PLTB Gas - Technical Toolboxesttoolboxes.com/documents/brochures/PLTB_Gas_Help_2014.pdf · PLTB Gas...
Transcript of PLTB Gas - Technical Toolboxesttoolboxes.com/documents/brochures/PLTB_Gas_Help_2014.pdf · PLTB Gas...
PLTB Gas
iii
Table of Contents
How to Export or Save Reports in Other Applications? ................................................................. 1
How to Export Report in Adobe Acrobat? ................................................................................. 1
How to Export Report to Microsoft Word? ................................................................................ 4
How to Export Report in Microsoft Outlook Express? .............................................................. 6
Gas Properties Calculations ............................................................................................................ 9
Gas Mixture Properties Calculations .......................................................................................... 9
Pipeline Facilities .......................................................................................................................... 11
Orifice Meters ........................................................................................................................... 12
Relief Valves: Reaction Force in an Open Discharge System .................................................. 19
Pipeline Compressors.................................................................................................................... 23
Centrifugal Compressor - Adiabatic Head ................................................................................ 23
Centrifugal Compressor - Required Adiabatic Horsepower ..................................................... 25
Centrifugal Compressor - Required Polytropic Horsepower .................................................... 27
Centrifugal Compressor - Fan Laws ......................................................................................... 29
Reciprocating Compressors - Capacity and Horsepower ......................................................... 30
Discharge Temperature ............................................................................................................. 33
Compressor Station Piping - Diameter and Gas Velocity ........................................................ 34
Local Atmospheric Pressure ..................................................................................................... 35
Accidental Gas Releases and Pipeline Rupture ............................................................................ 37
Accidental Gas Release through a Small Hole from Pressurized Gas Pipeline ........................ 37
Accidental Gas Release Rate from a Full-Bore Pipeline Rupture ............................................ 40
Natural Gas Pipeline Rupture - Depth, Radius, & Width of Crater .......................................... 43
PLTB Gas
iv
Gas Pipeline Hydraulics ................................................................................................................ 47
Steel Pipe - Design & Stress Analysis .......................................................................................... 57
Restrained Gas Pipeline - Stress Analysis ................................................................................ 59
Unrestrained Gas Pipeline Stress Analysis - Steel Pipe............................................................ 61
Flume Design ............................................................................................................................ 67
Natural Gas Pipeline Rupture - Depth, Radius, & Width of Crater .......................................... 79
Maximum Impact Load and Penetration Depth ........................................................................ 82
Pipeline Anchor Force Analysis ............................................................................................... 84
API - 1117 Movement of In-Service Pipelines ......................................................................... 86
Pipe Requirements for Horizontally Drilled Installation .......................................................... 90
Buoyancy Analysis and Concrete Coating Thickness .............................................................. 92
Buoyancy Analysis and Concrete Weights Spacing ................................................................. 94
Steel Pipeline Crossings .............................................................................................................. 105
API 1102 - PC PISCES ........................................................................................................... 105
Wheel Load Analysis .............................................................................................................. 123
Track Load Analysis ............................................................................................................... 130
Design of Uncased Pipeline Crossings ................................................................................... 137
Pipeline Testing & Miscellaneous .............................................................................................. 139
API 1104 - Appendix A: Weld Imperfection Assessment ...................................................... 139
API 1104 - Appendix A: Weld Imperfection Assessment ...................................................... 140
NiSource Blowdown Calculations .......................................................................................... 142
Pipeline Corrosion ...................................................................................................................... 147
Cathodic Protection ..................................................................................................................... 155
Table of Contents
v
Cathodic Protection Attenuation Calculation ......................................................................... 162
Polyethylene Pipe Design and Pipeline Crossings...................................................................... 165
Dead Load on PE Pipe - Prism, Marston and Combined Load .............................................. 165
Spangler's Modified Iowa Formula for PE Pipe ..................................................................... 167
Modulus of Soil Reaction (E') - Average Values for Iowa Formula ...................................... 168
Modulus of Soil Reaction (E') - Values of E' for Pipe Embedment ....................................... 169
Values of E'n Native Soil Modules of Soil Reaction .............................................................. 170
Soil Support Factor (Fs) .......................................................................................................... 171
Pipe Wall Compressive Stress (PE Pipe Crushing) ................................................................ 172
Distributed Static Surcharge Load Directly over Buried PE Pipe .......................................... 173
Distributed Static Surcharge Load not over Buried PE Pipe .................................................. 177
Live Load: Aircraft Load on Buried PE Pipe ......................................................................... 181
Index ........................................................................................................................................... 185
1
How to Export or Save Reports in Other
Applications?
How to Export Report in Adobe Acrobat?
Requirements: In order to export report to Adobe Acrobat, version 5.0 or 6.0 of Adobe
Acrobat must be installed on your computer.
1. On the report toolbar
select and click on the “Print…” button.
2. On the printer selection screen select Adobe PDF (or Adobe Distiller) and click
“Print” button
PLTB Gas
2
3. After you click “Print” button you will be prompted to save the file. Select the
directory/folder, rename the file and click “Save” button.
How to Export or Save Reports in Other Applications?
3
Technical Toolboxes, Inc.
PLTB Gas
4
How to Export Report to Microsoft Word?
Requirements: In order to export report to Microsoft Word or any other COM application
such as Visio, the application must be installed on your computer.
1. On the report toolbar
select and click on the “Copy” button.
2. Minimize application, open MS Word select “Edit” and then click “Paste”
Note: If report has more then one page, report should be exported page by page, to scroll
through pages use following
How to Export or Save Reports in Other Applications?
5
buttons on the report toolbar.
The imported report may need some additional editing.
Technical Toolboxes, Inc.
PLTB Gas
6
How to Export Report in Microsoft Outlook Express?
Requirements: In order to export report to your email client such as Microsoft Outlook
Express, the email software must be installed on your computer.
1. On the report toolbar
select and click on the “Copy” button.
2. Minimize application, open MS Outlook Express (or any other email client) select
“Edit” and then click “Paste”
How to Export or Save Reports in Other Applications?
7
Note: If report has more then one page, report should be exported page by page, to scroll
through pages use following
buttons on the report toolbar.
The imported report may need some additional editing.
Technical Toolboxes, Inc.
9
Gas Properties Calculations
Gas Mixture Properties Calculations
This module is based on the calculation procedures contained in the following documents:
- GPA Standard 2172, " Calculation of Gross Heating Value, Relative Density and
Compressibility Factor for Natural Gas Mixtures from Compositional Analysis."
- A.G.A . Transmission Measurement Committee Report No. 8
- API MPMS 14.2
Technical Toolboxes, Inc.
11
Pipeline Facilities
Regulator Station Sizing
Sizing of regulator is performed using Universal Gas Equation :
1. For Subsonic Flow
2. For Sonic Flow equation is reduced to:
Technical Toolboxes, Inc.
12
Orifice Meters
This module is developed in accordance with A.G.A. "Orifice Metering of Natural Gas and
Other Related Hydrocarbons "( A.G.A. Report No. 3 ). The results of the calculations fully
comply required number precision and rounding.
Technical Toolboxes, Inc.
Pipeline Facilities
13
Hot Tap Sizing
Scope:
When a compressible fluid, such as natural gas or air, is passed through an orifice, the rate of
flow is determined by the area of the orifice opening; the absolute upstream pressure is P1; and
the absolute downstream pressure is P2: unless the ratio P2/P1 equals or is less than the critical
ratio. When P2/P1 equals or is less than the critical ratio downstream pressure no longer effects
rate of flow through the orifice, and flow velocity at the vene contracta is equal to the speed of
sound in that fluid under that set of condition. This is commonly referred to as critical or sonic
flow. Orifice equations are therefore classified as "sonic" or "subsonic" equations.
1. 0 Critical Ratio-The equations for the critical ratio of a compressible gas is based on
P1 and the ratio, k of the specific heats of the gas for constant pressure, , and
constant volume .(See Table I for values of k.)
For natural gas this ratio is 0.55.
2. 0 Subsonic Orifice Flow Equation-Subsonic flow conditions exist where
.
M = 28.964 G
3. 0 Sonic Orifice Flow Equation-Sonic flow conditions exist where
14
These flow graphs are to be used as an aide in selecting the size and number of taps necessary to
flow a given amount of gas as various pressure drops across a hot tap opening. Under normal
circumstances, a pressure drop of approximately 1 psi across the top is ideal. Pipeline pressure or
size limitations may not allow a drop of 1 psi across the hot tap. The flow charts will provide the
amount of flow possible given the actual pressure drop up to and including 8 psi.
There are certain parameters which must be met in order to obtain accurate results from these
graphs. For a hot tap opening, the orifice is in a curved surface (the side of the pipeline being
tapped) and flow through the orifice enters the pipeline flow perpendicularly. The orifice
coefficient decreases the calculated flow value to adjust for this geometry. To calculate flow
through an orifice with geometry that differs from a hot tap, the orifice coefficient should be
adjusted to reflect the differing geometry. If the pipeline pressure varies substantially from 800
psig, the orifice flow equation (utilizing the actual pipeline pressure) should be used to determine
the flow volume. In special circumstances, when much larger pressure drops across the orifice
are encountered (P2< .55 P1), sonic flow formulations must be used to determine the flow
volume. For more detailed explanation of the orifice flow equation, foe both sonic and subsonic
flow, reference the Onshore Pipeline design Catalog of TI-59 software and the Design Procedure
Manual.
Where: A = Orifice area, square inches
Qm = Flow, standard cubic ft. per minute
M = Molecular weight of flowing gas
T = Inlet temperature,
K = Orifice coefficient, use
Z = Compressibility factor for inlet conditions,
(see AGA Report NO. 3 for Fpv.)
Technical Toolboxes, Inc.
Pipeline Facilities
15
Relief Valve: Sizing for Gas or Vapor Relief
CRITICAL FLOW BEHAVIOR
If a compressible gas is expanded across a nozzle, an orifice, or the end of a pipe, its velocity and
specific volume increase with decreasing downstream pressure. For a given set of upstream
conditions (using the example of a nozzle), the mass rate of flow through the nozzle will increase
until a limiting velocity is reached in the throat .It can be shown that the limiting velocity is the
velocity of sound in the flowing media at that location. The flow rate that corresponds to the
limiting velocity is known as the critical flow rate.
The absolute pressure ratio of the pressure in the throat at sonic velocity to the inlet
pressure is called critical pressure ratio. is known as the critical flow pressure.
Under critical flow conditions, the actual pressure in the throat cannot fall below the critical flow
pressure even if a much lower pressure exists downstream. At critical flow, the expansion from
throat pressure to downstream pressure takes place irreversibly with energy dissipated in
turbulence into the surrounding fluid.
The critical flow pressure ratio in absolute units may be estimated using the ideal gas
relationship in Equation 1:
(1)
Where:
The sizing equations for pressure relief valves in vapor or gas service fall into two general
categories depending on whether the flow is critical or subcritical. If the pressure downstream of
the throat is less than or equal to the critical flow pressure, , then critical flow will occur, and
the procedures in SIZING FOR CRITICAL FLOW should be applied. If the downstream
pressure exceeds the critical pressure, , then subcritical flow will occur, and procedure in
SIZING FOR SUBCRITICAL FLOW SHOULD BE APPLIED.
SIZING FOR CRITICAL FLOW
General
Pressure relief valves in gas or vapor service that operate under critical flow conditions may be
sized using Equations 2-4. Each of the equations may be used to calculate the effective discharge
area, A, required to achieve a required flow rate through a pressure relief valve. A valve that has
an effective discharge area equal to or greater than the calculated value of A is then chosen for
the application.
16
Where:
A = required effective discharge area of the valve, in square inches.
W = required flow through the valve, in pounds per hour.
C = coefficient determined from an expression of the ratio of the specific heats of the
gas or vapor at standard conditions. This can be obtained from Figure 26 or Table 9.
Note: See for applications that involve superimposed back pressure of a magnitude that will
cause critical flow.
T = relieving temperature of the inlet gas or vapor, in degrees Rankine
(degrees Fahrenheit + 460).
Z = compressibility factor for the deviation of the actual gas from a perfect gas,
a ratio evaluated at inlet conditions.
M = molecular weight of the gas or vapor. Various handbooks carry tables
of molecular weights of materials, but the composition of the flowing
gas or vapor is seldom the same as that listed in tables. This value should be
obtained from the process data. Table 8 lists values for same common fluids.
V = required flow through the valve, in standard cubic feet per minute at 14. 7
pounds per square inch absolute and .
G = specific gravity of gas referred to air = 1.00 for air at 14.7 pounds per square
inch absolute and .
The value of the coefficient C can be evaluated from the expression of the ratio of the specific
heats of the gas or vapor.
The ratio of specific heats of any ideal gas and possibly the ratio of specific heats of a diatomic
actual gas can be found in any acceptable reference work.
When k cannot be determined, it is suggested that C = 315.
SIZING FOR SUBCRITICAL FLOW: GAS OR
VAPOR OTHER THAN STEAM
General
Pipeline Facilities
17
When the ratio of back pressure to inlet pressure exceeds the critical pressure ratio , the
flow through the pressure relief valve is subcritical . Equation 5 - 7 may be used to calculate the
required effective discharge area for a conventional relief valve that has its spring setting
adjusted to compensate for superimposed back pressure and for sizing a pilot-operated relief
valve.
Note: Balanced-bellows relief valves that operate in the subcritical region should be sized using
Equations 2-4. The back pressure correction factor for this application should be obtain from the
valve manufacturer.
Where:
A = required effective discharge area of the valve, in square inches.
W = required flow through the valve, in pounds per hour.
=
k = ratio of the specific heats.
r = ratio of back pressure to upstream relieving pressure, .
Z = compressibility factor for the deviation of the actual gas from a perfect gas,
a ratio evaluated at inlet conditions.
T = relieving temperature of the inlet gas or vapor, in degrees Rankine (degrees
Fahrenheit + 460).
M = molecular weight of the gas or vapor. Various handbooks carry tables of
molecular weights of materials, but the composition of the flowing gas or vapor is
seldom the same as that listed in tables.
V = required flow through the valve, in standard cubic feet per minute at 14.7 pounds
per square inch absolute and .
G = specific gravity of gas referred to air = 1.00 for air at 14.7 pounds per square inch
absolute and .
References:
ASME - Boiler and Pressure Vessel Code, Section VIII
18
API Recommended Practice 520, Sixth Edition
Technical Toolboxes, Inc.
Pipeline Facilities
19
Relief Valves: Reaction Force in an Open Discharge System
Reference: API RP 520 Part 2
Technical Toolboxes, Inc.
20
Reinforcement of Welded Branch Connection
One of the first methods of providing branch connections was to stub a branch line into a run.
Sometimes a pad would also be used to reinforce the connections. The figure below shows a
header with pad-reinforced branch connections. Although tees and extrusions have generally
taken the place of reinforced branch connections, an example calculation is presented for the
occasional instance where the designer may want to use this type of connection.
Nomenclature:
Refer to figure for a physical representation of the applicable terms.
Pipeline Facilities
21
d = Outside diameter of branch pipe.
D = Outside diameter of the run.
E = The longitudinal joint factor determined in accordance with
49 CFR 192.105.
F = The design factor determined in accordance with 49 CFR
192.105.
