Equipment Component and Compliance
Corrugated Metal, w/ Asbestos
or corrugated metal, jacketed
with:
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
2.50
2.75
3.00
3.25
3.50
2900.
3700.
4500.
5500.
6500.
2.75
3.00
3.25
3.50
3.75
3700.
4500.
5500.
6500.
7600.
3.25
3.50
3.75
3.50
3.75
3.75
5500.
6500.
7600.
8000.
9000.
9000.
3.25
3.50
3.75
3.75
4.25
5500.
6500.
7600.
9000.
10100.
4.00
4.75
5.50
6.00
6.50
8800.
13000.
18000.
21800.
26000.
Corrugated Metal:
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
Flat metal, jacketed asbestos
filled
soft aluminum
soft copper or brass
iron or soft steel
Monel
4%-6% chrome
Stainless steels and nickel
alloys
Grooved Metal
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
Solid flat metal
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
800
CAESAR II User's Guide
Equipment Component and Compliance
Gasket Seating Stress
Specifies the initial seating stress required for the gasket being used. This entry is required
only if ASME stress calculations are to be performed.
The following table, extracted from Sect VIII Div. 1 gives gasket factors for some common
types of gaskets.
Gasket Materials and Contact Facings Notes
Table 2-5.1
Gasket Material
Self-energizing types (O rings,
metallic elastomer, and other
self-sealing types)
Gasket Factor
Seating Stress
m
y (^06)
0.
0.
Elastomers without fabric or a
high percent of asbestos fiber:
Below 75A Shore Durometer
.50
75A or higher Shore Durometer 1.00
0.
200.
Asbestos with Suitable Binder
1/8" thick
1/16" thick
1/32" thick
2.00
2.75
3.50
600.
3700.
6500.
Elastomers with cotton fabric
1.25
400.
Elastomers with Asbestos fabric
3 ply
2.25
2 ply
2.50
1 ply
2.75
2200.
2900.
3700.
Vegetable fiber
1.75
1100.
2.50
3.00
10000.
10000.
Spiral-wound, asbestos filled:
Carbon
Stainless, Monel, Nickel alloys
CAESAR II User's Guide
801
Equipment Component and Compliance
Corrugated Metal, w/ Asbestos
or corrugated metal, jacketed
with:
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
2.50
2.75
3.00
3.25
3.50
2900.
3700.
4500.
5500.
6500.
2.75
3.00
3.25
3.50
3.75
3700.
4500.
5500.
6500.
7600.
3.25
3.50
3.75
3.50
3.75
3.75
5500.
6500.
7600.
8000.
9000.
9000.
3.25
3.50
3.75
3.75
4.25
5500.
6500.
7600.
9000.
10100.
4.00
4.75
5.50
6.00
6.50
8800.
13000.
18000.
21800.
26000.
Corrugated Metal:
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
Flat metal, jacketed asbestos
filled
soft aluminum
soft copper or brass
iron or soft steel
Monel
4%-6% chrome
Stainless steels and nickel
alloys
Grooved Metal
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
Solid flat metal
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel
alloys
802
CAESAR II User's Guide
Equipment Component and Compliance
Nubbin Width or Ring
Specifies the nubbin width, if applicable. This value is required only for facing sketches 1c, 1d,
2 and 6 (FLANGE) equivalents 3, 4, 5, and 9). For sketch 9, this is not a nubbin width but the
contact width of the metallic ring.
Facing Sketch
Specifies the facing sketch number according to the following correlations, according to
Table 2-5-2 of the ASME code.
Facing Sketch
CAESAR II Equivalent
Description
1a
1
flat finish faces
1b
2
serrated finish faces
1c
3
raised nubbin-flat finish
1d
4
raised nubbin-serrated finish
2
5
1/64 inch nubbin
3
6
1/64 inch nubbin both sides
4
7
large serrations, one side
5
8
large serrations, both sides
6
9
metallic O-ring type gasket
This value is required for calculating the contact gasket width and the effective gasket
diameter, G.
Facing Column
Specifies the facing column number according to the following correlations:
Gasket Material
Self-energizing types (O rings, metallic elastomer, and other
self-sealing types)
Facing Column
2
Elastomers without fabric or a high percent of asbestos fiber:
Below 75A Shore Durometer
75A or higher Shore Durometer
CAESAR II User's Guide
2
2
803
Equipment Component and Compliance
Asbestos with Suitable Binder
1/8" thick
1/16" thick
1/32" thick
2
2
2
Elastomers with cotton fabric
2
Elastomers with Asbestos fabric
3 ply
2 ply
1 ply
2
2
2
Vegetable fiber
2
Spiral-wound, asbestos filled:
Carbon
Stainless, Monel, Nickel alloys
2
2
Corrugated Metal, w/ Asbestos or corrugated metal, jacketed with:
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel alloys
2
2
2
2
3.50
Corrugated Metal:
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel alloys
2
2
2
2
2
Flat metal, jacketed asbestos filled
soft aluminum
soft copper or brass
iron or soft steel
Monel
4%-6% chrome
Stainless steels and nickel alloys
2
2
2
2
2
2
Grooved Metal
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
Stainless steels and nickel alloys
804
2
2
2
2
2
CAESAR II User's Guide
Equipment Component and Compliance
Solid flat metal
soft aluminum
soft copper or brass
iron or soft steel
Monel or 4%-6% chrome
2
2
2
2
Stainless steels and nickel alloys
2
Material Data Tab
The following options are used to define material and stress-related data.
Topics
Flange Material .............................................................................. 805
Bolt Material ................................................................................... 805
Design Temperature ...................................................................... 805
Flange Allowable @ Design Temperature..................................... 806
Flange Allowable @ Ambient Temperature................................... 806
Flange Modulus of Elasticity @ Design ......................................... 806
Flange Modulus of Elasticity @ Ambient ....................................... 806
Bolt Allowable @ Design Temperature ......................................... 807
Bolt Allowable @ Ambient Temperature ....................................... 807
Flange Allowable @ Stress Multiplier ............................................ 807
Bolt Allowable Stress Multiplier ..................................................... 808
Flange Material
Displays the material database for flanges, taken from ASME Section VIII, Division 1.
Bolt Material
Displays the material database for bolting, taken from ASME Section VIII, Division 1.
Design Temperature
Specifies the flange design temperature. This value is required for ASME stress
calculations, and for ANSI B16.5/API rating table look-ups.
The design temperature is not used in the flexibility model of the flange.
CAESAR II User's Guide
805
Equipment Component and Compliance
Flange Allowable @ Design Temperature
Specifies the allowable stress for the flange material at the design temperature. This value
is required only if an ASME stress analysis of the flange is to be performed.
This value is available in the ASME Sect. VIII Div. 1 material database delivered with the
software. You can access the database by typing a material name in the Flange Material box
or by clicking Browse and selecting a material in the Material Selection list.
After it is in the database, fill in the spaces for database entry where the defaults are not
correct. Press F1 when the material inputs are satisfactory. The material selection can be
changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when
the cursor is on the appropriate material. When you select the material in this way, it becomes
the default for the next material database entry.
Flange Allowable @ Ambient Temperature
Specifies the allowable stress for the flange material at the ambient temperature. This value
is only required if an ASME stress analysis of the flange is to be performed.
This value is available in the ASME Sect. VIII Div. 1 material database delivered with the
software. You can access the database by typing a material name in the Flange Material box
or by clicking Browse and selecting a material in the Material Selection list.
After it is in the database, fill in the spaces for database entry where the defaults are not
correct. Press F1 when the material inputs are satisfactory. The material selection can be
changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when
the cursor is on the appropriate material. When you select the material in this way, it becomes
the default for the next material database entry.
Flange Modulus of Elasticity @ Design
Defines the value of the modulus of elasticity to be used for the determination of the Flange
Rigidity Factor "J", for the DESIGN case defined in Appendix S of the A93 addendum.
Flange Modulus of Elasticity @ Ambient
Defines the value of the modulus of elasticity to be used for the determination of the Flange
Rigidity Factor "J", for the SEATING case defined in Appendix S of the A93 addendum.
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CAESAR II User's Guide
Equipment Component and Compliance
Bolt Allowable @ Design Temperature
Indicates the allowable stress for the bolt material at the design temperature. This value is
only required if an ASME stress analysis of the flange is to be performed.
This value is available in the ASME Sect. VIII Div. 1 material database delivered with the
software. You can access the database by typing a material name in the Flange Material box
or by clicking Browse and selecting a material in the Material Selection list.
After it is in the database, fill in the spaces for database entry where the defaults are not
correct. Press F1 when the material inputs are satisfactory. The material selection can be
changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when
the cursor is on the appropriate material. When you select the material in this way, it becomes
the default for the next material database entry.
Bolt Allowable @ Ambient Temperature
Specify the allowable stress for the bolt material at the ambient temperature. This value is
only required if an ASME stress analysis of the flange is to be performed.
This value is available in the ASME Sect. VIII Div. 1 material database delivered with the
software. You can access the database by typing a material name in the Flange Material box
or by clicking Browse and selecting a material in the Material Selection list.
After it is in the database, fill in the spaces for database entry where the defaults are not
correct. Press F1 when the material inputs are satisfactory. The material selection can be
changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when
the cursor is on the appropriate material. When you select the material in this way, it becomes
the default for the next material database entry.
Flange Allowable @ Stress Multiplier
Applies the increased allowable (1.5) for the radial and tangential operating ASME flange
allowables. This increase is implied in B31.1 Appendix II Section 4.2.3 when it states that the
longitudinal hub, tangential and radial stress allowables are equal to the yield stress at
design temperature, which is essentially 1.5(S).
Prior to the 1992 edition of the ASME NC code, NC paragraph 3658.1(d) also stated that
the tangential and radial stress allowables could be increased by 50%. The 1992 edition of NC
eliminated this increase on these allowables.
CAESAR II User's Guide
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Equipment Component and Compliance
Bolt Allowable Stress Multiplier
Designates a factor by which to increase the operating bolt allowables.
Section VIII Division 2, Article 4-141 of the ASME Boiler and Pressure Vessel Code allows
for operating loads on bolts to equal two times the standard table allowables. In some cases,
this increase can be by as much as three times the table allowables.
Loads Tab
The following options are used to describe the imposed loads.
Topics
Design Pressure ............................................................................ 808
Axial Force ..................................................................................... 808
Bending Moment ........................................................................... 808
Disable Leakage Calculations ....................................................... 808
Disable Stress Calculations ........................................................... 809
Disable ANSI B16.5 Check ............................................................ 809
Design Pressure
Indicates the internal line pressure (lbs./sq.in.) in gage. This pressure is used in the
flexibility model of the flange in the ASME stress calculations and is the B16.5/API rating.
Axial Force
Defines the externally applied axial force applied to the flange joint by the attached piping.
The software does not include the effect of shear forces in the flexibility model.
Bending Moment
Specifies the external moment applied to the flange joint by the attached piping. If you have
two bending moments, SRSS them and enter the result here.
Disable Leakage Calculations
Turns off the leakage calculations performed by CAESAR II. Use this option if you want a
flange report, which only contains ASME Section VIII, Division 1, Appendix 2 results.
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CAESAR II User's Guide
Equipment Component and Compliance
Disable Stress Calculations
Turns off the flange stress calculations performed by CAESAR II. Use this option if you want a
flange report, which only contains leakage calculations and omits ASME Section VIII, Division
1, Appendix 2 results.
Disable ANSI B16.5 Check
Turns off the report for the ANSI B16.5 Equivalent Pressure check. This check compares the
equivalent pressure to the MAWP (as listed in ANSI B16.5) for the flange class and material.
The ANSI MAWP does not consider bolting or gasket properties, and it is not a good indicator
of the leakage characteristics of the flange.
Flange Rating
This is an optional input. It has been a common practice in the industry to use the ANSI B16.5
and API 605 temperature/pressure rating tables as a gauge for leakage. Because these rating
tables are based on allowable stresses and are not intended for leakage prediction, the
leakage predictions that resulted are a function of the allowable stress for the flange material,
not the flexibility, or modulus of elasticity, of the flange. To give you a comparison to the old
practice, the minimum and maximum rating table values from ANSI and API are stored and are
used to print minimum and maximum leakage safety factors that are predicted from this
method. An example of the output that you get upon entering the flange rating is shown below:
EQUIVALENT PRESSURE MODEL ————————-Equivalent
Pressure (lb./sq.in.) 1639.85 ANSI/API Min
Equivalent Pressure Allowed 1080.00 ANSI/API
Max Equivalent Pressure Allowed 1815.00
According to the older method, this shows that leakage occurred if a carbon steel flange is
used, and leakage does not occur if an alloy flange is used. Both flanges have essentially the
same flexibility tendency to leak.
The following input parameters are used only for the ASME Section VIII Division 1
stress calculations:











Flange Type



Flange Outside Diameter


Design Temperature


Small End Hub Thickness

Large End Hub Thickness


Hub Length


Flange Allowables




Bolt Allowables



Gasket Seating Stress
Optional Allowable Multipliers

Flange Face & Gasket Dimensions
CAESAR II User's Guide

809
Equipment Component and Compliance
Specify the Flange Type (on page 793) on the Flange (see "Flange Tab" on page 793) tab.
To acquire material allowables from the Section VIII, Division 1 material library, use the Flange
Material (on page 805) list on the Material Data (see "Material Data Tab" on page 805) tab.
An input listing for a typical flange analysis is shown below:
CA E S A R I I MISCELLANEOUS REPORT
ECHO Flange Inside Diameter [B](in.)
30.560 Flange Thickness [t](in.) 4.060
Flange Rating (Optional) 300.000
Bolt Circle Diameter (in.) 38.500
Number of Bolts 32.000
Bolt Diameter (in.) 1.500
Bolt Initial Tightening Stress(lb./sq.in.)
Effective Gasket Diameter [G] (in.)
33.888 Uncompressed Gasket Thickness
(in.) 0.063 Basic Gasket Width [b0] (in.)
0.375 Leak Pressure Ratio [m] 2.750
Effective Gasket Modulus(b./sq.in.) 300,000.000
Externally Applied Moment (optional)(in.lb.)
24,000.000 Externally Applied Force (optional)(lb.)
1,000.000 Pressure [P](lb./sq.in.) 400.000
The following inputs are required only if you wish to perform
stress calcs as per Sect VIII Div. 1
Flange Type (1-8, see ?-Help or Alt-P to plot)
1.000 Flange Outside Diameter [A](in.) 41.500
Design Temperature°F 650.000
Small End Hub Thickness [g0](in.) 1.690
Large End Hub Thickness [g1](in.) 3.440
Hub Length [h](in.) 6.620
Flange Allowable @Design Temperature(lb./sq.in.) 17,500.000
Flange Allowable @Ambient Temperature(lb./sq.in.)
17,500.000 Flange Modulus of Elasticity @Design(lb./sq.in.)
0.279E+08 Flange Modulus of Elasticity @Ambient(lb./sq.in.)
0.279E+08 Bolt Allowable @Design Temperature(lb./sq.in.)
25,000.000 Bolt Allowable @Ambient Temperature(lb./sq.in.)
25,000.000 Gasket Seating Stress [y](lb./sq.in.) 3,700.000
Flange Allowable Stress Multiplier 1.000
Bolt Allowable Stress Multiplier (VIII Div 2 41411.000 Disable Leakage Calculations (Y/N) N
Flange Face OD or Lapjt Cnt OD(in.) 34.500
Flange Face ID or Lapjt Cnt ID(in.) 33.000
Gasket Outer Diameter (in.) 36.000
Gasket Inner Diameter (in.) 33.000
Nubbin Width (in.)
Facing Sketch 1.000
Facing Column 2.000
Disable Leakage Calculations (Y/N) N
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CAESAR II User's Guide
Equipment Component and Compliance
Pipeline Remaining Strength Calculations (B31G)
Analysis > B31G evaluates corroded pipelines to determine when specific pipe segments
must be replaced. The original B31G document is conservative. CAESAR II performs additional
calculations to modify the original criteria. This additional work can be found in project report
PR-3805, by Battelle, Inc. The details of the original B31G criteria, as well as the modified
methods, are discussed in detail in this report.
CAESAR II determines the following values according to the original B31G criteria and
four modified methods. The values are



The hoop stress to cause failure



The maximum allowed operating pressure


The maximum allowed flaw length
The four modified methods vary in the manner in which the corroded area is estimated.
The methods are:








.85dL - Approximates the corroded area as 0.85 times the maximum pit depth times the flaw length.
Exact - Determines the corroded area numerically using the trapezoid method.

Equivalent - Determines the corroded area by multiplying the average pit depth by the flaw
length. Additionally, an equivalent flaw length (flaw length
 * average pit depth / maximum
pit depth) is used in the computation of the Folias factor.
Effective - Uses a numerical trapezoid summation; however, various sub-lengths of the total
flaw length are used to arrive at a worst case condition. If the sub-length that produces the
worst case
 coincides with the total length, the Exact and Effective methods yield the same
result.
To begin, specify a new job name in the New Job Name Specification dialog box or
click Browse to navigate to an existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
CAESAR II User's Guide
811
Equipment Component and Compliance
The software opens the Pipeline Remaining Strength Calculations (B31G) window. The
window consists of two input tabs--Data (see "Data Tab" on page 813) and Measurements
(see "Measurements Tab" on page 815).
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CAESAR II User's Guide
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After the data is entered, click Run Analysis
report is shown below:



to begin the computations. A typical output
For additional
 information or backup on these computations, an intermediate computation file is
generated.
For more information on the analysis methods used
 by this command, see the B31G
document or the Battelle project report PR-3-805.
CAESAR II User's Guide
813
Equipment Component and Compliance
Data Tab
Most of the data required by this processor is acquired through actual field
measurements.
Topics
Pipe Nominal Diameter .................................................................. 814
Pipe Wall Thickness ...................................................................... 814
Design Pressure ............................................................................ 814
Material Yield Strength .................................................................. 814
Material Specified Minimum Yield ................................................. 814
Flaw Length ................................................................................... 814
Measurement Increment ................................................................ 815
Factor of Safety (FS) ..................................................................... 815
Design Factor (S) .......................................................................... 815
Pipe Nominal Diameter
Specifies the pipe diameter.
Pipe Wall Thickness
Specifies the un-corroded pipe wall thickness.
Design Pressure
Specifies the design pressure. This value is the maximum pressure reported in the output section,
although the maximum allowed pressure may be less than the input design pressure.
Material Yield Strength
Defines the material yield strength. If this value is unknown, enter the specified minimum
yield strength in this cell.
Material Specified Minimum Yield
Defines the minimum yield strength.
Flaw Length
Indicates the length of flaw or anomaly. This value is a measured quantity, usually taken in
a straight line.
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CAESAR II User's Guide
Equipment Component and Compliance
Measurement Increment
Specify the measurement increment in this cell. This value defines how often along the flaw
length depth or thickness measurements are made.
The number of measurements should be calculated by ( flaw length / measurement increment
)+1
Factor of Safety (FS)
Defines the factor of safety. For those pipelines in which the maximum operating stress level
does not exceed 72% of the specified minimum yield strength, the safety factor is 100/72 =
1.39. The safety factor cannot be less than 1.0.
Design Factor (S)
Specifies the design factor from the applicable piping code.
Measurements Tab
You can enter a maximum of twenty pit measurements on the Measurements input screen.
CAESAR II User's Guide
815
Equipment Component and Compliance
First, you must define the measurements. Select Pits if the measurements are in pit depths.
Select Thicknesses if the measurements are remaining wall thicknesses.
Pit depths are required for the computations. If remaining thicknesses are specified, the
pit depths are computed from wall thickness - remaining thickness.
In the individual cells, enter the measurement obtained along the flaw length. The values
are based on the selection of Pits or Thicknesses.
Expansion Joint Rating
Analysis > Expansion Joint Rating computes a limit for the total displacement per corrugation of
an expansion joint. According to EJMA (Expansion Joint Manufacturers Association), the maximum
permitted amount of axial movement per corrugation is defined as erated where
ex + ey + eq < erated
The terms in the above equation are defined as:







ex = The axial displacement per corrugation resulting from imposed axial movements.
ey = The axial displacement per corrugation resulting from imposed lateral deflections.


eq = The axial displacement per corrugation resulting from imposed angular rotation, that is, bending.

erated = The maximum permitted amount of axial
movement per corrugation. You can find this value
in the expansion joint manufacturer’s catalog.
In addition, EJMA states, “Also, [as an expansion joint is rotated or deflected laterally] it should
be noted that one side of the bellows attains a larger projected area than the opposite side.
Under the action of the applied pressure, unbalanced forces are set up which tend to distort
the expansion joint further. In order to control the effects of these two factors a second limit is
established by the manufacturer upon the amount of angular rotation and/or lateral deflection
which may be imposed upon the expansion joint. This limit may be less than the rated
movement. Therefore, in the selection of an expansion joint, care must be exercised to avoid
exceeding either of these manufacturer’s limits.”
This module is intended to assist you in satisfying these limitations. This module computes the
terms defined in the above equation and the movement of the joint ends relative to each other.
These relative movements are reported in both the local joint coordinate system and the
global coordinate system.
To begin, specify a new job name in the New Job Name Specification dialog box or
click Browse to navigate to an existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
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CAESAR II User's Guide
Equipment Component and Compliance
The software opens the EJMA Expansion Joint window. The window consists of three input
screens--Geometry (on page 820), Displacements and Rotations (on page 821), and
Allowables (on page 821).
After the necessary data is entered, click Run Analysis
to begin the computations. After
processing completes, a report displaying both the input echo and the output calculations
are shown on a new tab called Output.
CAESAR II User's Guide
817
Equipment Component and Compliance
The units used for the coordinate and displacement values are the length units defined in
the active units file. Rotations are in units of degrees.
C A E S A R II MISCELLANEOUS REPORT ECHO
EJMA EXPANSION JOINT RATING
Node Number for “FROM” end 120.000
Node Number for “TO” end 125.000
Number of Convolutions 4.000
Flexible Joint Length (in.)4.447
Effective Diameter(in.)4.996
X Coordinate of “from” end (in.).000
Y Coordinate of “from” end (in.).000
Z Coordinate of “from” end (in.).000
X Coordinate of “to” end (in.)4.447
X Displacement of “from” end (in.).300
Y Displacement of “from” end (in.).250
Z Displacement of “from” end (in.).000
X Rotation of “from” end (deg).000
Y Rotation of “from” end (deg)1.222
Z Rotation of “from” end (deg).030
X Displacement of “to” end (in.)-.100
Y Displacement of “to” end (in.).120
Z Displacement of “to” end (in.).000
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CAESAR II User's Guide
Equipment Component and Compliance
X Rotation of “to” end (deg).000
Y Rotation of “to” end (deg)-.020
Z Rotation of “to” end (deg).890
OUTPUT:
AXIAL DISPLACEMENTS PER
CONVOLUTION Axial Displacement.100
Axial Displacement due to Lateral .133
Axial Displacement due to Rotation.016
Axial Displacement TOTAL.250
RELATIVE MOVEMENTS OF END “i” WITH RESPECT TO END “j”
(Local Joint Coordinate System)
Relative Axial Displacement, “x”.401
Relative Lateral Displacement, “y”.158
Relative Bending, “theta” (deg)1.511
Relative Torsion (deg) .019
RELATIVE MOVEMENTS OF END “i” WITH RESPECT TO END “j”
(Global Piping Coordinate System)
Relative X Displacement-.399
Relative Y Displacement-.132
Relative Z Displacement.095 Relative
Rotation about X (deg).000 Relative
Rotation about Y (deg)-1.242
Relative Rotation about Z (deg).860
In the previous output, the axial displacement total in the report is the total axial displacement
per corrugation due to axial, lateral, and rotational displacement of the expansion joint ends.
This is the value that is compared to the rated axial displacement per corrugation. If e (total) is
greater than the rated axial displacement per corrugation, then there is the possibility of
premature bellows failure. Be sure that the displacement rating from the manufacturer is on a
per corrugation basis. If it is not, multiply the axial displacement total by the number of
corrugations and compare this value to the manufacturer’s allowable axial displacement. Most
manufacturers allowed rating is for some set number of cycles (often 10,000). If the actual
number of cycles is less, then the allowed movement can often be greater. Similarly, if the
actual number of cycles is greater than 10,000, then the allowed movement can be smaller. In
special situations, contact the manufacturers because many factors can affect allowed bellows
movement.
The y in the report is the total relative lateral displacement of one end of the bellows with
respect to the other, and theta is the total relative angular rotation of one end of the bellows
with respect to the other. CAESAR II does not include x in the denominator for the lateral
displacement calculations as outlined in EJMA.
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Geometry
Topics
Node Number for "From" End ........................................................ 820
Node Number for "To" End ............................................................ 820
Number of Convolutions ................................................................ 820
Flexible Joint Length ...................................................................... 820
Effective Diameter ......................................................................... 820
Z Axis Up ....................................................................................... 821
Coordinates ................................................................................... 821
Node Number for "From" End
Identifies the node number that represents the From end of the expansion joint. This value
is used for labeling purposes.
Node Number for "To" End
Identifies the node number that represents the To end of the expansion joint. This value is
used for labeling purposes.
Number of Convolutions
Defines the number of convolutions in the expansion joint.
Flexible Joint Length
Specifies the flexible length of the bellows.
Effective Diameter
Specifies the diameter of the circle whose area is equal to the effective area of the
expansion joint. The effective ID can be estimated using the following equation:
1.13 * sqrt (Effective Area)
You can find the effective area of the joint in the manufacturer's catalog.
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Z Axis Up
Indicates that the z-axis is upward in your CAESAR II input file.
Coordinates
Defines the spatial coordinate at the appropriate end of the expansion joint
Displacements and Rotations
Defines the displacements and rotations at the appropriate end of the expansion joint.
These values typically come from the displacement report of a CAESAR II run.
Allowables
Specifies the allowed expansion joint movement (translation or rotation) on a per convolution
basis and for the entire bellows. Enter values using the following units of measure:
Axial
inches
Lateral
inches
Bending
inches or degrees
Torsional
inches or degrees
You can acquire this data using the vendor catalog.
Structural Steel Checks - AISC
Analyze > AISC performs AISC code check on structural steel elements. Compliance is
evaluated according to the AISC (American Institute of Steel Construction) code. This code
check uses the forces and moments at the ends of the structural members, computes stresses,
and allowables, and determines a unity check value. If the unity check value is less than 1.0,
the member is acceptable for the given loading conditions. CAESAR II performs the AISC unity
check according to either the 1977 or the 1989 edition of the AISC code.
Member properties are obtained from the AISC database and used to compute the actual
and allowable stress values for the axial and bending terms comprising the unity check
equations. The database must be either AISC77.BIN or AISC89.BIN and is set using Tools >
Configuration/Setup. For more information, see Configuration and Environment (on page 45).
There are a few differences between the 1977 and 1989 AISC Code Revisions that affect unity
check computation. The most noticeable difference is that the 1989 code provides a method
for computing the unity check on single angles. This procedure, which was not addressed in
the 1977 code, can be found in a special code section following the commentary. The steps
necessary to compute the unity check for single angles can be followed by reviewing the
message file (generated upon request).
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The other differences between these two code revisions deal with members in compression.
Several constants for Qs have been altered, and a new factor k c” has been added. “kc” is a
compression element restraint coefficient defined in the 1989 edition of the code.
Because of these code differences, CAESAR II stores the name of the active database in the
input file for the AISC module when the data file is first created. Attempting to switch
databases or compute unity checks on angles using the 1977 code generates error messages
and processing terminates. You are urged to consult the applicable AISC Manuals when using
this command.
To begin the unity check calculations, specify a new job name in the New Job
Name Specification dialog box or click Browse to navigate to an existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
The software displays the AISC window, which consists of two input screens:Global Input
(on page 824) and Local Member Data (see "Local Member Data Tab" on page 826).
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Output Reports
You can direct the output reports to the screen or to a printer. The output report begins with
a one page summary describing the current global data and units, as shown below.
The remaining pages in the output report show the data for the individual members. The last
column of the report contains the most important data (namely the unity check value) and
the governing AISC equation. A sample member output reports are shown below. The report
is applicable to jobs where sidesway is allowed.
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Global Input
The following options are used to enter data that applies to all members being evaluated.
Topics
Structural Code .............................................................................. 824
Allowable Stress Increase Factor .................................................. 824
Stress Reduction Factors Cmy and Cmz ...................................... 824
Young’s Modulus ........................................................................... 825
Material Yield Strength .................................................................. 825
Bending Coefficient ....................................................................... 825
Form Factor Qa ............................................................................. 825
Allow Sidesway .............................................................................. 825
Resize Members Whose Unity Check Value Is . . . ....................... 825
Minimum Desired Unity Check ...................................................... 826
Maximum Desired Unity Check ..................................................... 826
Structural Code
Identifies the code and year, typically matching the database in use. Slight variations in the
computations depend on which code year is selected. Single angles can only be checked
if AISC 1989 is selected.
Allowable Stress Increase Factor
Designates the multiplication factor applied to the computed values of the axial and bending
allowable stresses. Typically, this value is 1.0. However, in extreme events, such as
earthquakes and 100-year storms, the AISC code permits the allowable stresses to be
increased by a factor. Usually, a 1/3 increase is applied to the computed allowables, making
the allowable stress increase factor equal to 1.33. For more details see the AISC code, section
1.5.6.
Stress Reduction Factors Cmy and Cmz
Specifies the interaction formula coefficients (Cmy and Cmz) for the strong and weak axis of
the elements (in-plane and out-of-plane). Values include the following:



0.85 for compression members in frames subject to joint translation (sidesway).

For restrained compression members in frames braced against
sidesway and not subject to
transverse loading between supports in the plane of bending:
0.6 - 0.4(M1/M2)
but not less than 0.4, where (M1/M2) is the ratio of the smaller to larger moments at the ends,
of that portion of the member un-braced in the plane of bending under consideration.
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


For compression members in frames braced against joint translation in the plane of loading
and subject to transverse loading between supports, the value of Cmy can be determined
by rational analysis. Alternatively, the following values are suggested per the AISC code:


0.85 for members whose ends are restrained against rotation in the plane of bending.
1.0 for members whose ends are unrestrained against rotation in the plane of bending.


Young’s Modulus
Specifies the slope of the linear portion of the stress-strain diagram. For structural steel
this value is usually 29,000,000 psi.
Material Yield Strength
Defines the minimum yield stress of the steel being used. The term yield stress denotes the
minimum yield point (for those steels that have a yield point) or the minimum yield strength
(for those that do not have a yield point).
Bending Coefficient
Specifies the bending coefficient (Cb). Use 1.0 in computing the value of Fby and Fbz for use
in Formula 1.6-1a or when the bending moment at any point in an unbraced length is larger
than the moment at either end of the same length. Otherwise, Cb shall be:
Cb = 1.75 + 1.05(M1/M2) + 0.3(M1/M2)2
but not more than 2.3, where (M1/M2) is the ratio of the smaller to larger moments at the ends.
Form Factor Qa
Defines the allowable axial stress reduction factor equal to the effective area divided by
the actual area.
Consult the latest edition of the AISC code for the current computation methods for the
effective area.
Allow Sidesway
Controls the ability of a frame or structure to experience sidesway (joint translation). This
affects the computation of several of the coefficients used in the unity check equations.
Additionally, for frames braced against sidesway, moments at each end of the member are
required. Sidesway is allowed.
Resize Members Whose Unity Check Value Is . . .
Determines whether the AISC module attempts to resize specific members as a result of the
unity check computations. This option is most often used for an initial pass at optimization.
Selecting this option requires that you specify a minimum unity check and a maximum
unity check. If the computed unity check falls outside this range, the module resizes the
member appropriately. The final member size is shown in the output report.
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A resized member overwrites the initial input member size in the input file (input and output
share a common file). If member resizing occurs, check the final member size to ensure
the following:
1.
The selected member is commonly available.
2.
The selected member is optimal in its group.
3.
The selected member does not violate fabrication requirements for flange or web size.
Minimum Desired Unity Check
Defines the minimum acceptable unity check allowed. Accepted values are between 0.0
and 1.0. Members whose computed unity check value is less than this minimum are resized
to a smaller shape.
The Minimum Desired Unity Check value must be less than the Maximum Desired
Unity Check value. The recommended value for the minimum desired unity check is 0.7,
which allows lightly loaded members to be reduced in size.
Maximum Desired Unity Check
Defines the maximum acceptable unity check allowed. Accepted values are between 0.0 and
1.0. Members whose computed unity check value is greater than this maximum are resized to
a larger shape.
The Maximum Desired Unity Check value must be greater than the Minimum
Desired Unity Check value. The recommended value for the maximum desired unity check
is 0.9, which leaves a margin for loading inaccuracies.
Local Member Data Tab
The following options are used to enter local member data for each member being evaluated.
Topics
Member Start Node ....................................................................... 827
Member End Node ........................................................................ 827
Member Type................................................................................. 827
In-And Out-Of-Plane Fixity Coefficients Ky And Kz....................... 827
Unsupported Axial Length ............................................................. 828
Unsupported Length (In-Plane Bending) ....................................... 828
Unsupported Length (Out-Of-Plane Bending) ............................... 828
Double Angle Spacing ................................................................... 828
Young's Modulus ........................................................................... 828
Material Yield Strength .................................................................. 828
Axial Member Force ...................................................................... 828
In-Plane Bending Moment ............................................................. 829
Out-of-Plane Bending Moment ...................................................... 829
In-Plane “Small” Bending Moment ................................................ 829
In-Plane “Large” Bending Moment ................................................ 829
Out-of-Plane “Small” Bending Moment ......................................... 829
Out-of-Plane “Large” Bending Moment ......................................... 829
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Member Start Node
Identifies the start node, or “i” end, of a structural element. This option is required. Enter
an integer value between 1 and 32,000.
Member End Node
Identifies the member end node, or the “j” end, of a structural element. This option is required.
Enter an integer value between 1 and 32,000.
Member Type
Specifies the AISC shape label found in the AISC manual. The shape label is used to
acquire the member geometric properties from the database. For properties to be obtained,
the label you enter must match exactly the label in the database.
Because many of the angle labels can be found in the single angles, the double angles (long
legs back to back), and the double angles (short legs back to back), require an angle type to
tell them apart. Enter a D double angles with equal legs, and double angles with long legs back
to back. Enter a B for double angles with short legs back to back.
In-And Out-Of-Plane Fixity Coefficients Ky And Kz
Specifies the coefficients used to compute the strong and weak axis slenderness ratios.
Recommended values are listed in the following table:
End Conditions Theoretical K Recommended Design K
fixed-fixed
0.5
0.65
fixed-pinned
0.7
0.8
fixed-sliding
1.0
1.2
pinned-pinned
1.0
1.0
fixed-free
2.0
2.1
pinned-sliding
2.0
2.0
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Unsupported Axial Length
Defines the length used to determine the buckling strength of the member. Typically, this is
the total length of the member.
Unsupported Length (In-Plane Bending)
Defines the length of the member between braces or supports which prevent bending about
the strong axis of the member.
Unsupported Length (Out-Of-Plane Bending)
Defines the length of the member between braces or supports which prevent bending about
the weak axis of the member.
Double Angle Spacing
Indicates the gap or space separating the adjacent legs. The spacing, as defined in the
AISC manual, must be 0.0, .375, or .75-inches.
Young's Modulus
Specifies the slope of the linear portion of the stress-strain diagram. For structural steel this
value is usually 29,000,000 psi. This value of Young’s modulus overrides the Young's
Modulus (see "Young’s Modulus" on page 825) value specified on the Global Input tab.
Material Yield Strength
Defines the minimum yield stress of the steel being used. The term yield stress denotes the
minimum yield point (for those steels that have a yield point) or the minimum yield strength
(for those that do not have a yield point). This value of the material yield strength overrides the
Material Yield Strength (on page 825) value specified on the Global Input tab.
Axial Member Force
Specifies the force (tension or compression) that acts along the axis of the member. The sign of
the number is not significant because a worst case load condition is assumed, that is, all
positive loads.
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In-Plane Bending Moment
Specifies the maximum bending moment in the member (when sidesway is permitted) that
will cause bending about the strong axis Y-Y of the member. The sign of the number is not
significant because a worst case load condition of all positive loads is assumed
Out-of-Plane Bending Moment
Specifies the maximum bending moment in the member (when sidesway is permitted) that will
cause bending about the weak axis Z-Z of the member. The sign of the number is not
significant because a worst case load condition of all positive loads is assumed
In-Plane “Small” Bending Moment
Specifies the end moments for structures braced against sidesway. This value is the smaller of the
two in-plane bending moments that cause bending about the strong axis Y-Y of the member.
In-Plane “Large” Bending Moment
Specifies the end moments for structures braced against sidesway. This value is the larger
of the two in-plane bending moments which cause bending about the strong axis Y-Y of the
member.
Out-of-Plane “Small” Bending Moment
Specifies the end moments for structures braced against sidesway. This value is the smaller
of the two out-of-plane bending moments that cause bending about the weak axis Z-Z of the
member.
Out-of-Plane “Large” Bending Moment
Specifies the end moments for structures braced against sidesway. This value is the larger
of the two out-of-plane bending moments that cause bending about the weak axis Z-Z of the
member.
NEMA SM23 (Steam Turbines)
Analysis > NEMA SM23 evaluates piping loads on steam turbine nozzles. There are two
types of force/moment allowables computed during a NEMA run:



Individual nozzle allowables.
Cumulative equipment allowables.


