.90 161.80 163.40 161.80 154.40 160.00 154.40 158.30 160.00 159.00 152.10 156.70 133.50 156.50 147.80 133.50 155.50 147.90 124.80 129.20 124.80 120.10 150.50 153.00 141.30 118.50 119.50 145.70 147.30 145.70 131.30 140.90 143.30 140.90 126.00 136.00
163.00 165.30 166.50 166.40 166.20 165.10 158.00 165.00 165.00 162.00 161.80 161.80 160.00 161.80 161.30 160.00 158.30 158.20 156.80 156.80 150.00 135.00 156.70 155.50 135.20 135.20 129.20 135.00 155.50 154.30 150.50 127.90 127.70 150.40 148.00 147.30 145.70 145.80 145.80 143.30 140.70 140.70
14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9
138.47 12.01 12.10 74.08 123.82 12.00 7.03 209.12 149.91 58.14 169.05 147.00 21.80 192.57 146.55 45.06 141.66 82.65 373.95 142.46 136.28 76.66 58.37 115.85 100.72 61.42 37.56 70.53 173.77 140.19 89.56 56.94 38.29 145.53 134.46 8.70 130.39 119.22 66.23 52.08 167.46 127.83
0.14 0.01 0.01 0.07 0.12 0.01 0.01 0.21 0.15 0.06 0.17 0.15 0.02 0.19 0.15 0.05 0.14 0.08 0.37 0.14 0.14 0.08 0.06 0.12 0.10 0.06 0.04 0.07 0.17 0.14 0.09 0.06 0.04 0.15 0.13 0.01 0.13 0.12 0.07 0.05 0.17 0.13
o
49 Table 6-11 Thermal deflection for pipes complete segments (Continued) S. No
Pipe Line No.
L, ft
TIn, o C
Tout , o ( C)
∆T o ( C)
(α) = (mm*10 o -3 /m C)
Deflection ∆(mm)
Deflection ∆(m)
31 32
P-242 P-243 P-243-1 P-243-2 P-244 P-244-1 P-244-2 P-250 P-251 P-251-1 P-251-2 P-252 P-253 P-254 P-256 P-256-1 P-256-2 P-257 P-259 P-260 P-261 P-262 P-263 P-264 P-270 P-270-1 P-270-2 P-271
197 262 200 62 394 200 94 6.6 328 200 128 115 66 197 230 200 30 33 164 39 49 16 16 49 262 200 62 33
140.90 131.70 131.70 117.50 131.62 131.62 100.30 160.20 159.70 159.70 139.40 159.90 153.80 153.50 156.20 156.20 153.30 153.10 142.80 140.50 119.20 136.10 129.10 120.40 157.70 157.70 153.40 157.80
131.60 114.10 122.40 114.10 95.90 120.62 95.90 159.90 122.20 145.70 122.20 153.80 147.60 133.30 150.40 153.30 150.40 152.80 137.80 139.10 117.30 135.30 127.90 116.80 152.70 155.20 152.20 152.70
140.90 131.70 131.70 117.50 131.62 131.62 100.30 160.20 159.70 159.70 139.40 159.90 153.80 153.50 156.20 156.20 153.30 153.10 142.80 140.50 119.20 136.10 129.10 120.40 157.70 157.70 153.40 157.80
14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.9
126.09 156.75 119.65 33.09 235.58 119.58 42.83 4.80 237.95 145.09 81.06 83.53 46.11 137.37 163.20 141.91 20.89 22.95 106.39 24.89 26.53 9.89 9.38 26.80 187.69 143.28 43.20 23.66
0.13 0.16 0.12 0.03 0.24 0.12 0.04 0.00 0.24 0.15 0.08 0.08 0.05 0.14 0.16 0.14 0.02 0.02 0.11 0.02 0.03 0.01 0.01 0.03 0.19 0.14 0.04 0.02
33
34 35
36 37 38 39
40 41 42 43 44 45 46 47
48
6.3.8 Expansion Loops Calculations Based on thermal expansion calculated above, size of expansion loops was calculated below as [2]. L=
3EDo ∆ 144 S A
(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) = 14.9 × 10−3 × 60.98 × 169 = 153.55mm = 6.04in
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:
3 × 27.5 × 106 × 8.625 × 6.07 144 × 21400 L = 39.47 ft L=
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
P-208 P-208-1 P-208-2 P-209
8 8 8 2
Do,(in)
L, ft
Deflection (in)
Size of expansion loop, ft
Width of expansion Loop (ft)
Height of expansion loop(ft)