L = Height of the reinforcement zone
L is lesser of:
1. 2.5 , or
2. 2.5
P = The design pressure of the branch connection.
S = The yield strength of the component
being considered (i.e., run, branch or pad).
T = The temperature derating factor determined in accordance
with 49 CFR 192.105.
Reference:
ASME B31.8 Gas Transmission and Distribution Piping Systems, Appendix F
Technical Toolboxes, Inc.
23
Pipeline Compressors
Centrifugal Compressor - Adiabatic Head
CNGA/GPSA Compressibility Factor Approximation
This approximation will produce results sufficiently accurate for preliminary calculations.
Reference:
1. Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth
Edition
2. Compressor Station Operation, Book T-2, GEOP, American Gas Association
(A.G.A.)
24
3. Compressor Selection and Sizing, Royce N. Brown, Second Edition, Gulf
Professional Publishing
Technical Toolboxes, Inc.
Pipeline Compressors
25
Centrifugal Compressor - Required Adiabatic Horsepower
CNGA/GPSA Compressibility Factor Approximation
26
This approximation will produce results sufficiently accurate for preliminary calculations.
Brake Horsepower
Reference:
1. Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth
Edition
2. Compressor Station Operation, Book T-2, GEOP, American Gas Association
(A.G.A.)
3. Compressor Selection and Sizing, Royce N. Brown, Second Edition, Gulf
Professional Publishing
Technical Toolboxes, Inc.
Pipeline Compressors
27
Centrifugal Compressor - Required Polytropic Horsepower
CNGA/GPSA Compressibility Factor Approximation
28
This approximation will produce results sufficiently accurate for preliminary calculations.
Brake Horsepower
Reference:
1. Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth
Edition
2. Compressor Station Operation, Book T-2, GEOP, American Gas Association
(A.G.A.)
3. Compressor Selection and Sizing, Royce N. Brown, Second Edition, Gulf
Professional Publishing
Technical Toolboxes, Inc.
Pipeline Compressors
29
Centrifugal Compressor - Fan Laws
Reference:
1. Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth
Edition
Technical Toolboxes, Inc.
30
Reciprocating Compressors - Capacity and Horsepower
Piston Displacement
Reciprocating Compressor Volumetric Efficiency
Pipeline Compressors
31
32
CNGA/GPSA Compressibility Factor Approximation
This approximation will produce results sufficiently accurate for preliminary calculations.
Reciprocating Compressor Horsepower
Reference:
1. Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth
Edition
2. Compressor Station Operation, Book T-2, GEOP, American Gas Association
(A.G.A.)
3. Compressor Selection and Sizing, Royce N. Brown, Second Edition, Gulf
Professional Publishing
Technical Toolboxes, Inc.
Pipeline Compressors
33
Discharge Temperature
Ideal Discharge Temperature
Theoretical Discharge Temperature
Actual Discharge Temperature
Reference:
1. Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth
Edition
2. Compressor Station Operation, Book T-2, GEOP, American Gas Association
(A.G.A.)
3. Compressor Selection and Sizing, Royce N. Brown, Second Edition, Gulf
Professional Publishing
Technical Toolboxes, Inc.
34
Compressor Station Piping - Diameter and Gas Velocity
Note: Gas velocity in piping should not exceed 2,000 [ft/min].
Reference: Compressor Station Operation, Book T-2, GEOP, American Gas Association
(A.G.A.)
Technical Toolboxes, Inc.
Pipeline Compressors
35
Local Atmospheric Pressure
The local atmospheric pressure may be calculated using Smithsonian Metrological Tables:
Reference: American Gas Association, Report No.3, A.G.A. Catalog No. XQ9210
Technical Toolboxes, Inc.
37
Accidental Gas Releases and Pipeline
Rupture
Accidental Gas Release through a Small Hole from
Pressurized Gas Pipeline
When the hole diameter in pipeline is relatively small, the pipeline is considered as a tank.
Gas release rate would be calculated by the small hole model. Assumptions made are:
pressure inside the pipeline will not be affected by gas release; gas expansion is isentropic.
Therefore, the gas release rate is constant and equal to the initial maximum release rate.
The value of the release rate at the orifice depends on whether gas flow is choked/ sonic or
subsonic. This is defined by the critical pressure ratio (CPR)
Choked flow occurs when the ratio of the source gas pressure to the ambient atmospheric
pressure is equal to or greater than:
38
For many gases, k ranges from about 1.1 to about 1.4, and so sonic or choked gas flow
usually occurs when the source gas pressure is about 25 to 28 PSIA or greater. Thus, the
large majority of accidental gas releases will usually involve sonic/choked flow
Note: No general consensus is currently available for small hole size definition. However, a
number of methodologies are suggested:
World Bank (1985) suggests characteristic hole sizes for a range of process
equipment (e.g., for pipes 20% and 100% of pipe diameter are proposed).
Some analysts use 2 and 4-inch holes, regardless of pipe size.
Some analysts use a range of hole sizes from small to large, such as 0.2,1,4 and 6 inches and
full bore ruptures for pipes less than 6-inches in diameter.
Some analysts use more detailed procedures. They suggest that 90% of all pipe failures
result in a hole size less than 50% of the pipe area. The following approach may be
consider :
-For small bore piping use 5-mm and full-bore ruptures.
-For 2-6" piping use 5-mm, 25-mm and full-bore holes.
-For 8-12" piping use 5-, 25-, 100-mm and full-bore holes.
To convert lb/hr to SCFM
To convert lb/hr to SCFH
Accidental Gas Releases and Pipeline Rupture
39
References:
- Handbook of Chemical Hazard Analysis Procedures,
- Risk Management Program Guidance for Offsite Consequence
- API Recommended Practice 520, Sizing, Selection, and Installation of Pressure-Relieving
Devices in Refineries, Part I, American Petroleum Institute,
- API Recommended Practice 521, Guide for Pressure-Relieving and Depressuring
Systems, American Petroleum Institute,
- Crane Limited, Flow of Fluids through Valves, Fittings, and Pipe, Technical Paper No.
410-C, Crane Engineering Division
- Bosch, C.J.H. van den and N.J. Duijm, The Netherlands Organization of Applied
Scientific Research. Methods for the Calculation of Physical Effects, CPR 14E: Part (TNO
Yellow Book),
- Ramskill, P.K., Discharge Rate Calculation Methods or Use in Plant Safety Assessments,
Safety and Reliability
Technical Toolboxes, Inc.
40
Accidental Gas Release Rate from a Full-Bore Pipeline
Rupture
Reference:
- GRI-00/0189, A Model for Sizing High Consequence Areas Associated with Natural Gas
Pipelines, Gas Technology Institute
- PHMSA - Final Report TTO Number 13, Delivery Order DTRS56-02-D-70036, Michael
Baker Jr., Inc.
- PHMSA - Final Report TTO Number 14, Delivery Order DTRS56-02-D-70036, , Michael
Baker Jr., Inc.
- Crane Limited, Flow of Fluids through Valves, Fittings, and Pipe, Technical Paper No.
410-C, Crane Engineering Division
Technical Toolboxes, Inc.
Accidental Gas Releases and Pipeline Rupture
41
Pack in Pipeline
Pack in pipeline - Isolated pipe section Gas packed in isolated section of the pipeline can be calculated in the same way where,
P1 = P2 = Ps
42
Compressibility factor Z is calculated using procedure from Engineering Data Book, Volume II,
Gas Processor Association, Revised Tenth Edition, 1994
References:
1. Pipeline Design for Hydrocarbons Gases and Liquids, Committee of pipeline planning,
American Association of Civil Engineers, 1975
2. Engineering Data Book, Volume II, Gas Processor Association, Revised Tenth Edition,
1994
3. Pipeline Design & Construction, A Practical Approach, American Society of Mechanical
Engineers, 2000
Technical Toolboxes, Inc.
Accidental Gas Releases and Pipeline Rupture
43
Natural Gas Pipeline Rupture - Depth, Radius, & Width of
Crater
A. GASUNIE MODEL
This model applies to a guillotine rupture wherein two separate pipe ends exists after the
rupture.
Figure 1
44
The crater angles are determined from empirical equations:
Considering crater and dimensions shown in Figure 1. The equation of the ellipse is given
by
Differentiating this at the ground level and substituting for x gives
Evaluating this on the ground level and half crater depth gives
These can be solved simultaneously
The width of crater W is given by
B. NEN 3651 MODEL RADIUS OF THE CRATER
Model may be applied for guillotine type rupture, NEN 3651 define radius of the crater as:
Note: Units for pipe internal pressure p0 are in bars.
C. PRCI/GASUNIE/BATTELLE COMBINED MODEL
This model may be applied for guillotine type rupture only. Computation of the crater
depth in combined PRCI/Gasunie/Battelle model is the same as described above for
Gasunie model.
The crater width is calculated as:
Accidental Gas Releases and Pipeline Rupture
45
Reference:
1. Schram, W., “Prediction of Crater Caused by Underground Pipeline Rupture”,
N.V. Nederalandse Gasunie, Report TR/T 97.R.2515
2. NEN 3651, Annex A: “Determining Disturbance Zone Dimension”
3. PRCI L51861, “Line Rupture and Spacing of Parallel Lines”, Battelle Memorial
Institute
Technical Toolboxes, Inc.
47
Gas Pipeline Hydraulics
Gas Pipeline Hydraulics - A.G.A - Fully Turbulent Flow Equation
For the fully turbulent zone the transmission factor is determined from the Von Karman rough
pipe flow law.
Nomenclature
Technical Toolboxes, Inc.
48
Gas Pipeline Hydraulics - Colebrook - White Equation
The Colebrook-White equation is recommended for use by those unfamiliar with pipeline flow
equations, since it will produce the greatest consistency of accuracy
over the widest possible range of variables.
Nomenclature
Technical Toolboxes, Inc.
Gas Pipeline Hydraulics
49
Gas Pipeline Hydraulics - IGT Distribution Equation
Nomenclature
Technical Toolboxes, Inc.
50
Gas Pipeline Hydraulics - Mueller - High Pressure
The Mueller High Pressure equation is used in distribution systems with pressures greater than 1
psig.
Nomenclature
Technical Toolboxes, Inc.
Gas Pipeline Hydraulics
51
Gas Pipeline Hydraulics - Mueller - Low Pressure
The Mueller Low Pressure equation is used in distribution systems with pressures less than 1
psig.
Nomenclature
Technical Toolboxes, Inc.
52
Gas Pipeline Hydraulics - Panhandle - A Equation
The Panhandle A equation was originally developed from Reynolds numbers in the range of:
The average pipeline efficiency factor of 0.92 normally used in this Panhandle A equation was
obtained from actual empirical experience with the metered gas flow rates corrected to standard
conditions. The Panhandle A equation provides a reasonable approximation for partially
turbulent flow; however, for fully turbulent flow, the Panhandle A equation is not realistic. In the
fully turbulent region, the Panhandle B equation is recommended.
Pipeline efficiency factors used in the Panhandle equations should be reduced for smaller pipe
diameters. For large diameter lines, the efficiency factor may be as high as 0.98.
Nomenclature
Technical Toolboxes, Inc.
Gas Pipeline Hydraulics
53
Gas Pipeline Hydraulics - Panhandle - B Equation
The Panhandle B equation is used in the design of large high pressure, long transmission
pipelines. The Panhandle B equation is considered suitable for Reynolds numbers from:
Pipeline efficiency factors used in the Panhandle equations should be reduced for smaller pipe
diameters. For large diameter lines, the efficiency factor may be as high as 0.98.
Nomenclature
Technical Toolboxes, Inc.
54
Gas Pipeline Hydraulics - Pittsburgh Equation
The Pittsburgh equation is used in low pressure pipelines within the following range:
Nomenclature
Technical Toolboxes, Inc.
Gas Pipeline Hydraulics
55
Gas Pipeline Hydraulics - Spitzglass Equation
The Spitzglass equation is used with pipe diameters of 10" or less and with a range of pressure:
Nomenclature
Technical Toolboxes, Inc.
56
Gas Pipeline Hydraulics - Weymouth Equation
The Weymouth equation is one of the older equations, but is still widely used for distribution and
gathering systems. It was originally developed from data taken on small, low to medium pressure
pipelines. When it is used for larger, high pressure pipelines it is quite conservative, as it predicts
values for Q which could be 8-12% low
For gas transmission through long pipelines, the Weymouth equation is not recommended.
The Weymouth equation is typically used for flow conditions :
Nomenclature
Technical Toolboxes, Inc.
57
Steel Pipe - Design & Stress Analysis
Design Pressure - Steel Pipe
Note : For design limitations and definitions, see CFR Code Part 192 in the Standars and regulations
Regulations Module.
Technical Toolboxes, Inc.
58
Design Pressure - Steel Pipe
Note : For design limitations and definitions, see CFR Code Part 192 in the Standars and regulations
Regulations Module.
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
59
Restrained Gas Pipeline - Stress Analysis
Hoop Stress
Longitudinal Stress due to Internal Pressure
Longitudinal Stress due to Thermal Expansion
Nominal Bending Stress
Stress due to Axial Loading
Net Longitudinal Stresses
60
Combined Biaxial Stress
Reference: ASME B31.8 - 2010
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
61
Unrestrained Gas Pipeline Stress Analysis - Steel Pipe
Hoop Stress
Longitudinal Stress due to Internal Pressure
Nominal Bending Stress
Stress due to Axial Loading
Net Longitudinal Stresses
Reference: ASME B31.8 - 2010
Technical Toolboxes, Inc.
62
Design Pressure - Steel Pipe
Note : For design limitations and definitions, see CFR Code Part 192 in the Standars and regulations
Regulations Module.
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
63
Design Pressure - Steel Pipe
Note : For design limitations and definitions, see CFR Code Part 192 in the Standars and regulations
Regulations Module.
Technical Toolboxes, Inc.
64
Design Pressure - Plastic Pipe
Design pressure for plastic pipe is determined in accordance with either of the following
formulas :
Note :
For design limitations and definitions, see DOT Code 192 in the DOT & MMS Regulations
Module !
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
65
Design Pressure - Plastic Pipe
Design pressure for plastic pipe is determined in accordance with either of the following
formulas :
Note :
For design limitations and definitions, see DOT Code 192 in the DOT & MMS Regulations
Module !
Technical Toolboxes, Inc.
66
Hoop and Longitudinal Stress
Hoop stress is determined by Barlow's formula
Longitudinal stress
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
67
Flume Design
ESTIMATING ROUGHNESS COEFFICIENTS
This section describes a method for estimating the roughness coefficient n for use in
hydraulic computations associated with natural streams, floodways, and excavated
channels. The procedures applies to the estimation of n in Manning's formula .
The coefficient of roughness n quantifies retardation of flow due to roughness of channel
sides, bottom, and irregularities.
Estimation of n requires the application subjective judgement to evaluate five primary
factors:
- Irregularity of the surfaces of the channel sides and bottom;
- Variations in the shape and size of the channel cross sections;
- Obstructions in the channel;
- Vegetation in the channel;
- Meandering of the channel.
Procedure for estimating n
The procedure for estimating n involves selecting a basic value for a straight, uniform,
smooth channel in the existing soil materials, then modifying that value with each of the
five primary factors listed above.
In selecting the modifying values, it is important that each factor be examined and
considered independently.