Each individual suction, discharge, and extraction nozzle must satisfy the equation:
3F + M < 500De
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Equipment Component and Compliance
Where:
F = resultant force on the particular nozzle.
M = resultant moment on the particular nozzle.
De = effective nominal pipe size of the connection.
A typical discharge nozzle calculation is shown below
For cumulative equipment allowables, NEMA SM23 states that "the combined resultants of the
forces and moments of the inlet, extraction, and exhaust connections resolved at the centerline of
the exhaust connection", be within a certain multiple of Dc, where Dc is the diameter of an opening
whose area is equal to the sum of the areas of all of the individual equipment connections. A typical
turbine cumulative (summation) equipment calculation is shown below:
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SFX, SFY, and SFZ are the respective components of the forces from all connections
resolved at the discharge nozzle. FC(RSLT) is the result of these forces. SMX, SMY and SMZ
are the respective components of the moments from all connections resolved at the discharge
nozzle. Dc is the diameter of the equivalent opening as discussed above.
The software opens the NEMA SM23 window. Aside from the description, there is only one input
tab for the NEMA turbine. The Nema Input tab enables iterative addiction of an arbitrary
number of nozzles to the model. To add a nozzle, click Add Nozzle.
NEMA Turbine Example
Consider a turbine where node 35 represents the inlet nozzle and node 50 represents the
outlet nozzle. The output from a CAESAR II analysis of this piping system includes the forces
and moments acting on the pipe elements that attach to the turbine:
NODE
FX
FY
FZ
MX
MY
MZ
30
-108
-49
-93
73
188
603
35
108
67
93
162
-47
-481
50
-192
7
-11
369
-522
39
55
192
-63
11
78
117
-56
To find the forces acting on the turbine at points 35 and 50, reverse the sign of the forces
that act on the piping:
LOADS ON TURBINE @ 35 -108 -67 -93 -162 47 481
LOADS ON TURBINE @ 50 192 -7 11 -369 522 -39
Output Reports
The first page of the output is the input echo. The second page, as well as some of
the remaining pages, display the individual nozzle calculations. The last page displays
the summation calculations. The example below shows a sample input echo report.
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The actual number of output pages varies and depends on the number of nozzles defined
in the input.
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The NEMA output report for the above turbine example shows that the turbine passed. The
highest summation load is only 56% of the allowable. If the turbine had failed, **FAILED**
would have displayed, in red, under the STATUS column opposite to the load combination that
was excessive. The following two examples show sample NEMA output nozzle calculations and
NEMA output summation calculations, respectively.
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NEMA Input Data Tab
The following options are used to enter input data used to evaluate piping loads for
steam turbine nozzles.
Topics
Z-Axis Vertical................................................................................ 834
Cos X & Y ...................................................................................... 834
Nozzle Number .............................................................................. 834
Nozzle Type ................................................................................... 835
Nozzle Diameter ............................................................................ 835
DX .................................................................................................. 835
DY .................................................................................................. 835
DZ .................................................................................................. 836
Global Force FX ............................................................................ 836
Global Force FY ............................................................................ 836
Global Force FZ ............................................................................. 836
Global Moment MX ........................................................................ 836
Global Moment MY ........................................................................ 836
Global Moment MZ ........................................................................ 836
Select Load Jobs and Load Case ................................................. 837
Z-Axis Vertical
Controls the plane in which the Z-axis lies. By default, CAESAR II assumes the Y-axis is
vertical with the X- and Z-axes in the horizontal plane. If you select this option, the software
places the Z-axis in the vertical plane, and the X- and Y-axes are in the horizontal plane.
Cos X & Y
Specifies the direction cosines (X, Z) for the equipment shaft centerline. For example, if shaft
CL is along the Z-axis, the direction cosines are as follows:
cosine X = 0.0
cosine Z = 1.0
Nozzle Number
Identifies the node number that describes the nozzle flange connection. Enter a positive
number only.
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Nozzle Type
Identifies the nozzle type. This is used only for informational purposes in the output report.
Nozzle Diameter
Specifies the nozzle pipe nominal diameter.
DX
Specifies the X-distance from the force/moment resolution point to the nozzle.
NEMA SM 23 is ambiguous about the point of resolution of the combined forces and moments.
The resolution points are interpreted to be the following two points:
1.
The face of the flange at the exhaust nozzle connection.
2.
The intersection point of the exhaust nozzle centerline and the equipment shaft centerline.
In order to resolve the forces and moments at the current nozzle connection, enter the Xdistance from the current nozzle to each connection. Distance from the exhaust to the exhaust
nozzle is 0.0. In order to resolve the forces and moments at the intersection point of the exhaust
nozzle and the shaft centerlines, enter the X-distance from the intersection point to each
connection.
DY
Specifies the Y-distance from the force/moment resolution point to the nozzle.
NEMA SM 23 is ambiguous about the point of resolution of the combined forces and moments.
The resolution points are interpreted to be the following two points:
1.
The face of the flange at the exhaust nozzle connection.
2.
The intersection point of the exhaust nozzle centerline and the equipment shaft centerline.
In order to resolve the forces and moments at the current nozzle connection, enter the Ydistance from the current nozzle to each connection. Distance from the exhaust to the exhaust
nozzle is 0.0. In order to resolve the forces and moments at the intersection point of the exhaust
nozzle and the shaft centerlines, enter the Y-distance from the intersection point to each
connection.
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DZ
Specifies the Z-distance from the force/moment resolution point to the nozzle.
NEMA SM 23 is ambiguous about the point of resolution of the combined forces and moments.
The resolution points are interpreted to be the following two points:
1.
The face of the flange at the exhaust nozzle connection.
2.
The intersection point of the exhaust nozzle centerline and the equipment shaft centerline.
In order to resolve the forces and moments at the current nozzle connection, enter the Zdistance from the current nozzle to each connection. Distance from the exhaust to the exhaust
nozzle is 0.0. In order to resolve the forces and moments at the intersection point of the exhaust
nozzle and the shaft centerlines, enter the Z-distance from the intersection point to each
connection.
Global Force FX
Specifies the X-component of the force that the piping system exerts on the nozzle.
Global Force FY
Specifies the Y-component of the force that the piping system exerts on the nozzle.
Global Force FZ
Specifies the Z-component of the force that the piping system exerts on the nozzle.
Global Moment MX
Specifies the X-component of the moment that the piping system exerts on the nozzle.
Global Moment MY
Specifies the Y-component of the force that the piping system exerts on the nozzle.
Global Moment MZ
Specifies the Z-component of the force that the piping system exerts on the nozzle.
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Select Load Jobs and Load Case
Opens up a dialog box that you can use to navigate to the appropriate loads job or load case.
API 610 (Centrifugal Pumps)
Analyze > API 610 evaluates piping loads on centrifugal pumps. In October 2004, API
released the 10th edition of API 610 for centrifugal pumps for general refinery service. The API
610 load satisfaction criteria are outlined below:
If clause F.1.2 is satisfied, then the pump is acceptable. Clause F.1.2a states that the
individual component nozzle loads must fall below two times the allowables listed in the Nozzle
Loadings table (Table 4) shown below:
Further, F.1.2 b) and c) must also be satisfied.
Clause F.1.2b states that the resultant applied forces and moments acting on each pump
nozzle flange shall satisfy the equations F.1 and F.2 of the code. Referring to the API 610
report, you can determine whether F.1.2b is satisfied by comparing the Force/Moment to two. If
either resultant exceeds two, the nozzle status is reported as ** FAILED **.
The F.1.2c requirements give equations translating the applied component forces and moments
to the center of the pump. The requirements of these equations, and whether they have
satisfied API 610, are shown on the bottom of the report.
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To begin an analysis of piping loads on centrifugal pumps, specify a new job name in the
New Job Name Specification dialog box or click Browse to navigate to an existing job file. .
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
The software displays the API 610 window, which consists of three data input tabs: Input
Data (see "Input Data Tab" on page 843), Suction Nozzle (see "Suction Nozzle Tab" on page
846), and Discharge Nozzle (see "Discharge Nozzle Tab" on page 847).
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The following example is taken from the API 610 code and shows the review of an overhung
end-suction process pump in English units. The three CAESAR II input tabs are shown.
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An example of the processing output is shown below:
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API 610 Discharge Nozzle
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Input Data Tab
The following options are used to enter input data used to evaluate piping loads on
centrifugal pumps.
Topics
Vertical In-Line Pumps .................................................................. 844
Centerline Direction Cosine X ....................................................... 844
Centerline Direction Cosine Z........................................................ 844
Basepoint Node Number ............................................................... 845
Suction Nozzle Node Number ....................................................... 845
Suction Nozzle Nominal Diameter ................................................. 845
Suction Nozzle Type ...................................................................... 845
Discharge....................................................................................... 845
Discharge Nozzle Nominal Diameter ............................................ 845
Discharge Nozzle Type ................................................................. 845
Factor for Table 4 Allowables ........................................................ 846
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Vertical In-Line Pumps
Indicates that the pump is the vertical in-line type supported only by the attached piping. API
states that for the vertical in-line pump, you can use 2.0 times the loads from Table 4.
However, even if the pump fails the 2.0 Table 2 criteria, it may still pass. If the principal stress
on the nozzle is less than 6,000 psi, then that nozzle passes. If the principal stress on either
nozzle is greater than 6,000 psi, the overall status is reported as **FAILED**
In API 610 there is an example problem which illustrates the way stresses are computed
on these in-line pump nozzles. The two basic equations for determining stress are
Stresses (s) = Force / Area + Moment / Section Modulus
Shear Stresses (t) = Force / Area + Torque * distance / J
Where J is the polar moment of inertia.
In the second equation, both terms of the equation are always added together. On the other
hand, the Force/Area term in the first equation depends on the sign of the force (tension or
compression) that you enter in the force and moment spreadsheet. The sign of the force is
determined by Centerline Direction Cosine X (on page 844). For vertical in-line pumps, enter
the value in the direction extending from the discharge to the suction nozzle. The distances that
are usually entered for pedestal mounted pumps can be left blank because they are not used.
Centerline Direction Cosine X
Indicates one of the following, depending on whether Vertical In-Line Pumps is selected.

Vertical In-Line Pumps - Specifies the direction cosines (X,Z) for the nozzles. The positive
direction is from discharge to the
 suction nozzle. For example, if the nozzles are in the Xaxis, the direction cosines are:
cosine X=1.0
cosine Z=0.0

Horizontal Pumps - Specifies the direction cosines (X,Z) for the pump
 centerline. For
example, if the pump is along the Z-axis, the direction cosines are:
cosine X=0.0
cosine Z=1.0
Centerline Direction Cosine Z
Indicates one of the following, depending on whether Vertical In-Line Pumps is selected.

Vertical In-Line Pumps - Specifies the direction cosines (X,Z) for the nozzles. The positive
direction is from discharge to the
 suction nozzle. For example, if the nozzles are in the Xaxis, the direction cosines are:
cosine X=1.0
cosine Z=0.0

Horizontal Pumps - Specifies the direction cosines (X,Z) for the pump
 centerline. For
example, if the pump is along the Z-axis, the direction cosines are:
cosine X=0.0
cosine Z=1.0
844
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Equipment Component and Compliance
Basepoint Node Number
Identifies the node number that describes the intersection of the axis of the shaft and the
centerline of the pedestals. Enter only a positive value. This node does not have to appear
in any of the piping models but is used by API 610 as a point of reference on the pump
about which to sum moments.
In the 8th Ed. of the Standard, the base point refers to the center of the pump. The center of
the pump is defined by the intersection of the pump shaft centerline and a vertical plane
passing midway between the four pedestals.
Suction Nozzle Node Number
Identifies the node number that describes the suction nozzle flange connection. Enter only
a positive number.
Suction Nozzle Nominal Diameter
Defines the suction nozzle pipe nominal diameter.
Suction Nozzle Type
Specifies the location of the suction nozzle. Select Top, Side, or End. Each position
has different allowables.
For pumps with centerline along Y-axis (vertical), select Side.
Discharge
Identifies the node number that describes the discharge nozzle flange connection. Enter only
a positive number.
Discharge Nozzle Nominal Diameter
Defines the discharge nozzle pipe nominal diameter.
Discharge Nozzle Type
Specifies the location of the discharge nozzle. Select Top, Side, or End. Each position
has different allowables.
For pumps with centerline along Y-axis (vertical), select Side.
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Equipment Component and Compliance
Factor for Table 4 Allowables
Defines the factor by which all Table 4 allowables are multiplied. This value is between 1.0 and
2.0. Values less than 1.0 are replaced by a default factor of 1.0, while values larger than 2.0
are replaced by a default factor of 2.0. If left blank, a default value of 1.0 is used.
Typically, a value of 1.0 is used when evaluating individual nozzle loads. When checking
vertical in-line pumps, this value can be equal to 2.0. The value of 2.0 is also valid when suction
and discharge nozzle loads are evaluated together as defined in Appendix F of the API 610
Standard.
Suction Nozzle Tab
The following options are used to enter input data for suction nozzles.
Topics
DX .................................................................................................. 846
DY .................................................................................................. 846
DZ .................................................................................................. 847
Forces on Nozzle ........................................................................... 847
Moments on Nozzle ....................................................................... 847
DX
Specifies the distance between the suction nozzle and base point along the X-axis. Enter a
positive value if the suction nozzle X-coordinate is greater than that of the base point, that is,
if the suction nozzle is farther out on the positive X-axis.




When analyzing vertical in-line pumps, the X-, Y-, and Z-distances (DX, DY, and DZ) are not used.
The API 610 10th Edition defines the base point as the center of the pump. The center of
the pump is defined as the intersection of the pump
 shaft centerline and a vertical plane
passing through the center of the two pedestals.
DY
Specifies the distance between the suction nozzle and base point along the Y-axis. Enter a
positive value if the suction nozzle Y-coordinate is greater than that of the base point, that is,
if the suction nozzle is farther out on the positive Y-axis.



846

When analyzing vertical in-line pumps, the X, Y, and Z distances (DX, DY, and DZ) are not used.
The API 610 10th Edition defines the base point as the center of the pump. The center of
the pump is defined as the intersection of the pump
 shaft centerline and a vertical plane
passing through the center of the two pedestals.
CAESAR II User's Guide
Equipment Component and Compliance
DZ
Specifies the distance between the suction nozzle and base point along the Z-axis. Enter a
positive value if the suction nozzle Z-coordinate is greater than that of the base point, that is,
if the suction nozzle is farther out on the positive Z-axis.




When analyzing vertical in-line pumps, the X, Y, and Z distances (DX, DY, and DZ) are not used.
The API 610 10th Edition defines the base point as the center of the pump. The center of
the pump is defined as the intersection of the pump
 shaft centerline and a vertical plane
passing through the center of the two pedestals.
Forces on Nozzle
Identifies the X-, Y-, or Z-component of the force that the piping system exerts on the
suction nozzle.
Enter the forces in their global orientation. For vertical in-line pumps, the orientation of
the nozzle centerline is used to determine if the nozzle is in tension or compression.
Positive direction is from discharge to suction nozzle.
Moments on Nozzle
Identifies the X-, Y-, or Z-component of the moment that the piping system exerts on the
suction nozzle.
Discharge Nozzle Tab
The following options are used to enter input data used for discharge nozzles.
Topics
DX .................................................................................................. 848
DY .................................................................................................. 848
DZ .................................................................................................. 848
Forces on Nozzle ........................................................................... 849
Moments on Nozzle ....................................................................... 849
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Equipment Component and Compliance
DX
Specifies the distance between the discharge nozzle and base point along the X-axis. Enter a
positive value if the discharge nozzle X-coordinate is greater than that of the base point, that
is, if the discharge nozzle is farther out on the positive X-axis.




When analyzing vertical in-line pumps, the X-, Y-, and Z- distances (DX, DY, and DZ) are not used.
The API 610 10th Edition defines the base point as the center of the pump. The center of
the pump is defined as the intersection of the pump
 shaft centerline and a vertical plane
passing through the center of the two pedestals.
DY
Specifies the distance between the discharge nozzle and base point along the Y-axis. Enter a
positive value if the discharge nozzle Y-coordinate is greater than that of the base point, that
is, if the discharge nozzle is farther out on the positive Y-axis.




When analyzing vertical in-line pumps, the X-, Y-, and Z-distances (DX, DY, and DZ) are not used.
The API 610 10th Edition defines the base point as the center of the pump. The center of
the pump is defined as the intersection of the pump
 shaft centerline and a vertical plane
passing through the center of the two pedestals.
DZ
Specifies the distance between the discharge nozzle and base point along the Z-axis. Enter a
positive value if the discharge nozzle Z-coordinate is greater than that of the base point, that
is, if the discharge nozzle is farther out on the positive Z-axis.



848

When analyzing vertical in-line pumps, the X-, Y-, and Z-distances (DX, DY, and DZ) are not used.
The API 610 10th Edition defines the base point as the center of the pump. The center of
the pump is defined as the intersection of the pump
 shaft centerline and a vertical plane
passing through the center of the two pedestals.
CAESAR II User's Guide
Equipment Component and Compliance
Forces on Nozzle
Identifies the X-, Y-, or Z-component of the force that the piping system exerts on the
discharge nozzle.
Enter the forces in their global orientation. For vertical in-line pumps, the orientation of
the nozzle centerline is used to determine if the nozzle is in tension or compression.
Positive direction is from discharge to suction nozzle.
Moments on Nozzle
Identifies the X-, Y-, or Z-component of the moment that the piping system exerts on
the discharge nozzle.
API 617 (Centrifugal Compressors)
Analysis > API 617 evaluates piping loads on compressors. The requirements of this
standard are similar to those of NEMA SM-23 (1991). The allowable load values for API-617
are approximately 85% higher than the NEMA allowables.
To begin, specify a new job name in the New Job Name Specification dialog box or
click Browse to navigate to an existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
The software opens the API 617 window, which consists of the following five input tabs:
API 617 Input (see "API 617 Input Tab" on page 850)
Suction Nozzle (see "Suction Nozzle Tab" on page 852)
Discharge Nozzle (see "Discharge Nozzle Tab" on page 853)

























Extraction Nozzle #1 (see "Extraction Nozzle #1 Tab" on page 854)
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Equipment Component and Compliance





































API
Extraction Nozzle #2 (see "Extraction Nozzle #2 Tab" on page 856)
617 Input Tab
Topics
Node Number ................................................................................ 851
Nominal Diameter .......................................................................... 851
Node Number ................................................................................ 851
Nominal Diameter .......................................................................... 851
Node Number ................................................................................ 851
Nominal Diameter .......................................................................... 851
Node Number ................................................................................ 851
Nominal Diameter .......................................................................... 851
Equipment Centerline .................................................................... 851
Factor for Allowables ..................................................................... 852
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CAESAR II User's Guide
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Node Number
Indicates the node number that describes the suction nozzle flange connection. Enter a
positive number.
Nominal Diameter
Specifies the suction nozzle pipe nominal diameter.
Node Number
Indicates the node number that describes the extraction nozzle #1 flange connection. Enter
a positive number.
Nominal Diameter
Specifies the extraction nozzle #1 pipe nominal diameter.
Node Number
Indicates the node number that describes the discharge nozzle flange connection. Enter
a positive number.
Nominal Diameter
Specifies the discharge nozzle pipe nominal diameter.
Node Number
Indicates the node number that describes the extraction nozzle #2 flange connection. Enter
a positive number.
Nominal Diameter
Specifies the extraction nozzle #2 pipe nominal diameter.
Equipment Centerline
Indicates the direction cosines (X,Z) for the equipment shaft centerline. For example, if shaft
CL is along the Z-axis, the direction cosines are:
cosine X = 0.0
cosine Z = 1.0
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Equipment Component and Compliance
Factor for Allowables
Designates the multiplication factor by which all allowables are multiplied, if necessary
API 617 does not recommend the use of a multiplier. The code specifically states what
the allowables are.
Suction Nozzle Tab
The following options are used to enter input data for suction nozzles.
Topics
X Distance to Suction .................................................................... 852
Y Distance to Suction .................................................................... 852
Z Distance to Suction .................................................................... 852
X Force Acting on Suction Nozzle ................................................. 852
Y Force Acting on Suction Nozzle ................................................. 853
Z Force Acting on Suction Nozzle ................................................. 853
X Moment Acting on Suction Nozzle ............................................. 853
Y Moment Acting on suction Nozzle .............................................. 853
Z Moment Acting on Suction Nozzle ............................................. 853
X Distance to Suction
Specifies the X-distance from the largest suction/discharge nozzle to the suction nozzle.
Y Distance to Suction
Specifies the Y-distance from the largest suction/discharge nozzle to the suction nozzle.
Z Distance to Suction
Specifies the Z-distance from the largest suction/discharge nozzle to the suction nozzle.
X Force Acting on Suction Nozzle
Specifies the X-component of the force that the piping system exerts on the suction nozzle.
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Y Force Acting on Suction Nozzle
Specifies the Y-component of the force that the piping system exerts on the suction nozzle.
Z Force Acting on Suction Nozzle
Specifies the Z-component of the force that the piping system exerts on the suction nozzle.
X Moment Acting on Suction Nozzle
Specifies the X-component of the moment that the piping system exerts on the suction nozzle.
Y Moment Acting on suction Nozzle
Specifies the Y-component of the moment that the piping system exerts on the suction nozzle.
Z Moment Acting on Suction Nozzle
Specifies the Z-component of the moment that the piping system exerts on the suction nozzle.
Discharge Nozzle Tab
The following options are used to enter input data for discharge nozzles.
Topics
X Distance to Discharge ................................................................ 853
Y Distance to Discharge ................................................................ 854
Z Distance to Discharge ................................................................ 854
X Force Acting on Discharge Nozzle ............................................. 854
Y Force Acting on Discharge Nozzle ............................................. 854
Z Force Acting on Discharge Nozzle ............................................. 854
X Moment Acting on Discharge Nozzle ......................................... 854
Y Moment Acting on Discharge Nozzle ......................................... 854
Z Force Acting on Discharge Nozzle ............................................. 854
X Distance to Discharge
Specifies the X-distance from the largest suction/discharge nozzle to the discharge nozzle.
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Equipment Component and Compliance
Y Distance to Discharge
Specifies the Y-distance from the largest suction/discharge nozzle to the discharge nozzle.
Z Distance to Discharge
Specifies the Z-distance from the largest suction/discharge nozzle to the discharge nozzle.
X Force Acting on Discharge Nozzle
Specifies the X-component of the force that the piping system exerts on the discharge nozzle.
Y Force Acting on Discharge Nozzle
Specifies the Y-component of the force that the piping system exerts on the discharge nozzle.
Z Force Acting on Discharge Nozzle
Specifies the Z-component of the force that the piping system exerts on the discharge nozzle.
X Moment Acting on Discharge Nozzle
Specifies the X-component of the moment that the piping system exerts on the
discharge nozzle.
Y Moment Acting on Discharge Nozzle
Specifies the Y-component of the moment that the piping system exerts on the
discharge nozzle.
Z Force Acting on Discharge Nozzle
Specifies the Z-component of the force that the piping system exerts on the discharge nozzle.
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CAESAR II User's Guide
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Extraction Nozzle #1 Tab
The following options are used to enter input data for the extraction nozzle #1.
Topics
X Distance to Extraction Nozzle #1 ............................................... 855
Y Distance to Extraction Nozzle #1 ............................................... 855
Z Distance to Extraction Nozzle #1 ............................................... 855
X Force Acting on the Extraction Nozzle ....................................... 855
Y Force Acting on the Extraction Nozzle ....................................... 855
Z Force Acting on the Extraction Nozzle ....................................... 855
X Moment Acting on the Extraction Nozzle ................................... 855
Y Moment Acting on the Extraction Nozzle ................................... 856
Z Moment Acting on the Extraction Nozzle ................................... 856
X Distance to Extraction Nozzle #1
Specifies the X-distance from the largest suction/discharge nozzle to the extraction nozzle #1.
Y Distance to Extraction Nozzle #1
Specifies the Y-distance from the largest suction/discharge nozzle to the extraction nozzle #1.
Z Distance to Extraction Nozzle #1
Specifies the Z-distance from the largest suction/discharge nozzle to the extraction nozzle #1.
X Force Acting on the Extraction Nozzle
Specifies the X-component of the force that the piping system exerts on the extraction
nozzle #1.
Y Force Acting on the Extraction Nozzle
Specifies the Y-component of the force that the piping system exerts on the extraction
nozzle #1.
Z Force Acting on the Extraction Nozzle
Specifies the Z-component of the force that the piping system exerts on the extraction
nozzle #1.
X Moment Acting on the Extraction Nozzle
Specifies the X-component of the moment that the piping system exerts on the extraction
nozzle #1.
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Equipment Component and Compliance
Y Moment Acting on the Extraction Nozzle
Specifies the Y-component of the moment that the piping system exerts on the extraction
nozzle #1.
Z Moment Acting on the Extraction Nozzle
Specifies the Z-component of the moment that the piping system exerts on the extraction
nozzle #1.
Extraction Nozzle #2 Tab
The following options are used to enter input data for the extraction nozzle #2.
Topics
X Distance to Extraction Nozzle #2 ............................................... 856
Y Distance to Extraction Nozzle #2 ............................................... 856
Z Distance to Extraction Nozzle #2 ............................................... 856
X Force Acting on the Extraction Nozzle ....................................... 856
Y Moment Acting on Extraction Nozzle ......................................... 857
Z Force Acting on the Extraction Nozzle ....................................... 857
X Moment Acting on the Extraction Nozzle ................................... 857
Y Moment Acting on the Extraction Nozzle ................................... 857
Z Moment Acting on the Extraction Nozzle ................................... 857
X Distance to Extraction Nozzle #2
Specifies the X-distance from the largest suction/discharge nozzle to the extraction nozzle #2.
Y Distance to Extraction Nozzle #2
Specifies the Y-distance from the largest suction/discharge nozzle to the extraction nozzle #2.
Z Distance to Extraction Nozzle #2
Specifies the Z-distance from the largest suction/discharge nozzle to the extraction nozzle #2.
X Force Acting on the Extraction Nozzle
Specifies the X-component of the force that the piping system exerts on the extraction
nozzle #1.
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Y Moment Acting on Extraction Nozzle
Specifies the Y-component of the moment that the piping system exerts on |the
extraction nozzle #2.
Z Force Acting on the Extraction Nozzle
Specifies the Z-component of the force that the piping system exerts on the extraction
nozzle #1.
X Moment Acting on the Extraction Nozzle
Specifies the X-component of the moment that the piping system exerts on the extraction
nozzle #1.
Y Moment Acting on the Extraction Nozzle
Specifies the Y-component of the moment that the piping system exerts on the extraction
nozzle #1.
Z Moment Acting on the Extraction Nozzle
Specifies the Z-component of the moment that the piping system exerts on the extraction
nozzle #1.
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Equipment Component and Compliance
API 661 (Air Cooled Heat Exchangers)
Analysis > API 661 evaluates piping loads on air-cooled heat exchangers. These
calculations cover the allowed loads on the vertical, co-linear nozzles (item 9 in the figure
below) found on most single or multi-bundled air cooled heat exchangers. The following
figures from API 661 illustrate the type of open exchanger body analyzed by this standard.
The two requirements must be met for API 661compliance:



5.1.11.1 - Each nozzle in the corroded condition must be
capable of withstanding the
moments and forces defined in Heat Exchangers figure.
5.1.11.2 - The sum of the forces and moments on each fixed header, that is, each individual
bundle, must be less than 1,500 lb. transverse to the bundle, 2,500 lb. axial to the bundle,
and 3,000 pound axial on the nozzle centerline. The allowed moments are 3,000, 2,000,
and 4,000 ft.-lb., respectively. This recognizes that the application of these moments and
forces will cause movement and that this movement will tend to reduce the actual loads.
To begin, specify a new job name in the New Job Name Specification dialog box or
click Browse to navigate to an existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
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CAESAR II User's Guide
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The software opens the API 661 window, which consists of the following three screens for
input of project-specific data: Input Data (see "Input Data Tab" on page 860), Inlet Nozzle (see
"Inlet Nozzle Tab" on page 862), and Outlet Nozzle (see "Outlet Nozzle Tab" on page 863).
CAESAR II User's Guide
859
Equipment Component and Compliance
A typical API 661 report is shown below:
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CAESAR II User's Guide
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Input Data Tab
The following options are used to enter input data used to evaluate piping loads on aircooled heat exchangers.
Topics
Inlet Nozzle Node Number ............................................................ 861
Inlet Nozzle Nominal Diameter ...................................................... 861
Outlet Nozzle Node Number.......................................................... 861
Outlet Nozzle Nominal Diameter ................................................... 861
Table 4 Force and Moment Multiplier ............................................ 861
Resultant Force and Moment Multiplier ......................................... 861
Tube Bundle Direction ................................................................... 862
Inlet Nozzle Node Number
Indicates the inlet nozzle node number that is the connecting point between piping and
the exchanger. This entry is optional. If defined, enter a positive number.
Inlet Nozzle Nominal Diameter
Specifies the nominal diameter of the exchanger inlet connection.
Outlet Nozzle Node Number
Indicates the outlet nozzle node number that is the connecting point between piping and
the exchanger. This entry is optional. If defined, enter a positive number.
Outlet Nozzle Nominal Diameter
Specifies the nominal diameter of the exchanger outlet connection.
Table 4 Force and Moment Multiplier
Defines the Table 4 (Figure 6) Force and Moment multiplier. This is the value upon which the
passed or failed status is based. If you leave this option blank, the software uses a default
value of 1.0.
Resultant Force and Moment Multiplier
Indicates the resultant force and moment multiplier. The computed force and moment ratios are
compared to this value. If you leave this option blank, the software uses a default value of 1.0.
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Equipment Component and Compliance
Tube Bundle Direction
Specifies the CAESAR II global tube direction. If the X-direction is defined, the force and
moment allowables for the X- and Z-directions are flipped. The same applies to the
Resultant Force and Moment Multiplier allowables.
Inlet Nozzle Tab
The following options are used to enter input data for the inlet nozzle.
Topics
Y Distance from Nozzle Face to Header Center ........................... 862
X Force Applied to Inlet Nozzle ..................................................... 862
Y Force Applied to Inlet Nozzle ..................................................... 862
Z Force Applied to Inlet Nozzle ..................................................... 862
X Moment Applied to Inlet Nozzle ................................................. 863
Y Moment Applied to Inlet Nozzle ................................................. 863
Z Moment Applied to Inlet Nozzle ................................................. 863
Y Distance from Nozzle Face to Header Center
Designates the Y-dimension of the suction nozzle to the header center. This dimension must
be positive. Refer to Figure 5 in API 661. In the figure, the number 6 arrowhead points to the
approximate center of the header location.
X Force Applied to Inlet Nozzle
Specifies the X-force that the piping system exerts on the inlet nozzle.
Y Force Applied to Inlet Nozzle
Specifies the Y-force that the piping system exerts on the inlet nozzle. This component can
be considered a radial load.
Z Force Applied to Inlet Nozzle
Specifies the Z-force that the piping system exerts on the inlet nozzle.
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X Moment Applied to Inlet Nozzle
Specifies the X-moment that the piping system exerts on the inlet nozzle.
Y Moment Applied to Inlet Nozzle
Specifies the Y-moment that the piping system exerts on the inlet nozzle.
Z Moment Applied to Inlet Nozzle
Specifies the Z-moment that the piping system exerts on the Inlet nozzle.
Outlet Nozzle Tab
The following options are used to enter input data for the outlet nozzle.
Topics
Y Distance From Header Center to Nozzle Face .......................... 863
X Force Applied to Outlet Nozzle .................................................. 863
Y Force Applied to Outlet Nozzle .................................................. 863
Z Force Applied to Outlet Nozzle .................................................. 864
X Moment Applied to Outlet Nozzle .............................................. 864
Y Moment Applied to Outlet Nozzle .............................................. 864
Z Moment Applied to Suction Nozzle ............................................ 864
Y Distance From Header Center to Nozzle Face
Indicates the Y-dimension of the header center to the discharge nozzle. Refer to Figure 5 in API
661. In this figure, the number 6 arrowhead points to the approximate center of the
header location.
X Force Applied to Outlet Nozzle
Indicates the X-force which the piping system exerts on the outlet nozzle.
Y Force Applied to Outlet Nozzle
Specifies the Y-force that the piping system exerts on the outlet nozzle. This can be
considered a radial load.
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Equipment Component and Compliance
Z Force Applied to Outlet Nozzle
Specifies the Z-force that the piping system exerts on the outlet nozzle.
X Moment Applied to Outlet Nozzle
Specifies the X-moment that the piping system exerts on the outlet nozzle.
Y Moment Applied to Outlet Nozzle
Specifies the Y-moment which the piping system exerts on the outlet nozzle.
Z Moment Applied to Suction Nozzle
Specifies the Z-moment which the piping system exerts on the outlet nozzle.
Heat Exchange Institute
Analysis > HEI Standard evaluates the allowable loads on shell type heat exchanger nozzles.
To begin, specify a new job name in the New Job Name Specification dialog box or click
Browse to navigate to an existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
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Equipment Component and Compliance
The software opens the HEI STD window, in which you can enter the necessary input data.
The following example shows sample input for the HEI module:
Because the pressure is greater than zero, a pressure thrust force is computed and
combined with the radial force.
Section 3.14 of the HEI bulletin discusses the computational methods used to compute these
allowable loads. The method employed by HEI is a simplification of the WRC 107 method,
where the allowable loads have been linearized to show the relationship between the maximum
permitted radial force and the maximum permitted moment vector. If this relationship is plotted
(using the moments as the abscissa and the forces as the ordinate), a straight line can be
drawn between the maximum permitted force and the maximum permitted moment vector,
forming a triangle with the axes. For any set of applied forces and moments, the nozzle passes
if the location of these loads falls inside the triangle. Conversely, the nozzle fails if the location
of the loads falls outside the triangle.
Because the pressure is greater than zero, a pressure thrust force is computed and
combined with the radial force modified to include both the plot of the allowables and the
location of the current load set on this plot. The HEI bulletin states that the effect of internal
pressure has been included in the combined stresses; however, the effect of the pressure on
the nozzle thrust has not. This requires combination with the other radial loads. CAESAR II
automatically computes the pressure thrust and adds it to the radial force if Add Pressure
Thrust is selected on the HEI Nozzle (on page 866) tab.
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865
Equipment Component and Compliance
HEI Nozzle
The following options are used to enter input data for shell type heat exchanger nozzles.
Topics
Design Pressure ............................................................................ 866
Nozzle Outside Diameter ............................................................... 866
Shell Outside Diameter .................................................................. 866
Shell Thickness ............................................................................. 866
Material Yield Strength .................................................................. 866
Material Allowable Stress .............................................................. 867
Maximum Radial Force .................................................................. 867
Maximum Longitudinal Moment..................................................... 867
Add Pressure Thrust Force ........................................................... 867
Design Pressure
Sets the design pressure under which the vessel is operating. Enter a non-negative value.
Nozzle Outside Diameter
Sets the design pressure under which the vessel is operating. Enter a non-negative value.
Shell Outside Diameter
Indicates the outside diameter of the pressure vessel.
Shell Thickness
Defines the shell wall thickness. This software does not take any corrosion allowance
into consideration.
Material Yield Strength
Specifies the yield strength (Sy) of the shell material at the operating temperature. Refer to
ASME Section VIII Division 1 for this information. Enter a positive value. The yield strength
is greater than the allowable stress.
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Equipment Component and Compliance
Material Allowable Stress
Indicates the allowable stress of the shell material at the operating temperature, according
to ASME Section VIII Division 1. Enter a positive value.
Maximum Radial Force
Defines the shell wall thickness. This software does not take any corrosion allowance
into consideration.
Maximum Longitudinal Moment
Specifies the moment about the transverse axis of the vessel which the piping exerts on
the nozzle. Enter a non-negative value.
Add Pressure Thrust Force
Controls whether the thrust force generated by the internal pressure is included or ignored.
Select this option to include the pressure thrust force. To ignore this force,do not select
this option.
All versions prior to CAESAR II 3.21a always included the pressure thrust force in
analysis.
API 560 (Fired Heaters for General Refinery Services)
Analysis > API 560 evaluates piping loads on fired heaters. To begin, specify a new job
name in the New Job Name Specification dialog box or click Browse to navigate to an
existing job file.
All CAESAR II analyses require a job name for identification purposes. After you have
created, or opened, a job, you can enter input data on the Global Input and Local Member
tabs and Output menus to define, analyze, and review your data.
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Equipment Component and Compliance
The software opens the API 560 window. The window consists of one input tab on which you can
enter data for the tube nominal diameter and the forces and moments acting on the tube.
When you run the analysis, CAESAR II compares the input forces and moments to the allowables
as published in API 560. An example of the equipment report output is shown below.
T
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API 560 Input Data Tab
The following options are used to enter input data for the tube nominal diameter and the
forces and moments acting on the tube.
Topics
Tube Node Number ....................................................................... 869
Tube Nominal Diameter ................................................................. 869
Tube Axial Force ........................................................................... 869
Tube Horizontal Shear Force ........................................................ 869
Tube Vertical Shear Force ............................................................. 869
Tube Torsional Moment ................................................................. 870
Tube Horizontal Moment ............................................................... 870
Tube Vertical Moment ................................................................... 870
Tube Node Number
Identifies the node number for the tube that is being analyzed. Because there are many tubes
in a fired heater, analyze the most highly loaded tubes.
Tube Nominal Diameter
Indicates the nominal diameter of the tube.
Tube Axial Force
Specifies the axial force acting on the tube at the tube/header junction. If the tube direction is
X, then enter the FX value from the appropriate load case.
Tube Horizontal Shear Force
Specifies the horizontal force acting on the tube at the tube/header junction. If the tube
direction is X, then enter the FZ value from the appropriate load case.
Tube Vertical Shear Force
Specifies the vertical force acting on the tube at the tube/header junction. If the tube direction
is X, then enter the FY value from the appropriate load case.
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Tube Torsional Moment
Indicates the torsional moment acting on the tube at the tube/header junction. If the
tube direction is X, then enter the MX value from the appropriate load case.
Tube Horizontal Moment
Indicates the horizontal moment acting on the tube at the tube/header junction. If the
tube direction is X, then enter the MZ value from the appropriate load case.
Tube Vertical Moment
Indicates the vertical moment acting on the tube at the tube/header junction. If the tube
direction is X, then enter the MY value from the appropriate load case.
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S ECTION 1 4
Technical Discussions
In This Section
Rigid Element Application .............................................................. 871
In-Line Flange Evaluation .............................................................. 873
Cold Spring .................................................................................... 874
Expansion Joints ........................................................................... 876
Hanger Sizing Algorithm ................................................................ 878
Class 1 Branch Flexibilities ............................................................ 883
Modeling Friction Effects ............................................................... 885
Nonlinear Code Compliance.......................................................... 886
Sustained Stresses and Nonlinear Restraints ............................... 887
Static Seismic Inertial Loads ......................................................... 890
Wind Loads .................................................................................... 891
Hydrodynamic (Wave and Current) Loading ................................. 893
Evaluating Vessel Stresses ........................................................... 906
Inclusion of Missing Mass Correction ............................................ 910
Fatigue Analysis Using CAESAR II ............................................... 916
Pipe Stress Analysis of FRP Piping .............................................. 929
Code Compliance Considerations ................................................. 951
Local Coordinates .......................................................................... 991
Rigid Element Application
A piping element that is stiffer or heavier than pipe of the same size (for example, a flanged
valve) can be modeled as a rigid element in CAESAR II. CAESAR II sets the stiffness of a
rigid element based on the inside diameter defined for the pipe but with a wall thickness set to
ten times the entered value. Note that long “rigid” elements may bend.
Rigid elements in CAESAR II are rigid relative to the pipe around it. For example, if a 6-inch line ties
into a 72-inch heat exchanger and rigid elements are used to model the heat exchanger, those
exchanger elements are better represented by 72 inch pipe rather than 6 inch pipe.
Rigid Weight
Specifies a value for the weight of the rigid element. The rigid material weight is the weight of
the rigid excluding insulation, refractory, cladding, or fluid. If left blank, then the weight of the
rigid defaults to 0. A rigid element with zero weight is often used as a construction element,
used to move a centerline load to the shell wall, or used to model the effective stiffness and
thermal growth of a piece of equipment.
If left blank or 0, then the software does not add the additional weight due either to
insulation, refractory, cladding, or fluid.
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Fluid Weight in Rigid Elements
The fluid weight in a rigid element is assumed to be equal to the fluid weight in an
equivalent straight pipe of similar length and inside diameter.
Insulation Weight on Rigid Elements
The insulation weight for the rigid is assumed to be equal to 1.75 times the insulation for
an equivalent length of straight pipe of the entered outside diameter.
Total Weight on Rigid Elements
The total weight for rigid elements where the entered weight is zero will be zero.
The total weight for rigid elements where the entered weight is not zero is calculated as follows:
Weight = W u + W f + W r +1.75(W i+W c)
Where:
W u = User-defined rigid weight (the Thermal Expansion/Pipe Weight report will show
user-defined weight divided by entered length)
W f = Calculated fluid weight for equivalent straight pipe (this is reduced by refractory lining)
W r = Calculated refractory weight for equivalent straight pipe
W i = Calculated insulation cladding weight for equivalent straight pipe
W c = Calculated cladding weight for equivalent straight pipe
CAESAR II does not calculate stress on rigid elements. Forces and moments are not
normally printed for rigid elements however, you can select the appropriate check box found
in Environment>Special Execution Parameters from the Piping Input spreadsheet to print
these loads.
Modeling using Rigids
Zero-weight rigid elements are useful where modeling non-pipe components where
thermal growth or load transfer is important.
Use zero-weight rigids to model piping hardware such as expansion joint tie rods, base
plates, and trunnions.
You can also use these dummy rigids to provide connectivity between the centerline of an
element and the outside edge of the element. The most common example of this is when you
need to add a dummy rigid that runs from the node at the centerline of the vessel to the
outside wall where you want to connect the nozzle.
You can also model equipment using a series of rigid elements, joining nozzles to a body
and perhaps to a support point. This approach will properly distribute thermal strain through
the component based on this geometry and the entered element temperatures. For more
information on the use of these construction rigids, see the CAESAR II Applications Guide in
various sections as appropriate to a particular modeling technique.
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In-Line Flange Evaluation
Allows you to choose the method to use for evaluating flanges under load:



The Kellogg Equivalent Pressure Method

The ASME NC-365.8 Calculation for B16.5 Flanged Joints

Kellogg Equivalent Pressure Method
Converts piping axial forces and bending moments into an equivalent pressure on the flange.
After the conversion is complete, the software adds this equivalent pressure to the pressure
defined in the load case. It then compares this sum to the allowable pressure rating for the
flange at the appropriate temperature. (The pressure-temperature table is defined in the
model input and the temperature is specified in the Load Case Options.) The formula for the
total equivalent pressure displays below:
Peq = 16M/()G3 + 4F/ ()G2 + PD
Where:
Peq = total equivalent pressure (for checking against flange rating)
M = calculated bending moment on flange
G = diameter of effective gasket reaction
F = absolute value of the calculated axial force on flange
PD = pressure specified in the load case (for example, P1 for W+T1+P1)
The allowable pressure rating will be multiplied by the occasional load factor specified in
the Load Case Options.
ASME NC-3658.3 Calculation Method for B16.5
Flanged Joints with High Strength Bolting
Restricted to joints using flanges, bolting, and gaskets as specified in ANSI B16.5 that use bolting
materials having an S value at 100°F (38°C) greater than or equal to 20,000 psi (138 MPa).
CAESAR II uses the analysis method for Service Level A as stated in NC-3658.3(a)(2):
Mfs ≤ 3125(Sy/36,000)CAb
or
Mfd ≤ 6250(Sy/36,000)CAb
Where:
Mfs = Bending or torsional moment, whichever is greater, acting on the flange, and due to
weight, thermal expansion, sustained anchor movements, relief valve steady state thrust,
and other sustained mechanical loads. CAESAR II considers any moments developed
during a non-Occasional Load Case to be Mfs.
Mfd = Bending or torsional moment, whichever is greater, acting on the flange, as defined
for Mfs and but also including any dynamic loadings. CAESAR II considers any moments
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Technical Discussions
developed during an Occasional Load Case to be Mfd, effectively the doubling
flange capacity for Occasional loadings.
Sy = Yield strength of flange material at design temperature. CAESAR II allows evaluation
to be done using as many as 10 different temperatures; Sy/36,000; where Sy, is given in
psi, cannot be greater than 36,000 psi
C = Bolt circle diameter
Ab = Total cross sectional area of bolts
PD = Design pressure
CAESAR II calculates an Equivalent Stress S in the flange and compares it to Sy (or 2*Sy
for occasional load cases), in the following manner:
S = 36,000* Mfs / (CAb * 3125) ≤ Min(Sy, 36000)
(non-Occ)
S = 36,000 * Mfd / (CAb * 3125) ≤ 2.0 * Min(Sy, 36000)
(Occ)
For systems of units that do not express stress in psi, the software converts the 36,000 values
in the above equations to the appropriate set of units.
You can do flange evaluations in Static Analysis only.
Cold Spring
Cold spring is a method where you introduce pipe strain in the installed state to modify the
resulting strain in the operating state. Adding this preload is commonly used to adjust
(reduce) equipment load in the operating state. A cut short describes an intentional gap in the
pipe assembly requiring an initial tensile load to close the final joint. A cut long describes an
intentional overlap in the pipe assembly requiring an initial compressive load to close the final
joint. This initial gap or overlap is modeled as a cut short material or a cut long material,
respectively. CAESAR II reduces the cut short to zero length and doubles the cut long in any
load case that includes the “CS” load in the load case definition.
This initial cold pull is difficult to implement with any accuracy and, being used in systems that
operate in the creep range, their long term effect is difficult to control or even predict. Due to the
difficulty of properly installing a cold spring system, most piping codes recommend that you only
use two-thirds of the specified cold spring for equipment load calculations. You can calculate
the cold spring element length (ignoring equipment growth) by using the following equation:
Ci = xLi  dT
Where:
Ci = length of cold spring in direction i; where i is X, Y, or Z (inches)
Li = total length of pipe subject to expansion in direction i (inches)
= mean thermal expansion coefficient of material between ambient and operating
temperature (in/in/°F)
dT = change in temperature (°F)
x = percent cold spring
When x = 0%, there is no cold spring and there will be no reduction in the thermal strain found
in the operating load. When x = 100%, the operating load will have no thermal strain as all the
expected pipe strain will be realized in the installed state of the piping system. If x = 50%, the
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pipe strain will be shared equally by both the installed load and operating load. This percent
cold spring (x) is not the same term as the two-thirds allowance mentioned above.
No credit can be taken for cold spring in the stress calculations, because the expansion
stress provisions of the piping codes require the evaluation of the stress range, which is
unaffected by cold spring, except perhaps in the presence of non-linear boundary conditions, as
discussed below. The cold spring adjusts installed and operating loads and the stress mean,
but not the stress range used in most expansion stress calculations.
Cold Spring Considerations
You must consider several factors when using cold spring:







Verify that the
 cold reactions on equipment nozzles due to cold spring do not exceed nozzle
allowables.
Verify that the expansion stress range does not include the effect of the cold spring.
Verify that the cold spring value/tolerance is much greater than fabrication tolerances.


For elevated temperature cases, where cold spring is used to reduce operating equipment
load, using 
the hot modulus of analysis may also have a significant effect on the load
magnitude.
Modeling cold springs
1.
Specify the cold gaps or overlaps as elements defined as cut short or cut long
materials, respectively.
2.
Make the lengths of the cold spring elements only ⅔ of their actual lengths to implement
the code recommendations.
3.
Reset the material property on the element following the cold spring element.
4.
Analyze the cold spring system by running the following load cases:
Load Case 1 (OPE)
W+T1+P1+CS includes all of the design cold spring
Load Case 2 (OPE)
W+P1+CS includes all of the design cold spring but
not the temperature.
Load Case 3 (SUS)
W+P1 standard sustained case for code stress check
Load Case4 (EXP)
L1-L2 expansion case for code stress check.
Both the sustained loads and the operating loads must fall within the manufacturer’s
allowables for a specific piece of equipment.
5.
Verify that using cold spring in the ambient state does not overload a piece of
rotating equipment as the unit starts.
Material numbers 18 and 19 are used to signal CAESAR II that the element in the
spreadsheet represents a length of pipe that is to be cut short or long during fabrication.
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Other Applications for Cold Spring
While often used to reduce the magnitude of loads on equipment and restraints (see below),
you can also use cold spring to accelerate the thermal shakedown of the system in fewer
operating cycles.
Expansion Joints
Checking the expansion joint box on the element enables definition of an expansion joint for
that element. Expansion joints can be modeled as a single element across the flexible length of
the joint or as a zero length element at the midpoint of the expansion joint. Expansion joints
elements have a zero length if the Delta fields on the Pipe Element spreadsheet are left blank
or zero.
When an expansion joint has a defined length, CAESAR II builds the expansion joint as a
beam element using the element length with the entered expansion joint stiffnesses.
Four stiffness values define the expansion joint:



876

Axial



Transverse


Torsion


Bending
CAESAR II User's Guide
Technical Discussions
Examples of the Stiffnesses
Define Finite Length Joints
For expansion joints where flexible length is defined, the bending stiffness is defined by the
entered, flexible, length and the transverse stiffness of the joint. Some expansion joint catalogs
list what would be called bending flexibility rather than the required bending stiffness used in
CAESAR II. This bending flexibility is adequate for an expansion joint modeled by two rigid
elements that are pinned at the joint midpoint (a zero length expansion joint) but it is the wrong
value for a flexible beam element. To address this ambiguity, CAESAR II calculates and
applies a bending stiffness based on the entered expansion joint length and transverse
stiffness. We suggest that you only enter the bending term from manufacturers' catalogs when
using the zero-length expansion joint model or for rubber joint which do not follow beam
bending definitions.
Typically, expansion joint manufacturers do not supply torsional stiffness data. If the
manufacturer does not supply the data, enter a large torsional stiffness value, and verify that the
resulting load on the bellows is not excessive. When the piping system is tight, and the diameter
large, the magnitude of the large torsional stiffness can significantly affect the magnitude of the
torsion carried by the joints. For example, a stiffness of 100,000 in.lb./deg. and 1E12 in.lb./deg.
can produce considerably different torsional load results. Conservatively speaking, the tendency
is to use the larger stiffness except that the torsional stiffness value is probably closer to the
100,000 in.lb./deg. In instances where a large torsional stiffness value is important, you can get
a stiffness estimate from the manufacturer, or use the equation below to derive an estimate.
Use this equation to conservatively estimate torsional loads on the bellows and surrounding
equipment.
Where
 = 3.14159
Re = Expansion joint effective radius
t = Bellows thickness
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E = Elastic Modulus
 = Poisson’s Ratio
L = Flexible bellows length
When the expansion joint has a zero length, none of the expansion joint stiffnesses are
related. You must be sure that you enter a value in all of the Stiffness fields.
Calculate the Pressure Thrust
CAESAR II calculates the pressure thrust on the expansion joint if you type a value for the
bellows Effective ID on the Expansion Joint auxiliary dialog box. If there is no Effective ID,
the mathematical model for pressure thrust applies a force equal to the pressure multiplied by
the effective area of the bellows at the two nodes that define the expansion joint. The force can
open the bellows if the pressure is positive, and close the bellows if the pressure is negative.
You should note that this model does not correctly locate pressure load components in the
vicinity of the expansion joint. In most cases, the misapplied load does not affect the solution.
There are two components of the pressure thrust to apply in practice rather than the one
component applied in the model. The first component is equal to the pressure times the inside
area of the pipe and acts at the first change in direction of the pipe on either side of the
expansion joint. This load will tend to put the pipe wall between the change in direction and the
expansion joint in tension. The second component is equal to the pressure times the difference
between the bellows effective area and inside pipe area. This load acts at the end of the
expansion joint and tends to open the bellows up putting the pipe between the expansion joint
and the change in direction in compression. In the mathematical model, the full component of
the pressure thrust force is placed on the ends of the bellows instead of having a portion shifted
out on either side of the expansion joint.
Effective ID
The pressure area used to set the pressure thrust force on an expansion joint is provided by
the expansion joint manufacturer either as an effective area or effective inside diameter (ID). If
the pressure thrust load is to be included in the analysis, the Effective ID must be provided in
the expansion joint model definition. Any load case that includes a pressure term (for example,
…+P1…) will include a thrust force on either end of the expansion joint based on this effective
ID.
Hanger Sizing Algorithm
At locations that you define, CAESAR II will select a rigid, variable or constant effort support
using the automated procedure defined here. Attention here is focused on selecting a
variable (spring) support from a manufacturer’s catalog. Be sure to review and verify all
supports sized by CAESAR II.
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Spring Design Requirements
A rigid rod is selected if the vertical thermal growth at the location is less than the value
entered as “Rigid Support Displacement Criteria” and a constant support is selected if the
vertical thermal growth at the location is greater than the value entered as “Max. Allowed
Travel Limit”. Otherwise, CAESAR II selects the smallest single spring that satisfies all design
requirements provided in the hanger design data.
The spring design requirements are:
1.
Both the operating (typically hot) and the installed (typically cold) loads must be within
the allowed working range of the spring.
2.
The absolute value of the change in the load (the product of the travel and the
selected spring rate) divided by the design load must be less than the specified
"Allowable Load Variation" value. The default variation is 25%.
MSS SP-69 defines load variation as the ratio of the change in load and the operating
load. CAESAR II, in using the design load, will use the theoretical cold load (discussed
below), instead of the operating load, if the user selects "Cold Load" design.
3.
If you specify "Available Space", then this space must be greater than the basic height of
the spring selected. Positive values are compared with hanger height and negative values
are compared with spring can height.
If the software cannot find a single spring that satisfies the design requirements, it
searches for two identical springs that will each carry half the load. If the software cannot find
any springs that satisfies the design requirements, it recommends a constant effort support
for the location.
Restrained Weight Case
If you need to design a hanger, the first analysis case that you must run is the restrained
weight case. This case usually includes weight, pressure, and concentrated loads. Hanger hot
loads are calculated in the restrained weight case.
Run the restrained weight case
1.
Place rigid Y-restraints at each hanger location.
2.
Determine any anchors you want to designate as freed.
3.
Verify the freed anchors are properly released.
Loads on the Y-restraints at hangers, calculated from the restrained weight case, are
designated as the hanger hot design loads.
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Pre-Selection Load Case 2 – Setting Hanger
Deflection through the Operating Case
After the restrained weight case, you must run an operating analysis. The operating case
must always be the second load case in the set of defined analysis cases. You can define the
operating load cases for hanger design any way you see fit. CAESAR II recommends the load
cases it thinks you should run whenever it detects the first attempt to analyze a particular
system. You can accept or reject the recommendations. If you define your own hanger design
load cases, you must understand exactly what is done in the "restrained weight" and
operating passes of the hanger design algorithm.
Run an operating case
1.
Remove the Y-restraints.
2.
Insert the hot loads calculated from the hanger locations in the restrained weight analysis.
3.
Change any freed anchors from the restrained weight analysis to fixed.
The vertical displacement of the operating case at each hanger location defines the travel of
that particular hanger. If there are single directional restraints or gaps in the system and a
changed status in the operating case, then the hanger loads are redistributed.
When CAESAR II detects a nonlinear status change, it reruns the restrained weight case
with the restraints left as they were at the end of the operating case. To determine the updated
travel, you must calculate the new restraint loads and run another operating case.
Post-Selection Load Case (Optional) – Setting the
Actual Installed (Cold) Load
If you need to calculate the actual hanger installed loads, the third analysis level combination
case must define the weight configuration that exists in the field when a spring is installed.
Typically, this case includes weight without fluid contents and other live loads. The theoretical
cold, or installed load, is the load on the spring when the "unbalanced" installed load is applied
and the pipe is not allowed to displace vertically (the load will be "balanced" when the pipe is
in the operating or design position). The actual installed load may differ from the theoretical
installed load by (K)(d), where (K) is the spring stiffness and (d) is the displacement of the pipe
in the installed condition.
Calculate the actual installed load
880
1.
Install the hangers.
2.
Apply the theoretical cold load and all other loads (for example, empty weight) that will
be present when the springs are set.
3.
Calculate the position of all springs (d).
4.
Set the actual installed spring load based on this installed position (installed load
= Theoretical Cold Load - (K)(d)).
CAESAR II User's Guide
Technical Discussions
Create Spring Load Cases
Up to three load cases are needed for spring sizing:



"Restrained" Weight (required)


Operating (required)


Installed Weight (optional)

After the Hanger Algorithm runs the hanger load cases, it selects the hangers. The
program inserts the newly-selected springs into the piping system and includes them and
their preload (the Theoretical Cold Load) in the analysis of all remaining load cases.
Hanger installed loads are concentrated forces and are only included in subsequent load
cases that contain the hanger preload force set (+H).
You can specify any number of user-defined load cases after setting up the required spring
load cases.
Spring hanger design does not affect the ability of CAESAR II to check code compliance. In
load cases recommended by CAESAR II, the normal code compliance cases always follow the
set of load cases required for hanger design.
Multiple operating case spring hanger design implies that hanger loads and travels from
more than one operating case are included in the spring hanger selection algorithm.
Each spring in a multiple operating case hanger design has a Multiple Load Case Design
option. This design option tells CAESAR II how multiple loads and travels for a single hanger
are combined to get a single design load and travel. The set-up of the analysis cases is slightly
different for multiple operating case hanger design in that now there is more than one operating
case. You can use the Hanger Design Control dialog to specify the actual number of
operating cases.
The load cases that you analyze for multiple load case hanger design operating cases are:




Restrained Weight (this does not change)


Operating case #1




Operating case #9


Installed Weight (if requested)
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Constant Effort Support
Enables you to specify the support load for a constant effort hanger and define the hanger
location. This value is also included in all hanger design runs and all analysis cases
following the hanger cases that include the hanger preload force set in their formulation.
Including the Spring Hanger Stiffness in the
Design Algorithm
The operating cases for hanger travel are normally analyzed with no stiffness included at the
hanger locations. This is why these cases are traditionally referred to as "free thermal" cases.
However, when the piping system is very flexible, or the selected springs are very stiff, the
actual resulting spring loads in the installed condition can vary significantly from the
theoretically calculated results. With such a load change, perhaps this shorter, more accurate
spring deflection may allow a smaller spring selection. In that case, CAESAR II enables you to
include, using an iterative process, the stiffness of the selected springs in the operating cases
for hanger travel.
You can activate this trait for all new models through the Configure\Setup by setting the option
to Include Travel to As Designed. You can also activate this option for individual models on
the Load Case Options Tab (Static Analysis Dialog Box) (on page 537) tab by changing the
Hanger Stiffness option to As Designed.
Selecting this option could lead to convergence problems. If you use this option, be sure to
check the hanger load in the cold case in the field so that it matches the reported hanger
Cold Load.
You must always include the hanger preload force set H (the Theoretical Cold Load)
in subsequent load cases.
Applying thermal and displacement effects to the live loaded system should make an
installed hanger move to the hot, or balanced, load in this operating case.
Other Notes on Hanger Sizing
At times, CAESAR II indicates that certain hanger locations carry no load and selects “zero
load” constant effort supports at these locations. Typically, zero load constant effort
supports indicate poor hanger locations. It is important to not simply ignore these selections
as and other hangers selected in the vicinity of these “zero load” hangers have improper
operating loads assigned. Relocate or remove these “zero load” selections.
Unless you specifically designate your hanger design load cases with a KEEP status,
they display in the output reports as NOT ACTIVE.
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Class 1 Branch Flexibilities
This analytical option was added to CAESAR II for the following reasons:



Automatic local flexibilities at intersections help you bound the true solution. Because the
computer time to do an analysis is less expensive, more frequently you can run several
solutions of the same model using slightly different input techniques to determine the effect
of the modeling difference on the results. This gives you a degree of confidence in the
numbers you get. For example, structural steel supporting structures can be modeled to
see the effect of their stiffnesses, nozzle flexibilities can be added at vessel connections to
see how these features redistribute load throughout the model, friction is added to watch its
effect on displacements and equipment loads, and with CAESAR II you can include Class 1
intersection flexibilities. The characteristic that makes this option convenient to use is that
you can enable or disable the Class 1 flexibilities
using a single option in the setup file. No

other modification to the input required.
In WRC 329, there are a number of suggestions made to improve the stress calculations at
intersections. These suggestions are fairly substantial and are given in order of
importance. The most important item, as felt by E. Rodabaugh,
in improving the stress

calculations at intersections is given, in part, as follows:
"In piping system analyses, it may be assumed that the flexibility is represented by a rigid
joint at the branch-to-run centerlines juncture. However, you should be aware that this
assumption can be inaccurate and should consider the use of a more appropriate
flexibility representation."





Use of the Class 1 Branch Flexibility
 feature may be summarized as follows: Include the Class 1
Branch Flex option in the setup file.
Where reduced branch geometry requirements are satisfied, CAESAR II constructs a rigid
offset from the centerline of the header pipe to its surface, and then adds the local flexibility
of the header pipe, between the end of the offset, at the header, and the start of the branch.

Stresses computed for the branch are for the point at its connection with the header.
Where reduced branch geometry requirements are not satisfied, CAESAR II constructs a
rigid offset from the centerline of the header pipe to its surface. The branch piping starts
at the end of this rigid offset. There is NO local flexibility due to the header added. (It is
deemed to be insignificant.)
Stresses computed for the branch are for the point at its
connection with the header.
The reduced branch geometry requirements that CAESAR II checks
are d/D  0.5 and D/T  100.0
Where:
d = Diameter of Branch
D = Diameter of Header
T = Wall thickness of Header
If you use the Class 1 branch flexibilities, intersection models in the analysis become stiffer when
the reduced geometry requirements do not apply, and become more flexible when the reduced
geometry requirements do apply. Stiffer intersections typically carry more loads and thus have
higher stresses lowering the stress in other parts of the system that have been
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unloaded. More flexible intersections typically carry less load and thus have lower stresses.
This causes higher stresses in other parts of the system that have "picked up" the extra load.
The branch flexibility rules used in CAESAR II are taken from ASME III, Subsection NB, (Class 1),
1992 Edition, Issued December 31, 1992, from Code Sections NB-3686.4 and NB-3686.5.
When the reduced branch rules apply, use the following equations for the local stiffnesses:
TRANSLATIONAL:
AXIAL
=
RIGID
CIRCUMFERENTIAL
=
RIGID
LONGITUDINAL
=
RIGID
ROTATIONAL:
AXIAL
=
RIGID
CIRCUMFERENTIAL
=
(kx)d/EI
LONGITUDINAL
=
(kz)d/EI
Where:
RIGID
=
1.0E12 lb./in. or 1.0E12 in.lb./deg.
d
=
Branch Diameter
E
=
Young’s Modulus
I
=
Cross Section Moment of Inertia
D
=
Header Diameter
T
=
Header Thickness
Tb
=
Branch Fitting Thickness
kx
=
0.1(D/T)1.5[(T/t)(d/D)]0.5(Tb/T)
0.2(D/T)[(T/t)(d/D)]0.5(Tb/T)
kz
=
For more information, see WRC 329 Section 4.9 Flexibility Factors. A brief quote from
this section follows:
"The significance of "k" depends upon the specifics of the piping system. Qualitatively, if "k" is
small compared to the length of the piping system, including the effect of elbows and their kfactors, then the inclusion of "k" for branch connections will have only minor effects on the
calculated moments. Conversely, if "k" is large compared to the piping system length, then the
inclusion of "k" for branch connections will have major effects. The largest effect will be to
greatly reduce the magnitude of the calculated moments acting on the branch connection. To
illustrate the potential significance of "k’s" for branch connections, we use the equation
[above] to calculate "k" for a branch connection with D=30 in., d=12.75 in., and T=t=0.375 in.:
k = 0.1(80)1.5(0.425)0.5 * (1.0) = 46.6
This compares to the more typical rigid-joint interpretation that k=1, rather than k=46.6 !"
Further discussion in section 4.9 illustrates additional problems that can arise by overestimating the
stiffness at branch connections. Problems arise by believing "mistakenly" that the stress at the
intersection is too high. Further reference should be made to this section in WRC 329.
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Branch automatic flexibility generation can be used where the user has only defined the branch
element in the model, that is has left the header piping out of the analysis. In this case there will
be no "offset" equal to one-half of the header diameter applied to the branch end. A "partial
intersection" is one where either the header pipe is not modeled, is modeled with a single
element, or is part of a geometric intersection where the header pipes are not colinear. In the
case where there is no header pipe going to the intersection, there will be no modification to the
model for the class 1 branch flexibilities. When at least a single header pipe is recognized, the
local flexibility directions are defined by the branch alone and in accordance with the CAESAR
II defaults for circumferential and longitudinal directions for the branch and header. You must
build full intersection models at all times, not only when employing the class 1 branch flexibility.
In most cases, building full intersection models eliminates problems caused by the assumptions
necessary when a partial intersection is described.
In the equations in NB-3686.5 for tn, the thickness of the branch pipe is used in all cases.
When branches are skewed with respect to the header pipe, and where the two header pipes are
colinear, the local Class 1 flexibilities are still taken to be the longitudinal and circumferential
directions that are tangent to the header surface at its intersection with the branch.
Class 1 branch flexibilities can be formed at both ends of a single pipe element.
The offsets necessary to form the class 1 intersections are automatically generated by
CAESAR II. There is no extra input required by you to have CAESAR II build these
intersections.
If there are already user-defined offsets at an intersection end, the computed offset to get
from the header centerline to its surface along the centerline of the branch is added to the
already entered user offset.
Automatic offsets are generated providing that the distance from the header centerline to the
header surface along the branch centerline is less than or equal to 98% of the total pipe
straight length.
When an element with a bend designation is part of an intersection model, the offset
and flexibility calculations are not performed.
Modeling Friction Effects
There are two methods to solving friction problems:



Insert a force at the node which must be overcome for motion to occur.
Insert a stiffness which applies an increasing force up to the value of Mu * Normal Force.


CAESAR II uses the stiffness method.
If there is motion at the node under evaluation then the friction force is equal to Mu * Normal
force. However, because there is a non-rigid stiffness placed at that location to resist the initial
motion; the node could experience some displacement. The force at the node is the product of
the displacement and the stiffness. If the resultant force is less than the maximum friction force
(Mu * Normal Force) the node is assumed to be not sliding. As a result, you might see
displacements at nodes that have not achieved the "sliding" friction force in the output report.
The maximum value of the force at the node is the friction force (Mu * Normal force). After the
system reaches this value, the reaction at the node stops increasing. This constant force
value is then applied to the global load vector during the next iteration to determine the nodal
displacements. The example below explains what happens in a "friction" problem.
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1.
The default friction stiffness is 1,000,000 lb./in. To solve convergence problems,
consider decreasing this value.
2.
Until the calculated load at the node equals (Mu * Normal force), the restraint load is
the product of the displacement multiplied by the friction stiffness.
3.
Should the calculated load exceed the maximum value of the friction force, the friction
force stops increasing because a constant effort force opposite the sliding direction is
inserted in the model in place of the friction stiffness.
If you increase the friction stiffness in the setup file, the displacements at the node may
decrease slightly. Usually, this causes a re-distribution of the loads throughout the system
that could have an adverse effect on the solution convergence.
If problems arise during the solution of a job with friction at supports, reducing the friction
stiffness typically improves convergence. You must do several runs with varying values of
the friction stiffness to ensure the behavior of the system is consistent.
For more information on this subject, see "Inclusion of a Support Friction into a Computerized
Solution of a Self-Compensating Pipeline" by J. Sobieszczanski, published in the Transactions
of the ASME, Journal of Engineering for Industry, August 1972. A summary of the major
points of this paper is below.

Summary of J. Sobieszczanski’s ASME Paper

For dry friction, the friction force magnitude is a step function of displacement. This
discontinuity means the problem as
intrinsically nonlinear and eliminates the possibility
of using the superposition principle.