8.625 8.625 8.625 2
265 200 65 16
8.04 6.07 1.96 0.48
45.44 39.47 22.46 5.85
9 8 4 1
18 16 9 2
51 Table 6-12 Sizing of expansion loops (Continued) Pipe Line No.
NPS, D in
P-210 P-210-1 P-210-2 P-211 P-211-1 P-211-2 P-212 P-212-1 P-212-2 P-213 P-213-1 P-213-2 P-213-3 P-213-4 P-214 P-215 P-216 P-217 P-218 P-219 P-220 P-220-1 P-220-2 P-221 P-221-1 P-221-2 P-224 P-224-1 P-224-2 P-225 P-226 P-227 P-227-1 P-227-2 P-227-3 P-228 P-229 P-230 P-230-1 P-230-2 P-231 P-232 P-232-1 P-233
8 8 8 8 8 8 8 8 8 4 4 4 4 4 8 6 2 4 3 4 4 4 4 2 2 2 4 4 4 2 3 2 2 2 2 3 2 2 2 2 1 3 3 2
Do,(in)
L, ft
Deflection (in)
Size of expansion loop, ft
Width of expansion Loop (ft)
Height of expansion loop(ft)
8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 4.5 4.5 4.5 4.5 4.5 8.625 6.63 2.38 4.5 3.5 4.5 4.5 4.5 4.5 2.375 2.375 2.375 4.5 4.5 4.5 2.375 3.5 2.375 2.375 2.375 2.375 3.5 2.375 2.375 2.375 2.375 1.32 3.5 3.5 2.375
394 200 194 341 200 141 361 200 161 787 200 200 200 187 16 16 98 164 16 9.8 279 200 79 230 200 30 262 200 62 197 115 525 200 200 125 82 164 164 100 64 115 246 200 131
11.89 6.04 5.83 10.22 5.99 4.21 10.74 5.95 4.77 23.25 5.91 5.90 5.87 5.45 0.47 0.48 2.92 4.87 0.47 0.28 8.23 5.90 2.29 6.66 5.79 0.86 7.58 5.77 1.77 5.58 3.25 14.72 5.61 5.37 3.02 2.30 4.56 3.97 2.42 1.48 2.78 6.84 5.52 3.53
55.26 39.37 38.69 51.21 39.22 32.87 52.51 39.09 35.01 55.80 28.13 28.11 28.03 27.02 11.02 9.70 14.37 25.55 7.02 6.09 33.21 28.11 17.51 21.69 20.23 7.79 31.87 27.80 15.41 19.86 18.41 32.26 19.91 19.47 14.61 15.47 17.96 16.74 13.07 10.22 10.44 26.70 23.98 15.79
11 8 8 10 8 7 11 8 7 11 6 6 6 5 2 2 3 5 1 1 7 6 4 4 4 2 6 6 3 4 4 6 4 4 3 3 4 3 3 2 2 5 5 3
22 16 15 20 16 13 21 16 14 22 11 11 11 11 4 4 6 10 3 2 13 11 7 9 8 3 13 11 6 8 7 13 8 8 6 6 7 7 5 4 4 11 10 6
52
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)
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 o
0
Taking θ = 90 (b/c at lower and upper ends of expansion loops the bends are at 90 ) 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].