Step 1. Selection of basic value of n. Select a basic n value for straight, uniform, smooth
channel in the natural materials involved. The conditions of straight alignment, uniform
cross section, and smooth side and bottom surfaces without vegetation should be kept in
mind. Thus, basic n varies only with the material that forms the sides and bottom of the
channel. Select the basic n for natural or excavated channels from Table 8.04a. If the
bottom and sides of a channel consist of different materials, select an intermediate value.
Table 8.04a. Basic Value of Roughness Coefficient for Channel Materials
Soil Material Basic n
Channels in earth 0.02
Channels in fine gravel 0.024
Channels cut into rock 0.025
Channels in coarse gravel 0.028
Step 2.Selection of modifying value for surface irregularity. This factor is based on the
degree of roughness or irregularity of the surfaces of the channel sides and bottom.
Consider the actual surface irregularity, first in relations to the degree of surface
smoothness obtainable with the natural materials involved, and second in relation to the
depth of flow expected. If the surface irregularity is comparable to the best surface possible
for the channel materials, assign a modifying value zero. Irregularity induces turbulence
that calls for increased modifying values. Table 8.04b may be used as a guide to selection of
these modifying values.
Table8.04b. Modifying Value for Roughness Coefficient Due to Surface Irregularity of
Channels
Degree of Surface Comparable Modifying
68
Irregularity Value
Smooth The best obtainable for the material 0.000
Minor Well-dredged channels; slightly eroded
or scoured side slope of canals or
drainage channels 0.005
Moderate Fair to poorly dredged channels;
moderately sloughed or eroded side
slopes of canals or drainage channels 0.010
Severe Badly sloughed banks of natural channels:
badly eroded or sloughed sides of canals
or drainage channels; unshaped, jagged
and irregular surfaces of channels excavated
in rock 0.020
Source for Tables b-f: Estimating Hydraulic Roughness Coefficients
Step 3. Selection of modifying value for variations in the shape and size of cross sections. In
considering this factor, judge the approximate magnitude of increase and decrease in
successive cross sections as compared to the average. Gradual and uniform changes do not
cause significant turbulence. Turbulence increases with the frequency and abruptness of
alternation from large to small channel sections.
Shape changes causing the greatest turbulence are those for which flow shifts from side to
side in the channel. Select modifying values based on Table 8.04c.
Table 8.04c. Modifying Value for Roughness Coefficient Due to Variations of Channel
Cross Section
Character of Variation Modifying
Value
Changes in size or shape occurring
gradually 0.000
Large and small sections alternating
occasionally, or shape changes causing
occasional shift of main flow from side
to side 0.005
Large and small sections alternating
frequently, or shape changes causing
frequent shift of main flow from side
to side 0.010-0.015
Step 4. Selection of modifying value for obstructions. This factor is based on the presence
and characteristics of obstructions such as debris deposits, stumps, exposed roots, boulders,
and fallen and lodged logs. Take care that conditions considered in other steps not be
double-counted in this step.
In judging the relative effect of obstructions, consider the degree to which the obstructions
reduce the average cross-sectional area at various depths and the characteristic of the
obstructions. Shaped-edged or angular objects induce more turbulence than curved,
smooth-surfaced objects. Also consider the transverse and longitudinal position and
spacing of obstruction in the reach. Select modifying value based on Table 8.04d.
Table 8.04d. Modifying Value for Roughness Coefficient Due to Obstruction in the
Channel
Steel Pipe - Design & Stress Analysis
69
Relative Effect Modifying
of Obstruction Value
Negligible 0.000
Minor 0.010 to 0.015
Appreciable 0.020 to 0.030
Severe 0.040 to 0.060
Step 5. Selection of modifying value for vegetation. The retarding effect of vegetation is due
primarily to turbulence induced as the water flows around and between limbs, stems and
foliage and secondarily to reduction in cross section. As depth and velocity increase, the
force of flowing water tends to bend the vegetation. Therefore, the ability of vegetation to
cause turbulence is related to its resistance to bending. Note that the amount and
characteristics of foliage vary seasonally. In judging the retarding effect of vegetation,
consider the following: height of vegetation in relation to depth of flow, its resistance to
bending, the degree to which the cross section is occupied or blocked, and the transverse
and longitudinal distribution of densities and height of vegetation in the reach. Use Table
8.04e as a guide.
Table 8.04e. Modifying Value for Roughness Coefficient Due to Vegetation in the Channel
Vegetation and Flow Conditions Range in Modifying Value
Comparable to:
Low Effect 0.005 to 0.010
Dense growths of flexible turf grass or
weeds, such as Bermudagrass and Kentacky
bluegrass. Average depth of flow 2 to 3 times
the height of the vegetation.
Medium Effect 0.010 to 0.025
Turf grasses where the average depth of flow
is 1 to 2 times the heigth of vegetation
Stemmy grasses, weeds or tree seedlings
with moderate cover where the average
depth of flow is 2 to 3 times the height
of vegetation
Brushy growths, moderately dense, similar
to willow 1 to 2 years old, dormant season,
along side slopes of channel with no significant
egetation along the channel bottom, where the
hydraulic radius is greater then 2 ft
High Effect 0.025 to 0.050
Grasses where the average depth of flow is
about equal to the height of vegetation
Dormant seasons, willow or cottonwood
tree 8-10 year old, intergrown with some
weed and brush; hydraulic radius 2 to 4 ft
1. yr old, intergrown with some weeds in
70
full foliage along side slopes; no significant
egetation along channel bottom; hydraulic
radius 2 to 4 ft
Grasses where average depth of flow is less
than one-half the height of vegetation
Very High Effect 0.050 to 0.100
Growing season, bushy willows about 1-yr
old, intergrown with weeds in full foliage
along side slopes; dense grown of cattails
or similar rooted vegetation along channel
bottom; hydraulic radius greater than 4 ft
Growing season, tree intergrown with weeds
and brush, all in full foliage; hydraulic radius
greater than 4ft
Step 6 Computation of n for the reach. The first estimate of roughness for the reach
n , is obtained by neglecting meandering and adding the basic n value obtained in step 1
and modifying value from steps 2 through 5.
Step 7. Meander. The modifying value for meandering is not independent of the other
modifying values. It is estimated from the n obtained in step 6, and the ratio of the
meandering length to the straight length. The modifying value for meandering may be
selected from Table 8.04f.
Table 8.04f.Modifying Value for Roughness Coefficient Due to Meander of the Channel
Meander Ratio Degree of Modifying
Meandering Value
0.0 to 1.2 Minor 0.000
1. 2 to 1.5 Appropriable 0.15 n
1. 5 and greater Severe 0.30 n
Step 8. Computation of n for a channel reach with meandering. Add the modifying value
obtained in step 7, to n , obtained in step 6.
The procedure for estimating roughness for an existing channel is illustrated in Sample
Problem 8.04a.
Sample Problem 8.04a. Estimation of roughness coefficient for an existing channel.
Description of reach:
Steel Pipe - Design & Stress Analysis
71
Soil - Natural channel with lower part of banks and bottom yellowish gray
clay, upper part light silty clay.
Side slopes - Fairly regular; bottom uneven and irregular.
Cross section - Very little variation in the shape; moderate, gradual
ariation in size. Average cross section approximately trapezoidal with
side slopes about 1,5:1 and bottom width about 10 ft. At bankfull stage,
the average depth is about 8.5 ft and the average top width is about 35 ft.
Vegetation - Side slopes covered with heavy growth of poplar tree,
2. to 3 inches in diameter, large willows, and climbing vines; thick,
bottom growth of waterweed; summer condition with the vegetation
in full foliage.
Alignment - Significant meandering; total length of meandering
channel, 1120 ft; straight line distance, 800 ft.
Solution:
Step Description
Number n Value
1. Soil materials indicate minimum basic n 0.02
Modification for:
2. Moderately irregular surface 0.01
3. Change in size and shape judged insignificant 0.00
4. No obstructions indicted 0.00
5. Dense vegetation 0.08
6. Straight channel subtotal, n = 0.11
7. Meandering appreciable,
meandering ratio: 1120/800 = 1.4
Select 0.15 from Table 8.04f
8. Modified value =(0.15)(0.11) = 0.0165 or 0.02
Total roughness coefficient n = 0.13
Out-of-Bank Condition Channel and Flood Plain Flow
Work with natural floodways and streams often requires consideration of a wide range of
discharges. At high stages, both channel and overbank or flood plain flow may occur.
Usually, the retardance of the flood plain differs significantly from that of the channel, and
the hydraulic computations can be improved by subdividing the cross selection and
assigning different n values for flow in the channel and the flood plain. If conditions
72
warrant, the flood plain may be subdivided further. Do not average channel n with flood
plane n. The n value for in-bank flow in the channel may be averaged.
To compute a roughness coefficient for flood plain flow, consider all factors except
meandering. Flood plain n values normally are greater than channel values, primarily due
to shallower depths of flow. The two factors requiring most careful consideration in the
flood plain are obstructions and vegetation. Many flood plains have fairly dense networks
of obstructions to be evaluated. Vegetation should be judged on the basis of growing-season
conditions.
The overland flow portion of flow time may be determined from Figure 8.03a.The flow
time (in minutes) in the channel can be estimated by calculating the average velocity in feet
per minute and dividing the length (in feet) by the average velocity.
Table 8.03a Value of Runoff Coefficient (C) for Rational Formula
Land Use C Land Use C
Business: Lawns:
Downtown areas 0.70-0.95 Sandy soil, flat, 2% 0.05-0.10
Neighborhood areas 0.50-0.70 Sandy soil, ave., 2-7% 0.10-0.15
Sandy soil, steep, 7% 0.15-0.20
Residential: Heavy soil, flat, 2% 0.13-0.17
Single-family areas 0.30-0.50 Heavy soil, ave., 2-7% 0.18-0.22
Multi units, detached 0.40-0.60 Heavy soil, steep, 7% 0.25-0.35
Multi units, attached 0.60-0.75
Suburban 0.25-0.40 Agricultural land:
Bare packed soil
Industrial: Smooth 0.30-0.60
Light areas 0.50-0.80 Rough 0.20-0.50
Heavy areas 0.60-0.90 Cultivated rows
Heavy soil no crop 0.30-0.60
Parks, cemeteries 0.10-0.25 Heavy soil with crop 0.20-0.50
Sandy soil no crop 0.20-0.40
Play grounds 0.20-0.35 Sandy soil with crop 0.10-0.25
Pasture
Railroad yards areas 0.20-0.40 Heavy soil 0.15-0.45
Sandy soil 0.05-0.25
Unimproved areas 0.10-0.30 Woodlands 0.05-0.25
Streets:
Asphalt 0.70-0.95
Concrete 0.80-0.95
Brick 0.70-0.85
Drives and walks 0.75-0.85
Roofs 0.75-0.85
NOTE: The designer must use judgment to select the appropriate C value within the range
for the appropriate land use. Generally, large areas with permeable soils, flat slopes, and
dense vegetation should have lowest C values. Smaller areas with slowly permeable soils,
steep slopes, and sparse vegetation should be assigned highest V value.
Sources: American Society of Civil Engineers
Steel Pipe - Design & Stress Analysis
73
Step 4. Determine the rainfall intensity, frequency, and duration (Figure 8.03b through
8.03g - source: North Carolina State Highway Commission; Jan.1973). Select the chart for
the locality closest to your location. Enter the "duration" axis of the chart with the
calculated time of concentration,. . More vertically until you intersect the curve of the
appropriate design storm, then move horizontally to read the rainfall intensity factor, i, in
inches per hour.
Step 5. Determine peak discharge, Q , by multiplying the previously determined
factors using the rational formula (Sample Problem 8.03a)
Sample Problem 8.03a Determination of peak runoff rate using the rational method.
Q = CiA
Given:
Drainage area: 20 acres
Graded areas: 12 acres
Woodland: 8 acres
Maximum slope length: 400 ft
Average slope: 3% area bare
Location: Raleigh, NC
Find:
Peak runoff rate from 10-yr frequency storm
Solution:
(1) Drainage area: 20 acres (given)
(1) Determine runoff coefficient, C.
Calculate Weighted Average
Area C from Table 8.03a
Graded 12 x 0.45 = 5.4
Woodland 8 x 0.15 = 1.2
20 6.6
C = 6.6/20 = 0.33
1. Find the time of concentration, from Figure 8.03a using maximum
length of travel = 400ft and height of most remote point above outlet
= 400 ft x 3% = 12 ft; assuming overland flow on bare earth.
= 3.2 minutes.
NOTE: Any time of flow in channel should be added to the overland flow to
determine .
(1) Determine the rainfall intensity factor, i.
i = 8.0 inches/hr (from Figure 8.03e) using 10-yr storm,
5 min. duration.
(1) Q = C(i)(A)
Q = 0.33 (8.0)(20) = 52.8 cfs; Use 53 cfs
74
Table 8.05a
Maximum Allowable Design Velocity
For Vegetated Channels
Typical Soil Grass Lining Permissible Velocity
Channel Slope Characteristic for Established Grass
Application Lining (ft/sec)
0-5% Easily Erodible Bermudagrass 5.0
Non_plastic Tail fescue 4.5
(Sand & Silts) Bahiagrass 4.5
Kentucky bluegrass 4.5
Grass-legume mixture 3.5
Erosion Resistant Bermudagrass 6.0
Plastic Tall fescue 5.5
(Clay mixes) Bahiagrass 5.5
Kentucky bluegrass 5.5
Grass-legume mixture 4.5
5-10% Easily Erodible Bermudagrass 4.5
Non_plastic Tail fescue 4.0
(Sand & Silts) Bahiagrass 4.0
Kentucky bluegrass 4.0
Grass-legume mixture 3.0
Erosion Resistant Bermudagrass 5.5
Plastic Tall fescue 5.0
(Clay Mixes) Bahiagrass 5.0
Kentucky bluegrass 5.0
Grass-legume mixture 3.5
>10% Easily Erodible Bermudagrass 3.5
Non_plastic Tail fescue 2.5
(Sand & Silts) Bahiagrass 2.5
Kentucky bluegrass 2.5
Erosion Resistant Bermudagrass 4.5
Plastic Tall fescue 3.5
(Clay Mixes) Bahiagrass 3.5
Kentucky bluegrass 3.5
Source: USDA-SCS Modified
NOTE:
Selecting Channel Cross-Section Geometry
To calculate the required size of an open channel, assume the design flow is uniform and
does not vary with time. Since actual flow conditions change throughout the length of a
channel, subdivide the channel into design reaches and design each reach to carry the
appropriate capacity.
Steel Pipe - Design & Stress Analysis
75
The three most commonly used channel cross-section are "V"-shaped, parabolic, and
trapezoidal. Figure 8.05b gives mathematical formulas for the area, hydraulic radius and
top width of each of these shapes.
Table 8.05b Manning's n for Structure Channel Linings
Channel Lining Recommended
n values
Asphaltic concrete, machine placed 0.012
Asphalt, exposed prefabricated 0.015
Concrete 0.015
Metal, corrugated 0.024
Plastic 0.013
Shotcrete 0.017
Gabion 0.030
Earth 0.020
Erosion Control Blankets 0.030
Source: American Society of Civil Engineers (modified)
Design Procedure-Permissible Velocity
The following is a step-by-step procedure for designing a runoff conveyance channel using
Manning's equation and the continuity equation:
Step1. Determine the required flow capacity, Q, by estimating peak runoff rate for the
design storm (Appendix 8.03).