The friction loading on the pipe can be represented by an ordinary differential equation of
the fourth order with a variable coefficient that is a nonlinear function of both dependent and
independent variables. No solution in closed form is known for an equation of this type.
The solution has to be sought by means of numerical
 integration to be carried out
specifically for a particular pipeline configuration.
Dry friction
can be idealized by a fictitious elastic foundation, discretized to a set of elastic spring
supports.
A well-known property of an elastic system with dry friction constraints is that
it may attain several
static equilibrium positions within limits determined by the friction forces.
The whole problem then has clearly not a deterministic, but a stochastic character.

Nonlinear Code Compliance
You can adhere to nonlinear piping code compliance requirements by doing the following:
1.
Performing an operating and sustained analysis of the system and including with each
case the effect of nonlinear restraints.
2.
Subtracting the sustained case displacements from the operating case displacements to
find the displacement range.
3.
Calculating the expansion stresses from the displacement range solved for in step 2.
CAESAR II uses this method for calculating the expansion stress range. In addition, CAESAR II
scans your input and recommends load cases and combinations for performing the operating,
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sustained, and expansion stress calculations. This recommendation is useful when
performing spring hanger analysis of a multiple operating case system.
Sustained Stresses and Nonlinear Restraints
The proper computation of sustained stresses has been an issue since the late 1970s when
computerized pipe stress analysis programs first attempted to address the problem of nonlinear restraints. The existing piping codes offered little guidance on the subject, because their
criteria were developed during the era when all analyses were simplified to behave in a strictly
linear fashion. The problem arises because the codes require that a piping system be analyzed
separately for sustained loadings; you must determine which stresses are caused by which
loadings. Sustained loads are force loadings that are assumed not to change, while expansion
loadings are displacement loadings that vary with the system operating conditions.
Determination of the sustained loads is the simple part — most everybody agrees that those
forces consist of weight, pressure, and spring preloads. These forces remain relatively constant
as the piping system goes through its thermal growth. However, confusion occurs when the
status of nonlinear restraints change (pipes lift off of supports, gaps close, and so forth) as the
pipe goes from installed to operating state. In this case, you must determine which boundary
conditions to use when evaluating the applied forces. Or in other words, what portion of the
stress in the operating case is caused by weight loads, and what portion is caused by
expansion effects?
There is no corresponding confusion on the question of calculating expansion stresses,
because the codes are explicit in their instructions that the expansion stress range is the
difference between the operating and cold stress positions, both of which are known.
The obvious answer to this question by the developers of some pipe stress programs was that the
sustained stress calculation should be done using the operating, or hot boundary condition. This
compounded the problem in that the laws of superposition no longer held. In other words, the results
of sustained (W+P) and thermal (T) cases, when added together, did not equal the results of the
operating (W+P+T) case. One pioneering program, DYNAFLEX, attempted to resolve this by
introducing the concept of the "thermal component of weight" an oxymoron, in our opinion. Other
programs, notably those which came from the mainframe/linear analysis world, had to approximate
the behavior of these non-linear restraints. Their approach to the problem is to run an operating
case, obtain the restraint status, and modify the model according to these results. All subsequent
load cases analyzed use this restraint configuration. The fact that the laws of static superposition did
not hold was hopefully not noticed by the user. CAESAR II, on the other hand, represents
technology developed expressly for operation on the personal computer, and therefore incorporates
directly the effects of non-linear restraints. This is done by considering each load case
independently. The restraint configuration is determined for each load case by the program as it
runs, based upon the actual loads that are considered present.
Some users have asserted that there are actually two sustained load cases. In fact, there has
been a B31.3 code interpretation that indicates that the sustained stress may also be checked
with the operating restraint configuration. Calculating the sustained stresses using the
operating restraint status raises several other issues; what modulus of elasticity should be
used, and which sustained stresses should be used for occasional cases.
It is our assertion that there is only one sustained case (otherwise, it is not "sustained") there can
be, however, multiple sustained stress distributions. The two most obvious are those associated
with the cold (installed) and hot (operating) configurations; however, there are also numerous inbetween, as the piping system load steps from cold to hot. Whether the "true" sustained load case
occurs during the installed or operating case is a matter of the frame of
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reference. If an engineer first sees a system in its cold condition, and watches it expand to its
operating condition, it appears that the first case (because weight and pressure — primary loads
— are present) is the sustained case, and the changes he viewed are thermal effects (due to
heat up) — secondary loads due to displacements. If a second engineer first sees the same
system in the operating case and watches it cool down to the cold case, he may believe that the
first case he saw (the operating case) is the sustained case, and changes experienced from hot
to cold are the thermal expansion effects (the thermal stress ranges are the same in both
cases). Consider the further implications of cryogenic systems where changes from installed to
operating are the same as those experienced by hot systems when going from operating to
installed. After elastic shakedown has occurred, the question becomes clouded even further
due to the presence of thermally induced pre-stresses in the pipe during both the cold and hot
conditions. We feel either the operating or installed case (or some other one in-between) could
justifiably be selected for analysis as the sustained case, as long as the program is consistent.
We have selected the installed case (less the effect of cold spring) as our reference sustained case,
because thermal effects can be completely omitted from the solution (as intended by the code). This
best represents the support configuration when the sustained loads are initially applied. If the pipe
lifts off of a support when going from installed to operating, we view this as a thermal effect which is
— consistent with the piping codes’ view of thermal effects as the variation of stress distribution as
the piping system goes from cold to hot, and is explicitly corroborated by one code, an earlier edition
of the French petrochemical code, which states that weight stress distributions due to thermal growth
of the pipe should be considered as expansion stresses). For example, we feel that a change in a
rigid support load from 2,000 lbs to zero should be treated no differently than would be a variable
spring load changing from 6,000 lbs to 4,000 lbs (or another rigid support load going 2,000 lbs to 1
lb). In the former case, if the pipe became "overstressed", it would yield, and sag back to the support,
relieving the stress. This process is identical to the way that all other expansion stresses are relieved
in a piping system.
We are confident that our interpretation is correct. However, we understand that our users may
not always agree with us — that is why CAESAR II provides the greatest ability to custom tailor
the analysis to your individual specifications. If you want, you can analyze a "hot sustained"
case by adding two load cases to those normally recommended by CAESAR II. This is done by
assuming that the pipe expands first, and then the sustained loads are applied (this is of course
an idealized concept, but the stresses can only be segregated by segregating the applied
loads, so the sustained loads can only be applied either before, or after, the expansion loads).
Following are the default load cases, as well as those required for a "hot sustained."
Default
New
L1: W+P1+T1(OPE)
L1: W+P1+T1(OPE)
L2: W+P1(SUS)
L2: W+P1(SUS)
L3: L1-L2(EXP)
L3: T1(EXP)
L4: L1-L2(EXP)
L5: L1-L3(SUS)
In the new load case list, the second case still represents the cold sustained, while the
fourth case represents the expansion case (note that L1-L2, or W+P1+T1-W-P1, equals T1,
with non-linear effects taken into account). The third case represents the thermal growth of
the "weightless," non-pressurized pipe, against the non-linear restraints.
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The fifth case (L1-L3, or W+P1+T1-T1, equals W+P1) represents the application of weight and
pressure to that expanded case, or the "hot sustained" case. Note that when the piping system
is analyzed as above, the actual effects of the non-linear restraints are considered (they are
not arbitrarily removed from the model), and the laws of superposition still hold.
An alternative school of thought believes that a "hot sustained" is only valid if: (1) the
sustained, primary loads are applied, (2) all springs are showing their Hot Load settings, and
(3) any supports that lift off (or otherwise become non-active) have been removed from the
model. An analysis such as this is achievable by setting the "Keep/Discard" status of the
Restrained Weight case (the first hanger design load case) to "Keep", thus permitting the
results of that case to be viewable as for any other load case. The Restrained Weight case
automatically removes restraints that become non-active during the designated operating case,
and apply the Hot Load at each of the hanger locations.
Notes on Occasional Load Cases
Several piping codes require that you add the stresses from occasional loads (such as wind or
earthquake) to the sustained stresses (due to weight, pressure, and other constant loads)
before comparing them to their allowables. You can recreate this combination in CAESAR II
using the following load cases:
CASE #
1
W+P+H
(SUS):
Sustained stresses
2
WIND
(OCC):
Wind load set
3
U1
(OCC):
Uniform g load set for earthquake
4
L1+L2
(OCC):
Code stresses for wind
5
L1+L3
(OCC):
Code stresses for earthquake*
* Scalar Summation Method required
If you must model nonlinear effects in the system, the load case combinations are not so
straight forward. Friction, one-direction restraints, and double-acting restraints with gaps are the
nonlinear items which complicate modeling. For this example, we will use wind loading on a
long vertical run of pipe with a guide. Assume there is a 1-inch gap between the pipe and guide.
Under normal operation, the pipe moves ¾-inch towards the stop leaving a gap of 1-¾-inch on
either side of the pipe and a ¼-inch gap on the other side. If you analyze the wind loads alone,
the pipe is allowed to move 1-inch from its center point in the guide to the guide stop. Because
occasional loads are usually analyzed with the system in operation, the pipe may be limited to a
¼-inch motion as the gap is closed in one direction, and 1-¾-inch if the gap is closed in the
opposite direction. With nonlinear effects modeled in the system, the occasional deflections
(and stresses) are influenced by the operating position of the piping.
The following list of CAESAR II load cases takes this point into consideration. The load cases
displayed below are only for wind acting in one direction, that is, +X. Depending on the system,
the most critical loads could occur in any direction +/-X, +/-Z, or skewed in XZ. The intention of
the load case construction is to find the effect of the occasional load on the piping system in
the operating condition. The stress due to the moment change from the operating to the
operating plus wind case is added to the stress from the sustained case.
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CASE #
1
W+T1+P1
(OPE):
Operation analysis
2
W+P1
(SUS):
Sustained stresses
3
W+T1+P1+WIN
D1
(OPE):
Operating analysis with wind
4
L1-L2
(EXP):
Expansion stresses (Algebraic summation)
5
L3-L1
(OCC):
Net deflection of wind(Algebraic summation)
6
L2+L5
(OCC):
Code stresses for wind (Scalar summation)
Case 5 computes the isolated wind effect on the piping system in the operating condition.
Case 6 adds the stresses from Case 5 to the sustained stresses from Case 2.
Static Seismic Inertial Loads
Static earthquake loads are applied in a manner very similar to static wind loads. The static
loading magnitude is considered to be in direct proportion to the weight of the element.
Express earthquake load magnitudes in terms of the gravitational acceleration constant g. If
you model an earthquake with a 0.5-g load in the X direction, then half of the systems weight is
turned into a uniform load and applied in the X direction.
You create earthquake static load cases the same way you create wind occasional load cases.
Use the same load case, nonlinearity, and directional sensitivity logic. In some cases, the
client specifies the magnitude of the earthquake loading in g's and the direction(s). In other
cases, analysis is left to the discretion of the analyst. It is not unusual to see only X-Y or Z-Y
components of an earthquake. It is also not uncommon to see X, Y, and Z simultaneous
components.
Dynamic (response spectrum) evaluation of earthquake loads are discussed later in this
section, in the dynamic analysis and output sections, and in the screen reference section.
The ASCE #7 method for determining earthquake coefficients is described below. After you
calculate the earthquake coefficients, enter the g-factors as uniform loads on the piping
spreadsheet.
Calculate the horizontal seismic design force using equation 13.3-1 from ASCE 7 (10):
Fp = [(0.4 ap SDS W p) / (Rp / Ip)] (1 + 2 z / h)
But since W p is "component operating weight", Fp/W p = calculated (horizontal) acceleration,
aH, so;
aH = [(0.4 ap SDS) / ( Rp / Ip )] (1 + 2 z / h),
additionally;
aH  1.6 SDS Ip
and:
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aH  0.3 SDS Ip
Where:
ap = Component amplification factor, from Table 13.6-1
= 2.5 for "Piping"
SDS = Design elastic response acceleration at short period (0.2 sec), from Section 11.4.4
Rp = Component response modification factor, from Table 13.6-1
= 12.0 for "Piping in accordance with ASME B31... with joints made by welding
or brazing"; values range as low as 3.0 for other joints and for less ductile materials.
Ip = Component importance factor, from Section 13.1.3
= 1.5 for life-safety components, components containing hazardous material,
or components that are required for continuous operation; 1.0 for all others
z = Height in structure at point of attachment
h = Average roof height of structure
Wind Loads
You can define your own wind pressure profile or wind speed profile, or you can access
wind load data from the following wind codes:

ASCE7 2005

IBC 2006

AS/NZ 1170:2002

IS 875

Brazil NBR 6123

Mexico 1993

BS6399-97

NBC 2005

China GB 50009

UBC

EN 1991-1-4:2005

Generate Wind Loads
By defining a wind shape factor in the model input, CAESAR II allows you to define up to
four wind vectors in the Load Case Editor. Multiply the pipe exposed area by the equivalent
wind pressure and the pipe shape factor.
CAESAR II includes insulation thickness in the cladding. You must also consider the angle
to the wind with your calculations.
Determine the Equivalent Wind Pressure
There are three ways to determine the equivalent wind pressure:



Selecting a regional wind specification (by building code)


Use the Pressure versus Elevation Table Entry method


Use the Velocity versus Elevation Table Entry method
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
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Calculate the Total Wind Force on the Element
Calculate the total wind force on the element by using the following equation:
F=
PeqSA Where:
F = the total wind force on the element
Apply the wind force in the three global
directions as a function of the element
direction cosines.
Peq = the equivalent wind pressure (dynamic
pressure)
Calculate Peq for each end of the element and
then take the average.
The average applies uniformly over the
whole length of the element.
S = the pipe element wind shape factor
A = the pipe element exposed area as shown
in the figure to the right.
If you enter velocity versus elevation table data, then the program converts the velocity to
a dynamic pressure using the following equation:
P = 1/2 V2
Where V is the wind velocity and  is the air density.
Enter the Wind Shape Factor on the piping spreadsheet. For cylindrical elements, a value
between 0.5 and 0.7 is used. A value of 0.65 is typical. The wind shape factor as entered is
distributive. This means that the shape factor entered on a spreadsheet is carried forward
and applies for all following elements until zeroed or changed.
There is no need to enter the same shape factor on each piping spreadsheet. Zero or
disable the wind shape factor if the piping system runs inside of a building or similarly
protective structure.
Enter wind load parameters on the Wind Loads (see "Wind Loads Tab (Static Analysis Dialog
Box)" on page 543) tab of the Static Load Case Builder. You can enter up to four different
wind loads per analysis. These typically might be setup to model wind loads in the +X, -X, +Z,
and -Z directions.
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Elevation
It is important to set the proper elevation of the piping system (height above ground) when
running a wind analysis. When a wind shape factor is specified in the input, CAESAR II prompts
you for the elevation (and horizontal coordinates) of this first node. By default, CAESAR II
assigns the "From" node of the first element an elevation of 0.0. You can also use the
procedure below to set the reference wind elevation of the piping system.
Set the true elevation
1.
Click EDIT > GLOBAL.
A dialog appears.
2.
Enter the global coordinates of the first node in the system.
3.
Repeat step 2 for each (if any) disconnected section until you are finished.
You can specify and save the coordinates for up to 100 node points from the model.
Hydrodynamic (Wave and Current) Loading
Ocean waves are generated by wind and propagate out of the generating area. Ocean wave
generation is dependent on the wind speed, the duration of the wind, the water depth, and the
distance over which the wind blows the fetch length. There are several two dimensional wave
theories, but the three most widely used are the Airy (linear) wave theory, Stokes 5th Order wave
theory, and Dean's Stream Function wave theory. The latter two theories are non-linear wave
theories and provide a better description of the near surface effects of the wave.
Of course, wave motion is a three dimensional action but it can be adequately
represented by two dimensions. One dimension is the direction the wave travels, and the other
dimension is vertical through the water column. Two dimensional waves are not found in the
marine environment, but are somewhat easy to define and determine properties for. In
actuality, waves undergo spreading, in the third dimension. To understand this concept think
about a stone dropped in a pond. As the wave spreads, the diameter of the circle increases. In
addition to wave spreading, a real sea state includes waves of various periods, heights, and
lengths. To address these actual conditions you must use a sea spectrum that includes a
spreading function.
Airy (linear) wave theory assumes the free surface is symmetric about the mean water level.
Additionally, water particle motion is in a closed circular orbit, the diameter of which decays
with depth. You should take the term circular loosely because, the orbit varies from circular to
elliptical based on whether the wave is in shallow or deep water.
Additionally, for shallow water waves, the wave height to depth ratio (H/D) is limited to 0.78
to avoid breaking.
None of the wave theories address breaking waves.
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The figure below shows a typical wave and associated hydrodynamic parameters.









SWL - The still water level.


L - The wave length or horizontal distance between successive crests or troughs.
H - The wave height or vertical distance between the crest and trough.

D - The water depth or vertical distance from the bottom to the still water level.
 - The surface elevation measured from the still water level.


Ocean Wave Particulars
The Airy Wave Theory Implementation (on page 897) theory provides a good first
approximation to the water particle behavior. The nonlinear theories provide a better description
of particle motion, over a wider range depths and wave heights. Stokes 5tH Wave theory is
based on a power series. This wave theory does not apply the symmetric free surface
restriction. Additionally, the particle paths are no longer closed orbits, which mean there is a
gradual drift of the fluid particles, that is, a mass transport.
Stokes 5tH Order Wave theory however, does not adequately address steeper waves over a
complete range of depths. Dean’s Stream Function wave theory attempts to address this
deficiency. This wave theory employs an iterative numerical technique to solve the stream
function equation. The stream function describes not only the geometry of a two dimensional
flow, but also the components of the velocity vector at any point, and the flow rate between
any two streamlines.
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The most suitable wave theory is dependent on the wave height, the wave period, and the
water depth. Based on these parameters, the applicable wave theory can be determined from
the figure below (from API-RP2A, American Petroleum Institute - Recommended Practice 2A).
Applicable Wave Theory Determination
The limiting wave steepness for most deep water waves is usually determined by the
Miche Limit:
H / L = 0.142 tanh( kd )
Where:
H is the wave height
L is the wave length
k is the wave number (2)/L
d is the water depth
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Pseudo-Static Hydrodynamic Loading
You can model individual pipe elements that experience loading due to hydrodynamic effects.
Fluid effects can impose a substantial load on the piping elements in a manner similar to,
but more complex than wind loading.
Use wave theories and profiles to compute the water particle velocities and accelerations at
the node points. Then use, Morrison’s equation, F = ½ *  * Cd * D * U * |U| + /4 * * Cm * D2*
A to compute the force on the element.
Where:
- is the fluid density
Cd- is the drag coefficient
D - is the pipe diameter
U - is the particle velocity
Cm - is the inertial coefficient
A - is the particle acceleration
The particle velocities and accelerations are vector quantities that include the effects of any
applied waves or currents. In addition to the force imposed by Morrison’s equation, piping
elements are also subjected to a lift force and a buoyancy force. The lift force is defined as
the force acting normal to the plane formed by the velocity vector and the axis of the element.
The lift force is defined as:
Fl = ½ * * Cl * D * U2
Where:
 - is the fluid density

Cl - is the lift coefficient D
- is the pipe diameter U is the particle velocity
The buoyancy force acts upward and is equal to the weight of the fluid volume displaced by
the element.
A piping system can be described by using the standard finite element equation:
[K] {x} = {f}
Where:
[K] - is the global stiffness matrix for the entire
system {x} - is the displacement / rotation vector to
solve for {f} - is global load vector
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Calculate pseudo-static hydrodynamic loading
1.
Place the element loads generated by the hydrodynamic effects in their proper locations
in {f}, similar to weight, pressure, and temperature.
2.
Perform a standard finite element solution on the system of equations to finalize [K] and {f}.
3.
Use the resulting displacement vector {x} to compute element forces.
4.
Use the computed element forces to compute the element stresses.
Except for the buoyancy force, all other hydrodynamic forces acting on the element are a
function of the particle velocities and accelerations.
Airy Wave Theory Implementation
Airy Wave theory is also known as Linear Wave theory due to the assumption that the wave
profile is symmetric about the mean water level. Standard Airy Wave theory allows for the
computation of the water particle velocities and accelerations between the mean surface
elevation and the bottom. The Modified Airy Wave theory allows for the consideration of the
actual free surface elevation in the computation of the particle data. CAESAR II includes
both the standard and modified forms of the Airy wave theory.
To apply the Airy Wave theory, you must enter several descriptive parameters about the wave.
The software uses these parameters along with the Newton-Raphston iteration to determine
the wave length. Each wave has its own unique wave length that the program determines
solving the dispersion relation, shown below:
L = (gT2 / 2) * tanh(2D /
L) Where:
g - is the acceleration of gravity
T - is the wave period
D - is the mean water depth
L - is the wave length to solve for
After determining the wave length (L), you can determine any other wave parameters you
want. The parameters determined and used by CAESAR II are: the horizontal and vertical
particle velocities (UX and UY), the horizontal and vertical particle acceleration (AX and AY),
and the surface elevation above (or below) the mean water level (ETA). For more information
on the equations for these parameters, refer to any text which discusses ocean wave theories.
STOKES 5th Order Wave Theory Implementation
The Stokes Wave is a 5th order gravity non-linear wave. CAESAR II uses the solution
technique described in a paper published in 1960 by Skjelbreia and Hendrickson of the
National Engineering Science Company. The standard formulation as well as a modified
formulation, to the free surface, is available in CAESAR II Stokes 5th Order Wave Theory.
The solution follows a procedure very similar to that used in the Airy Wave Theory
Implementation (on page 897). You can determine the characteristic parameters of the wave
by using Newton-Raphston iteration, after finding the water particle values of interest.
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The Newton-Raphston iteration procedure solves two non-linear equations for constants beta
and lambda. After you determine these values, you can compute the other constants. After
computing all of the constants, use CAESAR II to compute: the horizontal and vertical
particle velocities (UX and UY), the horizontal and vertical particle acceleration (AX and AY),
and the surface elevation above the mean water level (ETA).
Stream Function Wave Theory Implementation
The solution to Dean's Stream Function Wave Theory used by CAESAR II is described in the
text by Sarpkaya and Issacson. As previously mentioned, this is a numerical technique to
solve the stream function. The solution subsequently obtained, provides the horizontal and
vertical particle velocities (UX and UY), the horizontal and vertical particle acceleration (AX
and AY), and the surface elevation above the mean water level (ETA).
Ocean Currents
In addition to the forces imposed by ocean waves, piping elements can also be subjected
to forces imposed by ocean currents. There are three different ocean current models in
CAESAR II: linear current, piece-wise, and power law profile.





The linear current profile assumes that the current velocity through the water
 column varies linearly
from the specified surface velocity (at the surface) to zero (at the bottom).
The piece-wise linear
profile employs linear interpolation between specific user-defined
depth/velocity points.
The power law profile decays the surface velocity to the 1/7 power.

While waves produce unsteady flow where the particle velocities and accelerations at a
point constantly change, currents produce a steady, non-varying flow.
Technical Notes on CAESAR II Hydrodynamic Loading
The input parameters necessary to define the fluid loading are described in detail in the next
section. The basic parameters describe the wave height and period, and the current velocity.
The most difficult to obtain, and also the most important parameters, are the drag, inertia, and
lift coefficients: Cd, Cm, and Cl. Based on the recommendations of API RP2A and DNV (Det
Norske Veritas), values for Cd range from 0.6 to 1.2, values for Cm range from 1.5 to 2.0. Values
for Cl show a wide range of scatter, but the approximate mean value is 0.7.
The inertia coefficient Cm is equal to one plus the added mass coefficient Ca. This added mass
value accounts for the mass of the fluid assumed to be entrained with the piping element.
In actuality, these coefficients are a function of the fluid particle velocity, which varies over the
water column. In general practice, two dimensionless parameters are computed that are used
to obtain the Cd, Cm, and Cl values from published charts. The first dimensionless parameter is
the Keulegan-Carpenter Number, K. K is defined as:
K = Um * T / D
Where:
Um = Maximum Fluid Particle Velocity
T = Wave Period
D = Characteristic Diameter of the Element
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The second dimensionless parameter is the Reynolds number, Re. Re is defined as
Re = U m * D / 
Where:
Um = Maximum Fluid Particle Velocity
D = Characteristic Diameter of the Element
= Kinematic Viscosity of the Fluid 1.26e-5 ft2/sec for Sea Water
After you calculate K and Re use the charts to obtain Cd, Cm, and Cl. For more information, see
Mechanics of Wave Forces on Offshore Structures by T. Sarpkaya. Figures 3.21, 3.22, and
3.25 are example charts, which display below.
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In order to determine these coefficients, the fluid particle velocity (at the location of interest)
must be determined. The appropriate wave theory is solved, and these particle velocities
are readily obtained.
Of the wave theories discussed, the modified Airy and Stokes 5th theories include a
modification of the depth-decay function. The standard theories use a depth-decay function
equal to cosh(kz) / sinh(kd),
Where:
k - is the wave number, 2 /L
L - is the wave length
d - is the water depth
z - is the elevation in the water column where the data is to be determined
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The modified theories include an additional term in the numerator of this depth-decay
function. The modified depth-decay function is equal to cosh(d) / sinh(kd),
Where:
- is equal to z / (d + h)
The term d represents the effective height of the point at which the particle velocity and
acceleration are to be computed. The use of this term keeps the effective height below the
still water level. This means that the velocity and acceleration computed are convergent for
actual heights above the still water level.
As previously stated, the drag, inertia, and lift coefficients are a function of the fluid velocity and
the diameter of the element in question. Note that the fluid particle velocities vary with both
depth and position in the wave train (as determined by the applied wave theory). Therefore,
these coefficients are in fact not constants. However, from a practical engineering point of view,
varying these coefficients as a function of location in the Fluid field is usually not implemented.
This practice can be justified when one considers the inaccuracies involved in specifying the
instantaneous wave height and period. According to Sarpkaya, these values are insufficient to
accurately predict wave forces, a consideration of the previous fluid particle history is
necessary. In light of these uncertainties, constant values for C d, Cm, and Cl are recommended
by API and many other references.
The effects of marine growth must also be considered. Marine growth has the following effects
on the system loading: the increased pipe diameters increase the hydrodynamic loading; the
increased roughness causes an increase in Cd, and therefore the hydrodynamic loading; the
increase in mass and added mass cause reduced natural frequencies and increase the
dynamic amplification factor; it causes an increase in the structural weight; and possibly causes
hydrodynamic instabilities, such as vortex shedding.
Finally, Morrison’s force equation is based the "small body" assumption. The term "small" refers to
the "diameter to wave length" ratio. If this ratio exceeds 0.2, the inertial force is no longer in phase
with the acceleration of the fluid particles and diffraction effects must be considered. In such cases,
the fluid loading as typically implemented by CAESAR II is no longer applicable.
Additional discussions on hydrodynamic loads and wave theories can be found in the
references at the end of this article.
Input: Specifying Hydrodynamic Parameters in CAESAR II
The hydrodynamic load analysis requires the specification of several measurable
parameters that quantify the physical aspects of the environmental phenomenon in question.
You can enter four different wave loads here. Use the Editing Load Case buttons to
move up or down between the Wave Load Input Spreadsheets.
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The necessary hydrodynamic parameters are discussed in the following paragraphs and
a CAESAR II hydrodynamic loading dialog is shown in the figure below.
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Current Data
Profile Type — Defines the interpolation method you want CAESAR II to use to determine the
current velocity as a function of depth. Available options for this entry are:

Power Law Profile — Determines the current velocity at depth D according to the equation:

Vd = Vs * [di / D]p
Where:
Vd - is the velocity at depth di
Vs - is the specified velocity at the surface
D - is the water depth
p - is the power, set to 1/7







Piece-wise Linear Profile — Performs a linear interpolation of a velocity verse depth table
that you must provide, to determine the current velocity at depth di. The table should
start at

the surface (a depth of zero) and progress in increasing depth to the sea bed.
Linear Profile — Performs a linear interpolation to determine the current velocity at depth
di. However, this method assumes the 
current velocity varies linearly from the specified
surface velocity to zero at the sea bed.
Current Speed — Defines the current speed at the surface. The units for this entry are
(length/time) as defined by
the active units file at the time of input. This value should
always be a positive entry.
Current Direction Cosines — Defines the direction of fluid transport due tothe current. These
fields are unit-less and follow the standard software global axis convention.
Wave Data
Wave Theory Indicator — Specifies which wave theory to use to compute the water
particle velocities and accelerations. The wave theories available are:
Standard Airy Wave — This is also known as linear wave theory. Discussion of this theory
can be found in the previously mentioned references.
Modified Airy Wave — This is a modification of the standard Airy theory which includes the
free surface effects due to the wave. The modification consists of determining a depth scaling
factor equal to the depth divided by the depth plus the surface elevation. Note that this scale
factor varies as a function of the location in the wave train.







Standard Stokes 5th Wave — This
 is a 5th order wave theory, also discussed in the
previously mentioned references.
Modified Stokes 5th Wave — This is a modification of
the standard Stokes 5th theory. The
modification is the same as applied to the Airy theory.
Stream Function Wave — This isDean’s Stream Function theory, also discussed in the
previously mentioned references.
Modified Stream Function Wave — 
This is Dean’s Stream Function theory, modified to directly
consider current in the wave solution.
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Stream Function Order — When the Stream Function theory is activated, the solution order
must be defined. Typical values for the stream function order range from 3 to 13, and must
be an odd value (see API-RP2A figure).
Water Depth — Defines the vertical distance (in units of length) from the still water level
the surface to the sea bed.
Wave Height — Defines the height of the incident wave. The height is the vertical distance
in units of length from the wave crest to the wave trough.
Wave Period — Defines the time span (in seconds) for two successive wave crests to pass
a fixed point.
Wave Kinematic Factor — Because the two dimensional wave theories do not account for
spreading, a reduction factor is often used for the horizontal particle velocity and
acceleration. Wave kinematic measurements support values in the range of 0.85 to 0.95.
Refer to the applicable offshore codes before using this item.
Wave Direction Cosines — Define the direction of wave travel. These fields are unit-less
and follow the standard software global axis convention.
Wave Phase Angle — Defines the position of the wave relative to the starting node of the
piping system. The phase angle is a measure (in degrees) of position in the wave train, where
0 is the wave crest, 180 is the wave trough, and 360 is the following crest. Because the wave
propagates over the piping structure, each point in the structure experiences all possible wave
phase angles. One analysis technique specifies the wave phase at the system origin, and then
the phase at each node point in the model is deter\-mined. From these exact phase locations,
the water particle data is computed from the wave theory.
Alternatively, a conservative engineering approach is to use the same phase angle usually
zero for all points in the model. This technique produces higher loads; however, the extra
conservatism is warranted when given the unknowns in specifying environmental data.
Seawater Data
Free Surface Elevation — Defines the height of the free surface from the global system origin. If the
system origin is at the free surface, this entry should be specified as zero. If the system origin is at
the sea bottom, this entry is equal to the water depth. By default, the first node in a CAESAR II
model is at an elevation of zero. You can change the elevation by pressing [Alt-+G].
Kinematic Viscosity — Defines the kinematic viscosity of water. This value is used to determine
the Reynolds number, which is subsequently used to determine the hydrodynamic coefficients
Cd, Cm, and Cl. Typical values of kinematic viscosity for sea water display below.
Temp Deg (F)
n(ft2/sec)
Temp (C)
n(m2/sec)
60
1.26e-5
15.556
1.17058e-6
50
1.46e-5
10.000
1.35639e-6
40
1.55e-5
4.444
1.44000e-6
30
2.00e-5
-1.111
1.85807e-6
Fluid Weight Density - Defines the weight density of the fluid. For sea water, this value
is approximately .037037 pounds per cubic inch (.001025 kg/cm3, 1.0256SG).
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Piping Element Data
Element Exposure — In implementing hydrodynamic loading in a software program, you must
be able to indicate that elements are either exposed to the fluid or not exposed to the fluid. In
CAESAR II, this is accomplished by a set of options, which indicate that the particular element
is exposed to hydrodynamic loads, wind loads, or not exposed. This specification carries
forward for all subsequent elements until changed.
Hydrodynamic Coefficients — Piping elements that are subjected to hydrodynamic loading
must have drag (Cd), inertia (Cm), and a lift (Cl) coefficient defined. The specification of these
items is optional. Alternatively, you can specify these values as constants to be applied to all
subsequent exposed elements, regardless of depth or phase position in the wave.
Alternatively, You can leave these values blank, which causes CAESAR II to interpolate their
values from the charts previously discussed.
Marine Growth — Defines the amount of marine growth on the piping elements. This value is
used to increase the diameter of the piping elements. The units for this field are the units of
the current diameter. The diameter used in the computation of the hydrodynamic forces is
equal to the pipe diameter plus twice the marine growth entry.
References
1.
Mechanics of Wave Forces On Offshore Structures, Turgut Sarpkaya and Michael
Isaacson, Van Nostrand Reinhold Co., 1982, ISBN 0-442-25402-4.
2.
Handbook of Ocean and Underwater Engineering, Myers, Holm, and
McAllister, McGraw-Hill Book Co., 1969, ISBN 07-044245 -2.
3.
Fifth Order Gravity Wave Theory, Lars Skjelbreia and James Hendrickson,
National Engineering Science Co., Pasadena, California, 1960.
4.
Planning and Design of Fixed Offshore Platforms, McClelland and Reifel, Van
Nostrand Reinhold Co., 1986, ISBN 0-442-25223-4.
5.
Intercomparison of Near-Bottom Kinematics by Several Wave Theories and Field and
Laboratory Data, R. G. Dean and M. Perlin, Coastal Engineering, #9 (1986), p399-437.
6.
A Finite Amplitude Wave on a Linear Shear Current, R. A. Dalrymple, Journal
of Geophysical Research, Vol 79, No 30, 1974.
7.
Application of Stream Function Wave Theory to Offshore Design Problems, R. G.
Dean, OTC #1613, 1972.
8.
Stream Function Representation of Nonlinear Ocean Waves, R. G. Dean, Journal
of Geophysical Research, Vol 70, No 18, 1965.
9.
American Petroleum Institute - Recommended Practice 2A (API-RP2A),
American Petroleum Institute, July 1993.
10. Improved Algorithm for Stream Function Wave Theory, Min-Chih Huang, Journal
of Waterway, Port, Coastal, and Ocean Engineering, January 1989.
11. Stream Function Wave Theory with Profile Constraints, Min-Chih Huang, Journal
of Waterway, Port, Coastal, and Ocean Engineering, January/February 1993.
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Evaluating Vessel Stresses
ASME Section VIII Division 2 — CAESAR II applies rules prior to the 2007 Edition — provides
a procedure to analyze the local stresses in vessels and nozzles. For this example, we will only
discuss the nozzle analysis approach.
Always refer to the applicable design code if any of the limits described in this section are
approached, or if any unusual material, weld, or stress situation exists, or there are non-linear
concerns such as the operation of material within creep range.
The first step is to determine if the elastic approach is satisfactory. To summarize, Section
AD-160 states that if the model meets all of the following conditions, then a fatigue analysis
is not required:
1.
The expected design number of full-range pressure cycles does not exceed the number of
allowed cycles corresponding to a Sa value of 3Sm (4Sm for non-integral attachments) on the
material fatigue curve. Sm is the allowable stress intensity for the material at the operating
temperature.
2.
The expected design range of pressure cycles other than startup or shutdown must be
less than ⅓ (¼ for non-integral attachments) the design pressure times (Sa/Sm), where Sa
is the value from the material fatigue curve for the specified number of significant pressure
fluctuations.
3.
The vessel does not experience localized high stress due to heating.
4.
The full range of stress intensities due to mechanical loads including piping reactions
does not exceed Sa, from the fatigue curve, for the expected number of load fluctuations.
After deciding if an elastic analysis is satisfactory, you must determine whether to take either a
simplified or a comprehensive approach to do the vessel stress analysis. For more information
on the simplified or the comprehensive approach, see ASME Section VIII Division 2-Elastic
Nozzle Simplified Analysis (see "ASME Section VIII Division 2-Elastic Nozzle Simplified Analysis
pre-2007" on page 910) or ASME Section VIII Division 2-Elastic Nozzle Comprehensive
Analysis (see "ASME Section VIII Division 2-Elastic Nozzle Comprehensive Analysis (pre2007)" on page 906). For more information on Section VIII Division 2 requirements, refer to the
latest version of the ASME code.
ASME Section VIII Division 2-Elastic Nozzle
Comprehensive Analysis (pre-2007)
To address the local allowable stress problem, you should have the endurance curve for
the material of construction and complete design pressure/temperature loading information.
Carefully consult the code before performing the local stress analysis if:



any elastic limit is approached

there is anything unusual in the nozzle/vessel connection design

The material Sm table and the endurance curve for carbon steels used in this
section are for illustration purposes. You should only use values taken directly from the code
in your design.
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There are three criteria you must satisfy before considering stresses in the vessel wall due
to nozzle loads within the allowables. The three criteria are summarized as:
Pm < kSmh
Pm + Pl + Pb< 1.5kSmh
Pm + Pl + Pb + Q < 3Smavg
Where Pm, Pl, Pb, and Q are the general primary membrane stress, the local primary membrane
stress, the local primary bending stress, and the total secondary stresses (membrane plus
bending), respectively; and k, Smh, and Smavg are the occasional stress factor, the hot material
allowable stress intensity, and the average material stress intensity (S mh + Smc) / 2.
The stress classification defined by the Section VIII Division 2 code in the vicinity of nozzles,
classifies the bending stress terms caused by any external load moments or internal pressure
in the vessel wall near a nozzle or other opening, as secondary stress Q, regardless of whether
they were caused by sustained or expansion loads. This definition causes P b to disappear and
leads to a more detailed classification:




Pl - Local primary membrane stress, which may include the following:





Pm - General primary membrane stress (primarily due to internal pressure)








Membrane stress due to internal pressure
Local membrane stress due to applied sustained forces and moments
Q - Secondary stresses, which may include the following:






Bending stress due to internal pressure
Bending stress due to applied sustained loads

Membrane stress due to applied expansion loads
Bending stress due to applied expansion loads


Each of the stress terms defined in the above classifications contains three parts: two stress
components in normal directions and one shear stress component. To combine these
stresses, the following rules apply:
1.
Compute the normal and shear components for each of the three stress types, that is, Pm,
Pl, and Q.
2.
Compute the stress intensity due to the Pm and compare it against kSmh.
3.
Add the individual normal and shear stress components due to Pm
resultant stress intensity and compare its value against 1.5kS mh.
4.
Add the individual normal and shear stress components due to P m, Pl, and Q, compute the
resultant stress intensity, and compare its value to against 3S mavg.
5.
Determine if there is an occasional load as well as a sustained load, these types can
be repeated using a value of 1.2 for k.
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and Pl; compute the
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These criteria can be readily found from Figure 4-130.1 of Appendix 4 of ASME Section VIII, Division
2 2004 and the surrounding text. Note that the primary bending stress term, Pb, is not applicable to
the shell stress evaluation, and therefore disappears from the Section VIII, Division
2 requirements. Using the same analogy, write the peak stress limit as:
Pl + Pb + Q + F < Sa
The preceding equation need not be satisfied, provided the elastic limit criteria of AD-160 is
met based on the statement explicitly given in Section 5-100, which is cited below:
"If the specified operation of the vessel meets all of the conditions of AD-160, no analysis for
cyclic operation is required and it can be assumed that the peak stress limit discussed in 4135 has been satisfied by compliance with the applicable requirements for materials, design,
fabrication, testing and inspection of this division."
Elastic Analyses of Shells near Nozzles Using WRC 107
Check vessel stresses in shells using WRC 107
1.
Check the geometric limitation to see whether WRC 107 is applicable.
2.
If yes, determine whether the elastic approach as outlined in Section VIII Division 2 AD160 is applicable.
3.
Compute the sustained, expansion, and occasional loads in the vessel shell due to
the applied nozzle loads.
4.
Consider the local restraint configuration to determine whether some or all the axial
pressure thrust load P * Ain should be added to the sustained and occasional loads. If you
choose, the program can automatically calculate the thrust load and add it to the applied
loads.
5.
Calculate the pressure stresses, Pm, on the vessel shell wall in both the longitudinal
and circumferential hoop directions for both sustained and occasional load cases.
Notice that two different pressure terms are required in carrying out the pressure stress
calculations. P is the design pressure of the system (sustained), while P var is the difference
between the peak pressure and the design pressure of the system, which is used to qualify
the vessel membrane stress under the occasional load case.
If you enter the pressure value, the software automatically calculates the P m stresses.
6.
The processor will calculate the Pl, and Q stresses as defined earlier.
If needed, you can simultaneously compute the local stresses due to sustained,
expansion, and occasional loads.
7.
Obtain the various stress components by combining the stress intensities computed
from applying the sustained, expansion, and occasional loads, if applicable.
8.
Then use stress intensities to carry out the stress summations.
If needed, use the results to determine the acceptability of the local stresses in the
vessel shell. Notice how CAESAR II provides the WRC 107 Stress Summation module
in line with the stress calculation routines.
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The equations used in CAESAR II to qualify the various stress components can be
summarized as follows:
Pm(SUS) < Smh
Pm(SUS + OCC) < 1.2Smh
Pm(SUS) + Pl(SUS) < 1.5Smh
Pm(SUS + OCC) + Pl(SUS + OCC) < 1.5(1.2)Smh
Pm(SUS + OCC) + Pl(SUS + OCC) + Q(SUS + EXP + OCC) < 1.5(S mc + Smh)
Description of Alternate Simplified ASME Section
VIII Division 2 Elastic Nozzle Analysis pre-2007
The most difficult problem associated with the comprehensive ASME Section VIII Division 2
nozzle/vessel analysis involves the pressure calculation. Hoop and longitudinal pressure
hand calculations are not considered reliable, and axial pressure loading on the junction is
often miscalculated or omitted. Another issue with the comprehensive calculation is the
amount of time it takes to organize and manipulate the stress data. For these reasons, an
alternate simplified approach was developed using three checks.
The first check, Pm due to pressure, must be  1.0 Smh. To eliminate the concern for pressure,
both the loading pressure term on the left side of the inequality and the allowable pressure
term on the right side of the inequality cancel out.
This assumes that the area of reinforcement around the nozzle satisfies the pressure
requirements. Also, let Pm equal the maximum value.
The second check, Pm + Pl + Pb, must be  1.5 Smh. Subtract the stress due to pressure, Pm, from
both sides of the inequality and assuming Pm equals Smh. This reduces the check to: Pl + Pb 
0.5 Smh (due to external sustained forces without pressure).
The third check, Pm + Pl + Q, is the root of the application controversy. There are three
schools of thought:





Pm+Pl+Q
is an operating loading condition, and as such, includes the loads due to pressure and
weight.
Pm+Pl+Q is the range of loads or the expansion loading condition, and as such, excludes the
effects of sustained,
or primary loads. Also, exclude the primary sustained loads like weight

and pressure.
Pm+Pl+Q is the range of loads and excludes the primary load weight, but includes the
varying pressure load at least in those thermal load cases where the systemgoes from a
startup ambient temperature and pressure condition to operating condition.
To simplify the calculation, assume that Pm, due to pressure, is included on both sides of the
Pm+Pl+Pb+Q < 3Sm inequality. Also, assume that the area reinforcement requirements are
exactly satisfied. Again, let Pm = Sm and subtract this term from the expansion allowable (P m +
Pl + Q < 3Sm) to provide a simplified allowable limit.
The expansion, operating, or both loads from the CAESAR II Restraint report (see
"Restraints" on page 569) must satisfy the computed stress requirement:
Pl + Pb + Q (operating or expansion excluding pressure) < 2S m.
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To summarize:
1.
Ensure proper nozzle reinforcement for pressure and assume pressure stresses are at
their maximum.
2.
Compare primary stresses without pressure to ½Smh.
3.
Compare stresses due to the sum of primary and secondary loads to 2Sm(avg); where Sm(avg)
is the average of the hot and cold allowable stress intensities S mh and Smc.
ASME Section VIII Division 2-Elastic Nozzle
Simplified Analysis pre-2007
1.
Perform a CAESAR II analysis of the piping loads on the vessel/nozzle junction. Use
WRC 297 flexibilities to compute loads more accurately, but less conservatively or do two
analyses, one with flexibilities and one without.
From this analysis you should have sustained, operating, and expansion loads on
the vessel/nozzle junction.
2.
Find Smh and Smc from the Sect. VIII allowable stress tables.
Smh is the vessel material hot allowable, and Smc is the vessel material cold allowable.
3.
Run WRC 107 with the sustained loads on the vessel/nozzle junction from CAESAR II,
and verify that the computed stress intensities are < 0.5 S mh.
This operation helps in conservatively considering bending stresses from internal
pressure and sustained moments and also lets you categorize the stresses and moment
as a primary classification. If the operation fails, review the stresses in more detail.
4.
Run WRC 107 with the operating loads on the vessel/nozzle junction from CAESAR II,
and verify that the computed stress intensities are < S mh + Smc.
5.
Run WRC 107 with the expansion loads on the vessel/nozzle junction from CAESAR II,
and verify that the computed stress intensities are < Smh + Smc.
Should any of the checks described fail, then perform the more comprehensive analysis of the
junction described earlier. For more information, see ASME Section VIII Division 2 - Elastic
Analysis of Nozzle Comprehensive Analysis (see "ASME Section VIII Division 2-Elastic
Nozzle Comprehensive Analysis (pre-2007)" on page 906).
Inclusion of Missing Mass Correction
The response of a system under a dynamic load is often determined by superposition of modal
results, with CAESAR II specifically providing the Spectral Analysis method for use. One of
the advantages of modal analysis is that usually only a limited number of modes are excited
and need be included in the analysis. The drawback to this method is that although
displacements may be obtained with good accuracy using only a few of the lowest frequency
modes, the force, reaction, and stress results may require extraction of far more modes,
possibly far into the rigid range, before acceptable accuracy is attained. The Missing Mass
option offers the ability to include a correction which represents the quasi-static contribution of
the higher order modes not explicitly extracted for the modal/dynamic response, thus providing
greater accuracy with reduced calculation time.
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The dynamic response of a linear multi-degree-of-freedom system is described by the
following equation:
Ma(t) + Cv(t) + Kx(t) = F(t)
Where:
M = n x n mass matrix of system
C = n x n damping matrix of system
K = n x n stiffness matrix of system
a(t) = n x 1, time-dependent acceleration vector
v(t) = n x 1, time-dependent velocity vector
x(t) = n x 1, time-dependent displacement vector
F(t) = n x 1, time-dependent applied force vector
Assuming harmonic motion and neglecting damping, the free vibration eigenvalue problem
for this system is
K - M2 = 0
Where:
= n x n mode shape matrix
2 = n x n matrix where each diagonal entry is the angular frequency squared of
the corresponding mode
The modal matrix can be normalized such that T M = I (where I is the n x n identity
matrix) and T  = 2.
Partition the modal matrix  into two sub-matrices:
= [e r ]
Where:
e = mode shapes extracted for dynamic analysis (that is., lowest frequency modes)
r = residual (non-extracted) mode shapes (corresponding to rigid response, or the "missing
mass" contribution)
The extracted mode shapes are orthogonal to the residual mode shapes, or:
eT x r = 0
The displacement components can be expressed as linear combinations of the mode shapes:
x = Y = e Ye + r Yr = xe + xr
Where:
x = Total System Displacements
x e = System Displacements Due to Extracted Modes
x r = System Displacements Due to Residual Modes Y
= Generalized Modal Coordinates
Ye = partition of Y Matrix Corresponding to Extracted Modes
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Yr = Partition of Y Matrix Corresponding to Residual Modes
The dynamic load vector can be expressed in similar terms:
F = K Y = K e Ye + Kr Yr = Fe +
Fr Where:
F = Total System Load Vector
Fe = Load Vector Due to Extracted Modes
Fr = Load Vector Due to Residual Modes Y
= Generalized Modal Coordinates
Ye = Partition of Y Matrix Corresponding to Extracted Modes Yr
= Partition of Y Matrix Corresponding to Residual Modes
Normally, modal superposition analyses completely neglect the rigid response the displacement
Xr caused by the load Fr. This response, of the non-extracted modes, can be obtained from the
system displacement under a static loading Fr. Based upon the relation\-ships stated above,
you can estimate Fr as follows:
F = K e Ye + K r Yr
Multiplying both sides byeT and considering that eT r = 0:
eT F = eT K e Ye + eT K r Yr = eT K e Ye
Substituting e2 for eT K e and solving for Ye:
eT F = e2 Ye
Ye = eT e-2 F
The residual force can now be stated as
Fr = F - K e Ye = F - eT K e e-2 F
As seen earlier
T M2 = I 2 = T K 
Substituting eT Me e2 for eT K e:
Fr = F - eT M e e2 e-2 F = F - eT Me F
Therefore, CAESAR II calculates the residual response (and includes it as the missing
mass contribution) according to the following procedure:
1.
The missing mass load is calculated for each individual shock load as:
F r = F -  eT M  e F





912
The load vector F represents the product of:
the force set vector and the rigid DLF for force spectrum loading;


the product of the mass matrix, ZPA, and directional vector for non-ISM seismic loads;
and the product of the mass matrix, ZPA, and displacement
matrix (under unit ISM support

displacement) for seismic anchor movement loads.
CAESAR II User's Guide
Technical Discussions
Note that the missing mass load will vary, depending upon the number of modes
extracted by the user and the cutoff frequency selected (or more specifically, the DLF
or acceleration corresponding to the cutoff frequency). "Rigid," for the purposes of
determining the rigid DLF, or the ZPA, may be designated by the user, through a setup
parameter, to be either the DLF/acceleration associated with the frequency of the last
extracted mode, or the true spectral DLF/ ZPA that corresponding to the largest
entered frequency of the input spectrum.
2.
The missing mass load is applied to the structure as a static load. The static structural
response is then combined (according to the user-specified combination method) with
the dynamically amplified modal responses as if it was a modal response. Actually this
static response is the algebraic sum of the responses of all non-extracted modes—
representing in-phase response, as would be expected from rigid modes.
3.
The Missing Mass Data report is compiled for all shock cases, whether missing mass is
to be included or not. The percent of mass active is calculated according to:
% Active Mass = 1 - ( Fr[i] /  F [i])
summed over i = 1 to n, where n is the number of modes included
The maximum possible percent that is theoretically possible for this value is of course 100%;
however numerical inaccuracies may occasionally cause the value to be slightly higher. If
the missing mass correction factor is included, the percent of mass included in the correction
is shown in the report as well.
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Because the CAESAR II procedure assumes that the missing mass correction represents the
contribution of rigid modes, and that the ZPA is based upon the spectral ordinate value at the
frequency of the last extracted mode, we recommend that you extract modes up to, but not far
beyond, a recognized "rigid" frequency. Choosing a cutoff frequency below the spectrum’s resonant
peak [point (1) below] provides a non-conservative result, because resonant responses may be
missed. Using a cutoff frequency higher than the peak (2), but still in the resonant range, will yield
conservative results, because the ZPA/rigid DLF will be overestimated. Extracting a large number of
rigid modes for calculation of the dynamic response may be conservative (4), because all available
modal combination methods (SRSS, GROUP, ABS, and so forth) give conservative results versus
the algebraic combination method which gives a more realistic representation of the net response of
the rigid modes. Based upon the response spectrum shown below, an appropriate cutoff point for the
modal extraction would be about 33 Hz (3).
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Maximum Stress Versus Extracted Loads
CAESAR II provides two options for combining the missing mass correction with modal
dynamic results SRSS and Absolute. The Absolute Combination method provides the more
conservative result and is based upon the assumption that dynamic amplification is going to
occur simultaneously with the maximum ground acceleration or force load. Literature
(References 1, 2) states that the modal and the rigid portions of the response to typical
dynamic loads are actually statistically independent, so that the SRSS Combination method is
a more accurate representation of reality. Because the SRSS Combination method is most
closely aligned to reality, CAESAR II defaults to this missing mass combination method.
References
1.
A. K. Gupta, Response Spectrum Method in Seismic Analysis and Design of
Structures, CRC Press, 1990
2.
K. M. Vashi, "Computation of Seismic Response from Higher Frequency Modes,"
ASME 80-C2/PVP-50, 1980
3.
O. E. Hansteen and K. Bell, "On the Accuracy of Mode Superposition Analysis in
Structural Dynamics," Earthquake Engineering and Structural Dynamics, Volume 7, John
Wiley & Sons, Ltd., 1979
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Fatigue Analysis Using CAESAR II
For most piping codes supported by CAESAR II, performing a fatigue analysis is an
extension to, rather than an explicit part of, the code requirements. However, it is an explicit
part of the IGE/TD/12 Pipework Stress Analysis for Gas Industry Plant code.
Fatigue Basics
Piping and vessels have been known to suffer from sudden failure following years of successful
service. Research done during the 1940s and 1950s, primarily advanced by A. R. C. Markl’s
"Piping Flexibility Analysis," published in 1955, provided an explanation for this phenomenon,
as well as design criteria aimed at avoiding failures of this type. The explanation was that
materials were failing due to fatigue, a process leading to the propagation of cracks, and
subsequent fracture, following repeated cyclic loading.
Steels and other metals are made up of organized patterns of molecules, known as crystal
structures. However, these patterns are not maintained throughout the steel producing an
ideal homogeneous material, but are found in microscopic isolated island-like areas called
grains. Inside each grain a pattern of molecules is preserved. From one grain boundary to the
next the molecular pattern is the same, but the orientations differ. As a result, grain
boundaries are high energy borders. Plastic deformation begins within a grain that is subject
to both a high stress and oriented such that the stress causes a slippage between adjacent
layers in the same pattern. The incremental slippages, called dislocations, cause local coldworking. On the first application of the stress, dislocations can move through many of the
grains that are in the local area of high stress. As the stress is repeated, more dislocations
move through their respective grains. Dislocation movement is impeded by the grain
boundaries. After multiple stress applications, the dislocations tend to accumulate at grain
boundaries. Eventually they become so dense that the grains "lock up" causing a loss of
ductility and thus preventing further dislocation movement. Subsequent applications of the
stress cause the grain to tear, forming cracks. Repeated stress applications cause the cracks
to grow. Unless abated, the cracks propagate with additional stress applications until sufficient
cross sectional strength is lost to cause a catastrophic failure of the material.
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You can estimate the fatigue capacity of a material through the application of cyclic
tensile/compressive displacement loads with a uniaxial test machine. A plot of the cyclic
stress capacity of a material is called a fatigue or endurance curve. These curves are
generated through multiple cyclic tests at different stress levels. The number of cycles to
failure usually increases as the applied cyclic stress decreases, often until a threshold stress,
known as the endurance limit, is reached below which no fatigue failure occurs, regardless of
the number of applied cycles. An endurance curve for carbon and low alloy steels, taken from
the ASME Section VIII Division 2 Pressure Vessel Code displays below:
Fatigue Analysis of Piping Systems
IGE/TD/12 does present specific requirements for true fatigue evaluation of systems subject to
a cyclic loading threshold. Furthermore, ASME Section III, Subsection NB and ASME Section
VIII Division 2 provide guidelines by which fatigue evaluation rules can be applied to piping and
other pressure retaining equipment. These procedures have been adapted, where possible, to
the methodology used by CAESAR II.
Perform fatigue analysis
1.
From the Allowable auxiliary dialog box, enter fatigue data or import it in from a text file.
You can also define your own fatigue curves as discussed later in this section. By doing
this, you assign the fatigue curve data to the piping material.
To help with your fatigue analysis, CAESAR II provides a number of commonly used
curves.
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2.
From either the Static or Dynamic Load Case Builders you must define, for every
fatigue load case, the number of anticipated cycles.
Also we have added a new FAT stress type.
3.
Unless explicitly defined in the applicable code, CAESAR II calculates the fatigue stress
the same way it calculates the stress intensity.
IGE/TD/12 is the only piping code supported by CAESAR II that has explicit
instructions for calculating fatigue stresses. For more information on IGE/TD/12, refer to
IGE/TD/12 (on page 987).
4.
Allowable fatigue stresses are interpolated logarithmically from the fatigue curve based
upon the number of cycles designated for the load case. For static load cases, the
calculated stress is assumed to be a peak-to-peak cyclic value (for example, thermal
expansion, settlement, pressure, and so forth), so the allowable stress is extracted directly
from the fatigue curve. For harmonic and dynamic load cases, the calculated stress is
assumed to be a zero-to-peak cyclic value (for example, vibration, earth\-quake, and so
forth), so the extracted allowable is divided by two prior to use in the comparison.
5.
The flip side of calculating the allowable fatigue stress for the designated number of cycles
is the calculation of the allowable number of cycles for the calculated stress level. You can
do this by logarithmically interpolating the "Cycles" axis of the fatigue curve based upon the
calculated stress value. Because static stresses are assumed to be peak-to-peak cyclic
values, the allowable number of cycles is interpolated directly from the fatigue curve.
Because harmonic and dynamic stresses are assumed to be zero-to-peak cyclic values,
the allow\-able number of cycles is interpolated using twice the calculated stress value.
6.
CAESAR II provides two reports for viewing the results of load cases for the FAT stress
type. The first of these is the standard Stress report that shows the calculated fatigue
stress and fatigue allowable at each node.
You can generate individual stress reports for each load case to show whether any of the
individual load cases in isolation fail the system
However, in those instances where there is more than one cyclic load case potentially
contributing to a fatigue failure, the Cumulative Usage report is appropriate. To generate this
report select all the FAT load cases that contribute to the overall system degradation. The
Cumulative Usage report lists for each node point the usage ratio actual cycle divided by
allowable cycles, and then sums these to obtain the total cumulative usage. A total greater
than 1.0 indicates a potential fatigue failure.
Static Analysis Fatigue Example
Consider a sample job that potentially has several different cyclic load variations:







Operating cycle from ambient 70°F to 500°F, 12,000 cycles anticipated

Shut down 
external temperature variation from ambient 70°F to -20°F, 200 cycles
anticipated
Pressurization to 1800 psig, 12,000 cycles anticipated


Pressure fluctuations of +/- 30 psi from the 1800 psig, 200,000 cycles anticipated
To do a proper fatigue analysis, you must group the load pairs that represent the worst-case
combination of stress ranges between extreme states. These load variations can be laid out in
graphical form. The figure below shows a sketch of the various operating ranges this system
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experiences. Each horizontal line represents an operating range. At the each end of each
horizontal line, the temperatures and pressures defining the range are noted. At the center
of each horizontal line, the number of cycles for each range is defined.
Using this sketch of the operating ranges, the four fatigue load cases can be determined. Case
1: Cover the absolute extreme, from -20°F and 0 psi to 500°F and 1830 psi. This occurs 200
times. As a result of this case, the cycles for the ranges defined must be reduced by 200. The
first range (-20, 0 to 70, 0) is reduced to zero, and has no contribution to additional load cases.
The second range (70, 0 to 500, 1800) is reduced to 11,800 cycles. The third and fourth
ranges are similarly reduced to 199,800 cycles.
These same steps can be used to arrive at cases 2 through 4, reducing the number
of considered cycles at each step. This procedure is summarized in the table below.
Segment
-20, 0 to 70, 0 70, 0 to 500, 1800 500, 1700 to 500,
1800
500, 1800 to 500, 1830
Initial
200
12,000
200,000
200,000
After 1
0
11,800
200,000
199,800
After 2
0
0
200,000
188,000
After 3
0
0
12,000
0
After 4
0
0
0
0
Case
This table is then used to set the load cases as cycles between the following load values:







Between -20°F, 0 psig and 500°F, 1830 psig (200 cycles)
Between 70°F, 0 psig and 500°F, 1830 psig (11,800 cycles)



Between 500°F, 1770 psig and 500°F, 1830 psig (188,000 cycles)
Between 500°F, 1770 psig and 500°F, 1800 psig (12,000 cycles)
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These temperatures and pressures are entered as operating conditions accordingly:
Next enter the fatigue curve data for the material. This is done by clicking Fatigue Curves to
activate the Material Fatigue Curve dialog box. This dialog box can be used to enter the
fatigue curve for the materials.
For IGE/ TD/12, you only need to enter five sets of fatigue curves for fatigue
classes D, E, F, G, and W.
920
1.
Enter up to eight Cycle versus Stress data points to define the curve. Interpolations
are made logarithmically.
2.
Enter Cycle/Stress pairs in ascending cycle order.
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3.
Enter stress values as the allowable stress range, rather than the allowable
Stress Amplitude.
You can enter fatigue curve data from a text file, by clicking Read from file. This displays a
list of all \CAESAR\SYSTEM\*.FAT files.
The following fatigue curve files are delivered with CAESAR II. You can also construct
additional fatigue curve files. For more information on fatigue curve files, see Appendix A below:

5-110-1A.FAT
ASME Section VIII Division 2 Figure 5-110.1, UTS < 80 ksi

5-110-1B.FAT
ASME Section VIII Division 2 Figure 5-110.1, UTS = 115-130 ksi

5-110-2A.FAT
ASME Section VIII Division 2 Figure 5-110.2, Curve A

5-110-2B.FAT
ASME Section VIII Division 2 Figure 5-110.2, Curve B

5-110-2C.FAT
ASME Section VIII Division 2 Figure 5-110.2, Curve C
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In this case for A106B low carbon steel operating at 500°F, 5-110-1A.FAT is the
appropriate selection. This populates the fatigue curve data boxes in the dialog box:
Error check the job, and set up your load cases.
The static load case builder offers a new stress type, FAT (fatigue). Selecting this stress
type does the following:
922
1.
Enables you to define the number of cycles for the load case. Dragging the FAT stress
type into the load case or clicking the Load Cycles button opens the Load Cycles field.
2.
Calculates the stress range as per the Fatigue Stress method of the applicable code.
This is the stress intensity for all codes except IGE/TD/12.
3.
Compares the calculated stress range to the full value extracted from the fatigue
curve. Indicates that the load case may be included in the Cumulative Usage report.
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The last four load cases represent the load set pairs defined earlier.
After you run the job the presence of a FAT stress type adds the Cumulative Usage
report to the list of available reports.
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You can check the fatigue stress range against the fatigue curve allowable for each load case
by selecting it along with the Stresses report. A review of each load case confirms that all
stress levels passed.
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However, this is not a true evaluation of the situation because it is not a case of either-or. The
piping system is subjected to all of these load cases throughout its expected design life, not
just one of them. Therefore, we must also review the Cumulative Usage (see "Cumulative
Usage Report" on page 579) report, which shows the total effect of all fatigue load cases, or
any user-selected combination, on the design life of the system. This report lists for each load
case the expected number of cycles, the allowable number of cycles (based upon the
calculated stress), and the Usage Ratio (actual cycles divided by allowable cycles). The Usage
Ratios are then summed for all selected load cases. If this sum exceeds 1.0, the system has
exceeded its fatigue capabilities. In this case, it is apparent that with the maximum cumulative
usage ratio of 0.87 at node 115, this system is not predicted to fail due to fatigue:
Fatigue Capabilities in Dynamic Analysis
Fatigue analysis capability is also available for harmonic and dynamic analyses. Harmonic load
cases are entered as they always have been. They can be designated as being stress type
FAT by entering the number of expected load cycles on the harmonic input dialog box:
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This produces the same types of reports as are available for the static analysis. They can
be processed as discussed earlier.
The only difference between the harmonic and static fatigue analyses is that for harmonic jobs
the calculated stresses are assumed to be zero-to-peak calculations so that they are
compared to only half of the stress value extracted from the fatigue curve. Likewise, when
creating the Cumulative Usage report, the number of allowable cycles is based upon twice
the calculated stress.
For other dynamic applications (response spectrum and time history), the stress type can
be identified as fatigue by selecting the stress type from the drop list for the Load Case or
Static/Dynamic Combination, and by entering the number of expected cycles in the provided
field.
Note that as with the harmonic analyses, the calculated stresses are assumed to be zero-topeak calculations so that they are compared to only half of the stress value extracted from
the fatigue curve. Likewise, when creating the Cumulative Usage report, the number of
allowable cycles is based upon twice the calculated stress.
Creating the .FAT Files
The .FAT file is a text file, containing the data points necessary to describe the fatigue curve for the
material, for both butt welded and fillet welded fittings. A sample FAT file is shown below.
* ASME SECTION VIII DIVISION 2 FATIGUE CURVE
* FIGURE 5-110.1
* DESIGN FATIGUE CURVES FOR CARBON, LOW ALLOY, SERIES 4XX,
* HIGH ALLOY AND HIGH TENSILE STEELS FOR TEMPERATURES NOT
* EXCEEDING 700 F
* FOR UTS  80 KSI
*
0.5000000 - STRESS MULTIPLIER (PSI); ALSO CONVERTS AMPLITUDE TO FULL RANGE
*
10
580000.0
100
205000.0
1000
83000.0
10000
38000.0
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100000
500000
1000000
0
*
20000.0
13500.0
12500.0
0.0
You can create this text file by using any text editor. Lines beginning with an * are treated as
comment lines. It is good practice to use comment lines so that the data can be tied to a
specific material curve.
The first data line in the file the stress multiplier. This value is used to adjust the data values
from "zero to peak" to "peak to peak" or to convert the stress levels to psi. The entered values
are divided by this number. For example, if the stress values in the file represent the stress
amplitude, in psi, rather than a range, this "stress multiplier" should be 0.5. Following the
stress multiplier is the Fatigue Curve Data table. This table consists of eight lines, of two
columns. The first column is the Cycle column, and the second is the Stress column. For
each value in the cycle column, a corresponding stress value from the material fatigue curve is
listed in the stress column.
Fatigue curves intended for use with IGE/TD/12 are built slightly different. The first data line
contains three values: the stress multiplier, a modulus of elasticity correction, and a modulus of
elasticity multiplier (the correction factor is divided by this to convert to psi). After the files are
read in, the modulus of elasticity correction is inserted into the appropriate field on the Fatigue
Curve dialog. IGE/TD/12 fatigue files also include five sequential fatigue curves, Fatigue Class
D, E, F, G, and W, rather than one. You can use optional comment lines to separate the tables.
The comments help with the readability of the data file. You can best determine the format of
the IGE/TD/12 fatigue files by reviewing the contents of the TD12ST.FAT file.
In all tables, the number of cycles increases as you work down the table. If you do not
have enough data to use all eight lines, fill the unused lines with zeroes.
Calculation of Fatigue Stresses
For IGE/TD/12 the computation of fatigue stresses is detailed in Section 5.4.4 of that code.
This section of the code states: "The principal stress in any plane can be calculated for any set
of conditions from the following formula:"
Where:
Sh = Hoop stress
Sa = Axial stress
Sq = Shear stress
"This should be used for establishing the range of stress, due regard being paid to the direction
and sign." For all other piping codes in CAESAR II, the fatigue stress is computed as the
stress intensity, as follows:
3D Maximum Shear Stress Intensity (Default)
SI = Maximum of:



S1OT - S3OT


S1OB - S3OB
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


Max(S1IT,RPS) - Min(S3IT,RPS)


Max(S1IB,RPS) - Min(S3IB,RPS)
Where:
S1OT=Maximum Principal Stress, Outside Top
= (SLOT+HPSO)/2.0+(((SLOT-HPSO)/2.0)2+TSO2)1/2
S3OT=Minimum Principal Stress, Outside Top
=(SLOT+HPSO)/2.0-(((SLOT-HPSO)/2.0)2+TSO2) 1/2
S1IT=Maximum Principal Stress, Inside Top
=(SLIT+HPSI)/2.0+(((SLIT-HPSI)/2.0)2+TSI2) 1/2
S3IT=Minimum Principal Stress, Inside Top
=(SLIT+HPSI)/2.0-(((SLIT-HPSI)/2.0)2+TSI2) 1/2
S1OB=Maximum Principal Stress, Outside Top
=(SLOB+HPSO)/2.0+ (((SLOB-HPSO)/2.0)2+TSO2) 1/2
S3OB=Minimum Principal Stress, Outside Bottom
=(SLOB+HPSO)/2.0- (((SLOB-HPSO)/2.0)2+TSO2) 1/2
S1IB=Maximum Principal Stress, Inside Bottom
=(SLIB+HPSI)/2.0+ (((SLIB-HPSI)/2.0)2+TSI2) 1/2
S3IB=Minimum Principal Stress, Inside Bottom
=(SLIB+HPSI)/2.0- (((SLIB-HPSI)/2.0)2+TSI2) 1/2
RPS=Radial Pressure Stress, Inside
HPSI=Hoop Pressure Stress (Inside, from Lame's Equation)
HPSO=Hoop Pressure Stress (Outside, from Lame's Equation)
SLOT=Longitudinal Stress, Outside Top
SLIT=Longitudinal Stress, Inside Top
SLOB=Longitudinal Stress, Outside Bottom
SLIB=Longitudinal Stress, Inside Bottom
TSI=Torsional Stress, Inside
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TSO=Torsional Stress, Outside
Pipe Stress Analysis of FRP Piping
Underlying Theory
The behavior of steel and other homogeneous materials has been long understood, permitting
their widespread use as construction materials. The development of the piping and pressure
vessel codes (Reference 1) in the early part of this century led to the confidence in their use in
piping applications. The work of Markl and others in the 1940’s and 1950’s was responsible for
the formalization of today’s pipe stress methods, leading to an ensuing diversification of piping
codes on an industry by industry basis. The advent of the digital computer, and with it the
appearance of the first pipe stress analysis software (Reference 2), further increased the
confidence with which steel pipe could be used in critical applications. The 1980’s saw the
wide spread proliferation of the microcomputer, with associated pipe stress analysis software,
which in conjunction with training, technical support, and available literature, has brought
stress analysis capability to almost all engineers. In short, an accumulated experience of close
to 100 years, in conjunction with ever improving technology has led to the utmost confidence
on the part of today’s engineers when specifying, designing, and analyzing steel, or other
metallic, pipe.
For fiberglass reinforced plastic (FRP) and other composite piping materials, the situation is not
the same. Fiberglass reinforced plastic was developed only as recently as the 1950’s, and did
not come into wide spread use until a decade later (Reference 3). There is not a large base of
stress analysis experience, although not from a lack of commitment on the part of FRP vendors.
Most vendors conduct extensive stress testing on their components, including hydrostatic and
cyclic pressure, uni-axial tensile and compressive, bending, and combined loading tests. The
problem is due to the traditional difficulty associated with, and lack of understanding of, stress
analysis of heterogeneous materials. First, the behavior and failure modes of these materials
are highly complex and not fully understood, leading to inexact analytical methods and a
general lack of agreement on the best course of action to follow. This lack of agreement has
slowed the simplification and standardization of the analytical methods into universally
recognized codes BS 7159 Code Design and Construction of Glass Reinforced Plastics Piping
(GRP) Systems for Individual Plants or Sites and UKOOA Specification and Recommended
Practice for the Use of GRP Piping Offshore being notable exceptions. Second, the
heterogeneous, orthotropic behavior of FRP and other composite materials has hindered the
use of the pipe stress analysis algorithms developed for homogeneous, isotropic materials
associated with crystalline structures. A lack of generally accepted analytical procedures has
contributed to a general reluctance to use FRP piping for critical applications.
Stress analysis of FRP components must be viewed on many levels. These levels, or scales,
have been called Micro-Mini-Macro levels, with analysis proceeding along the levels
according to the "MMM" principle (Reference 4).
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Micro-Level Analysis
Stress analysis on the "Micro" level refers to the detailed evaluation of the individual
materials and boundary mechanisms comprising the composite material. In general, FRP
pipe is manufactured from laminates, which are constructed from elongated fibers of a
commercial grade of glass, E-glass, which are coated with a coupling agent or sizing prior to
being embedded in a thermosetting plastic material, typically epoxy or polyester resin.
This means, on the micro scale, that an analytical model must be created which simulates the
interface between these elements. Because the number and orientation of fibers is unknown
at any given location in a FRP sample, the simplest representation of the micro-model is that
of a single fiber, extending the length of the sample, embedded in a square profile of matrix.
Micro Level GRP Sample -- Single Fiber Embedded in Square Profile of Matrix
Evaluation of this model requires use of the material parameters of:
1.
the glass fiber
2.
the coupling agent or sizing layer normally of such microscopic proportion that it may
be ignored
3.
the plastic matrix
It must be considered that these material parameters might vary for an individual material
based upon tensile, compressive, or shear applications of the imposed stresses, and typical
values vary significantly between the fiber and matrix (Reference 5):
Young's Modulus Ultimate Strength
Coefficient of Thermal Expansion
tensile (MPa)
tensile (MPa)
m/m/ºC
3
Glass Fiber 72.5 x10
1.5 x 103
5.0 x 10-6
Plastic
Matrix
.07 x 103
7.0 x 10-6
Material
2.75 x 103
The following failure modes of the composite must be similarly evaluated to:


930

failure of the fiber



failure of the coupling agent layer


failure of the matrix
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


failure of the fiber-coupling agent bond


failure of the coupling agent-matrix bond
Because of uncertainties about the degree to which the fiber has been coated with the
coupling agent and about the nature of some of these failure modes, this evaluation is typically
reduced to:



failure of the fiber



failure of the matrix


failure of the fiber-matrix interface
You can evaluate stresses in the individual components through finite element analysis of the
strain continuity and equilibrium equations, based upon the assumption that there is a good
bond between the fiber and matrix, resulting in compatible strains between the two. For
normal stresses applied parallel to the glass fiber:
f = m = af / Ef = am / Em
af = am Ef / Em
Where:
f = Strain in the Fiber
 = Strain in the Matrix
af = Normal Stress Parallel to Fiber, in the Fiber
Ef = Modulus of Elasticity of the Fiber
am = Axial Normal Stress Parallel to Fiber, in the Matrix
Em = Modulus of Elasticity of the Matrix
Due to the large ratio of the modulus of elasticity of the fiber to that of the matrix, it is
apparent that nearly all of the axial normal stress in the fiber-matrix composite is carried by
the fiber. Exact values are (Reference 6):
af = L / [ + (1-)Em/Ef]
am = L / [Ef/Em + (1-)]
Where:
L = nominal longitudinal stress across composite
 = glass content by volume
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The continuity equations for the glass-matrix composite seem less complex for normal
stresses perpendicular to the fibers, because the weak point of the material seems to be
limited by the glass-free cross-section, shown below:
Stress Intensification in Matrix Cross-Section
For this reason, it would appear that the strength of the composite would be equal to that of
the matrix for stresses in this direction. In fact, its strength is less than that of the matrix due to
stress intensification in the matrix caused by the irregular stress distribution in the vicinity of
the stiffer glass. Because the elongation over distance D1 must be equal to that over the longer
distance D2, the strain, and thus the stress at location D1 must exceed that at D2 by the ratio
D2/D1. Maximum intensified transverse normal stresses in the composite are:
Where:
b = intensified normal stress transverse to the fiber, in the composite
 = nominal transverse normal stress across composite
m = Poisson's ratio of the matrix
Because of the Poisson effect, this stress produces an additional 'am equal to the
following:
'am = Vmb
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Shear stress can be allocated to the individual components again through the use of continuity
equations. It would appear that the stiffer glass would resist the bulk of the shear stresses. However,
unless the fibers are infinitely long, all shears must eventually pass through the matrix in order to get
from fiber to fiber. Shear stress between fiber and matrix can be estimated as
Where:
ab = intensified shear stress in composite
T = nominal shear stress across composite
Gm = shear modulus of elasticity in matrix
Gf = shear modulus of elasticity in fiber
Determination of the stresses in the fiber-matrix interface is more complex. The bonding agent
has an inappreciable thickness, and thus has an indeterminate stiffness for consideration in
the continuity equations. Also, the interface behaves significantly differently in shear, tension,
and compression, showing virtually no effects from the latter. The state of the stress in the
interface is best solved by omitting its contribution from the continuity equations, and simply
considering that it carries all stresses that must be transferred from fiber to matrix.
After the stresses have been apportioned, they must be evaluated against appropriate failure
criteria. The behavior of homogeneous, isotropic materials such as glass and plastic resin,
under a state of multiple stresses is better understood. Failure criterion for isotropic material
reduces the combined normal and shear stresses (a, b, c, ab, ac, bc) to a single stress, an
equivalent stress, that can be compared to the tensile stress present at failure in a material
under uniaxial loading, that is, the ultimate tensile stress, Sult.
Different theories, and different equivalent stress functions f(a, b, c, ab, ac, bc) have been
proposed, with possibly the most widely accepted being the Huber-von Mises-Hencky
criterion, which states that failure will occur when the equivalent stress reaches a critical value
the ultimate strength of the material:
eq = {1/2 [(a - b)2 + (b - c)2+ (c - a)2 + 6(ab2+ ac2+ bc2)}  Sult
This theory does not fully cover all failure modes of the fiber in that it omits reference to
direction of stress, that is, tensile versus compressive. The fibers, being relatively long and thin,
predominantly demonstrate buckling as their failure mode when loaded in compression.
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The equivalent stress failure criterion has been corroborated, with slightly non-conservative
results, by testing. Little is known about the failure mode of the adhesive interface, although
empirical evidence points to a failure criterion which is more of a linear relationship between the
normal and the square of the shear stresses. Failure testing of a composite material loaded
only in transverse normal and shear stresses are shown in the following figure. The kink in the
curve shows the transition from the matrix to the interface as the failure point.
Mini-Level Analysis
Mini-Level Analysis Fiber Distribution Models
Although feasible in concept, micro level analysis is not feasible in practice. This is due to the
uncertainty of the arrangement of the glass in the composite the thousands of fibers that might
be randomly distributed, semi-randomly oriented, although primarily in a parallel pattern, and
of randomly varying lengths. This condition indicates that a sample can truly be evaluated only
on a statistical basis, thus rendering detailed finite element analysis inappropriate.
For mini-level analysis, a laminate layer is considered to act as a continuous hence the
common reference to this method as the "continuum" method, material, with material properties
and failure modes estimated by integrating them over the assumed cross-sectional distribution,
which is, averaging. The assumption regarding the distribution of the fibers can have a marked
effect on the determination of the material parameters. Two of the most commonly postulated
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distributions are the square and the hexagonal, with the latter generally considered as being
a better representation of randomly distributed fibers.
The stress-strain relationships, for those sections evaluated as continua, can be written as:
aa = aa/EL - (VL/EL)bb - (VL/EL)cc
bb = -(VL/EL)aa + bb/ET - (VT/ET)cc
cc = -(VL/EL)aa - (VT/ET)bb + cc/ET
ab = ab / 2 GL
bc = bc / 2 GT
ac = ac / 2 GL
Where:
ij = strain along direction i on face j
ij, ab = stress (normal, shear) along direction i on face j
EL = modulus of elasticity of laminate layer in longitudinal direction
VL = Poisson’s ratio of laminate layer in longitudinal direction
ET = modulus of elasticity of laminate layer in transverse direction
VT = Poisson’s ratio of laminate layer in transverse direction
GL = shear modulus of elasticity of laminate layer in longitudinal direction GT
= shear modulus of elasticity of laminate layer in transverse direction
These relationships require that four modules of elasticity, EL, ET, GL, and GT, and two Poisson’s
ratios, VL and V, be evaluated for the continuum. Extensive research (References 4 - 10) has
been done to estimate these parameters. There is general consensus that the longitudinal
terms can be explicitly calculated; for cases where the fibers are significantly stiffer than the
matrix, they are:
EL = EF + EM(1 - )
GL = GM +/ [ 1 / (GF - GM) + (1 -) / (2GM)]
VL = VF + VM(1 - )
You cannot calculate parameters in the transverse direction. You can only calculate the upper
and lower bounds. Correlations with empirical results have yielded approximations (Reference
5 and 6):
ET = [EM(1+0.85f2) / {(1-VM2)[(1-f)1.25 + f(EM/EF)/(1VM2)]} GT = GM (1 + 0.6) / [(1 - )1.25 +  (GM/GF)] VT
= VL (EL / ET)
Use of these parameters permits the development of the homogeneous material models that
facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer.
The resulting stresses can be allocated to the individual fibers and matrix using relationships
developed during the micro analysis.
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Macro-Level Analysis
Macro to Micros Stress Conversion
Where Mini-level analysis provides the means of evaluation of individual laminate layers,
Macro-level analysis provides the means of evaluating components made up of multiple
laminate layers. It is based upon the assumption that not only the composite behaves as a
continuum, but that the series of laminate layers acts as a homogeneous material with
properties estimated based on the properties of the layer and the winding angle, and that
finally, failure criteria are functions of the level of equivalent stress.
Laminate properties may be estimated by summing the layer properties (adjusted for
winding angle) over all layers. For example
Where:
ExLAM = Longitudinal modulus of elasticity of laminate
tLAM = thickness of laminate
E⊥k = Longitudinal modulus of elasticity of laminate layer k
Cik = transformation matrix orienting axes of layer k to longitudinal laminate
axis Cjk = transformation matrix orienting axes of layer k to transverse laminate
axis tk = thickness of laminate layer k
After composite properties are determined, the component stiffness parameters can be
determined as though it were made of homogeneous material that is, based on
component cross-sectional and composite material properties.
Normal and shear stresses can be determined from 1) forces and moments acting on the
cross-sections, and 2) the cross-sectional properties themselves. These relationships can
be written as:
aa = Faa / Aaa ± Mba / Sba ± Mca / Sca
bb = Fbb / Abb ± Mab / Sab ± Mcb / Scb
cc = Fcc / Acc ± Mac / Sac ± Mbc / Sbc
ab = Fab / Aab ± Mbb / Rab
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ac = Fac / Aac ± Mcc / Rac
ba = Fba / Aba ± Maa / Rba
bc = Fbc / Abc ± Mcc / Rbc
ca = Fca / Aca ± Maa / Rca
cb = Fcb / Acb ± Mbb / Rcb
Where:
ij = normal stress along axis i on face j
Fij = force acting along axis i on face j
Aij = area resisting force along axis i on face j
Mij = moment acting about axis i on face j
Sij = section modulus about axis i on face j
ij = shear stress along axis i on face j
Rij = torsional resistivity about axis i on face j
Using the relationships developed under macro, mini, and micro analysis, these stresses can
be resolved back into local stresses within the laminate layer, and from there, back into
stresses within the fiber and the matrix. From these, the failure criteria of those microscopic
components, and hence, the component as a whole, can be checked.
Implementation of Macro-Level Analysis for Piping Systems
The macro-level analysis described above is the basis for the preeminent FRP piping codes in
use today, including Code BS 7159 (Design and Construction of Glass Reinforced Plastics
Piping Systems for Individual Plants or Sites) and the UKOOA Specification and
Recommended Practice for the Use of GRP Piping Offshore.
BS 7159
BS 7159 uses methods and formulas familiar to the world of steel piping stress analysis in
order to calculate stresses on the cross-section, with the assumption that FRP components
have material parameters based on continuum evaluation or test. All coincident loads, such as
thermal, weight, pressure, and axial extension due to pressure need be evaluated
simultaneously. Failure is based on the equivalent stress calculation method. Because one
normal stress (radial stress) is traditionally considered to be negligible in typical piping
configurations, this calculation reduces to the greater of (except when axial stresses are
compressive):
(when axial stress is greater than hoop)
(when hoop stress is greater than axial)
A slight difficulty arises when evaluating the calculated stress against an allowable, due to the
orthotropic nature of the FRP piping normally the laminate is designed in such a way to make the
pipe much stronger in the hoop, than in the longitudinal, direction, providing more than one
allowable stress. This difficulty is resolved by defining the allowable in terms of a design strained,
rather than stress, in effect adjusting the stress allowable in proportion to the strength
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in each direction. In other words, the allowable stresses for the two equivalent stresses
above would be (ed ELAMX) and (ed ELAMH) respectively. In lieu of test data, system design
strain is selected from Tables 4.3 and 4.4 of the Code, based on expected chemical and
temperature conditions.
Actual stress equations as enumerated by BS 7159 display below:
1.
Combined stress straights and bends:
C = (f 2+ 4S2)0.5
dELAM
or
C = (X2 + 4S2)0.5 dELAM
Where:
ELAM = modulus of elasticity of the laminate; in CAESAR II, the first equation uses the
modulus for the hoop direction and in the second equation, the modulus for the
longitudinal direction is used.
C = combined stress
Φ = circumferential stress
= ΦP + ΦB
S = torsional stress
= MS(Di + 2td) / 4I
X = longitudinal stress
= XP + XB
ΦP = circumferential pressure stress
= mP(Di + td) / 2 td
ΦB = circumferential bending stress
= [(Di + 2td) / 2I] [(Mi SIFΦi)2 + Mo SIFΦo)2] 0.5 for bends, = 0 for straights
MS = torsional moment on cross-section Di = internal pipe diameter
td = design thickness of reference laminate
I = moment of inertia of pipe
m = pressure stress multiplier of component
P = internal pressure
Mi = in-plane bending moment on cross-section
SIFΦi= circumferential stress intensification factor for in-plane moment
M = out-plane bending moment on cross-section
SIFΦo = circumferential stress intensification factor for out-plane moment
XP = longitudinal pressure stress
= P(Di+ td) / 4 td
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XB = longitudinal bending stress
= [(Di + 2td) / 2I] [(Mi SIFxi)2 + Mo SIFxo)2]0.5
SIFxi = longitudinal stress intensification factor for in-plane moment
SIFxo = longitudinal stress intensification factor for out-plane moment
2.
Combined stress branch connections:
CB = ((ΦP + bB)2 + 4SB2)0.5 d ELAM
Where:
CB = branch combined stress
ΦP = circumferential pressure stress
= mP(Di + tM) / 2 tM
bB = non-directional bending stress
= [(Di + 2td) / 2I] [(Mi SIFBi)2 + Mo SIFBo)2]0.5
SB = branch torsional stress
= MS(Di + 2td) / 4I
tM = thickness of the reference laminate at the main run
SIFBi = branch stress intensification factor for in-plane moment
SIFBo = branch stress intensification factor for out-plane moment
3.
When longitudinal stress is negative (net compressive):
Φ - VΦx x Φ ELAMΦ
Where:
VΦx = Poisson’s ratio giving strain in longitudinal direction caused by stress in circumferential
direction
Φ = design strain in circumferential direction
ELAMΦ= modulus of elasticity in circumferential direction
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BS 7159 also dictates the means of calculating flexibility and stress intensification (k- and i) factors for bend and tee components, for use during the flexibility analysis.
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BS 7159 imposes a number of limitations on its use, the most notable being: the limitation of a
system to a design pressure of 10 bar, the restriction to the use of designated design
laminates, and the limited applicability of the k- and i- factor calculations to pipe bends (that is,
mean wall thickness around the intrados must be 1.75 times the nominal thickness or less).
This code appears to be more sophisticated, yet easy to use. We recommend that its
calculation techniques be applied even to FRP systems outside its explicit scope, with the
following recommendations:





Pressure stiffening of bends
 should be based on actual design pressure, rather than
allowable design strain.
Design strain should be based on manufacturer’s test and
 experience data wherever possible
(with consideration for expected operating conditions).
Fitting k- and i- factors should be based on manufacturer’s test or analytic data, if available.

UKOOA
The UKOOA Specification is similar in many respects to the BS 7159 Code, except that it
simplifies the calculation requirements in exchange for imposing more limitations and
more conservatism on the piping operating conditions.
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Rather than explicitly calculating a combined stress, the specification defines an idealized
envelope of combinations of axial and hoop stresses that cause the equivalent stress to
reach failure. This curve represents the plot of:
(x / x-all)2 + (hoop / hoop-all)2 - [x hoop / (x-all hoop-all)] 1.0
Where:
x-all = allowable stress, axial
hoop-all = allowable stress, hoop
The specification conservatively limits you to that part of the curve falling under the line
between x-all (also known as sa(0:1)) and the intersection point on the curve where hoop is twice sx-(a
natural condition for a pipe loaded only with pressure), as shown in the following figure.
An implicit modification to this requirement is the fact that pressure stresses are given a factor
of safety (typically equal to 2/3) while other loads are not. This gives an explicit requirement of:
Pdes  f1 f2 f3 LTHP
Where:
Pdes = allowable design pressure
f1 = factor of safety for 97.5% lower confidence limit, usually
0.85 f2 = system factor of safety, usually 0.67
f3 = ratio of residual allowable, after mechanical
loads = 1 - (2 ab) / (r f1 LTHS)
ab = axial bending stress due to mechanical loads
r = a(0:1)/a(2:1)
a(0:1) = long term axial tensile strength in absence of pressure load
a(2:1) = long term axial tensile strength under only pressure loading
LTHS = long term hydrostatic strength (hoop stress allowable)
LTHP = long term hydrostatic pressure allowable
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This has been implemented in the CAESAR II pipe stress analysis software as:
Code Stress
ab (f2 /r) + PDm / (4t)
Code Allowable

(f1 f2 LTHS) / 2.0
Where:
P = design pressure
D = pipe mean diameter
t = pipe wall thickness
K and i-factors for bends are to be taken from the BS 7159 Code, while no such factors are
to be used for tees.
The UKOOA Specification is limited in that shear stresses are ignored in the evaluation
process; no consideration is given to conditions where axial stresses are compressive; and
most required calculations are not explicitly detailed.
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FRP Analysis Using CAESAR II
Practical Applications
CAESAR II has had the ability to model orthotropic materials such as FRP almost since its
inception. It also can specifically handle the requirements of the BS 7159 Code, the UKOOA
Specification, and more recently ISO 14692. FRP material parameters corresponding to those of
many vendors’ lines are provided with CAESAR II. You can pre-select these parameters to be
the default values whenever FRP piping is used. Other options, as to whether the BS 7159
pressure stiffening requirements should be carried out using design strain or actual strain can
be set in CAESAR II’s configuration module as well.
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Selecting material 20 — Plastic (FRP) – activates CAESAR II’s orthotropic material model and
brings in the appropriate material parameters from the pre-selected materials. The orthotropic
material model is indicated by the changing of two fields from their previous isotropic values:
Elastic Modulus (C) changes to Elastic Modulus/axial and Poisson's Ratio changes to
Ea/Eh*Vh/a. These changes are necessary because orthotropic models require more material
parameters than do isotropic. For example, there is no longer a single modulus of elasticity for
the material, but now two: axial and hoop. There is no longer a single Poisson’s ratio, but
again two: Vh/a (Poisson’s ratio relating strain in the axial direction due to stress-induced strain
in the hoop direction) and Va/h (Poisson’s ratio relating strain in the hoop direction due to
stress-induced strain in the axial direction). Also, unlike isotropic materials, the shear modulus
does not follow the relationship G = 1 / E (1-V), so that value must be explicitly input.
To minimize input, a few of these parameters can be combined due to their use in the program.
Generally, the only time that the modulus of elasticity in the hoop direction or the Poisson’s
ratios is used during flexibility analysis is when calculating piping elongation due to pressure
(note that the modulus of elasticity in the hoop direction is used when determining certain
stress allowables for the BS 7159 code):
dx = (x / Ea - Va/h * hoop / Eh) L
Where:
dx
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x
= longitudinal pressure stress in the piping element
E
= modulus of elasticity in the axial direction
Va/h
= Poisson’s ratio relating strain in the axial direction due to stressinduced strain in the hoop direction
hoop = hoop pressure stress in the piping element
Eh
= modulus of elasticity in the hoop direction
L
= length of piping element
This equation can be rearranged, to require only a single new parameter, as:
dx = (x - Va/h hoop * (Ea / Eh )) * L / Ea
In theory, that single parameter, Vh/a is identical to (Ea / Eh * Va/h) giving: dx = (x Vh/ahoop) * L / Ea
The shear modulus of the material is required in ordered to develop the stiffness matrix. In
CAESAR II, this value, expressed as a ratio of the axial modulus of elasticity, is brought in from the
pre-selected material, or can be changed on a problem-wise basis using the Special Execution
Parameter (see "Special Execution Parameters" on page 287) dialog box accessed by the
Environment menu from the piping spreadsheet (see figure). This dialog box also shows the
coefficient of thermal expansion (extracted from the vendor file or user entered) for the material, as
well as the default laminate type, as defined by the BS 7159 Code:





Type 1 – All chopped strand
 mat (CSM) construction with an internal and an external surface
tissue reinforced layer.
Type 2 – Chopped strand mat (CSM) and
 woven roving (WR) construction with an internal and an
external surface tissue reinforced layer.
Type 3 – Chopped strand mat (CSM) and
 multi-filament roving construction with an internal and an
external surface tissue reinforced layer.
The latter is used during the calculation of flexibility and stress intensification factors for
piping bends.
You can enter bend and tee information by using the auxiliary spreadsheets.
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You can also change bend radius and laminate type data on a bend by bend basis, as
shown in the corresponding figure.
Specify BS 7159 fabricated and molded tee types by defining CAESAR II tee types 1 and 3
respectively at intersection points. CAESAR II automatically calculates the appropriate
flexibility and stress intensification factors for these fittings as per code requirements.
Enter the required code data on the Allowables auxiliary spreadsheet. The program provides
fields for both codes, number 27 – BS 7159 and number 28 – UKOOA. After selecting BS
7159, CAESAR II provides fields for entry of the following code parameters:
SH1 through SH9 = Longitudinal Design Stress = d ELAMX
Kn1 through Kn9 = Cyclic Reduction Factor (as per BS 7159 paragraph 4.3.4)
Eh/Ea = Ratio of Hoop Modulus of Elasticity to Axial Modulus of Elasticity
K = Temperature Differential Multiplier (as per BS 7159 paragraph 7.2.1)
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After selecting UKOOA, CAESAR II provides fields for entry of the following code parameters:
SH1 through SH9 = hoop design stress = f1 * LTHS
R1 through R9 = ratio r = (a(0:1) / a(2:1))
f2 = system factor of safety (defaults to 0.67 if omitted)
K = temperature differential multiplier (same as BS 7159)
These parameters need only be entered a single time, unless they change at some point in
the system.
Performing the analysis is simpler than the system modeling. <Product> evaluates the operating
parameters and automatically builds the appropriate load cases. In this case, three are built:





Operating includes pipe and fluid weight, temperature, equipment displacements, and
pressure. This case is used to determine maximum code stress/strain, 
operational
equipment nozzle and restraint loads, hot displacements, and so forth.
Cold (same as above, except excluding temperature and
 equipment movements). This case is used to
determine cold equipment nozzle and restraint loads.
Expansion (cyclic stress range between the cold and hot case).
 This case may be used to evaluate
fatigue criteria as per paragraph 4.3.4 of the BS 7159 Code.
After analyzing the response of the system under these loads, CAESAR II displays a menu of
possible output reports. Reports may be designated by selecting a combination of load case
and results type (displacements, restraint loads, element forces and moments, and stresses).
From the stress report, you can determine at a glance whether the system passed or failed the
stress criteria.
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For UKOOA, the piping is considered to be within allowable limits when the operating stress falls
within the idealized stress envelope this is illustrated by the shaded area in the following figure.
Conclusion
A pipe stress analysis program with worldwide acceptance is now available for evaluation of
FRP piping systems as per the requirements of the most sophisticated FRP piping codes.
This means that access to the same analytical methods and tools enjoyed by engineers using
steel pipe is available to users of FRP piping design.
References
1.
Cross, Wilbur, An Authorized History of the ASME Boiler an Pressure Vessel Code,
ASME, 1990
2.
Olson, J. and Cramer, R., "Pipe Flexibility Analysis Using IBM 705 Computer Pro\-gram
MEC 21, Mare Island Report 277-59," 1959
3.
Fiberglass Pipe Handbook, Composites Institute of the Society of the Plastics Indus\try, 1989
4.
Hashin, Z., "Analysis of Composite Materials a Survey," Journal of Applied Mechanics,
Sept. 1983
5.
Greaves, G., "Fiberglass Reinforced Plastic Pipe Design," Ciba-Geigy Pipe Systems
6.
Puck, A. and Schneider, W., "On Failure Mechanisms and Failure Criteria of FilamentWound Glass-Fibre/Resin Composites," Plastics and Polymers, Feb. 1969
7.
Hashin, Z., "The Elastic Moduli of Heterogeneous Materials," Journal of Applied
Mechanics, March 1962
8.
Hashin, Z. and Rosen, B. Walter, "The Elastic Moduli of Fibre Reinforced Materials,"
Journal of Applied Mechanics, June 1964
9.
Whitney, J. M. and Riley, M. B., "Elastic Properties of Fiber Reinforced
Composite Materials," AIAA Journal, Sept. 1966
10. Walpole, L. J., "Elastic Behavior of Composite Materials: Theoretical
Foundations," Advances in Applied Mechanics, Volume 21, Academic Press, 1989
11. BS 7159: 1989 British Standard Code of Practice for Design and Construction of
Glass Reinforced Plastics GRP Piping Systems for Individual Plants or Sites.
12. UK Offshore Operators Association Specification and Recommended Practice for the Use
of GRP Piping Offshore., 1994
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Code Compliance Considerations
This section comprises general notes that cover code compliance. The first several pages
contain information that applies to all of the codes. The last pages contain code-specific
discussions. Review the general notes, highlighting those that apply to your problem.
Also, review the notes for the piping code that you need.
Configuration and Environment (on page 45) gives details about the various parameters that
you can use in the CAESAR II setup file. Many of these parameters are discussed from an
"application point-of-view" in the text that follows. For more information on the CAESAR II setup
file, see Configuration and Environment (on page 45).
General Comments on Configuration Settings' Effect
on Piping Code Calculations
Stress Intensification Factors (SIF) for all codes
Use the table below to determine which SIF value you need.
If you have...
then use an SIF Value of ...
threaded joints
2.3
double welded slip-on flanges
1.2
lap joint flanges with B16.9 stub
ends
1.6
Calculate Bonney Forge sweepolet and insert weldolet fittings
Use the Weld ID on the SIF & TEE Auxiliary dialog box to calculate the sweepolet and
insert weldolet fittings.
If you can verify that the welds for these fittings are finished or dressed, then specifying the
weld ID lowers the SIF.
Bend SIF overrides
User-defined bend SIF overrides affect the entire cross section of the bend, and as such you
cannot use them to specify a single point on the bend curvature. You must specify the SIFs for
the bend TO node. CAESAR II will apply this SIF, in place of the code SIF, over the entire
bend curvature, from weldline to weldline.
The default value for Fiberglass-Reinforced Plastic (FRP) bend and intersection SIFs is 2.3.
Use this value for all user-modified bends and intersections. The default flexibility factor value
for FRP bends is 1.0. If you modify these values, and generate the SIFs using the steel fatigue
tests you might not be able to use them as a basis for SIFs with FRP fittings.
CAESAR II does not permit the use of SIF values less than 1.0.
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WRC 329
The only piping codes that cannot take advantage of the WRC 329 options, or the option to
use the ASME NC and ND rules for reduced intersections, are BS806 and the Swedish Power
Method 1. These codes do not use the effective section modulus, and any extrapolation of the
ASME methods into these codes is unwarranted.
There is a small difference between Use WRC329 and Reduced Intersection = WRC329.
Use Use WRC329 for all full and reduced intersections that are not welding tees or reinforced
tees. Use Reduced Intersection =WRC329 for reduced fittings that are not welding tees or
reinforced fabricated tees. A fitting is reduced when d/D is less than 0.975.
WRC 329 impact on use with B31.3, B31.4, B31.11, or B31.1 (1967) codes
1.
Include torsional stresses in all stress calculations (sustained and occasional).
2.
Use a torsional SIF of (r/R) io.
3.
Compute i(ib) use 0.6(R/T)2/3 [1+0.5(r/R)3](r/rp).
4.
For i(ob) use 1.5(R/T)2/3 (r/R)1/2 (r/rp) and i(ob)(t/T)>1.5
when (r/R) < 0.9 use 0.9(R/T)2/3 (r/rp) and i(ob)(t/T)>1.0 when
(r/R) = 1.0 and use interpolation when 1.0 > (r/R) > 0.9
5.
For ir use 0.8 (R/T)2/3 (r/R), and ir > 2.1
6.
If the radius at the junction provided is greater than the larger of t/2 or T/2, then divide
the calculated SIFs by 2.0, but with ib>1.5 and ir>1.5.
WRC 329 impact on use with B31.1, B31.8, ASME III NC, ASME III ND, Navy 505, Z183,
Z184, or Swedish Method 2 codes
1. For ib use 1.5(R/T)2/3 (r/R)1/2 (r/rp), and ib(t/T)>1.5
when (r/R) < 0.9
use 0.9(R/T)2/3 (r/rp), and ib(t/T)>1.0
when (r/R) = 1.0 and
use interpolation when 1.0 > (r/R) > 0.9
2.
For ir use 0.8 (R/T)2/3 (r/R), and ir > 2.1
3.
If a radius at the provided junction is greater than the larger of t/2 or T/2, then divide
the calculated SIFs by 2.0, but with ib>1.5 and ir>1.5.
Bonney Forge Sweepolets tend to be a little more conservative because they are used for
fittings in the nuclear industry. Bonney Forge Sweepolet equations can generate SIFs less than
one because they are stronger than the girth butt weld used as the unity basis for the code
fitting SIFs. CAESAR II does not permit SIFs of less than 1.0. If you generate a Bonney Forge
Sweepolet SIF that is less than 1.0, the default value 1.0 is used.
The Bonney Forge SIF Data came from the technical flyer: "Bonney Forge Stress
Intensification Factors" Bulletin 789/Sl-1, Copyright 1976.
Although CAESAR II allows the specification of two element intersections, you cannot specify
two SIFs at a single node and get an increased SIF. For example, you cannot specify a
socket weld SIF and an intersection SIF at the same point.
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Stress calculations for under-specified fittings
For two element joints use the largest diameter and the smallest wall thickness, when
discrepancies exist between the two adjoining pipes. For two element fittings modeled as
socket welds use the largest wall thickness. Both of these selections generate the largest SIFs
and the most conservative stress calculations for under-specified fittings.
The mismatch given for girth butt welds is the average mismatch and not the maximum
mismatch. You must verify that any maximum mismatch requirements are satisfied.
If a fillet leg is given in conjunction with a socket weld SIF definition, then both socket weld
types result in the same SIF.
B31.3 sustained case SIF
The B31.3 sustained case SIF factor in the setup file affects all of the following codes: B31.4,
B31.8, B31.11, Navy 505, Z662, and B31.1 (1967). The default value for the B31.3 SUS
case SIF factor is 1.0.
Corrosion
Calculate the corroded effective section modulus by using (r2)te
Where:
r is the average cross sectional radius of the non-corroded
pipe (te) is the corroded thickness.
Select the thickness (te) based on the non-corroded thicknesses of the branch and header,
in other words, the lesser of Th and iTb. The resulting value has the corrosion subtracted from it
before the effective section modulus calculation is made.
Always use the corroded wall thickness to calculate the Maximum Shear Stress regardless
of the setting of the All Stress Cases Corroded option located in the setup file.
Using more than one Piping Code
If you use different piping codes in one job, the code that displays at the top of the Output
Stress report is the last code used during model input. SIFs, allowables, and code
equations are all computed in accordance with the code that varies with the input.
When there are multiple piping codes in the same piping job, and a piping code change occurs at an
intersection, if the intersection is completely defined with three pipes framing into the intersection
then the piping code used to generate the SIF equations will be that one associated with the first
header pipe framing into the intersection. If the intersection is only partially defined, then the piping
code will be selected from the first pipe framing into the intersection point.
Axial Stress in the Expansion Stress Range
The ASME piping codes primarily combine moments for thermal expansion stresses. When there is
any tendency for large axial forces to exist in the pipe these code equations are not adequate. An
example of this is for buried or partially buried pipe. Here the axial stresses can be very high. B31.4
directs you to compute a longitudinal stress for completely restrained pipe. CAESAR II enables you
to specify just how much of the pipe is buried. This longitudinal stress is then added to the stress
calculations for thermal and contributes to a failure prediction that might have otherwise been
ignored. Similar effects can be achieved in CAESAR II by using the axial
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soil restraint and telling the setup file to include F/A components in the stress calculations. Be
aware that for any type of problem, if large axial loads are developed because of the design,
the piping code might not be adequately considering it.
Application of Torsion in Stress Calculations
The piping codes that do not, by default, include torsion in the sustained or occasional
stress calculations display below:
B31.3
Navy 505
B31.4
Z662
B31.8
B31.1 (1967)
B31.11
GPTC/Z380
These codes tell you to add the longitudinal stresses due to weight, pressure, and other
sustained loadings so torsion is not added. Torsional shear stresses are not longitudinal
stresses. You can request that torsion is added into the sustained and occasional stress
equations by including the Add Torsion in SL Stress option in the setup file. The torsion
stress is still not intensified as it is in the power piping codes. This lack of intensification is
considered an oversight and is corrected in WRC 329. You can include this fix by running any
of the above codes and including the Use WRC330 option in the setup file.
Radius Entry for Mitered Joints
The radius given in CAESAR II is always the equivalent closely spaced miter radius. Only
use the radius calculation for widely spaced miters in the piping codes after breaking the
widely spaced miter bend down into individual single cut miters as recommended.
Reduced intersection calculations
Use reduced intersection calculations when d/D < 0.975.
Where:
d = Outside Diameter of the Branch
D = Outside Diameter of the Header
B31.1 and the ASME Section III piping codes provide stress intensification factors for reduced
branch ends. None of the other piping codes provide these SIFs. The Reduced Intersection
option in the setup file enables other piping code users to access improved SIFs for reduced
fittings. You should review the notes associated with the B31.1 and the ASME Section III
codes that follow to verify that any other parameters or input associated with the reduced
intersection calculations are set as necessary.
Pressure Stiffening
If you request pressure stiffening for those codes that do not normally provide it, CAESAR
II applies pressure stiffening for all bends and for both miter types.
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Occasional Load Factors
The defaults occasional load factor from the setup file used in the evaluation of the
allowable stress, display the text that follows for each of the piping codes.











































B31.1: The occasional load factor is 1.15.
B31.3: The occasional load factor is 1.33.