∑F
x
= P1 A1 − P2 A2 cos θ − ( FB ) x = m × (V2 − V1 ) F
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
9.33 lbf/sec
Provided
7.981 in
Table 6-1
0.0361 lb/in3
Appendix Table A-14
Mass flow rate, m Diameter of pipie, D1 = D2 Density of Water, ρwater
(6.4)
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: ( FB ) x = P1 A1 + m × V1 F
( FB ) x = 193.3 × 50 + 9.33 × 116 ×12 F
( FB ) x = 12.994kips F
Similarly finding the force in x- direction, using impulse momentum equation below [8],
∑F
y
= P1 A1 sin θ − P2 A2 + ( FB ) y = m × (V2 − V1 sin θ ) F
(6.5)
As V1 = V2 and P1A1 sin (θ) = 0, therefore the above equation become: ( FB ) y = P2 A2 F
( FB ) y = 14.7 × 50.03 F
( FB ) y = 735.44lb F
( FB ) = ( FB ) x 2 + ( FB ) y 2 F
Resultant force
F
F
( FB ) = (12994) 2 + (735.44) 2 F
( FB ) = 13.014kips F
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; P2 = P1 − ( Z1 − Z 2 ) × ρ
g gc
(6.6)
Table 6-14 Input data
Parameter Value V1 = V2 = V 116 ft/sec g 32.17 ft/sec2 gc 32.17 lbm-ft/lbf-sec2
Z1 – Z2 P1
Reference/ Reason From Table 6-1 Acceleration due to gravity Gravitational constant
12 ft
Height of an expansion loop for the first bend
193.3 psi
From Table 6-1
55 Using Equation (6.6) and obtaining the value of pressure at outlet of the expansion loop. P2 = 193.3 − 12 × 0.0361 ×
32.17 32.17
P2 = 192.868 psi
Using Equation (6.4) for force in x-direction,
∑F
x
= P1 A1 − P2 A2 cos θ − ( FB ) x = m × (V2 − V1 ) F
(6.4)
As V1 = V2, and P2A2cosθ = 0 as θ = 900, so the above equation becomes
( FB ) x = P1 × A1 F
( FB ) x = 9.67lb F
Using Equation (6.5) for force in y- direction
∑F
y
= P1 A1 sin θ − P2 A2 + ( FB ) y = m × (V2 − V1 sin θ ) F
(6.5)
As V1 = V2 and P1A1 sin (θ) = 0, for θ = 0o therefore the above equation becomes:
( FB ) y = P2 × A2 F
( FB ) y = 9.643lb F
The resultant force comes out be ( FB ) = ( FB ) x 2 + ( FB ) y 2 F
F
F
( FB ) = (9.67) 2 + (9.643) 2 F
( FB ) = 13.65lb F
θ = 450 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) Expansion rate (co-efficient)( α)
27.5 x 106 psi 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
F =
12 × E × I × ∆ L3
(7.1)
57 M =
Moment:
6× E× I× ∆ L2
(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]: ∆n =
Ln 3∆ T ΣL i 3
(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
Length of
Direction of
Magnitude of
Resisting
section (ft)
expansion
expansion
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
Segment
For Vertical Section of pipe Table 7-3 Vertical section magnitude of expansion and direction
Segment F-G
Length of
Direction of
Magnitude of
Resisting
section (ft)
expansion
expansion
segments
16
Y
0.361in
A-F
Thermal stress developed at on Anchor support A [2]
σ t = E × α × ∆T
(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
σ T = 27.5 × 106 × 14.4 × 10−6 × 169 σ T = 69.25Ksi ∆x absorbed by leg F-G, using Equation (7.3) ∆n = Ln3∆T/ΣLi3 Ln = LFG = 16 ft (From Table 7.2)
(7.3)
59 Li = 16 ft, ∆T = 2.17 in (From Table 7-2) 163 × 2.17 163 ∆x = 2.17in ∆x =
Fx across F-G by using Equation (7.1) Fx=
12EI∆ L3
(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 12×27.5×106 ×72.5×2.17 (16×12)3 Fx=7335lb Fx=