Step2. Determine the slope and select channel geometry and lining.
Step3. Determine the permissible velocity for the lining selected, or the desired velocity, if
paved. (see Table 8.05a,pg. 8.05.4)
Step 4. Make an initial estimate of channel size - divide the required Q by the permissible
velocity to reach a "first try" estimate of channel flow area. Then select a geometry, depth
and top width to fit site conditions.
Step 5. Calculate the hydraulic radius, R, from channel geometry (Figure 8.05b,pg.8.05.5).
Step 6. Determine roughness coefficient n.
Structural Lining - see Table 8.05, pg. 8.05.6
Grass Lining:
. Determine retardance class for vegetation from Table 8.05c, pg.8.05.8
To meet stability requirement, use retardance for newly mowed condition
( generally C and D). To determine channel capacity, use at least one retardance class
higher.
. Determine n from Figure 8.05c, pg.8.05.7
.
Step 7. Calculate the actual channel velocity and required, V, using Manning's equation
(Figure 8.05a, pg. 8.05.3), and calculate channel capacity, Q, using the continuity equation.
Step 8. Check results against permissible velocity and required design capacity to
determine if design is acceptable.
Step 9. If design is not acceptable, alter channel dimension as appropriate. For trapezoidal
channels, this adjustment is usually made by changing the bottom width.
Sample Problem 8.05a Design of a grass-lined channel
Channel summary
Trapezoidal shape, Z = 3, B = 3 ft, d = 1,5 ft, grade = 2%
76
Note: In Sample Problem 8.05a the "n-value" is first choosen based on a permissible
velocity and not a design velocity criteria. Therefore the use of table 8.05c may not be
accurate as individual retardance class charts when a design velocity is the determining
factor.
Tractive Force Procedure
The design of riprap-lined channel and temporary channel linings is based on analysis of
tractive force.
NOTE: The procedure is for uniform flow in channels and is not to be used for design of
deenergizing devices and may not be valid for larger channels.
To calculated the required size of an open channel, assume the design flow is uniform and
does not vary with time. Since actual flow conditions change through the length of a
channel, subdivide the channel into design reaches as appropriate.
PERMISSIBLE SHEAR STRESS
The permissible shear stress, , is the force required to initiate movement of the lining
material. Permissible shear stress for the liner is not related to the erodibility of the
underlying soil. However, if the lining is eroded or broken, the bed material will be exposed
to the erosive force of the flow.
COMPUTING NORMAL DEPTH
The first step in selecting an appropriate lining is to compute the design flow depth (the
normal depth) and determine the shear stress.
Normal depth can be calculated by Manning's equation as shown for trapezoidal channel
in Figure 8.05d. Values of the Manning's roughness coefficient for different ranges of depth
are provided in Table 8.05e for temporary lining and Table 8.05f for riprap. The coefficient
of roughness generally decrease with increase flow depth.
Table 8.05e Manning's Roughness Coefficient for Temporary Lining Materials
n value for Depth Ranges
0-0.5 ft 0.5-2.0 ft >2.0 ft
Lining Type
Woven Paper Net 0.016 0.015 0.015
Jute Net 0.028 0.022 0.019
Fiberglass Roving 0.028 0.021 0.019
Straw with Net 0.065 0.033 0.025
Curled Wood Mat 0.066 0.035 0.028
Synthetic Mat 0.036 0.025 0.021
Adapted from: FHWA-HEC 15, pg.37-April 1988
Table 8.05f Manning's Roughness Coefficient
n-value
n value for Depth Ranges
Lining Category Lining Type 0-0.5 ft 0.5-2.0 ft 2.0 ft
(0-15 cm) (15-60cm) (>60cm)
Rigid Concrete 0.015 0.013 0.013
Grouted Riprap 0.040 0.030 0.028
Stone Masonry 0.042 0.032 0.030
Soil Cement 0.025 0.022 0.020
Steel Pipe - Design & Stress Analysis
77
Asphalt 0.018 0.016 0.016
Unlined Bare Soil 0.023 0.020 0.020
Rock Cut 0.045 0.035 0.025
Gravel Riprap 1-inch (2.5 cm) 0.044 0.033 0.030
2-inch (5-cm) 0.066 0.041 0.034
Rock Riprap 6-inch (15-cm) 0.104 0.069 0.035
12-inch (30-cm) -- 0.078 0.040
Note:Values listed are representative values for the respective depth ranges. Manner's
roughness coefficient, n, vary with the flow depth.
DETERMINING SHEAR STESS
Shear stress, T, at normal depth is computed for lining by the following equation:
T = yds
= Permissible shear stress
where:
T = shear stress in
y = unit weight of water, 62.4
d = flow depth in ft
s = channel gradient in ft/ft.
If the permissible shear stress, , given in Table 8.05g is greater than the computed shear
stress, the riprap or temporary lining is considered acceptable. If a lining is unacceptable,
select a lining with a higher permissible shear stress and repeat the calculations for normal
depth and shear stress. In some cases it may be necessary to alter channel dimensions to
reduce the shear stress.
Computing tractive force around a channel bend requires special considerations because
the change in flow direction imposes higher shear stress on the channel bottom and banks.
The maximum shear stress in a bend, , is given by the following equation:
where:
The value of is related to the radius of curvature of the channel at its center line, ,
and the bottom width of the channel, B, Figure 8.05e. The length of channel requiring
protection downstream from a bend, , is a function of the roughness of the lining
material and the hydraulic radius as shown in Figure 8.05f.
Table 8.05g Permissible Shear Stresses for Riprap and Temporary Liners
Permissible Unit Shear Stress, T
Lining Category Lining Type
Temporary Woven Paper Net 0.15
78
Jute Net 0.45
Fiberglass Roving:
Single 0.60
Double 0.85
Straw with Net 1.45
Curled Wood Mat 1.55
Synthetic Mat 2.00
Erosion Control Blankets 2.25
Gravel Riprap 1 0.33
2. 0.67
Rock Riprap 6 2.00
9 3.00
12 4.00
15 5.00
15 6.00
21 7.80
24 8.00
Adapted From FHWA, HEC-15, April 1983, pgs. 17 & 37.
Design Procedure-Temporary Liners
The following is a step-by-step procedure for designing a temporary liner for a channel.
Because temporary liners have a short period of service, the design Q may be reduced. For
liners that are needed for six months or less, the 2-yr frequency storm is recommended.
Step 1. Select a liner material suitable for site conditions and application. Determine
roughness coefficient from manufacturer's specifications or Table 8.05e, pg.8.05.10.
Step 2. Calculate the normal flow depth using Manning's equation.Check to see that depth
is consistent with that assumed for selection of Manning's in Figure 8.05d, pg.8.05.11.For
smaller runoffs Figure 8.05d is not as clearly defined. Recommended solutions can be
determined by using the Manning equation.
Step 3. Calculate shear stress at normal depth.
Step 4. Compare computed shear stress with the permissible shear stress for the liner.
Step 5. If computed shear is greater than permissible shear, adjust channel dimension to
reduce shear or select a more resistant lining and repeat step 1 through 4.
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
79
Natural Gas Pipeline Rupture - Depth, Radius, & Width of
Crater
A. GASUNIE MODEL
This model applies to a guillotine rupture wherein two separate pipe ends exists after the
rupture.
Figure 1
80
The crater angles are determined from empirical equations:
Considering crater and dimensions shown in Figure 1. The equation of the ellipse is given
by
Differentiating this at the ground level and substituting for x gives
Evaluating this on the ground level and half crater depth gives
These can be solved simultaneously
The width of crater W is given by
B. NEN 3651 MODEL RADIUS OF THE CRATER
Model may be applied for guillotine type rupture, NEN 3651 define radius of the crater as:
Note: Units for pipe internal pressure p0 are in bars.
C. PRCI/GASUNIE/BATTELLE COMBINED MODEL
This model may be applied for guillotine type rupture only. Computation of the crater
depth in combined PRCI/Gasunie/Battelle model is the same as described above for
Gasunie model.
The crater width is calculated as:
Steel Pipe - Design & Stress Analysis
81
Reference:
1. Schram, W., “Prediction of Crater Caused by Underground Pipeline Rupture”,
N.V. Nederalandse Gasunie, Report TR/T 97.R.2515
2. NEN 3651, Annex A: “Determining Disturbance Zone Dimension”
3. PRCI L51861, “Line Rupture and Spacing of Parallel Lines”, Battelle Memorial
Institute
Technical Toolboxes, Inc.
82
Maximum Impact Load and Penetration Depth
A. Maximum Impact Load
B. Penetration Depth
Steel Pipe - Design & Stress Analysis
83
Reference: “Guidelines for the Design of Buried Steel Pipe” American Lifeline Alliance
Technical Toolboxes, Inc.
84
Pipeline Anchor Force Analysis
Tensile stress due to Poisson effect:
Compressive stress due to temperature change:
Net longitudinal stress at the beginning point ( A ) of the transition:
Net longitudinal stress at the end point ( B ) of transition:
Net strain at point B, will be:
Soil resistance force based on Wilburs formula for average soil:
Length of transition zone:
Steel Pipe - Design & Stress Analysis
85
Total pipe movement at point B will be:
Anchor force:
Reference:
"Pipe Line Industry", Wilbur, W.E., February 1963
"Theory of Elasticity", Timoshenko, S.
Technical Toolboxes, Inc.
86
API - 1117 Movement of In-Service Pipelines
TOTAL LONGITUDINAL STRESS
The total longitudinal stress in the pipe can be estimated
With the following equation:
Where:
LONGITUDINAL TENSILE STRESS DUE TO INTERNAL PRESSURE
The longitudinal tensile stress in the pipe due to internal pressure may be estimated with
the following equation:
Where:
LONGITUDINAL TENSILE STRESS DUE TO TEMPERATURE CHANGE
The longitudinal tensile stress in the pipe due to a change
in the temperature may be estimated with following
equation:
Where:
If the pipe's temperature at installation time is not known,
Steel Pipe - Design & Stress Analysis
87
it should be reasonably estimated.
LONGITUDINAL FLEXURE STRESS DUE TO EXISTING ELASTIC CURVATURE
When a pipeline is laid to conform elastically to a given trench profile, the pipeline will
experience induced flexural stress in amount proportional to its curvature. In hilly terain,
where slopes are unstable, or where soils are subject to frost heave or liquefaction, the
pipeline is likely to experience stress of unpredictable and varying magnitude. This stress
(S )can range from near-yield-strength levels in tension to near-bulking levels in
compression. This existing stress should be considered prior to a movement operation.
EXISTING LONGITUDINAL STRESS
The existing longitudinal stress in a pipeline will normally be in the range of-10,000 psi to
20,000 psi. In the flat or gently rolling terrain where soils are not subject to frost heave or
liquefaction, the pipeline will experience only the longitudinal tensile stress due to internal
pressure and temperature as discussed above.
The existing longitudinal stress in the pipe may be estimated
With following equation:
Where:
S = longitudinal stress in the pipe due to existing elastic curvature, in psi.
LONGITUDINAL STRESS DUE TO BENDING
The longitudinal stress in the pipe due to bending may be
estimated with following equation:
Where:
w = net uniformly distributed load required to achieve the desired mid-span vertical
deflection of the pipe [not full weight of the pipe and fluid], in pounds per inch.
L = minimum trench length required to reach the mid-span vertical deflection of the
pipe , in inches.
S = elastic section modulus of the pipe, in inches .
LONGITUDINAL STRESS DUE TO ELONGATION
The longitudinal stress in the pipe due to elongation caused by the movement operation
may be estimated with the following equation:
Where:
= mid-span deflection of the pipe, in feet.
88
L = minimum trench length required to reach the mid-span deflection of the pipe , in
feet.
The effects of this stress may be offset by an elastic compressive stress existing in the
pipeline prior to the moving because of slack.
AVAILABLE LONGITUDINAL BENDING STRESS
The longitudinal stress available for bending may be estimated with the following equation:
Where:
S = longitudinal stress available for bending, psi.
F = design factor.
SMYS = specified minimum yield strength of the pipe, in psi.
TRENCH LENGTH
The minimum trench length required to achieve a particular mid-span deflection of the
pipe without exceeding the longitudinal stress limit can be determined with the following
equation, based on elastic free deflection theory, which treats the pipe as a single-span
beam that is fixed at both ends andthat has a uniformly distributed load:
L=
TRENCH (OR DISPLACEMENT) PROFILE
A profile for the moved portion of the pipeline should be designed to minimize induced
bending stress concentrations. Therefore, to obtain acceptable longitudinal stress
distribution due to bending, the deflection at any point along the trench profile can be
determined with the following equation:
Where:
= vertical deflection of the pipe at distance x, in feet.
x = distance along the length of the trench from the
starting point of the pipe deflection, in feet.
SUPPORTING SPACING
Based on a four-span, uniformly loaded beam, the maximum free span between supports
can be determined with the following equation:
L =
Where:
L = maximum free span between pipe supports, in feet.
d = inside diameter of the pipe, in inches.
Reference: API RP 1117 "Movement of In-Service Pipeline", Second Edition, August 1996
Steel Pipe - Design & Stress Analysis
89
Technical Toolboxes, Inc.
90
Pipe Requirements for Horizontally Drilled Installation
1. Determine Hoop Stress:
1. Determine Overburden Stress:
1. Determine Total Circumferential Stress:
1. Determine Bending Stress:
1. Determine Total Combined Stress and select max value:
Steel Pipe - Design & Stress Analysis
91
1. Determine calculated design factor:
1. Determine maximum pull force:
1. Determine minimum bend radius - entry & exit at installation:
1. Maximum SMYS for hydrostatic pressure:
1. Determine maximum cantilever length
1. Determine maximum allowable hydrostatic test pressure:
Technical Toolboxes, Inc.
92
Buoyancy Analysis and Concrete Coating Thickness
1. Determine bare pipe weight:
2. Determine total volume of pipe in air including corrosion and concrete coating:
3. Determine Volume of corrosion coating:
4. Determine volume of concrete coating:
5. Determine total weight of pipe in air, including weight of corrosion and concrete
coating:
6. Determine weight of displaced water
7. Determine the difference :
Steel Pipe - Design & Stress Analysis
93
8. Determine bulk specific gravity:
Technical Toolboxes, Inc.
94
Buoyancy Analysis and Concrete Weights Spacing
Buoyant Force
Weight of Steel Pipe in the Air
Weight of Pipe Coating in the Air
Weight of Product in the Pipe
Downward Force of the Pipe
Net Controlling Force
Steel Pipe - Design & Stress Analysis
95
Downward Force of the Concrete Weight
Concrete Weight Spacing
Unit Weights:
Fresh water 62.42
Salt water 64.0
Concrete 140
Steel 490
PE Coating 59.30
FBE Coating 89.89
Wood lagging 26.84
Reference: “Pipeline Geo-Environmental Design and Geohazard Management”, ASME,
2008, Edited by Moness Rizkalla
Technical Toolboxes, Inc.