∆y absorbed by leg A-F using equation (7.3)
Ln = LAF = 96 ft Li = 96 ft, ∆T = 0.3616 in 963 × 0.3616 963 ∆y = 0.3616in ∆y =
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 F =
12 × E × I × ∆ L3
(7.1)
12×27.5×106 ×72.5×.3616 (96×12)3 Fy=5.65lb Fy=
Moment about Z-axis by using Equation (7.2) Mz=
6EI∆ L2
(7.2)
6×27.5×106 ×72.5×0.3616 (96×12) 2 Mz=3259.5lb-in Mz=
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 ∆y, A − B = 0.0837in ∆y, A − B =
Force and thermal moment in section AB using Equation (7.1) and (7.2) 12×27.5×106 ×72.5×0.0837 266.643 Fy,A-B =105.633lb Fy,A-B =
Mz,A-B =14.083×103 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 (∆y,total ) = 0.3616 in LAC = 44.44 ft
(7.3)
61 LAF = 96 ft 0.36166 × 44.44 96 = 0.167in
∆y, B −C = ∆y, B −C
For force in section B-C using Equation (7.1) F =
12 × E × I × ∆ L3
(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 12×27.5×106 ×72.5×0.167 266.643 Fy,B-C =210.76lb Fy,B-C =
For thermal moment in section B-C using Equation (7.2) M =
6× E× I× ∆ L2
(7.2)
Mz,B-C =28.098×103 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 ∆y,C − D = 0.251in
∆y,C − D =
For force in section C-D using Equation (7.1) F =
12 × E × I × ∆ L3
Modulus of Elasticity (E) = 27.5 x 106 psi Moment of Inertia (I) = 72.5 in4
(7.1)
62 L = 22.22 ft = 266.64 in 12×27.5×106 ×72.5×0.251 266.643 Fy,C-D =316.78lb Fy,C-D =
For thermal moment in section C-D using Equation (7.2) M =
6× E× I× ∆ L2
(7.2)
Mz,C-D =42.232×103 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 0.3616×88.88 96 ∆y,D-E =0.3348in ∆y,D-E =
For force in section C-D using Equation (7.1) F =
12 × E × I × ∆ L3
Modulus of Elasticity (E) = 27.5 x 106 psi Moment of Inertia (I) = 72.5 in4 L = 22.22 ft = 266.64 in 12×27.5×106 ×72.5×0.3348 Fy,D-E = 266.643 Fy,D-E =421.71lb For thermal moment in section C-D using Equation (7.2) M =
6× E× I× ∆ L2
Mz,D-E =56.2×103 lb-in For section E-F
(7.2)
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 = 0.3616in
∆y, E − F = ∆y, E − F
And similarly using Equation (7.1) for force in section E-F and Equation (7.2) for thermal moment 12×27.5×106 ×72.5×0.3616 266.643 Fy,E-F =455.6lb Fy,E-F =
Mz,E-F =60.74×103 lb-in
Vertical force on support A, B, C, D and E Fy,A =105.633lb Fy,B =Fy,A +
Mz AB Mz BC + L AB L BC
Fy,B =105.633+
(7.5)
14082 28098 + 266.64 266.64
Fy,B =264.62lb
Similarly using Equation (7.5) for supports C, D, and E in the same way as above, Fy,C =210.76+
28098 42232 + 266.64 266.64
Fy,C =474.52lb
Fy,D =421.52+
42232 56200 + 266.64 266.64
Fy,D =792.26lb 56200 60740 + 266.64 266.64 Fy,E =895.78lb Fy,E =455.6+
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 16 3 × 2.17 in 16 3 = 2.17 in
∆x across AF =
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 ∆x, A− B = 0.50in ∆x, A− B =
For force in section A-B using Equation (7.1) F =
12 × E × I × ∆ L3
(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 12×27.5×106 ×72.5×2.17 . 266.643 Fx,A-B =631lb Fx,A-B =
Thermal expansion produced in section B-C using Equation (7.3) ∆x, (B-C) = (∆y,total x LAC )/LAF (∆y,total ) = 0.3616 in LAC = 44.44 ft
(7.3)
65 LAF = 96 ft For Section B-C
2.17 × 44.44 96 = 1.004in
∆x, B −C = ∆x, B −C
For force in section B-C using Equation (7.1) F =
12 × E × I × ∆ L3
(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 12×27.5×10 6 ×72.5×1.004 266.64 3 Fx, B-C =1267lb Fx, B-C =
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 ∆x,C − D = 1.5in ∆x,C − D =
For force in section C-D using equation given below F =
12 × E × I × ∆ L3
(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 12×27.5×106 ×72.5×1.5 266.643 Fx,C-D =1893lb Fx,C-D =
And similarly for section D-E and E-F using Equation (7.1) for force and Equation (7.3) for thermal expansion
66 2.17×88.88 96 ∆x,D-E =2.00in ∆x,D-E = For section D-E
12×27.5×106 ×72.5×2 266.643 Fx,D-E =2524.1lb Fx,D-E =
2.17×96 96 ∆x,E-F =2.17in ∆x,E-F =
For section D-E
12×27.5×106 ×72.5×2.17 266.643 Fx,E-F =2738.645lb Fx,E-F =
Axial forces on every support A, B, C, D, and E separately are:
Fx, A = 631lb (From above calculation) For every support in the middle of other support following equation is used [3]. Fx,B =
( FA-B +FB-C )
(7.6)
2
Fx,B =(631+1267)/2=949lb And similarly for support C, D and E using Equation (7.6) Fx,C =(1267+1893)/2=1580lb Fx,D =(1893+2524.1)/2=2208.5lb Fx,E =(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].
iM C ≤ S A + f (Sh − SL ) Z
(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
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
1
Appendix Table A13
f
i
Equation (7.7), after putting values from above table gives the following comparison; 1 × 60740 ≤ 21400 + 1 × (14400 − 1297.098) 16.8 4.032 × 103 ≤ 34.502 × 103 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
w( x) = − M 0 〈 x〉 −2 + R0 〈 x〉 −1 − w〈 x〉 0 − R1 〈 x − a〉 −1 − M 1 〈 x − L〉 −2 V ( x) = − M 0 〈 x〉 −1 + R0 〈 x〉 0 − w〈 x〉1 − R1 〈 x − a〉 0 − M 1 〈 x − L〉 −1
(7.8)
M ( x) = − M 0 〈 x〉 0 + R0 〈 x〉1 − w〈 x〉 2 − R1 〈 x − a〉1 − M 1 〈 x − L〉 0
Integrating the moment equation twice and putting boundary conditions we get
EIy ( x) = −
M 0 〈 x〉 2 R0 〈 x〉 3 w〈 x〉 4 + − =0 2 6 24
(7.9)
As for segment AB, x = L1 = 266.64 in
M 0 〈l1 〉 2 R0 〈l1 〉 3 w〈l1 〉 4 − + − =0 2 6 24 −35548.44M 0 + 3159545.774 R0 − 877634043.8 = 0
(7.10)
For Segment B-C
Figure 7-5 Segment A-B-C
EIy (l2 ) = − M 0 〈l2 〉 2 +
R0 〈l2 〉 3 R1 〈l2 − l1 〉 3 w〈l2 〉 4 + − =0 6 6 24
−142193.78M 0 + 252766366.2 R0 + 3159545.78 R1 − 1.404e10 = 0 (7.11)
70 Similarly for segment C-D
EIy (l3 ) = − M 0 〈l3 〉 2 +
R0 〈l3 〉 3 R1 〈l3 − l1 〉 3 R2 〈l3 − l2 〉 3 w〈l3 〉 4 + − =0 6 6 6 24
−320000M 0 + 85333333.33R0 + 25287743.4 R1 + 3159545.78 R2 − 7.11e11 = 0
(7.12)
For segment D-E
EIy (l4 ) = − M 0 〈l4 〉 2 +
R0 〈l4 〉 3 R1 〈l4 − l1 〉 3 R2 〈l4 − l2 〉 3 R3 〈 L4 − l3 〉 3 w〈l4 〉 4 + + − =0 6 6 6 6 24
−568775.12 M 0 + 202210929.5 R0 + 85307735.9 R1 + 252776366.2 R2 +
(7.13)
3156702.75 R3 − 2.246e11 = 0
Now taking summation of moment at left end of right end support M 0 + R0 l4 + R1 (l4 − l1 ) + R2 (l4 − l2 ) + R3 (l4 − l3 ) − wl1 (l4 − a ) − w(l2 − l1 )(l4 − b) − w(l3 − l2 )(l4 − c) − w(l4 − l3 )(l4 − d ) − w
x2 − P× x = 0 2