96
Bending Stress and Deflection in Pipelines
FIXED ENDS SUPPORTS
y = maximum deflection, feet
S = maximum bending stress, PSI
W= unit weight, pounds per foot
L = length, feet
E = modulus of elasticity, PSI
steel = 30,000,000
plastic(dupont) = 100,000
plastic(plexco) = 125,000
cast iron = 15,000,000
copper = 15,000,000
D = outside diameter, inches
d = inside diameter, inches
SIMPLE SUPPORTS y = 5 times y for fixed ends
S = 1.5 times S for fixed ends
CANTILEVER SUPPORT y = 48 times y for fixed ends
S = 6 times S for fixed ends
S and y on the schematics indicate the points of
MAXIMUM stress and deflection.
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
97
Maximum Allowable Pipe Span Length
Step 1: Variables Definition D - Pipe Outside Diameter [in]
W - Weight [lb/ft], includes water weight if hydrostatic testing is specified
MOAP - Maximum Allowable Operating Pressure [psi],
MOP - Maximum Operating Pressure [psi],
t - Pipe Wall Thickness [in]
SMYS - Specified Minimum Yield Strength or Grade of Steel [psi] ,
E - Modulus of Elasticity ( 29000 ksi )
H - Hoop Stress, [psi]
B - Bending Stress [psi]
M - Bending Moment [ft-lb]
L - Span Length [ft]
d - Deflection [in]
Step 2: Calculate Hoop Stress
Where P = MOP
Step 3: Calculate Maximum Allowable Bending Stress Solve Von Mises Equation through Quadratic Equation, and than solve for
Bending Stress B
Step 4: Calculate Maximum Allowable Bending Moment
Step 5: Calculate Maximum Span Length L, due to bending
Step 6: Calculate Maximum Span Length L, due to deflection
98
Important Notes : Maximum Operating Pressure (MOP) Must Be Less Then Maximum Operating Pressure
(MAOP)
Maximum Allowable Operating Pressure is calculated in accordance to DOT Code Part 192
using design factors
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
99
Blasting Analysis
SCOPE
This procedure describes the method for calculating the stresses caused by underground blasting
near an existing pipeline(s). The equations used follows guidelines set forth in CFR Title 49, Part
192.
BASIC CONSIDERATIONS
Blasting near an existing operating pipeline frequently occurs for a variety of reasons. Whenever
these underground explosion occur, they create circumferential and longitudinal stresses in
adjacent pipelines.
These stresses must be estimated to determine the possibility of damaging the pipelines.
This procedure describes the method for calculating the combined stresses on a pipeline in the
vicinity of blasting, those stresses being hoop stress due to internal pressure in the pipeline and
circumferential and longitudinal stresses due to blasting. In some instances, blasting may occur
near pipelines that are under the influence of circumferential and longitudinal stresses caused by
excessive backfill overburden (>10 Ft. of cover) or surface traffic. These situations require
special analysis and are not addressed in this standard procedure.
This procedure assumes that the blasting occurs at one location - a point charge. A blasting plan
may consists of a series of point charge blasts with a small delay between each blast. A biaxial
stress state exists when blasting occurs. These stresses are combined stress state.
Knowledge of soil (rock) conditions and construction methods is necessary to make sound
engineering judgements about each blasting situation. The following information is usually
required:
1. Description (trade name) of the explosive.
1. Method of detonation.
1. Delay time and weight of charge per delay.
1. Distance from pipeline.
1. Alignment Drawing No.and Survey Station or Mile Post.
1. Predominant rock type between the detonation point and the pipelines.
1. Diameter, wall thickness and SMYS of all pipelines in the vicinity of the blasting.
1. MAOP and the actual operating pressure of all pipelines in the vicinity of the blasting.
1. Class Location.
Frequently a series of blasts will be detonated with a small delay between each blast. It is
necessary to analyze the delay time with respect to seismic velocity to insure that each shock
100
wave arrives at the pipeline separately. In general, a minimum delay time of 25 milliseconds
(0.025 seconds) will assure that there is no compounding of shock waves. If seismic velocities
are low (1,000 - 2,500 ft./sec. ) a longer delay time may be required. Conversely, if delay times
are significantly less than 25 milliseconds, information about the expected seismic velocities
should be obtained. A sample calculation detailing the use of delay times and seismic velocities
is included with the example calculations.
II. EQUATIONS FOR CHARGE BLASTING ANALYSIS
The hoop stress due to internal pressure is calculated as follows:
The circuferential and longitudinal stresses caused by a point charge underground explosion are
calculated as follow:
The hoop stress and circumferential stress are combined as follows:
The combined stress level (S) is calculated as follow:
The longitudinal bending stress occurs in tension on the outside of the bend and in
compression on the inside of the bend. Tensile stress is represented with a positive value for ;
conversely, compressive stress takes a negative value for . The negative value for is used
Steel Pipe - Design & Stress Analysis
101
when calculating the combined stress level (S). This will result in a larger ( more conservative)
combined stress level.
The allowable combined stress design factor (DFa) should be applied to the SMYS as follows:
S, psi < SMYS x DFa, where
S = Combined stress level, psi
SMYS = Specified Minimun Yield Strength of pipe, psi
DFa =Allowable Combined Stress Design Factor
The calculated combined stress design factor (DFc) should be determined as follows:
An unsafe blasting condition may be rectified in several ways. They include reducing the pounds
of explosive per delay, increasing the distance away from pipeline, using an explosive with a
lower energy release ratio, or reducing the pressure in the pipeline. It is normally impractical to
reduce the pipeline pressure.
Technical Toolboxes, Inc.
102
Bending Stress in Pipelines Caused by Fluid Flow Around Pipeline
S = bending stress, PSI
w = unit weight of fluid, pounds per cubic feet
@ 59 degree and 14.7 PSI:
air = 0.07651
water = 62.4
D =outside diameter of pipe, inches
d = inside diameter of pipe, inches
V = velocity of fluid, feet per second
L= length of pipe, feet
BENDING STRESS IN PILING
CAUSED BY FLUID FLOW
AROUND PILING
D = outside diameter of piling, inches
Technical Toolboxes, Inc.
Steel Pipe - Design & Stress Analysis
103
THERMAL EXPANSION OF PIPELINES - LINEAR
E = elongation, in.
C = coefficient of linear expansion, inches per in per degrees F
L = length, feet
MATERIAL COEFFICIENT
steel 6.80E - 06
cast iron 6.60E - 06
copper 9.00E - 06
plastic 9.0E - 05
water 1.15E - 04
LONGITUDINAL STRESS
DUE TO TEMPERATURE CHANGES
S = stress, psi
E = modulus of elasticity, psi
C = coefficient of linear expansion, inches per inch per degrees F
Technical Toolboxes, Inc.
104
Thrust at Blow-off
Technical Toolboxes, Inc.
105
Steel Pipeline Crossings
API 1102 - PC PISCES
A.) PROGRAM SCOPE
API 1102 - PC PISCES (Personal Computer Pipeline Soil Crossing Evaluation System)
program is based on the design methodology resulting from the research and has been
implemented in the program to aid pipeline designers in analyzing existing uncased
pipelines and designing new uncased pipelines that cross beneath railroads and highways.
The details of the full design methodology can be found in “Technical Summary and
Database for Guidelines for Pipelines Crossing Beneath Railroads and Highways” (GRI-
91/0285, Final Report) and should have been read and understood. The design
methodology used in program follows directly the approach given in API RP 1102. Concise
summaries of the Cornell/GRI Guidelines are given in “Guidelines for Pipelines Crossing
Beneath Highways” (Stewart, et al., 1991b) and “Guidelines for Pipelines Crossing Beneath
Highways”. API RP 1102 should be available to the user for additional documentation and
preferences, and supplement the information provided by the program help and graphical
display of the design curves.
This design methodology relates to steel pipelines installed using trenchless construction
methods, in particular auger boring, with the crossing perpendicular to the railroad or
highway. The design methodology used in the program is such the pipelines having
diameters of D = 2 to 42 in. (51 to 1067 mm) can be analyzed. The wall thickness to
diameter ratios must be within the range of tw/D = 0.01 to 0.08.
Railroad crossings can be analyzed for depths of cover H = 6 to 14 ft (1.8 to 4.3 m).
Highway crossings can be analyzed for depth of cover H = 4 to 10 ft (in accordance with
API 1102) and H = 3 to 10 ft (PC-PISCES). The loading condition for railroads is based for
four axel distributed to the track surface, and would develop from the trailing and leading
axles sets form sequential cars. Highway loadings are based on both single and tandem-axle
truck loading configurations.
B.) LIST OF SYMBOLS
Bd - Bored diameter of crossing
Be - Burial factor for circumferential stress from earth load
D - Pipe outside diameter
E - Longitudinal joint factor
E' - Modulus of soil reaction
Ee - Excavation factor for circumferential stress from earth load
Er - Resilient modulus of soil
Es - Youngs modulus of steel
F - Design factor
Fi - Impact factor
FS1- Factor of safety for Seff
FS2 - Factor of safety for girth welds
FS3- Factor of safety for longitudinal welds
GHh- Geometry factor for cyclic circumferential stress from highway vehicular load
GHr - Geometry factor for cyclic circumferential stress from rail load
106
GLh - Geometry factor for cyclic longitudinal stress from highway vehicular load
GLr - Geometry factor for cyclic longitudinal stress from rail load
H - Depth to the top of the pipe
KHe - Stiffness factor for circumferential stress from earth load
KHh - Stiffness factor for cyclic circumferential stress from highway vehicular load
KHr - Stiffness factor for cyclic circumferential stress from rail load
KLh - Stiffness factor for cyclic longitudinal stress from highway vehicular load
KLr - Stiffness factor for cyclic longitudinal stress from rail load
L - Highway axle configuration factor
LG - Distance of girth weld from centerline
MAOP - Maximum allowable operating pressure
NH- Double track factor for cyclic circumferential stress
NL - Double track factor for cyclic longitudinal stress
Nt - Number of tracks at railroad crossing
Ps - Single axle wheel load
Pt - Tandem axle wheel load
P - Internal pipe pressure
R - Highway pavement type factor
RF- Longitudinal stress reduction factor for fatigue
Seff- Total effective stress
SFG- Fatigue resistance of girth weld
SFL - Fatigue resistance of longitudinal weld
SHe - Circumferential stress from earth load
SHi - Circumferential stress from internal pressure
SHiB - Circumferential stress from internal pressure calculated using the Barlow formula
S1- Maximum circumferential stress
S2- Maximum longitudinal stress
S3 - Maximum radial stress
SMYS - Specified minimum yield strength
T- Temperature derating factor
T1- Installation temperature
T2- Operating temperature
tw- Pipe wall thickness
w - Applied design surface pressure
T- Coefficient of thermal expansion
r- Unit weight of soil
SHh - Cyclic circumferential stress from highway vehicular load
SHr - Cyclic circumferential stress from rail load
SLh - Cyclic longitudinal stress from highway vehicular load
SLr - Cyclic longitudinal stress from rail load
s - Poissons ratio of steel
C. PROGRAM AND VARIABLES LIMITATIONS
C.1.) DIAMETER.
The diameter, D, is the outside pipe diameter, and has units of inches. The range of D is
2.0000 to 42.000 in. The default value is D = 12.750 in.
C.2.) MAXIMUM ALLOWABLE OPERATING PRESSURE, MAOP
Steel Pipeline Crossings
107
The maximum allowable operating pressure, MAOP, is used as the design internal pressure
for calculating circumferential stress due to internal pressurization, and has units of psi.
The range for MAOP is 0000 to 5000 psig.
C.3.) SPECIFIED MINIMUM YIELD STRENGTH, SMYS
The specified minimum yield strength, SMYS, has a range of allowable values covering
steel grades A25 (SMYS = 25000 psi) to X-80 (SMYS = 80000 psi). The SMYS is also used
to establish the girth and longitudinal weld fatigue endurance limits.
C.4.) DESIGN FACTOR, F
Although 49 CFR 192 or 195, establishes a design factor, F, the user can input another F
value. The range for F is from 0.10 to 1.00. The default design factor is F = 0.72.
C.4.) LONGITUDINAL JOINT FACTOR, E
The longitudinal joint factor, E, depends on the type of pipe welds. The input screen limits
E to either 0.60, 0.80, or 1.00, consistent with the values given in 49CFR192, Section
192.113. The default value is E = 1.00.
C.5.) INSTALLATION TEMPERATURE, T1
The installation temperature, T1 is given in F . This value is used with T2 to determine
thermal stress effects. The range of T1 is from -20 to 450 F.
C.6.) OPERATING TEMPERATURE, T2
The operating temperature, T2 is give in F. The T2 value is used to determine the
temperature derating factor, T. T2 also is used with T1 to determine thermal stress effects.
The range for T2 is from -20 to 450 F.
C.7.) WALL THICKNESS, tw
The pipe wall thickness, tw has units of inches. The wall thickness to diameter ratios must
be within the range of tw/D = 0.01 to 0.08.
C.8.) DEPTH OF CARRIER PIPE, H
The depth of the carrier pipe, H, given it ft, is measured from the top of tie to the pipeline
crown for railroads and from the top of pavement to the pipeline crown for highways. The
limits on H are:
6ft <= H <= 14 ft for railroads, and
4ft <= H <= 10 ft for highways (API 1102); 3ft <= H <= 10 ft for highways (PC-PISCES)
These are the depth limits for the live load design curves. The depth, H, also is used to
establish the impact factor, Fi used in the design methodology.
C.9.) BORED DIAMETER, Bd
The bored diameter, Bd (Bd in RP 1102), has units of inches. The minimum value is Bd =
D, and the maximum value is Bd = D + 6 in. The default value is Bd = D + 2 in.
C.10.) SOIL TYPE FOR THE EARTH LOAD
The soil type for the earth load calculations is either A or B. See Figure 4 in API RP 1102,
C.11.) MODULUS OF SOIL REACTION. E'
The modulus of soil reaction, E', has units of ksi. The minimum value allowed is E = 0.2 ksi,
and the maximum recommended value for auger bored installations is E = 2.0 ksi. The
maximum input value for E is 8.0 ksi. When an E value greater than 2.0 ksi is used, a
warning will be displayed that the value is beyond the normal range of E' for auger bored
installations. See details in API RP 1102.
C.12.) SOIL RESILIENT MODULUS, Er
The soil resilient modulus, Er has units of ksi. The minimum allowable value is Er = 5.00
ksi, and the maximum allowable value is Er = 20.0 ksi. These are the limits for the live load
108
design curves. See Table 3 in API RP 1102 or The default value is Er = 10.0 ksi, as
recommended in API RP 1102.
C.13.) SOIL UNIT WEIGHT, r
The soil unit weight, r, has units of pcf, and can range from 0 to 150 pcf. The default value
is r = 120 pcf.
C.14.) TYPE OF LONGITUDINAL WELD
The type of longitudinal weld is used with the SMYS to establish the longitudinal weld
fatigue endurance limit, SFL. The choices for the type of longitudinal seam weld are SAW
or ERW. See Table 3 in API RP 1102 for the influence of longitudinal weld type and SMYS
on the seam weld fatigue endurance limits. The default type of longitudinal weld is SAW.
C15.) GIRTH WELD DISTANCE, LG (RAILROAD ONLY)
The girth weld distance, LG has units of ft and can range from 00 to 99 ft. The LG distance
is used to determine the longitudinal stress reduction factor, RF , needed for the girth weld
fatigue calculations. See Figure 18 A and 18 B in API RP 1102 for the RF values as
dependent on LG, H, and D. When a double track crossing is being analyzed, the
recommended value for LG is less than 5 ft. For LG less than 5 ft, longitudinal stress
reduction factors are not used.
C.16.) NUMBERS OF TRACKS, Nt (RAILROAD ONLY)
The number of tracks, Nt is used to determine whether a single or double track railroad
crossing will be analyzed. The Nt value determines the single or double track NH and NL
factors for circumferential and longitudinal live load pipelines stresses, respectively. The
default value is Nt = 1.
C.17.) E - TYPE RAIL LOADING (RAILRAOD ONLY)
The E - Type rail loading is used to determine the applied surface stress, w, for railroad
crossings. The range for the E type lading is from E - 00 to E - 99. can also be entered,
which causes the surface load, w, to be 1.0 psi. The default value is E - 80 loading, as
recommended in API RP 1102.
C.18.) DESIGN SINGLE WHEEL LOAD, Ps (HIGHWAY ONLY)
The design single wheel load, Ps , has units of kips, and can range from 0.00 to 20.0 kips.
The pavement type, design wheel loads, diameter, and depth are used to establish the
pavement type factor, R, and axle configuration factor, L. The default value is Ps = 12.0
kips, as recommended in API RP 1102.
C.19.) DESIGN TANDEM WHEEL LOAD, Pt (HIGHWAY ONLY)
The design tandem wheel load, Pt (, has units of kips, and can range from 0.00 to 20.0 kips.
The pavement type, design wheel loads, diameter, and depth are used to establish the
pavement type factor, R, and axle configuration factor, L. The default value is Ps = 10.0
kips, as recommended in API RP 1102.
C.20.) PAVEMENT TYPE (HIGHWAY ONLY)
The pavement type for highway crossings can be either flexible , none, or rigid . The
pavement type, design wheel loads, diameter and depth are used to establish the pavement
type factor, R, and axle configuration factor, L. The default pavement type is flexible.
C.21.) YOUNGS MODULUS, Es
Youngs modulus of the steel carrier pipe, Es (Es in RP 1102), has units of ksi. The range is
from 29 000 to 31 000 ksi. The default value is Es = 30 000 ksi.
C.22.) POSSIONS RATIO, s
Steel Pipeline Crossings
109
Possions ratio of the steel carrier pipe, s , is used to assess thermal and longitudinal
stresses due to the circumferential earth load and internal pressure stresses. The allowable
range is from 0.25 to 0.30. The default value is s = 0.30.
C.23.) COEFFICIENT OF THERMAL EXPANSION, T
The coefficient of thermal expansion of the steel carrier pipe T , is given for temperature
is F, and is used to assess longitudinal thermal stresses. The range is from 0.0000060 to
0.0000080 per F. The default value is T = 0.0000065 per F.
D. DESIGN CURVES
110
Steel Pipeline Crossings
111
112
Steel Pipeline Crossings
113
114
Steel Pipeline Crossings
115
116
Steel Pipeline Crossings
117
118
Steel Pipeline Crossings
119
120
Steel Pipeline Crossings
121
122
Technical Toolboxes, Inc.
Steel Pipeline Crossings
123
Wheel Load Analysis
SCOPE:
The Wheel Load Analysis Program was designed to calculate the overburden and vehicle
loads on buried pipe with a Single Layer System (soil only) or a Double Layer Systems
(timbers, pavement and soil). The information used to design this program was taken from
the Battelle Petroleum Technology Report on "Evaluation of Buried Pipe Encroachments"
which considered the theoretical work done by M.G. Spangler on overburden and vehicle
loads on buried pipe.
REQUIRED INFORMATION:
1. Values for all of the following variables:
H - cover, vertical depth from the ground to the top of the pipe (ft.)
B - trench width (ft.)
Ds - weight per unit volume of backfill (lbs./ft.³)
D - outside diameter of the pipe (in.)
Lw - concentrated surface load (lbs.) (Wheel Load) (see Section 4, Page 11)
H1 - thickness of the pavement layer (in.) (see Figure 2)
SMYS - specified minimum yield stress of the pipe (psi.)
P - pipe internal pressure (psi.)
T - pipe wall thickness (in.)
2. The Design Class of the pipeline being analyzed (1-3) which is used to find the
Maximum Allowable Combined Stress (% SMYS), see Table I.
3. The Soil Type which is used to find the friction force coefficients (Km), see Table II.
124
4. The Pavement Type which is used to find the impact factor (I), see Table III, and the
elastic constants for layered media analysis (E1, E2, G1, & G2), see Table IV &
Figure 2.
5. The Crossing Construction Type which is used to find the bedding constants for
buried pipe (Kb & Kz), see Table V & Figure 3.
REQUIRED INFORMATION IF LONGITUDINAL BENDING STRESS OCCURS:
6. All the above information along with values for the following variables:
X - longitudinal distance over which deflection occurs (ft.)
Y - vertical deflection (in.)
Table I
Steel Pipeline Crossings
125
Maximum Allowable Combined Stress
Maximum Maximum
Design Operating Allowable Allowable
Class Class Internal Combined
Stress Stress
(%) (%)
1. 1. 72 80
1. 72 80
2 2 62 72
2 3. 62 72
3 3 50 62
3 4. 50 62
Figure 1 shows a cross sectional view of a pipe buried in a trench. As a first estimate of the
soil load on the pipe it could be assumed that the backfill soil slides down the trench walls
without friction. Additionally assume that all soil above the pipe is supported by the pipe
itself and that the backfill soil on either side of the pipe does not assist in this support.
These assumptions are very conservative but they help a great deal in initial understanding
of the method of solution. The assumptions yield a soil load on the pipe equal to the weight
of the backfill soil above the pipe. This analysis provides an estimate of soil loads on the
buried pipe if nothing else is known about the system.
The basic analysis developed by M.G. Spangler follows similar arguments to that given
above. In this analysis, Spangler includes frictional forces between the trench wall and the
backfill. This permits the weight of the overburden to be partially carried by the
surrounding soil and reduces the total soil load on the pipe. The resulting equations for
calculating the pipe load due to overburden are as follows:
Cd - trench coefficient.
B - trench width (ft.).
H - cover, vertical depth from the ground to the top of the pipe (ft.).
Km - coefficient of friction force between the backfill soil and the trench wall.
Cd determines how much load is carried by the pipe. If there is no soil friction Cd becomes
equal to H/B and the entire backfill load must be supported by the pipeline.
The term Km provides a coefficient of friction force between the backfill soil and the
trench wall. A high value of Km implies that friction between the backfill and trench wall is
high and the weight of the backfill is supported largely by the wall friction. A low value
implies that there is little friction encountered and the backfill is allowed to settle more
such that the weight must be supported by the pipe. Table II provides values of Km used in
the program for five different soil types. Also in Table II are examples of values for Ds, the
126
density which is the weight per unit of backfill, which may be used if an actual value is not
known. Note: If a value for Ds is already given use that value instead of the one in Table II.
Table II
Friction Force Coefficients For Various Soils
Soil Type Km Ds
(lbs/ft³)
(1) Granular Materials without Cohesion 0.1924 90-100
(2) Sand and Gravel 0.165 110-120
(3) Saturated Top Soil 0.150 110-120
(4) Clay 0.130 110-120
(5) Saturated Clay 0.110 120-130
The soil types and coefficients given in this table represent the range that could normally
be expected. Saturated clay has little internal friction so that it has the smallest value for
Km. This implies that almost all of the soil load is carried by the pipe. Granular materials
have a great deal more internal friction. Their value of Km is higher which leads us to the
conclusion that the pipe carries less of the backfill load. Spangler, in his work, recommends
using the value for clay in most instances. Higher values may be used when there is
adequate evidence that the internal friction is higher and warrants a higher value of Km.
Spangler's recommendation provides a conservative estimate for common buried pipe
situations. Marsh and bog areas, however, have friction properties more similar to
saturated clay such that a value for Km equal to 0.110 should be used in these areas.
Wc - load per unit length of the pipe due to overburden (lbs./in.).
B - trench width (ft.).
Ds - density which is the weight per unit of backfill (lbs./ft.³).
H - cover, vertical depth from the ground to the top of the pipe (ft.).
Km - coefficient of friction force between the backfill soil and the trench wall.
A Pavement Type must be determined in order to select an Impact Factor (I) to be used in
the Wv equation. Table III provides Impact Factor values for the three different pavement
types used in this program. A Pavement Type is also used to select the elastic constants for
layered media analysis. The variables E1 & G1 will be used to represent the elastic
constants for the top layer and E2 & G2 will be used to represent the elastic constants for
the soil. See Figure 2 for a visual explanation of the elastic constants for the top layer and
the soil. These values will also be used in the Wv equation. Table IV provides the values for
the three different pavement materials used in this program.
Table III
Impact Factor
Pavement Type Factor
(I)
No Pavement 1. 5
Steel Pipeline Crossings
127
Asphalt 1. 3
Timber Mats (2" x 12" minimum) 1.2
Concrete 1.0
Wv - average load per unit length of pipe for vehicular load (lbs./in.).
D - outside diameter of the pipe (in.).
E1 - modulus of elasticity of the top (timber or pavement) layer (lbs./in.²).
E2 - modulus of elasticity of the soil cover (lbs./in.²).
G1 - Poisson's ratio of the top (timber or pavement) layer.
G2 - Poison's ratio of the soil cove
H - thickness of the pavement layer plus the depth of the soil from the pavement interface
to thetop of the pipe (ft.). (See Figure 2)
H1 - thickness of the pavement layer ("0" is used when there is no pavement) (in.).
H2 - depth of the soil from the pavement interface to the top of the pipe (ft.).
I - impact factor.
Lw - concentrated surface load (a value of 16,000 lbs. is recommended when the maximum
is unknown), wheel load in lbs..
Examination of equation Wv shows that this equation also may be used with a Single Layer
System because the Pavement Material on the Top Layer chosen is "Soil", which makes E1
equal to E2, G1 equal to G2, and H1 equal to zero which cancels out the second and third
part of the equation. Thus when there is no pavement layer the revised equation will
provide a solution for soil cover only. Table IV provides the values for E1, E2, G1 & G2
that will be used in the program.
Table IV
Elastic Constants for Layered Media Analysis
Pavement E
Material (psi.) G
(1) No Pavement (Soil Only) 1. 5 x 104 0.35
(2) Asphalt 1. 0 x 105 0.40
(3) Timber Mats (2" x 12" 1. 2 x 106 0.25
(4) Concrete 2. 0 x 10 6 0.15
Sc - circumferential stress due to pipe wall deflection (PSI).
D - outside diameter of the pipe (in.).
E - pipe material modulus of elasticity (2.9 x 107).
128
Kb - bending coefficient which is a function of the crossing construction types.
Kz - deflection coefficient which is a function of the crossing construction types.
P - pipe internal pressure (PSI).
T - pipe wall thickness (in.).
Wc - load per unit length of pipe due to overburden (lbs./in.).
Wv - average load per unit length of pipe for vehicular load (lbs./in.).
Note that the equation Sc includes pressure in the denominator so that bending stresses are
reduced by increasing pressure.
Equation Sc, as well as equation St, have two constants which depend upon the bedding
material upon which the pipe is placed. This bedding material is based on the crossing
construction type. When the pipe is placed on a rigid bedding such as an Open Cut-Rock,
little soil deformation occurs so that the load application area on the bottom is very small.
However if the pipe is placed on soil, the support conforms to the pipe somewhat and the
load is distributed over a larger area (See Figure 3). The latter case produces less pipe
stress and is preferable. Spangler's formulation includes both of these possibilities in order
to provide a conservative estimate for the rigid bedding case without penalizing the soil
bedding case. It does so by varying the constants Kb and Kz. Spangler's recommended
values for the constants are provided in Table V.
Table V
Bedding Constants for Buried Pipe
Width of
Uniform Crossing
Soil Reaction Construction
(Degrees) _ Type Kz Kb
0 (1) Open Cut-Rock 0.110 0.294
30 (2) Open Cut 0.108 0.235
90 (3) Bored 0.096 0.157
Sh - hoop stress due to internal pressure (PSI).
D - outside diameter of the pipe (in.).
P - pipe internal pressure (PSI).
T - pipe wall thickness (in.).
St is the total circumferential stress in the pipe wall due to pressure (hoop) stress and
bending stresses resulting from circumferential flexure caused by external loads measured
in PSI. The first term on the right hand side of the equation is the formula for hoop stress
due to internal pressure (Sh) and the second term is the formula for circumferential stress
due to pipe wall deflection (Sc).
Longitudinal Bending Stress (Sb) is when the overburden and vehicle loads on buried
pipelines will cause pipe settlement into the soil in the bottom of the trench. This settlement
occurs because soil is not as stiff as the pipe and will deform easily as the pipe is "pushed"
downward. Under uniform soil conditions and overburden loading, the pipe will settle
Steel Pipeline Crossings
129
evenly into the trench bottom along its entire length. Soil is not generally uniform,
however, and regions of "softer" soil will occur adjacent to regions of stiff soil, so that the
pipe will settle unevenly and hence bending will occur. A load that is applied on only one
portion of a pipeline will cause the section of pipe under the load to settle more than the
unloaded pipe, such that bending will also result. Longitudinal bending stress occurs in
tension on the outside of the bend and in compression on the inside of the bend. Tensile
stress is represented with a positive value for Sb; conversely, compressive stress takes a
negative value for Sb. The longitudinal bending stress is calculated as follows:
Sb - longitudinal bending stress (PSI).
D - outside diameter of the pipe (in.).
E - pipe material modulus of elasticity (2.9 x 107).
X - longitudinal distance over which deflection occurs (ft.).
Y - vertical deflection (in.).
A negative value will be used when calculating the total combined stress (S). This will result
in a larger (more conservative) combined stress. Note: If longitudinal bending stress does
occur, click onto the designated box next to "Longitudinal Bending Stress" . If the box is
not marked then the program will assume "0" for Sb.
S - total combined stress by Von Mises (PSI).
Sb - longitudinal bending stress (PSI).
St - total circumferential flexure caused by external loads (PSI).
Note that if longitudinal bending stress is not present then the S will equal St.
The final calculation is % SMYS. This is calculated to determine if the current conditions
exceed the Maximum Allowable Combined Stress determined by Transcontinental Gas
Pipe Line Corporation.
S - total combined stress by Von Mises (PSI).
SMYS - specified minimum yield stress of the pipe (PSI).
References:
ASME B31.8 "Gas Transmission and Distribution Systems"
"Evaluation of Buried Pipe Encroachments", BATTELLE, Petroleum Technology Center,
1983
Technical Toolboxes, Inc.
130
Track Load Analysis
SCOPE:
The Track Load Program was designed to calculate the overburden and track loads on
buried pipe with a Single Layer System (soil only). The information used to design this
program was taken from the Battelle Petroleum Technology Report on "Evaluation of
Buried Pipe Encroachments" which considered the theoretical work done by M.G.
Spangler on overburden and vehicle loads on buried pipe.
REQUIRED INFORMATION:
1. Values for all of the following variables:
H - cover, vertical depth from the ground to the top of the pipe (ft.)
B - trench width (ft.)
Ds - weight per unit volume of backfill (lbs./ft.³)
D - outside diameter of the pipe (in.)