M 0 + 1066.56 R0 + 800 R1 + 533.28 R2 + 266.64 R3 − 2369952.574 = 0
(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
R0 + R1 + R2 + R3 + R4 = wL + 800
(7.15)
R4 = 1591 lb Plotting shear force and bending moment diagram for the beam solved above
0
267
507
747
987
Pipe Length
Figure 7-6 Shear Force Diagram
1118
800 600 400 200 0 -200 -400 -600 -800
Shear Force
Shear Force Diagram
71
Bending Moment Daigram 10000 0 0
267
507
747
987
1118
-10000 -20000 -30000
Bending Moment
20000
-40000
Pipe length
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].
SL =
PDo 0.75i × M A + ≤ 1.0S h 4t 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 Sh i
32700in.lb Mmax at x = 800 in (above calculation) 14400ps
Appendix Table A1
1
Appendix Table A13
72
Equation (7.16) become;
193.7 × 8.625 0.75 × 1 × 32700 + ≤ 1.0 × 14400 4 × 0.322 16.8 2756.92 ≤ 14400 2.75 × 103 ≤ 14.4 × 103
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].
S = 0.75 × i × 12 × (
WL2 × (1.5G ) 8× 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)
C=
1 =0.12 15 T
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) V = 1×1×1.5 × 0.12 ×1.5 × 10000 V = 2700lb
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].
PDo 0.75i ( M A + M B ) + ≤ KSh 4t 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; 193.7 × 8.625 0.75 × 1× (32700 + 108.482 × 16.8) + ≤ 1.2 × 14400 4 × 0.322 16.8 2.838 × 103 ≤ 17.280 × 103 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
Vertical static load
Value, lb
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=wxL
(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) 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
(8.5)
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
Diameter(D), in
Value
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].
λc =
Fy kl × r E
(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,
λc =
2 × 3.28 36 × 103 × 1.51 29 × 106
λc = 0.487 ≤ 1.15 If the critical load factor is less than 1.15, then Equation (8.8) can be used to calculate the critical force [7].
(
2
)
Fcr = 0.658λc × Fy
(8.8)
Fcr = 35.598kips Pallowable = φ × Pn = φ × Fcr × A
(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) Pallowable = 0.85 × 32.598 × 3.17 Pallowable = 87.835kips 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 ⎛ fa ⎜ ⎝ Fa
⎞ ⎛ fb ⎞ ⎟ + ⎜ ⎟ 〈1.0 ⎠ ⎝ Fb ⎠
(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 MC I
fb =
(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 7.32 fb = 7.48ksi fb =
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) 〈1.0 0.2459〈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,
∑F
y
=0
(8.12)
86 Ry = Fy Ry = 585.74
(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]. y=
Fl 3 3EI
(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
29 x 106 psi Appendix Table A2
E
Using Equation (8.13), deflection in column comes out to be; 3714 × (3.28 × 12)3 3 × 29 × 106 × 7.23 y = 0.306in y=
For combined axial and bending stress [7]:
σ max =
P LC + ( Feq ) A I
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
(8.14)
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.