SMYS - specified minimum yield stress of the pipe (psi.)
P - pipe internal pressure (psi.)
T - pipe wall thickness (in.)
2. Values for the following information about the track:
Lt - operating weight of the object crossing the pipeline with tracks (lbs.)
Tw - width of standard track shoe (in.)
Tl - length of track on the ground (ft.)
Tg - track gauge (ft.)
3. The Design Class of the pipeline being analyzed (1-3) which is used to find the
Maximum Allowable Combined Stress (% SMYS), see Table I.
4. The Soil Type which is used to find the friction force coefficients (Km), see Table II.
5. The Crossing Construction Type which is used to find the bedding constants for
buried pipe (Kb & Kz), see Table V & Figure 3.
Steel Pipeline Crossings
131
REQUIRED INFORMATION IF LONGITUDINAL BENDING STRESS OCCURS:
6. All the above information along with values for the following variables:
X - longitudinal distance over which deflection occurs (ft.)
Y - vertical deflection (in.)
In compliance with the Transcontinental Gas Pipe Line Corporation specification on Road
Crossing Analysis Procedure, the following table will be used to determine the maximum
allowable stress for a particular design class which will be given as a variable:
Table I
Maximum Allowable Combined Stress
Maximum Maximum
Design Operating Allowable Allowable
Class Class Internal Combined
Stress Stress
(%) (%)
1. 1. 72 80
1. 72 80
2 2 62 72
2 3. 62 72
3 3 50 62
3 4. 50 62
132
As a first estimate of the soil load on the pipe it could be assumed that the backfill soil
slides down the trench walls without friction. Additionally assume that all soil above the
pipe is supported by the pipe itself and that the backfill soil on either side of the pipe does
not assist in this support. These assumptions are very conservative but they help a great
deal in initial understanding of the method of solution. The assumptions yield a soil load on
the pipe equal to the weight of the backfill soil above the pipe. This analysis provides an
estimate of soil loads on the buried pipe if nothing else is known about the system.
The basic analysis developed by M.G. Spangler follows similar arguments to that given
above. In this analysis, Spangler includes frictional forces between the trench wall and the
backfill. This permits the weight of the overburden to be partially carried by the
surrounding soil and reduces the total soil load on the pipe. The resulting equations for
calculating the pipe load due to overburden are as follows:
Cd - trench coefficient.
B - trench width (ft.).
H - cover, vertical depth from the ground to the top of the pipe (ft.).
Km - coefficient of friction force between the backfill soil and the trench wall.
Cd determines how much load is carried by the pipe. If there is no soil friction Cd becomes
equal to H/B and the entire backfill load must be supported by the pipeline.
The term Km provides a coefficient of friction force between the backfill soil and the
trench wall. A high value of Km implies that friction between the backfill and trench wall is
high and the weight of the backfill is supported largely by the wall friction. A low value
implies that there is little friction encountered and the backfill is allowed to settle more
such that the weight must be supported by the pipe. Table II provides values of Km used in
the program for five different soil types. Also in Table II are examples of values for Ds, the
density which is the weight per unit of backfill, which may be used if an actual value is not
known. Note: If a value for Ds is already given use that value instead of the one in Table II.
Table II
Friction Force Coefficients For Various Soils
Soil Type Km Ds
(lbs/ft³)
(1) Granular Materials without Cohesion 0.1924 90-100
(2) Sand and Gravel 0.165 110-120
(3) Saturated Top Soil 0.150 110-120
(4) Clay 0.130 110-120
(5) Saturated Clay 0.110 120-130
The soil types and coefficients given in this table represent the range that could normally
be expected. Saturated clay has little internal friction so that it has the smallest value for
Km. This implies that almost all of the soil load is carried by the pipe. Granular materials
have a great deal more internal friction. Their value of Km is higher which leads us to the
conclusion that the pipe carries less of the backfill load. Spangler, in his work, recommends
using the value for clay in most instances. Higher values may be used when there is
adequate evidence that the internal friction is higher and warrants a higher value of Km.
Steel Pipeline Crossings
133
Spangler's recommendation provides a conservative estimate for common buried pipe
situations. Marsh and bog areas, however, have friction properties more similar to
saturated clay such that a value for Km equal to 0.110 should be used in these areas.
Wc - load per unit length of the pipe due to overburden (lbs./in.).
B - trench width (ft.).
Ds - density which is the weight per unit of backfill (lbs./ft.³).
H - cover, vertical depth from the ground to the top of the pipe (ft.).
Km - coefficient of friction force between the backfill soil and the trench wall.
The Impact Factor (I) for a track load calculation with a single layer system is always going
to be 1.5. The reason for this is that the impact factor for soil is 1.5 and that is the only
thing that separates the track from the pipe in a single layer system.
Calculating track load is somewhat different from calculating a wheel load because the
load of a track expands over a larger area rather than a single point as does the wheel load.
The information needed from the track are the operating weight (Lt) of the object crossing
the pipeline with tracks is measured in lbs., the width of the standard track shoe (Tw)
measured in inches, the length of the track on the ground (Tl) measured in ft., and the
track gauge (Tg) measured in ft .
The weight of a track can be considered as a uniformly distributed load applied at the top
of the soil over an area equal to the length of the track on the ground times the width of the
standard track shoe. On the basis of this assumption, the unit pressure at a point on the top
of the line pipe or casing pipe directly beneath the center of the area may be estimated by
means on Newmarks Integration of Boussinesq equation. Newmark determined the
pressure at a point in the undersoil at any elevation below one corner of the rectangular
area over which unit loads are uniformly applied, and gave influence coefficients
corresponding to the Influence Factor m and Influence Factor n.
H - cover, vertical depth from the ground to the top of the pipe (ft.).
Tw - width of standard track shoe (in.).
H - cover, vertical depth from the ground to the top of the pipe (ft.).
Tl - length of the track on the ground (ft.).
These two factors are used by M.G. Spangler in the table called "Influence Coefficients for
Solution of Holl's and Newmark's Integration of the Boussinesq Equation for Vertical
Stress", see Table VI. Both of the influence factors will be rounded off to the nearest 0.01 in
order to cross reference Table VI.
134
Qd - maximum static pressure on the pipe directly under the center of the object with
tracks
(lbs./ft.²).
Ic - Influence Coefficient selected from Table VI.
Lt - operating weight of the object crossing the pipeline with tracks (lbs.)
Tl - length of the track on the ground (ft.).
Tw - width of standard track shoe (in.).
The equation for Qd is widely employed in structural work to estimate the unit pressure on
a deep soil stratum below a foundation, it appears to be appropriate for this problem. The
constant equal to 0.5 will be multiplied by Lt to get the operating load of one track.
Wt - total track load on the pipe (lbs./in.).
D - outside diameter of the pipe (in.).
I - impact factor of 1.5.
Qd - calculated result from equation Qd (lbs./ft.²).
Dividing the part of the equation (I * Qd) by twelve gives the load per linear inch of pipe.
Dividing the outside diameter of the pipe by twelve converts D, which is measured in
inches, into units of feet.
Sc - circumferential stress due to pipe wall deflection (PSI).
D - outside diameter of the pipe (in.).
E - pipe material modulus of elasticity (2.9 x 107).
Kb - bending coefficient which is a function of the crossing construction types.
Steel Pipeline Crossings
135
Kz - deflection coefficient which is a function of the crossing construction types.
P - pipe internal pressure (PSI).
T - pipe wall thickness (in.).
Wc - load per unit length of pipe due to overburden (lbs./in.).
Wt - total track load on the pipe (lbs./in.).
Note that the equation Sc includes pressure in the denominator so that bending stresses are
reduced by increasing pressure.
Equation Sc, as well as equation St, have two constants which depend upon the bedding
material upon which the pipe is placed. This bedding material is based on the crossing
construction type. When the pipe is placed on a rigid bedding such as an Open Cut-Rock,
little soil deformation occurs so that the load application area on the bottom is very small.
However if the pipe is placed on soil, the support conforms to the pipe somewhat and the
load is distributed over a larger area (See Figure 3). The latter case produces less pipe
stress and is preferable. Spangler's formulation includes both of these possibilities in order
to provide a conservative estimate for the rigid bedding case without penalizing the soil
bedding case. It does so by varying the constants Kb and Kz. Spangler's recommended
values for the constants are provided in Table V.
Table V
Bedding Constants for Buried Pipe
Width of
Uniform Crossing
Soil Reaction Construction
(Degrees) _ Type Kz Kb
0 (1) Open Cut-Rock 0.110 0.294
30 (2) Open Cut 0.108 0.235
90 (3) Bored 0.096 0.157
Sh - hoop stress due to internal pressure (PSI).
D - outside diameter of the pipe (in.).
P - pipe internal pressure (PSI).
T - pipe wall thickness (in.).
St is the total circumferential stress in the pipe wall due to pressure (hoop) stress and
bending stresses resulting from circumferential flexure caused by external loads measured
in PSI. The first term on the right hand side of the equation is the formula for hoop stress
due to internal pressure (Sh) and the second term is the formula for circumferential stress
due to pipe wall deflection (Sc).
Longitudinal Bending Stress (Sb) is when the overburden and vehicle loads on buried
pipelines will cause pipe settlement into the soil in the bottom of the trench. This settlement
occurs because soil is not as stiff as the pipe and will deform easily as the pipe is "pushed"
downward. Under uniform soil conditions and overburden loading, the pipe will settle
evenly into the trench bottom along its entire length. Soil is not generally uniform,
136
however, and regions of "softer" soil will occur adjacent to regions of stiff soil, so that the
pipe will settle unevenly and hence bending will occur. A load that is applied on only one
portion of a pipeline will cause the section of pipe under the load to settle more than the
unloaded pipe, such that bending will also result. Longitudinal bending stress occurs in
tension on the outside of the bend and in compression on the inside of the bend. Tensile
stress is represented with a positive value for Sb; conversely, compressive stress takes a
negative value for Sb. The longitudinal bending stress is calculated as follows:
Sb - longitudinal bending stress (PSI).
D - outside diameter of the pipe (in.).
E - pipe material modulus of elasticity (2.9 x 107).
X - longitudinal distance over which deflection occurs (ft.).
Y - vertical deflection (in.).
A negative value will be used when calculating the total combined stress (S). This will result
in a larger (more conservative) combined stress. Note: If longitudinal bending stress does
occur, click onto the option box. If the box is not marked then the program will assume "0"
for Sb.
S - total combined stress by Von Mises (PSI).
Sb - longitudinal bending stress (PSI).
St - total circumferential flexure caused by external loads (PSI)
Note that if longitudinal bending stress is not present then the S will equal St.
The final calculation is % SMYS. This is calculated to determine if the current conditions
exceed the Maximum Allowable Combined Stress determined by Transcontinental Gas
Pipe Line Corporation.
S - total combined stress by Von Mises (PSI).
SMYS - specified minimum yield stress of the pipe (PSI).
References:
ASME B31.8 "Gas Transmission and Distribution Systems"
"Evaluation of Buried Pipe Encroachments", BATTELLE, Petroleum Technology Center,
1983
Technical Toolboxes, Inc.
Steel Pipeline Crossings
137
Design of Uncased Pipeline Crossings
This method is proven and acceptable and can be used in the cases when the crossing
conditions for design are out of the scope and the limitations of API RP 1102 and PC-
PISCES.
Reference: GPTC Guide for Transmission and Distribution Systems, A.G.A.
Technical Toolboxes, Inc.
139
Pipeline Testing & Miscellaneous
API 1104 - Appendix A: Weld Imperfection Assessment
Please see API Standard 1104, Welding of Pipelines and Related Facilities, Appendix A,
Option 2 for the background of the assessment procedure.
Technical Toolboxes, Inc.
140
API 1104 - Appendix A: Weld Imperfection Assessment
Please see API Standard 1104, Welding of Pipelines and Related Facilities, Appendix A,
Option 2 for the background of the assessment procedure.
Technical Toolboxes, Inc.
Pipeline Testing & Miscellaneous
141
Gas Pipeline Pressure Testing - Maximum Pressure Drop
Technical Toolboxes, Inc.
142
NiSource Blowdown Calculations
The details of calculation procedure for this application are provided in electronic
document SWRI Report No. 87-2 and can be accessed by clicking the button “SWRI
Report No. 87-2”.
Technical Toolboxes, Inc.
Pipeline Testing & Miscellaneous
143
Purging Calculations
Method "A"
1. Find flow rate through the blow-off valve by using the formula for critical velocity,
Q = K
where Q = flow rate, MSCFH
K = flow coefficient, MSCF/(h x psi absolute)
P2 = pressure just upstream of blow-off valve, psi
2. From rearranged Weymouth formula to find an estimate pressure value of necessary to
maintain this flow rate:
3. Recommended purge time is 2T. The minimum purge time in minute is
or
where D = inside diameter of pipe, in
L = length of purge section, mi
C
C = (0.0361)D (1-h Weymouth coefficient in MSCF/h x mi)
Pm = average pressure, psi absolute
P1 = pressure at upstream end of section, psi absolute
P 2= pressure at downstream end of section, psi absolute (just
upstream of blow-off valve)
K = 1-h blow-off coefficient for standard blow-off sizes,
MSCF/ ( h x psi absolute)
One-Hour-Blow-off Coefficient for Standard Blow-off Sizes: Blow-off size, in. K, MSCF /(h x psi absolute)
144
1 0.75
2 3.0
3 6.0
4 13.5
6 24.0
8 47.0
10 72.0
where c = conversion constant = 60/14.73 = 4.07
V = actual volume of pipe section purged, thousand ft , where
pipe section is assumed to be filed with air prior to purge
K = blow-off coefficient, MSCF /(h x psi absolute)
P1 = pressure at upstream end of section, psi absolute
P1 = pressure at downstream end of section, psi absolute, just
upstream of blow-off valve
The volume of gas lost, MSCF, is
where V = actual volume of pipe action purged, thousand ft ,where
pipe section is assumed to be filled with air prior to purge;
equal to (0.028798)D , D in inches, L in miles
P1 = pressure at upstream end of section, psi absolute
P2 = pressure at downstream end of section, psi absolute
( just upstream of blow-off valve)
C , with C = (0.0361)D , D in inches, L in miles
K = 1-hour blow-off coefficient for standard blow-off sizes,
MSCF/(h x psi absolute)
Method "B"
where V = actual volume of pipe purged, thousand ft , where
pipe section is assumed to be filled with air prior to purge;
equal to(0.028798)D L, D in inches, L in miles
P = pressure of downstream end of section, psi absolute
( just upstream of blow-off valve)
t = actual time of purge, minutes
K = 1-h blow-off coefficient for standard blow-off sizes,
MSCF/ (h x lb/in absolute)
Technical Toolboxes, Inc.
Pipeline Testing & Miscellaneous
145
Pack in Pipeline
Pack in pipeline - Isolated pipe section Gas packed in isolated section of the pipeline can be calculated in the same way where,
P1 = P2 = Ps
146
Compressibility factor Z is calculated using procedure from Engineering Data Book, Volume II,
Gas Processor Association, Revised Tenth Edition, 1994
References:
1. Pipeline Design for Hydrocarbons Gases and Liquids, Committee of pipeline planning,
American Association of Civil Engineers, 1975
2. Engineering Data Book, Volume II, Gas Processor Association, Revised Tenth Edition,
1994
3. Pipeline Design & Construction, A Practical Approach, American Society of Mechanical
Engineers, 2000
Technical Toolboxes, Inc.
147
Pipeline Corrosion
EVALUATION OF MAOP IN CORRODED AREAS - ANSI B.31.G -1991
Computation of A
If the measured maximum depth of the corroded area is greater than 10 % of the nominal wall
thickness, and the measured longitudinal extent of the corroded area is greater than the value
determined by Equation (2), calculate:
where
Lm = measured longitudinal extent of the corroded area(inches).
D = nominal outside diameter of the pipe(inches).
t = nominal wall thickness of the pipe, in. Additional wall thickness required
for concurrent external loads shall not be included in calculation.
COMPUTATION OF P’
(a) For values of Less Than or Equal to 4.0.
where
= the safe maximum pressure for the corroded area
d = measured maximum depth of corroded area, in.
may not exceed P
P = the greater of either the established MAOP or
Where
S = specified minimum yield strength (SMYS), psi
F = appropriate design factor from ASME B31.4, ASMEB31.8, or ASME B31.11
T = temperature derating factor from the appropriate B31 Code(if not listed, T = 1)
D = nominal outside diameter of the pipe(inches).
T = nominal wall thickness of the pipe(inches). Additional wall thickness required
for concurrent external loads shall not be included in the calculations.
(b) For Value of A Greater Than 4.0
MAOP and
If the established MAOP is equal to or less than , the corroded region may be used for service at
that MAOP. If the established MAOP is greater than , then a lower MAOP should be established
not to exceed , or the corroded region should be repaired or replaced.
Technical Toolboxes, Inc.
148
DETERMINATION OF MAXIMUM ALLOWABLE LONGITUDINAL EXTENT OF
CORROSION - ANSI B.31.G - 1991
The depth of a corrosion pit may be expressed as a percent of nominal wall thickness of pipe by:
% pit depth = 100 (1)
where
d = measured maximum depth of the corroded area(inches).
t = nominal wall thickness of pipe(inches). Additional wall thickness required for concurrent
external loads shall not be included in the calculation.
A contiguous corroded area having a maximum depth of more then 10 % but less than 80 % of
the nominal wall thickness of the pipe should not extend along the longitudinal axis of the pipe
for a distance greater than that calculated from:
(2)
where
L = maximum allowable longitudinal extent of the corroded area(inches).
D = nominal outside diameter of the pipe(inches).
B = a value which may be determined from :
(3)
except that B may not exceed the value 4. If the corrosion depth is between 10% and 80%, use B
= 4.0 in Equation (2).
Technical Toolboxes, Inc.
Pipeline Corrosion
149
Rate of Electrical Current Flow Through the Corrosion Cell
Technical Toolboxes, Inc.
150
Relationship Between Resistance and Resistivity
Technical Toolboxes, Inc.
Pipeline Corrosion
151
Electrolyte Resistance from the Surface of an Electrode to any Distance
Technical Toolboxes, Inc.
152
Ohm's Law for Corrosion Current
Technical Toolboxes, Inc.
Pipeline Corrosion
153
Electrical Resistance of a Conductor
Technical Toolboxes, Inc.
155
Cathodic Protection
Estimated Life of a Magnesium Anode
Technical Toolboxes, Inc.
156
Resistance to Earth of an Impressed Anode Ground Bed
Technical Toolboxes, Inc.
Cathodic Protection
157
Rudenberg Formula
Vx - Potential at x in volt caused by grounds anode current
I - Ground anode current in amperes
- Earth resistivity in ohm-centimeters
y - Length of anode in earth in feet
x - distance from ground anode in feet
If x greater then 10y then,
Technical Toolboxes, Inc.
158
Single Vertical Anode Resistance to Earth and Typical Installation
R - Anode resistance to earth [ohm]
- Soil resistivity [ohm-cm]
L - Anode length [ft.]
d - Anode diameter [ft.]
s - Anode spacing in feet
h - Earth surface - Anode [ft.]
Technical Toolboxes, Inc.
Cathodic Protection
159
Resistance to Earth of Multiple Vertical Anodes in Parallel
R - Anode resistance to earth [ohm]
- Soil resistivity [ohm-cm]
L - Anode length [ft.]
d - Anode diameter [ft.]
N - Number of anodes in parallel
s - Anode spacing in feet
h - Earth surface - Anode [ft.]
Technical Toolboxes, Inc.
160
Single Horizontal Anode Resistance to Earth and Typical Installation
R - Anode resistance to earth [ohm]
- Soil resistivity [ohm-cm]
L - Anode length [ft.]
d - Anode diameter [ft.]
s - Anode spacing in feet
h - Earth surface - Anode [ft.]
Technical Toolboxes, Inc.
Cathodic Protection
161
Required Number of Anodes and Total Current Requirement
Technical Toolboxes, Inc.
162
Cathodic Protection Attenuation Calculation
Cathodic Protection
163
For typical pipeline with multiple drain points (anodes) with uniform spacing of 2L The
potential and current are given:
Reference:
1. Uhlig's Corrosion Handbook (2nd Edition) Edited by: Revie, R. Winston © 2000
John Wiley & Sons
2. ISO 15589-2 Petroleum and Natural gas Industries Cathodic Protection Pipeline
Transportation Systems
3. Pipeline Corrosion and Cathodic Protection, Third Edition, Gulf Publishing
Company
Technical Toolboxes, Inc.
164
Power Consumption of a Cathodic Protection Rectifier
Note : The formula is approximate, and based on 48% efficiency of rectifier.
Technical Toolboxes, Inc.
165
Polyethylene Pipe Design and Pipeline
Crossings
Dead Load on PE Pipe - Prism, Marston and Combined
Load
A. Prism Load
B . Marston Load (ASCE Manual No.60)
Typical Value for
Soil Typical Value for
Saturated clay 0.110
Ordinary clay 0.130
Saturated top soil 0.150
Sand and gravel 0.165
166
Clean granular soil 0.192
C. Combined Prism and Marston Load
For flexible pipe, a more conservative method is to use a soil pressure load in between
prism and Marston load:
Reference:
1. “Soil Engineering”, Third Edition, Spangler, M.G. and Handy, R.L., Intext
Educational Press
2. “Structural Mechanics of Buried Pipes”, Watkins, R.K, and Loren, R, A,
3. “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition,
Plastic Pipe Institute, Inc.
Technical Toolboxes, Inc.
Polyethylene Pipe Design and Pipeline Crossings
167
Spangler's Modified Iowa Formula for PE Pipe
Reference:
1. “Soil Engineering”, Third Edition, Spangler, M.G. and Handy, R.L., Intext
Educational Press
2. “Structural Mechanics of Buried Pipes”, Watkins, R.K, and Loren, R, A,
3. “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition,
Plastic Pipe Institute, Inc.
Technical Toolboxes, Inc.
168
Modulus of Soil Reaction (E') - Average Values for Iowa
Formula
Reference: “Modulus of Soil Reaction Values for Buried Flexible Pipe”, Journal of the
Geotechnical Engineering Division, ASCE, Vol. 103, No GT 1, Howard, A.K.
Technical Toolboxes, Inc.
Polyethylene Pipe Design and Pipeline Crossings
169
Modulus of Soil Reaction (E') - Values of E' for Pipe
Embedment
Reference:
“Evaluation of Modulus of Soil Reaction E and its Variation with Depth”, Report No.
UCB/GT/82-02,
Technical Toolboxes, Inc.
170
Values of E'n Native Soil Modules of Soil Reaction
Technical Toolboxes, Inc.
Polyethylene Pipe Design and Pipeline Crossings
171
Soil Support Factor (Fs)
Reference:
“Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition, Plastic Pipe
Institute, Inc.
Technical Toolboxes, Inc.
172
Pipe Wall Compressive Stress (PE Pipe Crushing)
Reference:
1. “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition,
Plastic Pipe Institute, Inc.
Technical Toolboxes, Inc.
Polyethylene Pipe Design and Pipeline Crossings
173
Distributed Static Surcharge Load Directly over Buried PE
Pipe
1. Dead/Earth Load
A. Prism Load
B . Marston Load (ASCE Manual No.60)
C. Combined Prism and Marston Load
174
For flexible pipe, a more conservative method is to use a soil pressure load in between
prism and Marston load:
2. Distributed Static Surchage Load
This method is using Boussinesq equation for pressure acting on pipe crown.
Influence coefficient is selected from the table below:
Polyethylene Pipe Design and Pipeline Crossings
175
3. Pipe Deflection is calculated using Spangler's Modified Iowa Formula:
4. Pipe Wall Compressive Stress
176
Reference:
1. “Soil Engineering”, Third Edition, Spangler, M.G. and Handy, R.L., Intext
Educational Press
2. “Structural Mechanics of Buried Pipes”, Watkins, R.K, and Loren, R, A,
3. “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition,
Plastic Pipe Institute, Inc.
Technical Toolboxes, Inc.
Polyethylene Pipe Design and Pipeline Crossings
177
Distributed Static Surcharge Load not over Buried PE Pipe
1. Dead/Earth Load
A. Prism Load
B . Marston Load (ASCE Manual No.60)
C. Combined Prism and Marston Load
178
For flexible pipe, a more conservative method is to use a soil pressure load in between
prism and Marston load:
2. Distributed Static Surchage Load not over PE Pipe
This method is using Boussinesq equation for pressure acting on pipe crown.
Polyethylene Pipe Design and Pipeline Crossings
179
Influence coefficient is selected from the table below:
3. Pipe Deflection is calculated using Spangler's Modified Iowa Formula:
180
4. Pipe Wall Compressive Stress
Reference:
1. “Soil Engineering”, Third Edition, Spangler, M.G. and Handy, R.L., Intext
Educational Press
2. “Structural Mechanics of Buried Pipes”, Watkins, R.K, and Loren, R, A,
3. “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition,
Plastic Pipe Institute, Inc.
Technical Toolboxes, Inc.
Polyethylene Pipe Design and Pipeline Crossings
181
Live Load: Aircraft Load on Buried PE Pipe
1. Dead/Earth Load
A. Prism Load
B . Marston Load (ASCE Manual No.60)
C. Combined Prism and Marston Load
182
For flexible pipe, a more conservative method is to use a soil pressure load in between
prism and Marston load:
2. Live Load: Aircraft Load on Buried PE Pipe
3. Pipe Deflection is calculated using Spangler's Modified Iowa Formula:
Polyethylene Pipe Design and Pipeline Crossings
183
4. Pipe Wall Compressive Stress
Reference:
184
1. “Soil Engineering”, Third Edition, Spangler, M.G. and Handy, R.L., Intext
Educational Press
2. “Structural Mechanics of Buried Pipes”, Watkins, R.K, and Loren, R, A,
3. “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition,
Plastic Pipe Institute, Inc.
Technical Toolboxes, Inc.
185
Index
A
A.G.A - Fully Turbulent Flow .................. 47
AccidentalFullBore ................................... 40
AccidentalSmallHole ................................ 37
Adobe .......................................................... 1
API 1102 - Steel Pipelines Crossing
Railroads and Highways ..................... 105
API 1104 - Appendix A
Weld Imperfection Assessment .. 139, 140
API 1117 - Movement of In-Service
Pipeline ................................................. 86
B
Blasting Analysis ...................................... 99
Buoyancy Analysis and Concrete Coating
Thickness .............................................. 92
Buoyancy Analysis and Concrete Weight
Spacing .................................................. 94
Bureau of Reclamation Average E' Values
for Iowa Formula ................................ 168
C
Cathodic Protection Attenuation Calculation
............................................................. 162
Centrifugal Compressor - Adiabatic Head 23
Centrifugal Compressor - Fan Laws ......... 29
Centrifugal Compressor - Required
Adiabatic Horsepower .......................... 25
Centrifugal Compressor - Required
Polyitropic Horsepower ........................ 27
Colebrook - White..................................... 48
Compressor Station Piping - Diameter and
Gas Velocity.......................................... 34
D
Dead Load on PE Pipe - Prism, Marston and
Combined Load ................................... 165
Design Pressure - Plastic Pipe............. 64, 65
Design Pressure - Steel Pipe ... 57, 58, 62, 63
Discharge Temperature ............................. 33
Distributed Static Surcharge Load not over
PE Pipe ................................................ 178
Distributed Static Surcharge Load over PE
Pipe ..................................................... 173
E
Electrical Resistance of a Conductor ...... 153
Electrolyte Resistance from the Surface of
an Electrode to any Distance............... 151
Estimated Life of a Magnesium Anode .. 155
F
Flume Design ............................................ 67
186
G
Gas Pipeline Pressure Testing - Maximum
Pressure Drop ...................................... 141
Gas Properties Calculations ........................ 9
GPTC Guide Pipeline Crossings ............. 137
H
Hoop Stress ............................................... 66
Hot Tap Sizing .......................................... 13
I
IGT ............................................................ 49
ImpactLoad ............................................... 82
L
Live Load
AASHTO H20 Load on Buried PE Pipe -
Flexible or no Pavement
Aircraft Load on Buried PE Pipe .... 183
Local Atmospheric Pressure ..................... 35
M
MaxSpan ................................................... 97
Mueller - High Pressure ............................ 50
Mueller - Low Pressure ............................. 51
Multiple Vertical Anode in Parallel ........ 159
N
NiSource Blowdown Calculations .......... 142
O
Ohm's Law for Corrosion Current .......... 152
Orifice Meters ........................................... 12
Outlook Express .......................................... 6
P
Pack in Pipeline................................. 41, 145
Panhandle - A ............................................ 52
Panhandle - B ............................................ 53
Pipe Requirements for Horizontally Drilled
Installation............................................. 90
Pipe Wall Compressive Stress (PE Pipe
Crushing)............................................. 172
Pipeline Anchor Force Analysis ............... 84
Pipeline Purging - Gas Volume Lost ...... 143
Pipeline Rupture Analysis................... 43, 79
Pittsburgh .................................................. 54
Power Consumption of a Cathodic
Protection Rectifier ............................. 164
R
Rate of Electrical Current Flow Through the
Corrosion Cell ..................................... 149
Reciprocating Compressors - Capacity and
Horsepower ........................................... 30
Regulator Station Sizing ........................... 11
Reinforcement of Welded Branch
Connection ............................................ 20
Index
187
Relationship Between Resistance and
Resistivity ........................................... 150
Relief Valve Sizing ................................... 15
Relief Valves
Reaction Force ...................................... 19
Required Number of Anodes and Total
Current Requirement ........................... 161
Resistance to Earth of an Impressed Anode
Ground Bed ......................................... 156
Restrained Gas Pipeline - Stress Analysis 59
Rudenberg Formula ................................ 157
S
Soil Support Factor (Fs) .......................... 171
Spangler's Modified Iowa Formula ......... 167
Spitzglass .................................................. 55
T
Thrust at Blow-off................................... 104
Track Load Analysis ............................... 130
U
Unrestrained Gas Pipeline Stress Analysis -
Steel Pipe .............................................. 61
V
Values of E' for Pipe Embedment ........... 169
Values of E'n Native Soil Modules of Soil
Reaction .............................................. 170
W
Weymouth ................................................. 56
Wheel Load Analysis .............................. 123
Word ........................................................... 4