σ max = 184.7 + 11492.647 σ max = 11.677kips
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], Bearing − pressure = ±
(
M BN 2
6
(8.15)
)
Where M = Bending moment = 24.36 kips-in (From above calculations) B = N = Sided of the plate = 15 inch ±
(
M BN 2
=±
6
24.38 ×12 = ±0.519kips 15 ×152 6
) (
)
{Bearing pressure due to + {Bearing pressure Concentric load} 2.768
due to moment} +
519.0
-
519.0
pressure of concrete} <
1050 1050
< -517.07
Thus the plate area is satisfactory
{Allowable bearing
< 522.3
2.768
<
<
1050 1050
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]. tp = 2×l ×
fp
(8.16)
Fy
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: N − Do 15 − 4.5 = = 5.25in 2 2 B − Do 15 − 4.5 n= = = 5.25in 2 2 m=
Therefore l = 5.25 in and putting all the values in the above Equation (8.16):
t p = 2 × 5.25 × 2.61
36000
t p = 0.09in
8.5.3 Thickness due to bending moment The bearing pressure at a distance m = 5.25 in 5.25 × 522.3 15 = 182.8 psi
f p) m = f p) m
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=σxZ
(8.17)
Taking the section modulus and bearing pressure of the two sections, Equation (8.17) becomes, fp ⎤ ⎡ f p) M = B × m 2 ⎢ m1 + ⎥ 3⎦ ⎣ 6 ⎡ 339.5 522.3 ⎤ + M = 15 × 5.252 ⎢ 3 ⎥⎦ ⎣ 6 M = 39.37in − kips The thickness required to resist this moment [7]: tp =
6× M B × σ all
(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 × 39.37 15 × 27 t p = 1.18in tp =
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 1 15 × 15 × 1 in 4 The total force on base plate and then force per bolt; 24.36 M = = 29.98kips d 9.75 12 Force = 29.98 = 7.5kips 4 Bolt F=
Allowable stress for bolts = 21ksi Nominal area of bolt = 7.5/21 = 0.357 in2 Diameter of bolt
D =
4 × 0.357
π = 0.68 in
D ≈ 0.75 in
And Bolt length by using bearing stress equation [7]. L=
F
bolt D ×π ×σ
using value of force and diameter of bolts as calculated
(8.19)
93 7.5 × 103
bolt 0.75 × π × 160 L = 19.89in L=
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 15 × 15 × 1
Base plate size Distances of column from edges, m = n Bolt diameter of anchor rod, D
1 in 4
5.25 in 0.75 in = 3/4 in
Hole diameter
1
5 = 1 .6 2 5 in 8
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
Width across plate, in
Height, in
Thread length,
(D)
(F)
(H)
in
3/4
1¼
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.
9200 Von Mises Stresses
9000 8800 8600 8400 8200 8000 7800 0
10000
20000
30000
40000
Num ber of Elem ents
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 A36
A325 Rock Wool Carbon Steel Water
Parameters
Value
Modulus of Elasticity Yield strength Allowable Stress Density Yield strength Bearing Strength Design Factor Tensile Strength Density Density Density
29 Mpsi 36 ksi 21 ksi 0.284 lb/in3 92 ksi 160 psi 0.75 120 ksi 0.003434 lb/in3 0.284 lb/in3 0.0361 lb/in3
Table A-15 Insulation factor (inch)
NPS, (in)/ Insul. Thickness(in) 1 2 3
1
1-1/2
2
3
4
5
6
8
0.057 0.16 0.23
0.066 0.21 0.29
0.08 0.21 0.37
0.1 0.25 0.44
0.21 0.3 0.51
0.15 0.34 0.58
0.3 0.38 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.