B31.4: This is 0.8Sy as
defined in the most recent edition of B31.4. OCC does not affect a B31.4
analysis in CAESAR II.
B31.5: The occasional load factor is 1.33.

B31.8: Occasional cases are not specifically defined. If you enter an OCC load
case the allowable
defaults to 1.0 times the sustained allowable stress in other words OCC=1.0.
B31.11: This is 0.88Sy 
as defined in the most recent edition of B31.11 OCC does not affect a B31.11
analysis in CAESAR II.
ASME Section III NC and ND: The default value of OCC is 1.2, the occasional stress
allowable is 1.8 (1.2 X 1.5)Sh but not greater than 1.5Sy. If OCC is 1.5 or 2.0, the
allowable is set to the minimum of 2.25Sh/1.8Sy
(Level C) or 3.0Sh/2.0Sy (Level D). Note

in the latter two cases, enter Sm for Sh.
Navy 505: Occasional cases are 
not addressed but defaults to the method used in B31.1, and an
OCC value of 1.15 is the default.
Z662: The occasional case is not defined, but
if you make an entry the allowable for the case
defaults to 1.0 times the sustained allowable.
BS806: The occasional load case is not defined, but if you make an entry the allowable
stress for the OCC load case is KSh. This is the occasional
load factor times the

sustained allow\-able. The default value for k is 1.0.
Swedish Method 1: OCC is not used. The load cases
are not differentiated. The same
allowable Sigma(ber)/1.5 is used for all load cases.
Swedish Method 2: Uses an OCC default of 1.2 as recommended in the Swedish Piping Code.
B31.1(1967): OCC default is 1.15.



Stoomwezen: OCC default is 1.2.
RCC-M C&D: OCC default is 1.2.
CODETI: OCC default is 1.15.


NORWEGIAN: OCC default is 1.2.


FBDR: OCC default is 1.15
BS 7159: The occasional load case is not defined.
UKOOA: The occasional load case is not defined.


IGE/TD/12: Table 4 of the code addresses
occasional stress increases. The occasional factor in
the setup file has no bearing on this code.
EN-13480: The occasional
load factor varies from 1.0 to 1.8, depending on the loading. Refer to
Section 12.3.3 for details.
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




GPTC/Z380: Occasional cases are not specifically defined. If you enter an OCC load
 case the
allowable defaults to 1.0 times the sustained allowable stress in other words OCC=1.0.
HPGSL: The occasional load factor is 1.33.
JPI: The occasional load factor is 1.33.


You can change the occasional load factor from the program defaults by using the setup file.
Enter the value as a percent. To get an occasional load factor of 1.5, you must type 50.0.
Code-Specific Notes
B31.1
Calculate pressure stiffening using B31.1
Pressure stiffening is defined by default in the code. You can exclude pressure stiffening on
bends in the analysis by including the Use Pressure Stiffening=No option in the setup file.
Flanged end modifications using B31.1
Modifications resulting from flanged ends are permitted in the code providing the bend is not a
widely spaced miter. CAESAR II does not verify the B31.1 criteria "B" length for closely
spaced miters.
B31.1 does not by default add F/A into the stress calculation. F/A and the pressure stresses
are added to the bending stress, whether the tensile or compressive component of bending, to
produce the largest longitudinal stress component. This is true for all codes where the addition
of axial and pressure terms are concerned. You can include the axial force terms into the code
stress by inserting the Add F/A In Stress=Yes option in the setup file.
The F/A forces are structural forces developed in the pipe independent of the pressure
PD/4t forces.
Calculate reduced branch stress intensification factors (SIFs) using B31.1
In 1980, B31.1 added a reduced branch SIF equation to Appendix D. This equation came from
ASME Section III. However, B31.1 continued to use the effective section modulus calculation
for the branch. The ASME Section III rules clearly stated that the branch section modulus, not
the effective section modulus should be used with the new SIF. B31.1 continued use of the
effective section modulus produced unnecessarily high calculated stresses. This error was
corrected in the 1989 version of B31.1. Prior to CAESAR II version 3.0, you had two options:



Use the pre-1980 version of the B31.1 SIF rules


Use the very conservative post-1980 B31.1 SIF rules
These options also exist in version 3.0 and later except that the section modulus problem is
corrected. If you need to run version 3.0 and later without the section modulus correction,
then include the B31.1 Reduced Z Fix=No option in the setup file.
Calculate reduced intersection branch using B31.1
Reduced intersection branch SIFs were not intended for reinforced or welding tees. Conservative
results are produced, but the original researchers did not intend for SIFs to be used for these
fittings. You can disable the reduced branch fitting calculations for reinforced or
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welded tees by including the No Reduced SIF for RFT and WLT option in the setup file.
This produces less conservative results, but can in some cases be justified.
B31.1 102.3.2 (c) says to divide the allowable stresses coming from the stress tables
in Appendix A by the applicable weld joint factors listed in Paragraph 102.4.3.
Calculate the B31.1 stress allowables
Use the equations below to calculate the stress allowables.
Expansion Allowable = f [ (1.25/Eff)(Sc+Sh) - Sl ]
Sustained Allowable = Sh/Eff
Occasional Allowable = Sh/Eff * (Occ)
Where:
f = Cyclic Reduction Factor
Eff = Longitudinal Weld Joint Efficiency
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress
Sl = Sustained Stress
Occ = Occasional Load Factor Default is 1.15
Calculate stress intensification factors (SIFs) for intersections using B31.1
Inplane and outplane SIFs for intersections are the same.
B31.1 reducer default values
The default flexibility factor value is 1.0. Use the following equation to determine the SIF value:
maximum of 2.0 or 0.5 + .01*Alpha* SQRT(D2/t2).
Where:
D1- Diameter of the Large End
t1- Thickness of the Large End
D2 - Diameter of the Small End
t2 - Thickness of the Small End
Alpha - the Reducer Cone Angle in Degrees.
Where:
Alpha = atan[ 0.5 * (D1-D2) / (length of the sloped portion of the reducer) ]
Alpha is the slope of the reducer transition in degrees. If left blank, the value is set from an
estimated slope equal to the arc tangent times 1/2 the change in diameters times sixty percent
of the entered reducer length.
Alpha cannot exceed 60° and the larger of D1/t1 and D2/t2 cannot exceed 100.
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B31.3
Flanged end modifications using B31.3
Modifications resulting from flanged ends are permitted in the code providing the bend is not
a widely spaced miter.
Calculate stress intensification factors (SIFs) for intersections using B31.3
In-plane and out-plane SIFs for intersections are separate and unique.
B31.3 piping code gives the equation for the expansion stress. Because that equation does not
include the longitudinal stress due to axial loads in the pipe, CAESAR II does not include the
F/A component of the stress in the expansion stress equation. The code also says that you can
add the F/A component where it is significant. Change this by including the Add F/A In Stress
option in the setup file. The F/A longitudinal stress components are added by default to the code
stress component for all other stress categories.
B31.3 girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate socket welds using B31.3
B31.3 makes no distinction between socket welds with undercut and socket welds without
undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for
all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3 for
all B31.3 socket welds.
Calculate the B31.3 stress allowables
Use the equations below to calculate the stress allowables.
Expansion Allowable = f [ (1.25)(Sc+Sh) - Sl ]
Sustained Allowable
Occasional Allowable =
= Sh
Sh * (Occ)
Where:
f = Cyclic Reduction Factor
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress (as selected)
Sl = Sustained Stress
Occ = Occasional Load Factor Default is 1.33
Calculate corroded stress using B31.3
By default, B31.3 applied corrosion to section modulus calculation for sustained and
occasional stress calculation. Specifying All Stress Cases Corroded in the setup file performs
the corroded stress calculations for all stress calculations.
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Calculate pressure effects on miters using B31.3
Pressure effects on miters are allowed in the B31.3 piping code.
B31.3 reducer default values
The default SIF value is 1.0. The default flexibility factor value is 1.0.
B31.4
Calculate pressure stiffening using B31.4
Pressure stiffening is defined by default in the code. You can exclude pressure stiffening on
bends in the analysis by including the Use Pressure Stiffening on Bends in the setup file.
Flanged end modifications using B31.4
Modifications resulting from flanged ends are permitted in the code providing the bend is not
a widely spaced miter.
B31.4 girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate stress intensification factors (SIFs) for intersections using B31.4
In-plane and out-plane SIFs for intersections are separate and unique.
Calculate the B31.4 stress allowables
Use the equations below to calculate the stress allowables.
Expansion Allowable = (0.72)(Sy)
Sustained Allowable = (0.75)(0.72)(Sy)
Occasional Allowable = (0.8)(Sy)
Operating Allowable = (0.9)(Sy) if the axial stress is compressive, no code check is done
if axial stress tensile
Where:
Sy = Specified Minimum Yield Stress
B31.4 does not use EFF, (found in the Allowable Stress auxiliary field). The minimum
yield stress is all that is required to compute flexibility stress allowables.
Calculate effective section modulus using B31.4
B31.4 has no provision for using an effective section modulus calculation at intersections.
Calculate liberal allowable using B31.4
B31.4 does not include a provision for the liberal allowable. This particular option is not used for
B31.4 stress allowable calculations. The occasional load factor, used in the other piping codes
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for determining the allowable stress for occasional load sets, is not used in B31.4, as the
default allowable stress is 0.8 times the minimum yield stress.
CAESAR II assumes that 419.6.4(b) establishes a requirement for the allowable operating
stress at 90% of Sy; when the net axial stress is compressive (for example, when
longitudinal pressure stresses can be ignored in underground pipes). The last sentence in
the paragraph establishes that: "Beam bending stresses shall be included in the longitudinal
stress for those portions of the restrained line which are supported above ground." You have
two options for including the axial stress in your analyses:
1.
Include axial friction restraints and include the ADD_F/A parameter into the setup file.
Set Fac to 0.001 to indicate that the line is buried, so longitudinal pressure stresses are
not present, so the hoop stress component must be considered.
2.
Use the Fac value to have CAESAR II compute the "axially-restrained" stress and include it
during stress calculations. If you enter a nonzero Fac value, then multiply the pressure plus
axial loads in the pipe by (1-Fac). This gives a more realistic estimation of the axial stress
in the pipe when you include both of the effects above.
Paragraph 419.6.4(b) requires 1) the reduction of the axial expansion stress by the
product of Poisson's ratio and the pressure hoop stress, and 2) the addiction of the hoop stress
to the axial stress. The latter represents the calculation of stress intensity when the axial stress
is compressive, implying that there is no longitudinal pressure stress in buried pipe (the
pressure loads are transmitted directly to the soil). CAESAR II handles this case in the
Operating Load Case, where the hoop stress is added in and the allowable stress is set to 0.9
Sy whenever the axial stress is compressive. If Fac is 0.001, the piping element is considered
buried, so the longitudinal pressure stress is replaced by the product of Poisson’s ratio and the
hoop stress, in keeping with the spirit of paragraph 419.6.4(b). "Fac" is automatically set to
0.001 when B31.4 pipe is sent through the Buried Pipe Modeler. The stress due to axial force
is also included for these elements.
The Fac variable should probably not be set to 1.0 with B31.4 and thermal expansion cases
where you are going from one thermal state to another state. In other words, where the case
is of the form: L1-L2, and both L1 and L2 contain temperatures. In this case, the thermal
expansion used in the restrained pipe calculation comes from the last thermal specified in the
load case definition. In the example above the thermal expansion associated with the L2 load
case.
The Base Hoop Stress On OD flag in the setup file is used by B31.4 when the hoop stress is
calculated for the restrained pipe longitudinal stress calculation. The default is to base the
hoop stress calculation on the average diameter, and the equation PD/2t. In the mechanical
stress calculations the hoop stress is based on the inside diameter.
This is the hoop stress that is printed in the extended CAESAR II Stress report.
B31.4 reducer default values
The default SIF value is 1.0. The default Flexibility Factor value is 1.0.
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B31.4 Chapter IX
Chapter IX presents the offshore requirements of the B31.4 (on page 959).
Calculate Stress Intensification Factors (SIFs), flexibility factors, and section moduli
Calculate all SIFs, flexibility factors, and section moduli exactly as stated in the standard
B31.4 code.
Calculate stress using B31.4 Chapter IX
Use the uncorroded wall thickness to make stress calculations.
Calculate load cases using B31.4 Chapter IX
There is no provision for a code check for the expansion load case, so no expansion cases are
generated under this code. Operating, sustained, or occasional load cases are treated
identically. Do three stress calculations for these load cases, each with a different allowable
limit. The Stress Report displays the calculation causing the highest percent of allowable
along with its specific allowable. These three stress checks are:
Hoop Stress: Sh  F1 Sy
Longitudinal Stress: |SL| 0.8 Sy
Equivalent Stress: Se 0.9 Sy
Where:
Sh = (Pi – Pe) D / 2t
Pi = Internal Pressure
Pe = External Pressure
D = Outer Diameter
t = Wall Thickness
F1 = Hoop Stress Design Factor 0.60 or 0.72, see Table A402.3.5(a) of the B31.4
Code Sy = Specified Minimum Yield Strength
SL = Sa + Sb or Sa - Sb, whichever results in greater stress
value Sa = Axial Stress Positive Tensile and Negative
Compressive Sb = Bending Stress
Se = 2[((SL - Sh)/2)2 + St2]1/2
St = Torsional Stress
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B31.5
B31.5 reducer default values
The default SIF value is 1.0. The default flexibility factor value is 1.0.
B31.8
Restrained Pipe (as defined in Section 833.1):
For Straight Pipe:
Both SL and SC < 0.9ST (OPE)
Both SL, and SC < 0.9ST (SUS)
SL < 0.9ST and Sc < ST (OCC)
and
* The Stress Report displays the calculation causing the highest percent of allowable
along with its specific allowable.
For All Other Components
SL < 0.9ST (OPE, SUS, OCC)
Unrestrained Pipe (as defined in Section 833.1):
SL < 0.75ST (SUS, OCC)
SE < f[1.25(SC + SH) – SL] (EXP)
Where:
SL = SP + SX + SB
SP = 0.3SHoop (for restrained pipe); 0.5SHoop (for unrestrained pipe)
SX = R/A
SB = MB/Z (for straight pipe/bends with SIF = 1.0); MR/Z (for other components)
SC = Max (|SHoop – SL|, sqrt[SL2 – SLSHoop + SHoop2])
MR = sqrt[(0.75iiMi)2 + (0.75ioMo)2 + Mt2]
SE = ME/Z
ME = sqrt[(0.75iiMi)2 + (0.75ioMo)2 + Mt2]
S = Specified Minimum Yield Stress
T = Temperature Derating Factor
SH = 0.33SUT
SC = 0.33SU
SU = Specified Minimum Ultimate Tensile Stress
B31.8 distinguishes between restrained and unrestrained piping for the purposes of stress
computations. To implement B31.8 you must define which sections of the piping system are
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restrained, as per Code Section 833.1. In general, restrained piping is piping in which the soil
or supports prevent axial displacement of flexure at bends. Conversely, unrestrained piping is
piping that is free to displace axially or flex at bends. For more information, see Section 833.1.
Processing a B31.8 model through the Buried Pipe Modeler designates the buried sections as
restrained.
For restrained pipe, B31.8 specifies that the operating case stresses should include the thermal
axial stress component, a constant stress due to linear thermal expansion, but exclude thermal
bending stresses from the SB component. Because CAESAR II cannot go back and segregate
internal thermal forces and moments from those of other loads, the thermal axial stresses are
calculated and included as part of SX (as opposed to added as a constant), and thermal
bending stresses are conservatively included in SB.
Bending stress SB is defined differently for straight pipe or "large-radius" bends than it is for
other components. CAESAR II resolves the ambiguity of exactly what constitutes a "largeradius" bend by considering any bend having an SIF of 1.0 as being a "large-radius" bend.
Occasional load default values
The occasional load default value for B31.8 is 1.111 (1/0.9) and is only applied to the
allowable for SC combined stress calculated only in straight pipes. The allowable in this case is
ST as opposed to 0.9ST. There is no provision for increasing or decreasing this allowable.
In the case of occasional stresses in straight pipes, there are potentially two stresses (SL
and SC) to be compared against two different allowable limits. CAESAR II only prints the one
that provides the greater ratio of calculated stress versus allowable stress. You can visually
determine which stress prints by examining the magnitude of the allowable.
Calculate pressure stiffening using B31.8
Pressure stiffening is included by default in the code. You can exclude pressure stiffening
on bends in the analysis by setting the Use Pressure Stiffening switch in the setup file.
Modifications to the flexibility factor and Stress Intensification Factor (SIF) using B31.8
Modifications to the flexibility factor and SIF of bends resulting from flanged ends are
permitted by the code.
Calculate socket welds using B31.8
B31.8 makes no distinction between socket welds with undercut and socket welds without
undercut. Unless you are specifying a fillet weld leg length, use a default SIF value of 2.1 for
all B31.8 socket welds.
Using reducers with B31.8
Use of reducers is subject to the following limitations:



Alpha the reducer cone angle is limited to 60°

The larger of D1/SQRT(t1) and D2/SQRT(t2) cannot exceed 100 where
 D1/t1 and D2/t2 are the
diameters and thicknesses of the large and small ends, respectively.
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B31.8 Chapter VIII
Chapter VIII discusses the offshore requirements of B31.8. For more information, see B31.8 (on
page 962)
Calculate the Stress Intensification Factors (SIFs), flexibility factors, and section
moduli using B31.8 Chapter VIII
Calculate all SIFs, flexibility factors, and section moduli exactly as in the standard B31.8 Code.
Make all stress calculations using the non-corroded wall thickness for the hoop and
longitudinal stresses. Use the corroded thickness for the combined stress.
Calculate the expansion load case using B31.8 Chapter VIII
There is no provision for a code check for the expansion load case, so no expansion cases
are generated under this code.
Calculate the operating, sustained, or occasional load cases using B31.8 Chapter VIII
Operating, sustained, or occasional load cases are treated identically. For these load cases,
you must perform three stress calculations, each with specific allowable limits. The stress
calculation causing the highest percent of allowable displays in the stress report along with its
specific allowable. The stress checks are:
Hoop Stress: Sh  F1ST
Longitudinal Stress: |SL|  0.8S
Equivalent Stress: Se  0.9S
Where:
Sh = (Pi – Pe) D / 2t
Pi = Internal Pressure
Pe = External Pressure
D = Outer Diameter
t = Wall Thickness
F1 = Hoop Stress Design Factor 0.50 or 0.72 see Table A842.22 of B31.8
S = Specified Minimum Yield Strength
T = Temperature Derating Factor see Table 841.116A of B31.8
The product of S and T, the yield stress at operating temperature, is required in
the SH field of the CAESAR II Input:
SL = Maximum Longitudinal Stress Positive Tensile and Negative Compressive
Se = 2[((SL - Sh)/2)2 + Ss2]1/2
Ss = Torsional Stress
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B31.9 Notes
Paragraph 919.4.1.b states that for analysis methods follow B31.1. For more information,
refer to B31.1.
B31.11
Calculate pressure stiffening using B31.11
Pressure stiffening is included by default in the code. You can exclude pressure stiffening
on bends in the analysis by setting the Use Pressure Stiffening switch in the setup file.
Flanged end modifications using B31.11
Modifications resulting from flanged ends are permitted in the code provided the bend is not
a widely spaced miter.
B31.11 girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate stress intensification factors (SIFs) for intersections using B31.11
In-plane and out-plane SIFs for intersections are separate and unique.
Calculate the B31.11 allowable stresses
Use the equations below to calculate the stress allowables.
Expansion Allowable = (0.72)(Sy)
Sustained Allowable = (0.75)(0.72)(Sy)
Occasional Allowable = (0.88)(Sy)
Operating Allowable = (0.9)(Sy) if the axial stress is compressive; no code check done if
the axial stress is tensile
Where:
Sy = Specified Minimum Yield Stress
B31.11 does not use EFF, found on the Allowable Stress Auxiliary field. The minimum
yield stress is all that is required to compute flexibility stress allowables.
Calculate effective section modulus using B31.11
B31.11 has no provision for using an effective section modulus calculation at intersections.
Calculate liberal allowable using B31.11
B31.11 does not include a provision for the liberal allowable. This option is not used for
B31.11 stress allowable calculations. The occasional load factor, used in the other piping
codes for determining the allowable stress for occasional load sets, is also not used in B31.11,
as the allowable stress is 0.88 times the minimum yield stress.
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CAESAR II assumes that 1119.6.4(b) establishes a requirement for the allowable operating
stress at 90% of Sy when the net axial stress is compressive (when longitudinal pressure
stresses can be ignored in underground pipes). The last sentence in the paragraph establishes
that: "Beam bending stresses shall be included in the longitudinal stress for those portions of
the restrained line which are supported above ground." You have two options for including this
axial stress in your analyses:
1.
Include axial friction restraints and include the Add F/A option in the setup file. Set Fac
to 0.001 to indicate that the line is buried, so longitudinal pressure stresses are not
present, and so the hoop stress component is considered.
2.
Use Fac to tell CAESAR II to compute the axially-restrained stress and include it during
stress calculations. If you enter a nonzero Fac, the pressure plus axial loads in the pipe
are multiplied by (1-Fac). This gives a more realistic estimation of the axial stress in the
pipe when you have included both of the effects above.
Paragraph 1119.6.4(b) requires 1) the reduction of the axial expansion stress by the
product of Poisson’s ratio and the pressure hoop stress, and 2) the addition of the hoop stress
to the axial stress. The latter represents the calculation of stress intensity when the axial stress
is compressive, implying that there is no longitudinal pressure stress in buried pipe (the
pressure loads are transmitted directly to the soil). CAESAR II handles this case in the
operating load case, where the hoop stress is added in and the allowable stress is set to 0.9 Sy
whenever the axial stress is compressive. If Fac is 0.001, the piping element is considered
buried, so the longitudinal pressure stress is replaced by the product of Poisson’s ratio and the
hoop stress, in keeping with the spirit of paragraph 1119.6.4(b). Fac is automatically set to
0.001 when B31.11 pipe is sent through the buried pipe modeler (on page 483). The stress due
to axial force is also included for these elements.
Do not set Fac to 1.0 when using B31.11with thermal expansion cases where you are going
from one thermal state to another state. In other words where the case is of the form: L1-L2,
and both L1 and L2 contain temperatures. In this case the thermal expansion used in the
restrained pipe calculation comes from the last thermal specified in the load case definition. In
the example above the thermal expansion associated with the L2 load case.
When calculating the hoop stress for the restrained pipe longitudinal stress calculation use the
Base Hoop Stress On option in the setup file. The default is to base the hoop stress
calculation on D = average diameter in the equation PD/2t. In mechanical stress calculations
the hoop stress is based on the inside diameter. This is the hoop stress that displays in the
extended CAESAR II Stress report.
B31.11 reducer default values
The default SIF value is 1.0. The default flexibility factor value is 1.0.
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ASME III Subsections NC and ND
Calculate pressure stiffening using NC and ND
Pressure stiffening is not defined by default in this code. You can include pressure stiffening on
bends in the analysis by including the Use Pressure Stiffening=Yes option in the setup file.
Flanged end modifications using NC and ND
Modifications resulting from flanged ends are permitted in this code providing the bend is not
a widely spaced miter.
Minimum SIF for reinforced and unreinforced fabricated tees using NC and ND
The minimum SIF for reinforced and unreinforced fabricated tees is 2.1.
Calculate B1 and B2 using NC and ND
Calculate B1 and B2 according to the equations in ASME NC and ND.
Calculate liberal allowable using NC and ND
If you are using this piping code and define a dynamic load case as a “Expansion”, a request
for Liberal Allowable is ignored and the (Sh-Sl) term is removed from the allowed limit (see
below). This is a programming decision rather than an interpretation of the piping code or a
recommendation for doing dynamic analysis.
Calculate stress intensification factors (SIFs) for intersections using NC and ND
Inplane and outplane SIFs for intersections are the same.
Using WRC 329 with NC or ND
For all intersections that are not welding tees or reinforced fabricated tees use the
equation *r2*t to calculate the approximate section modulus for the stress calculations.
This includes all reduced intersections and all d/D ratios.
Determine the branch SIF using NC or ND
If you do not want to use the branch SIF of the Code for welding and reinforced reducing
tees, include the No Reduced SIF for RFT and WLT flag in the setup file.
Calculate the NC and ND stress allowables
Use the equations below to calculate the stress allowables.
Expansion Allowable = f(1.25Sc + 0.25Sh) + (Sh-Sl)
Sustained Allowable = 1.5Sh If not at an intersection
Occasional Allowable = 1.8Sh not greater than 1.5Sy, if OCC=1.2;
2.25Sh not greater than 1.8Sy, if OCC=1.5;
3.0Sh not greater than 2.0Sy, if OCC=2.0
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Where:
f = Cyclic Reduction Factor
Sc = Cold Allowable
Sh = Hot Allowable
Sl = Sustained Stress from PD/4t+0.75iMb
Sy = Material Yield Stress
OCC = Occasional Factor from the CAESAR II configuration file
Calculate two pipe intersections using NC and ND
For two pipe intersections, for example butt welds or socket welds, B1 and B2 factors are 1.0.
If the ratio of the average branch to average run radius is less than 0.5, then apply the reduced
intersection rules to the B1 and B2 calculations regardless of the intersection type. If the
reduced intersection rules do not apply then use the following rules for butt welded fittings:
B2b = 0.4 * (R/T)**2/3 but not < 1.0
B2r = 0.5 * (R/T)**2/3 but not < 1.0
You can modify the values for B1 and B2 for any node in the SIF&TEE auxiliary field. Any
changes you make to B1 and B2 on an auxiliary field only apply for that element, regardless
of whether the node is an intersection or not.
Calculate the ratio of r/R using NC and ND
When r/R < 0.5 use the following equations for B1 and B2:
B2b = 0.50 C2b but not < 1.0
B2r = 0.75 C2r but not < 1.0
C2b = 3(R/T)2/3 (r/R)1/2 (t/T)(r/rp), but not < 1.5
C2r = 1.15(r/t)1/4 but not < 1.5
Branch SIFs using NC and ND
WRC 329 produces smaller branch SIFs than ASME NC and ND, and the same run SIFs. The
branch SIFs are smaller by a factor of 2. This is when d/D<0.5 and WRC 329 corrects the Mob
(out of plane bending) inconsistency when d/D is between 0.5 and 1. In the lower ranges of
d/D ratios WRC 329 is less conservative than the present codes and in the higher ranges
WRC 329 is more conservative than the present codes.
Calculate Pvar using NC and ND
Pvar represents the difference between the operating pressure and Pmax, which is used in eq
11. CAESAR II forms occasional stresses by adding the sustained stress including pressure,
and the occasional stress including the stress difference between the operating pressure
and the peak pressure.
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Limit for expansion stress range
To satisfy equations 10 or 11, the expansion stress, iMc/Z, must remain below the maximum
of either f(1.25Sc + 0.25Sh) or f(1.25Sc + 0.25Sh) + (Sh-Sl) where Sl is the sustained stress
as defined by equation 11: Sl= PDo/4tn+0.75iMa/Z.
Calculate moment summations using NC and ND
The approach taken by CAESAR II for moment summations at inter\-sections to satisfy
equations 8 and 9 is to use the SRSS of the moments at each end of the pipe framing into the
intersection. You do not have to adhere to the cumulative moment summation rules for a single
intersection as per NB 3683.1. In addition, use the effective section modulus rules of NC and
ND for all intersection stress calculations like equations 8 and 9. Use subsection NB to get the
values for B1 and B2 only, and to compute the local flexibility if requested. Because of the use
of this approach in CAESAR II, there is no allowable calculated for intersection points and
sustained or occasional loads.
Determine sustained case SIF using NC and ND
Do not use the SIF in the ASME class 2 or 3 sustained stress calculations.
NC and ND reducer default values
The default flexibility factor value is 1.0. Use the following equation to determine the SIF value:
2.0 max or 0.5 + .01*alpha* SQRT(D2/t2).
Where:
D1- Diameter of the Large End
t1- Thickness of the Large End
D2 - Diameter of the Small End
t2 - Thickness of the Small End
Alpha - the reducer cone angle in degrees
Where:
Alpha = atan[ 0.5 * (D1-D2) / (length of the sloped portion of reducer) ]
Alpha is the slope of the reducer transition in degrees. If left blank, the value is set from an
estimated slope equal to the arc tangent times 1/2 the change in diameters times sixty percent
of the entered reducer length.
Alpha cannot exceed 60º. The larger of D1/t1 and D2/t2 cannot exceed 100.
B1=.5 if alpha  30º, 1.0 if 30º < alpha  60º; B2 = 1.0.
There is an error in the code, the code states note 12 however, they meant note 14.
Alpha cannot exceed 60º.
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CANADIAN Z662
Calculate pressure stiffening using Z662
Pressure stiffening is not defined by default in the code. You can include pressure stiffening on
bends in the analysis by including the Use Pressure Stiffening=Yes option in the setup file.
Flanged end modifications using Z662
Modifications resulting from flanged ends are permitted in the code providing the bend is not
a widely spaced miter.
Pad thickness using Z662
There is no limit in Z662 for the beneficial effect of the pad on an intersection. Most codes
limit the pad thickness to 1.5 times the header thickness. For Z662, CAESAR II does not limit
the pad thickness.
Z662 girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
In-plane and out-plane stress intensification factors for intersections are the same.
Calculate socket welds using Z662
Z662 makes no distinction between socket welds with undercut and socket welds without
undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for
all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3.
Calculate effective section modulus using Z662
Z662 has no provision for using an effective section modulus calculation at intersections.
Calculate the CANADIAN Z662 allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable = (0.72)(T)(Sy)
Sustained Allowable = (Fac)(T)(L)(Sy)
Occasional Allowable = (Occ)(Fac)(T)(L)(Sy)
Operating Allowable = 0.9(T)(Sy), if pipe is buried and axial stress is compressive
Operating Allowable = (T)(Sy), if pipe is not buried and axial stress is compressive
Where:
Sy = Specified Minimum Yield Stress
Fac = Construction Design Factor
T = Temperature De-rating Factor
Occ = Occasional Load Factor (Default is 1.0)
L = Location Factor
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CAESAR II assumes that Section 4.6.2 of the Z662 code establishes a requirement for the
allowable operating stress of 0.9 x S x T whenever the net axial stress is compressive in the
absence of bending stress, and an allowable operating stress of S x T when the net axial
stress is compressive in the presence of bending stress.
Section 4.6.2 requires the following:
1.
The reduction of the axial expansion stress by the product of Poisson’s Ratio and
the pressure hoop stress.
2.
The addition of the hoop stress to the axial stress.
The latter represents the calculation of stress intensity when the axial stress is compressive,
implying that there is no longitudinal pressure stress in buried pipe (the longitudinal pressure
thrust loads are transmitted directly to the soil). CAESAR II handles these requirements, in
the operating load case, in the following manner:
1.
If FAC is 1.0, the piping system is fully restrained in the axial direction as described
in Section 4.6.2.1, and the operating stress is calculated as:
Sh + E a (T2 - T1) - v Sh < 0.9 S x T
2.
If FAC is 0.001, the piping system is buried, but the soil supports are modeled (rather than
just assumed to be fully rigid). This setting removes the longitudinal pressure stress from
the equation (as described above), and takes bending stresses into consideration, as
required by Section 4.6.2.2.1. In this case, the operating stress is calculated as:
Sh +Fax/A + Sb - v Sh < S x T
3.
If FAC is 0.0, the piping system is either not restrained, or is a freely spanning or above
ground portion of a restrained line, as described in Section 4.6.2.2.1. In this case, the
longitudinal pressure stress is restored, so this formula only comes into effect if the net
axial stress including pressure is compressive, in which case the operating stress is
calculated as:
Sh +Slp + Fax/A + Sb < S x T
4.
CAESAR II does not do an operating code stress check for those elements for which the
net axial stress is longitudinal.
5.
CAESAR II does not check for buckling, as required by Section 4.6.2.2.2.
Z662 reducer default values
The default SIF value is 1.0. The default flexibility factor value is 1.0.
NAVY 505
Calculate pressure stiffening using Navy 505
Pressure stiffening is not defined by default in the Code. You can include pressure stiffening
on bends in the analysis by including the parameter Use Pressure Stiffening in the setup file.
Flanged end modifications using Navy 505
Modifications resulting from flanged ends are permitted in the code providing the bend is not
a widely spaced miter.
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Navy 505 girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate effective section modulus using Navy 505
Navy 505 has no provision for using an effective section modulus calculation at intersections.
Calculate stress intensification factors (SIF)s for intersections using Navy 505
In-plane and out-plane SIFs for intersections are the same.
Calculate liberal allowable using Navy 505
Navy 505 has no provision for a liberal allowable, that is, adding the difference between Sh
and Sl to the allowed expansion stress range. This feature from the control parameter
spreadsheet has no effect on 505 runs.
Calculate cold and the hot allowable using Navy 505
Navy 505 uses longitudinal weld joint efficiency (Eff) to compute the cold and the hot
allowable stress. The use of this parameter is subject to some speculation however.
Calculate the Navy 505 allowable for occasional loads
Navy 505 has no specific allowable for occasional loads. An occasional load factor (k), similar
to the B31.1 code is used, and the occasional allowable calculated from kSh.
Calculate the Navy 505 allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable = [f(1.25Sc + 0.25Sh)]/Eff
Sustained Allowable = Sh/Eff
Occasional Allowable = k*Sh/Eff
Where:
f = Cyclic Reduction Factor
Eff = Joint Efficiency (Not explicitly in the Code)
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress
k = Occasional Load Factor, Defaults to 1.15
Use the B31.3 SUS Case SIF Factor option to multiply the SIFs for sustained and
occasional loads to be more in line with the current B31.1 practice.
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BS806
For BS806, the maximum hot stress case is considered to be the operating load case.
Operating load case allowables are only given as per BS806 when the creep rupture strength
governs the stress range allowable. See BS806 sect 4.11.2.
Stress Intensification Factors (SIFs) using BS806
BS806 SIFs printed are labeled fti and fto for bends, and Bi and Bo for intersections.
Calculate pressure stiffening using BS806
Pressure stiffening is not defined by default in the code. You can include pressure stiffening
on bends in the analysis by including the Use Pressure Stiffening option in the setup file.
Pad thickness using BS806
There is no limit in BS806 for the beneficial effect of the pad on an intersection. Most codes
limit the pad thickness to 1.5 times the header thickness. For BS806, CAESAR II does not limit
the pad thickness.
Flanged end modifications using BS806
The code permits modifications due to flanged ends for all bend types. This includes closely
and widely spaced mitered bends.
BS806 girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate the BS806 allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable = lesser of (H)(Sc)+(H)(Sh) <or> (H)(Sc)+F
Sustained Allowable = Sy
Occasional Allowable = (Sy)(Occ)
Operating Allowable = S avg rupture at design temperature
Where:
H = Multiplication Factor 0.9 or 1.0 from CAESAR II
Sc = 0.2% Proof Stress at Room Temperature
Sh = 0.2% Proof Stress at Design Temperature
F = Mean Stress to Failure in Design Life at Design Temperature
Occ = Occasional Load Factor Default is 1.0
Calculate pressure at intersections using BS806
The pressure calculation at the intersections is made as required in BS806 4.8.5.1 Eq. (17). The
pressure stress as per Eq. (17) is computed and then combined with the bending and torsional
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moment at each of the intersection ends 1, 2 and 3 respectively. The m factor is computed as
required with a value of n=1, in other words, for non-interacting intersections. BS806 does
not address reducers for SIF calculations.
Other BS806 Notes
When there is more than one thermal case to evaluate, read the following note
carefully concerning CAESAR II and the application of BS806.
Regarding BS806 4.11.3.1 paragraph 2, for sectionalized systems: CAESAR II only
makes the moment summation on a load case by load case basis, and does not take the
largest moments for an axis for any combination of load cases. The CAESAR II method is
designed to enable you to set up and combine the effects of each of the load transients that the
piping system undergoes. This method, for the most part is used in the B31/ASME piping
codes. The BS806 method is conservative in that it uses what is basically a shakedown
approach and computes a single worst case moment difference. The CAESAR II method
satisfies the shakedown theory but, also computes the moment range for each different load
traversed. The BS806 method of combining the maximum moment range is more conservative.
The BS806 method also eliminates the need to know where on the pipe the stress is the
highest. Use the moment tables in Appendix F, to get the moment difference between any two
load cases. However, you cannot use the moment tables to get the maximum moment
difference for any of the three moment axes as requested by the sectionalized piping rules. To
satisfying 4.11.3.1(a) CAESAR II uses the moment difference between the cold and the hot
case to compute the stress.
You can only enter a single modulus of elasticity for a single element in each job. Different
elements can have different moduli of elasticity, but you cannot vary that modulus between
load cases in the same run. Also, you cannot use cold and a hot moduli of elasticity in the
same run at this time.
For BS806 in 4.11.5.2 the value of n is 1.0.for all branches of the non-interacting type. See
the fourth paragraph 4.11.4.2 for the definition of n for interacting branches.
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The CAESAR II equation modeling of the BS806 SIF curves for bends displays in the
following plots.
Swedish Method 1 and 2
Calculate pressure stiffening using Swedish Method 1 and 2
Pressure stiffening is not defined by default in the code. You can include pressure stiffening
on bends in the analysis by including the parameter Use Pressure Stiffening in the setup file.
Flanged end modifications using Swedish Method 1 and 2
Modifications resulting from flanged ends are permitted in the code providing the bend is not
a widely spaced miter.
WRC329 recommendations
Swedish Method 1 cannot take advantage of the WRC 329 recommendations. WRC 329,
if requested, is ignored.
Calculate effective section modulus using Swedish Method 1
Swedish Method 1 has no provision for using an effective section modulus calculation
at intersections.
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Calculate stress intensification factors (SIFs) for intersections using Swedish codes
Inplane and outplane SIFs for intersections are the same.
Swedish Code item 9 is dealt with as a US tapered transition. Also, items 10 and 11 in
the Swedish table 9:2 correspond to items 8 and 9 in the CAESAR II nomenclature.
Calculate the allowable stress limits using Method 1
Use the equations below to calculate the stress allowables.
Sber = lesser of Sh or F
Allowable = (Fac)(Sber) / 1.5
Where:
Sh = Yield Stress at Temperature
F = Creep Rupture Stress at Temperature
Fac = Usually 1.5 for Pre-stressed Pipe Use 1.35.
Calculate the allowable stress limits using Method 2
Expansion Allowable = f ( 1.17S1 + 0.17S2 )
Sustained Allowable = Sh
Occasional Allowable = Occ * Sh
Where:
f = Cyclic Reduction Factor
S1 = Lesser of Sc or 0.267Sy
S2 = Lesser of Sh or 0.367Sy
Sc = Allowable Stress at Room Temperature (Stn2)
Sh = Allowable Stress at Design Temperature (Stn1)
Sy = Ultimate Tensile Strength at Room Temperature
Occ = Occasional Load Factor Default is 1.2
Default girth butt welds for Swedish Method codes
If the weld is ground flush inside and out then the default SIF value for a girth butt weld is 1.0.
Pressure Variation in Swedish Codes
Swedish methods 1 and 2 Beta in the code is entered in the Pvar field on the Allowable
Stress Auxiliary dialog box. Enter the value for Pvar in percent, for example 10.0 for ten
percent. If left blank, the default is 10.0 percent.
Limits on the reasonable Betas that you may enter for the Swedish piping code is 10% to 25%.
Anything less than 0.1 is taken to be 10% and anything entered greater than 0.25 is taken to
be 25%.
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Pressure Stress in Swedish Codes
Include the Use PD/4t option in the setup file to tell CAESAR II to use the thin walled
equations for stress calculations for Swedish Method 1 code compliance.
Default occasional load factor for Swedish Method 2
The default value for the occasional load factor for Swedish Method 2 is 1.2.
Pad thickness using the Swedish Method 1 and 2
The pad thickness on an intersection reduces stresses up to pad thickness of 2.5 times
the header wall thickness.
Calculate reducers using the Swedish Method 1 and 2
The default value for the flexibility factor is 1.0 and the equation to calculate reducer SIFs is:
2.0 max or 0.5 + .01*alpha* SQRT(D2/t2)
Where D1 and t1 are the diameter and thickness of the large end and D2 and t2 are
the diameter and thickness of the small end.
Alpha is the reducer cone angle in degrees.
Where:
Alpha = atan[ 0.5 * (D1-D2) / (0.60 * length of sloped portion of the reducer) ]
Alpha is the slope of the reducer transition in degrees. If left blank, the value is set from an
estimated slope equal to the arc tangent times 1/2 the change in diameters times sixty percent
of the entered reducer length.
Other Swedish Notes
If you are using Swedish Method 1 to calculate the CAESAR II allowable, assume that the
SIGMA(tn) multiplier is 1.5 for piping that is not pre-stressed. If you use pre-stressed or cold
sprung pipe change Fac on the Allowable Stress Auxiliary field to 1.35 as per the
Swedish code.
Use the corroded section modulus for all stress calculations as per the definition of Di in
the Swedish code.
B31.1 (1967)
Calculate full-sized intersections for both the header and the branch using B31.1 (1967)
B31.1 (1967) uses ii = io for full-sized intersections for both the header and the branch, and
for reduced intersections uses ii = 0.75io + 0.25 for both the header and the branch.
Calculate pressure stiffening using B31.1 (1967)
Pressure stiffening is not defined by default in this code. You can include pressure stiffening
on bends in the analysis by including the Use Pressure Stiffening option in the setup file.
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Flanged end modifications using B31.1 (1967)
Modifications resulting from flanged ends are permitted in the code providing the bend is not
a widely spaced miter.
B31.1 (1967) girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate socket welds using B31.1 (1967)
B31.1 (1967) makes no distinction between socket welds with undercut and socket welds without
undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for all
others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3.
Calculate the B31.1 (1967) allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable = f [ (1.25/Eff)(Sc+Sh) - Sl ]
Sustained Allowable = Sh/Eff
Occasional Allowable = Sh/Eff * Occ
Where:
f = Cyclic Reduction Factor
Eff = Longitudinal Weld Joint Efficiency
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress
Sl = Sustained Stress
Occ = Occasional Load Factor (Default is 1.15)
Stoomwezen
978
Sc
= The yield stress at room temperature is referred to as Re in the code.
Sh1
= The yield stress at design temperature is referred to as Re (um) in the
code.
Sh2
=
not used
Sh3
=
not used
FN
= The average creep stress to produce one percent set is referred to as
Rrg in the code. F2 is the average creep tensile stress to produce
rupture and is referred to as Rmg in the code. F3 is the minimum creep
tensile stress to produce rupture and is referred to as Rmmin in the
code.
Eff
= The cyclic reduction factor is referred to as Cf in the code.
CAESAR II User's Guide
Technical Discussions
Sy
= The tensile strength at room temperature is referred to as Rm in the
code.
Fac
= A constant whose value is either 0.44 or 0.5. For more information, refer
to Stoomwezen Section 5.2.
Pvar
= The Cm coefficient in the code whose value is usually 1.0.
Calculating reducers using Stoomwezen
Stoomwezen does not mention reducers for Stress Intensification Factor (SIF) calculations.
RCC-M Subsection C and D
Calculate pressure stiffening using RCC-M Subsection C and D
Pressure stiffening is not defined by default in the code. You can enable pressure stiffening on
bends in the analysis by including the Use Pressure Stiffening option in the configuration file.
Flanged end modifications using RCC-M
Modifications resulting from flanged ends are permitted providing the bend is not a
widely spaced miter.
Calculate stress intensification factors (SIFs) for intersections using RCC-M
Inplane and outplane SIFs for intersections are the same for these piping codes.
Calculate SIF for branch connection using RCC-M
If you do not want to use the SIF for branch connections, found in Figure C3680.1 of the code
for welding and reinforced reduced tees, include the No Reduced SIF For RFT and WLT
option in the configuration file.
Calculate the RCC-M allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable
= F (1.25Sc + 0.25Sh)+(Sh SSL)
Sustained Allowable
= Sh
Occasional Allowable = OCC * Sh
OCC defaults to 1.2 for Level
B
OCC defaults to 1.8 for Level
C
OCC defaults to 2.4 for Level
D
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Where:
F = Cyclic Reduction Factor
Sc = Cold Allowable
Sh = Hot Allowable
SSL = Sustained Stress (PD/4t + 0.75i Mb/Z)
OCC = Occasional Factor from the CAESAR II configuration file
Calculate Pvar using RCC-M
Pvar represents the difference between the operating pressure and Pmax, which is used in eq
10. To satisfy equations 7 or 8 use iMc/Z stress as the maximum of either F(1.25Sc + 0.25Sh) or
F(1.25Sc + 0.25Sh) + (Sh - Ssl) where Ssl is the sustained stress as defined by equation 6.
Calculate reducers using RCC-M
For reducers RCC-M states that the flexibility factor is 1.0. The code also states that the SIF is:
The minimum of 2.0 or 0.5 + .01*alpha* SQRT(D2/t2)
Where:
D2 - Diameter of the Small End
t2 - Thickness of the Small End
Alpha is the reducer cone angle in degrees.
If not specified:
Alpha = atan[ 0.5 * (D1-D2) / (0.60 * length of the reducer element) ]
Alpha cannot exceed 60° and the larger of D1/t1 and D2/t2 cannot exceed 100.
CODETI
Modifications resulting from flanged ends using CODETI
Modifications resulting from flanged ends are permitted in the code for all bends,
including widely spaced miters.
Calculate stress intensification factors (SIFs) for intersections using CODETI
CODETI provides two separate equations to calculate the in-plane and out-plane SIFs
for intersections.
Calculate expansion stress using CODETI
CODETI provides an equation to calculate the expansion stress. This equation does not include
calculations for the longitudinal stress due to axial loads in the pipe. CAESAR II does not
include the F/A longitudinal stress component for stress in the expansion stress equation. You
can change this by setting Add F/A In Stress to the configuration file. The program adds the
F/A longitudinal stress component, by default, to the code stress component for all other stress
categories.
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Calculate the CODETI allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable = F [1.25 (Sc + Sh)] - Sl
Sustained Allowable = Sh
Occasional Allowable = OCC * Sh
Where:
F = Cyclic Reduction Factor
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress
Sl = Sustained Stress
OCC = Occasional Load Factor from Configuration - Defaults to 1.15
Pressure stiffening using CODETI
Pressure stiffening of bends is automatically included as directed by the code. You can disable
pressure stiffening on bends in the analysis by excluding the Use Pressure Stiffening option
in the configuration file.
SIFs and flexibility coefficients using CODETI
Flexibility coefficients and SIFs are phased in for bends with an included angle between 15°
and 45°. The default value for bends smaller than 15° is 1.0.
SIFs and fabricated tees using CODETI
To determine the SIF of a fabricated tee having an angle of incidence other than 90°divide it
by (sin a)3/2
CODETI recommended occasional load factor values
Recommended occasional load factor values are 1.15, 1.2, and 1.3, as per Code Table C3.3.
CODETI requires that when "the design temperature is such that the creep
characteristics are determinant, and if a section of the piping presents locally weaker
characteristics," the sum of the primary and secondary stresses must not exceed the value
flexibility factor (from Section C1.4.3). CAESAR II does not implement this requirement and
is left for you to verify.
CODETI reducer default values
The default SIF value is 1.0. The default flexibility factor value is 1.0.
Norwegian (TBK 5-6)
Calculate pressure stiffening using TBK 5-6
Pressure stiffening of bends is required for flexibility factors only and is done by default. You can
disable pressure stiffening by excluding the Use Pressure Stiffening option in the setup file.
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You can enable pressure stiffening for stress intensification factors (SIF)s as well by
including the Use Pressure Stiffening option.
Expansion stress in TBK 5-6
Summing the longitudinal component F/A into the stress calculation is not defined by default
in the code. You can enable the axial force term in the code stress by including the Add F/A
In Stress option in the configuration file.
The code uses a circumferential weld strength factor (Z) when calculating longitudinal
pressure stress. Enter this value as Eff.
Calculate cyclic reduction factor using TBK 5-6
You can calculate the cyclic reduction factor using the following equation: F = (7000/Ne)0.2
Where
Ne = Number of Anticipated Cycles
F may be as high as 2.34 but not greater than 1.0 when Rm governs the expansion
stress allowable.
Calculate SIFs for bends and intersections using TBK 5-6
In-plane and out-of-plane SIFs for bends and intersections use the same stress equation.
Calculate the Norwegian allowable stress limits
Use the equations below to calculate the stress allowables.
Expansion Allowable = Sr + F2 - SSUS
Sustained Allowable = F2
Occasional Allowable = Occ * F2
Where:
Sr =
Minimum of 1.25F1 + 0.25F2; Fr * Rs - F2; or Fr (1.25 R1 + 0.25 R2) The latter for higher
temperatures; above 425°C for austenitic stainless steel, or above 370°C for other
materials.
F2 =
Hot Allowable Stress (entered in Sh)
OCC
Occasional Load Factor from the configuration file (defaults to 1.2)
SSUS = Sustained Stress
982
F1 =
Allowable Stress at Ambient (entered in Sc)
Fr =
Cyclic Reduction Factor
RS =
Permissible Extent of Stress for 7000 Cycles (from Code Table 10.2)
R1 =
Lesser of F1 and 0.267 RM
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Technical Discussions
R2 =
Lesser of F2 and 0.367 RM
Rm =
Ultimate Tensile Strength at room temperature
Calculate SIFs using TBK 5-6
As of this writing, SIFs or fitting types 6 (branch with raised edge radius), 7 (branch on locally
thickened pipe), 13 (conical reducer with knuckles), and 14 (reducer without knuckles) have
not been implemented in CAESAR II so you must enter them manually. The Norwegian code
offers an alternative stress analysis method in Appendix D. However, CAESAR II does not
implement this method.
TBK 5-6 reducer default values
Calculate the SIFs by using the following equation: 2.0 max or 0.5 + .01*alpha* SQRT(D2/t2).
Where:
D2 - Diameter of the Small End
t2 - Thickness of the Small End
alpha - the slope of the reducer
TBK 5-6 flexibility factor default value
The default flexibility factor value is 1.0.
FDBR
FDBR is similar to B31.1 in most requirements. For more information, see B31.1.
Calculate reinforced tees using FDBR
FDBR limits the pad thickness to a maximum equal to the header thickness. If you enter a
pad thickness that is greater than the header thickness the program overrides it with the
header thickness.
Calculate reduced intersections using FDBR
Treat intersections similar to ASME NC. For more information, see ASME NC.
Calculate butt welds using FDBR
Use either 1.0 or 1.8 depending on the thickness.
Calculate flexibility analysis using FDBR
You must use the Hot Modulus of Elasticity in your flexibility analysis.
Calculate the expansion case allowable stress using FDBR
Additionally, when computing the expansion case allowable stress you must include the ratio
of Ehot to Ecold. You can override the program computed ratio by manually entering a value
for Fac.
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Calculate reducers using FDBR
The value for the flexibility factor is 1.0 and the equation to calculate reducer SIFs is:
2.0 max or 0.5 + .01*alpha* SQRT(D2/t2)
Where:
D1 - Diameter of the Large End
t1 - Thickness of the Large End
D2 - Diameter of the Small End
t2 - Thickness of the Small End
Alpha - Reducer Cone Angle in Degrees
When not entered:
Alpha = atan[ 0.5 * (D1-D2) / (0.60 * length of the reducer element) ]
Alpha cannot exceed 60° and the larger of D1/t1 and D2/t2 cannot exceed 100.
BS 7159
BS 7159 for Fiberglass Reinforced Plastic (FRP) pipe requires that you evaluate the operating
load case only. You must verify the following operating load case combined stress
requirements are met:
If Sx is tensile:
(OPE)
and
(OPE)
or
if Sx is compressive:
If Fx/A > P(Dm)/(4t) and it is compressive
(OPE)
and
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(OPE)
Circumferential Stress
for straight pipes
for bends
for tees
Dm and t are always for the Run Pipe
Calculate the allowable stress limits using BS 7159
BS 7159 allowables are based on material design strain d. Therefore allowable stresses differ
in the axial and hoop directions by the ratio of the axial and hoop moduli of elasticity:
Sh = dEx
SHOOP = (dEx) (Eh/Ex)
Enter the ratio Eh/Ex in the allowable stress Eff field. If left blank, the value defaults to 1.0
for isotropic materials.
Calculate pressure stiffening using BS 7159
Pressure stiffening of bends is done assuming the bends are fully pressurized up to the
design strain of the components. You can exclude pressure stiffening on bends by including
the Use Pressure Stiffening option in the configuration file.
BS 7159 does not by default add F/A into the stress calculation (unless this puts an element
into compression as described above). Use the Add F/A in Stress option to tell CAESAR II to
include the axial force term into the code stress.
Calculate the fatigue factor using BS 7159
The fatigue factor Kn is used inversely relative to the cyclic reduction factor in most codes, so
its value should be greater than or equal to 1.0 (allowable stress is divided by this number). K n
is calculated as:
Kn = 1.0 + 0.25 (As/n) (Log10(n) - 3.0)
Where:
As = Stress Range During Fatigue Cycle
n = Maximum Stress During Fatigue Cycle
n = Number of Cycles During Design Life
Enter Kn in the Cyclic Reduction Factor fields.
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BS 7159 requires that you consider the thermal strain of the pipe material as being from 80% 85% below the true material strain due to insulation effects of the pipe wall. Enter this
reduction factor K in the allowable stress FAC field. If left blank, this value defaults to 1.0.
Calculate the stress intensity and flexibility factors of bends using BS 7159
The stress intensity and flexibility factors of bends vary based on laminate type:





All chopped strand
 mat (CSM) construction with internal and external surface tissue
reinforced layer.
CSM and woven
roving (WR) construction with internal and external surface tissue
reinforced layer.
CSM and multi-filament
roving construction with internal and external surface tissue

reinforced layer.
You can enter the laminate type in the Bend Type field, or set the type default on the
Special Execution Parameter dialog box.
Calculate SIFs for Reducers using BS 7159
BS 7159 does not mention reducers for SIF calculations.
UKOOA
The United Kingdom Offshore Operators Association (UKOOA) Specification and Recommended
Practice for the Use of GRP Piping Offshore is similar in many respects to the BS 7159, except
that it simplifies the calculation requirements in exchange for imposing more conservatism on the
piping operating conditions. Rather than explicitly calculating a combined stress, the specification
defines an idealized envelope of combinations of axial and hoop stresses which cause the
equivalent stress to reach failure. This curve represents the plot of:
(x / -all)2 + hoop / hoop-all)2 - [x hoop / (x-all hoop-all)] 1.0
Where:
x-all = Allowable Stress Axial
hoop-all = Allowable Stress Hoop
The specification conservatively limits you to that part of the curve falling under the line between
x-all also known as a(0:1) and the intersection point on the curve where hoop is twice x a natural
condition for a pipe loaded only with pressure. An implicit modification to this requirement is the
fact that pressure stresses are given a factor of safety typically equal to 2/3 while other stresses
are not. This gives an explicit requirement of:
Pdes f1 f2 f3 LTHP
Where:
Pdes = Allowable Design Pressure
f1 = Factor of Safety for 97.5% Lower Confidence Limit Usually
0.85 f2 = System Factor of Safety Usually 0.67
f3 = Ratio of Residual Allowable After Mechanical Loads
= 1 - (2 sab) / (r f1 LTHS)
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sab = Axial Bending Stress Due to Mechanical Loads
r = a(0:1) / a(2:1)
a(0:1) = Long Term Axial Tensile Strength In Absence Of Pressure Load
a(2:1) = Long Term Axial Tensile Strength Under Pressure Loading Only
LTHS = Long Term Hydrostatic Strength Hoop Stress Allowable
LTHP = Long Term Hydrostatic Pressure Allowable
This is implemented in the CAESAR II using the following equations:
Code Stress
ab (f2 /r) + PDm / (4t)
Code Allowable

(f1 f2 LTHS) / 2.0
Where:
P = Design Pressure
Dm = Pipe Mean Diameter
t = Pipe Wall Thickness
On the Allowable auxiliary dialog box, the product of f1 and LTHS is entered in the SH1, SH2,
SH3 fields; r is entered in the F1, F2, F3 fields; f2 is entered in the Eff field; and the temperature
reduction factor K (described for BS 7159 above) is entered in the Fac field if omitted, it
defaults to 1.0. K- and i-factors for bends and tees, and bending and pressure stresses are
calculated as described for the BS 7159.
Calculate SIFs using UKOOA
UKOOA refers to BS 7159 for SIF calculations.
IGE/TD/12
CAESAR II performs calculations as per the IGE/TD/12 Edition 2 code requirements. The
complexity of these requirements far exceeds what can be described here. We recommend that you
acquire a copy of this code from the International Institution of Gas Engineers & Managers.
Det Norske Veritas (DNV)
This code is entitled "Rules for Submarine Pipeline Systems." The Allowable Stress Design
(ASD) provisions of the code are implemented here, rather than the limit state requirements.
Calculate the Stress Intensification Factors (SIFs), flexibility factors, or section
moduli using DNV
DNV does not provide any guidance on calculating SIFs, flexibility factors, or section moduli.
An informal poll of DNV experts and users was taken and the decision was made to use the
B31.1 Power Code. Make all stress calculations using the corroded wall thickness.
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Calculate the expansion load case using DNV
There is no provision for a code check for the expansion load case, so no expansion cases
are generated under this code.
Calculate the operating, sustained, or occasional load cases using DNV
Treat the operating, sustained, or occasional load cases identically. For these load cases,
you must perform three stress calculations with different allowable limits. The stress
calculation causing the highest percent of allowable is reported in the stress report, along
with its specific allowable. These stress checks are:
Hoop Stress:
Sh ns SMYS
Hoop Stress:
Sh nu SMTS
Longitudinal Stress:
SL  n SMYS
Equivalent Stress:
Se  n SMYS
Where:
Sh = (Pi – Pe) (D – t) / 2t
Pi = Internal Pressure
Pe = External Pressure
D = Outer Diameter
t = Wall Thickness
ns = Hoop Stress Yielding Usage Factor; see Tables C1 and C2 of the DNV
Code SMYS = Specified Minimum Yield Strength at Operating Temperature
nu = Hoop Stress Bursting Usage Factor; see Tables C1 and C2 of the DNV
Code SMTS = Specified Minimum Tensile Strength at Operating Temperature
SL = Maximum Longitudinal Stress
n = Equivalent Stress Usage Factor; see Table C4 of the DNV Code
Se = [Sh2 + SL2 - ShSL + 3t2]1/2
t = Torsional Stress
Calculate reducers using DNV
DNV does not mention reducers for SIF calculations.
EN-13480
Flexibility calculations using EN-13480
EN-13480 uses the hot modulus of elasticity in the flexibility calculations (Sect 12.1.7.2).
The expansion allowable stress is subsequently modified by the ratio of Eh/Ec.
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Calculate the flexibility stresses using EN-13480
EN-13480 provides two methods of determining the flexibility stresses. The CAESAR II default
implementation is to use Sections 12.3.2 through 12.3.6, which perform an SRSS of the
bending moments with a single SIF. As an alternative, the flexibility stresses can be determined
by distinguishing between in and out of plane bending, using distinct SIFs, as discussed in
Section 12.3.1. The option to implement this alternative can be found on the "SIF & Stress" tab
of the configuration module.
EN-13480 pressure stiffening
EN-13480 does not consider pressure stiffening effects on bends.
GPTC/Z380
The recommendations of this code apply only to above ground steel piping through
450°F. GPTC/Z380 and B31.8, prior to 2004, recommendations are similar in many ways.
The differences between GPTC/Z380 and B31.8 display below:







The longitudinal
joint factors vary slightly between B31.8 Table 841.115a and GPTC/Z380 Table

192.113.
The design factor in B31.8 Table 841.114b provides more detail than GPTC/Z380 Table 192.11.

The allowable for the combined stress calculation in
GPTC/Z380 Section 192.159-1.5e includes
a "0.75" factor, while B31.8 Section 833.4 does not.

GPTC/Z380 uses a single stress intensification factor (SIF) for both in-plane and
out-of-plane loads, while B31.8 distinguishes between in-plane and out-of-plane SIFs.
ISO-14692
ISO-14692 addresses the analysis of Fiber Reinforced Plastic (FRP) pipe. Qualification is
based on the comparison of actual stresses, hoop and axial, to a failure envelope. See BS 7159
(on page 984) for the CAESAR II approach for FRP pipe analysis.
HPGSL
Calculate stress intensification factors (SIFs) for intersections using HPGSL
HPGSL provides two separate equations to calculate the in-plane and out-plane
stress intensification factors (SIFs) for intersections.
Calculate expansion stress using HPGSL
HPGSL provides an equation to calculate the expansion stress. This equation does not include
calculations for the longitudinal stress due to axial loads in the pipe. CAESAR II does not
include the F/A longitudinal stress component for stress in the expansion stress equation. You
can change this by including the Add F/A In Stress option in the configuration file. The program
adds the F/A longitudinal stress component, by default, to the code stress component for all
other stress categories.
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HPGSL girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate socket welds using HPGSL
HPGSL makes no distinction between socket welds with undercut and socket welds without
undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for
all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3.
Calculate the HPGSL stress allowables
Use the equations below to calculate the stress allowables.
Expansion Allowable =
f [ (1.25/Eff)(Sc+Sh) - Sl ]
Sustained Allowable
Sh/Eff
=
Occasional Allowable =
(Occ)*Sh/Eff
Where:
f = Cyclic Reduction Factor
Eff = Weld Joint Efficiency Minimum Wall Thickness Only
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress
SI = Sustained Stress
Occ = Occasional Load Factor Default is 1.33
When specifying a corrosion allowance, do not use a corrosion value in the sustained
and occasional stress calculations.
HPGSL reducer default values
The default SIF value is 1.0. The default Flexibility Factor value is 1.0.
HPGSL Pressure effects
Pressure effects on miters are allowed in this piping code.
JPI
Calculate stress intensification factors (SIFs) for intersections using JPI
JPI provides two separate equations to calculate the in-plane and out-plane SIFs
for intersections.
Calculate expansion stress using JPI
JPI provides an equation to calculate the expansion stress. However, this equation does not
include calculations for the longitudinal stress due to axial loads in the pipe. CAESAR II does not
include the F/A longitudinal stress component for stress in the expansion stress equation.
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The program adds the F/A longitudinal stress component, by default, to the code
stress component for all other stress categories.
JPI girth butt welds default value
The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs.
Calculate socket welds using JPI
JPI makes no distinction between socket welds with undercut and socket welds without
undercut. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3.
Calculate the JPI Stress allowables
Expansion Allowable
= f [ (1.25/Eff)(Sc+Sh) - Sl
]
Sustained Allowable
= Sh/Eff
Occasional Allowable
= (Occ)*Sh/Eff
Where:
f = Cyclic Reduction Factor
Eff = Weld Joint Efficiency minimum wall thickness only
Sc = Cold Allowable Stress
Sh = Hot Allowable Stress
SI = Sustained Stress
Occ = Occasional Load Factor Default - 1.33
When specifying a corrosion allowance, do not use a corrosion value in the sustained
and occasional stress calculations.
JPl reducer default value
The default SIF value is 1.0. The default Flexibility Factor value is 1.0.
Pressure effects and JPl
Pressure effects on miters are allowed in this piping code.
Local Coordinates
Many analytical models in engineering are based upon being able to define a real physical
object mathematically. This is accomplished by mapping the dimensions of the physical
object into a similar mathematical space. Mathematical space is usually assumed to be either
two-dimensional or three-dimensional. For piping analysis, the three dimensional space is
necessary, because almost all piping systems are three dimensional in nature.
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Two typical three-dimensional mathematical systems are shown below in Figure 1. Both of
these systems are "Cartesian Coordinate Systems". Each axis in these systems is
perpendicular to all other axes.
Figure 1 – Typical Cartesian Coordinate Systems
In addition, for these Cartesian coordinate systems the "right hand rule" is used to define
positive rotation about each axis and the relationship, or ordering, between the axes. Before
illustrating the "right hand rule", there are several traits of the systems in Figure 1 that should
be noted.









Each axis can be thought of as a "number line", where the zero point is the point where all of
the axes intersect. While only
the positive side of each axis is shown in Figure 1, each axis
has a negative side as well.
The direction of the arrow heads indicates the positive direction of each axis.

In Figure 1, the X-axis has one arrowhead, the Y-axis has two arrowheads, and the Z-axis
has three arrowheads. The circular arcs labeled RX, RY, and RZ define
the direction of
positive rotation about each axis. (This point will be dis\-cussed later.)
Any point in space can be mapped to these coordinate systems by using its position along
the number lines. For example, a point 5 units down the X-axis would have a coordinate
of (5.0, 0.0, 0.0). A point 5 units
down the X-axis and 6 units down the Y-axis would have
a coordinate of (5.0, 6.0, 0.0).
Notice that if the system on the right side of Figure 1 is rotated
a positive 90-degrees about the X
axis, the result is the system on the left side of Figure 1.
The coordinate system on the left side of Figure 1 is the default CAESAR II global coordinate
system. In this system, the X and Z axes define the horizontal plane, and the Y-axis is vertical.
The other coordinate system in Figure 1 can be obtained in CAESAR II by selecting the
Z-axis Vertical option, discussed later in this section.
All further discussion in this section targets this default coordinate system, unless other\wise noted.
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Other Global Coordinate Systems
There are other types of coordinate systems that can be used to mathematically map a
physical object.





A Polar coordinate
 system maps points in a two dimensional space using a radius and a rotation
angle (r, theta).
A Cylindrical coordinate system maps points using a radius, a rotation angle, and an
elevation (r, theta, z). The origin in this system could be considered the center of the
bottom of a cylinder. Cylindrical
coordinates are convenient to use when there is an axis of

symmetry in the model.
A Spherical coordinate system maps points using a radius and two rotation angles (r, theta,
phi). The origin in this system could be considered the center of a sphere. Spherical
coordinatesare convenient to use when there is a point which is the center of symmetry in
the model.
Typically, none of these coordinate systems are easily used to map piping systems. Most
piping software deals exclusively with the Cartesian coordinate system.
The Right Hand Rule
In the Cartesian coordinate system, each axis has a positive and a negative side, as previously
mentioned. Translations, straight-line movement, can be defined as movement along these axes.
Rotation can also occur around these axes, as illustrated by the arcs in Figure 1.
A standard rule must be applied in order to define the direction of positive rotation about these
axes. The right hand rule is used as the standard. Put the thumb of your right hand along the
axis, in the positive direction of the axis. The direction your fingers curl is positive rotation
about that axis. This is best illustrated in Figure 2.
Figure 2 – The Right Hand Rule
The right hand rule can also be used to describe the relationship between the three axes.
Mathematically, the relationship between the axes can be defined as:
X cross Y = Z (EQ 1)
Y cross Z = X (EQ 2)
Z cross X = Y (EQ 3)
Where cross indicates the vector cross product.
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Physically, using your right hand, what do the above equations mean? This question is
best answered by Figure 3.
Figure 3 – The Right Hand Rule - Continued
The left pane of Figure 3 corresponds to vector equation 3 above. Similarly, the center pane in
Figure 3 also corresponds to vector equation 3 above. The right pane in Figure 3 corresponds
to vector equation 2 above. All panes of Figure 3 refer to the left hand image of Figure 1.
Straight-line movement along any axis can be therefore described as positive or negative,
depending on the direction of motion. This straight-line movement accounts for three of the
six degrees of freedom associated with a given node point in a model.
Analysis of a model requires the discretization of the model into a set of nodes and
elements. Depending on the analysis and the element used, the associated nodes have certain
degrees of freedom. For pipe stress analysis, using 3D Beam Elements, each node in the
model has six degrees of freedom.
The other three degrees of freedom are the rotations about each of the axes. In accordance with the
right hand rule, positive rotation about each axis is defined as shown in Figures 1 and 2.
When modeling a system mathematically, there are two coordinate systems to deal with, a
global or model coordinate system and a local (or elemental) coordinate system. The global
or model coordinate system is fixed, and can be considered a constant characteristic of the
analysis at hand. The local coordinate system is defined on an elemental basis. Each element
defines its own local coordinate system. The orientation of these local systems varies with the
orientation of the elements.
An important concept here is the fact that local coordinate systems are defined by, and
therefore associated with, elements. Local coordinate systems are not defined for, or
associated with, nodes.
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Pipe Stress Analysis Coordinate Systems
As noted previously, most pipe stress analysis computer programs use the 3D Beam Element.
This element can be described as an infinitely thin stick, spanning between two nodes. Each
of these nodes has six degrees of freedom three translations and three rotations. Piping
systems models are constructed by defining a series of elements, connected by nodes. These
pipe elements are typically defined as vectors, in terms of delta dimensions referenced to a
global coordinate system. Several example pipe elements are shown below in Figure 4.
Figure 4 - Example Pipe Elements
For most pipe stress applications, there are two dominant global coordinate systems to choose
from, either Y-axis or Z-axis up. These two systems are depicted in Figure 1. As previously
noted, the global coordinate system is fixed. All nodal coordinates and element delta
dimensions are referenced to this global coordinate system. For example, in Figure 4 above, the
pipe element spanning from node 10 to node 20 is defined with a DX (delta X) dimension of 5 ft.
Additionally, node 20 has a global X coordinate 5 ft. greater that the global X coordinate of node
10. Similar statements could be made about the other two elements in Figure 4, only
these elements are aligned with the global Y and global Z axes.
In CAESAR II, you can choose between the two global coordinate systems shown in Figure 1.
By default, the CAESAR II global coordinate system puts the global Y-axis vertical, as shown
in the left half of Figure 1, and in Figure 4. There are two ways to change the CAESAR II
global coordinate system so that the global Z-axis is vertical.
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The first method is to modify the configuration file in the current data directory. This can be
accomplished from the Main Menu, by selecting Tools>Configure Setup. After the
configuration dialog appears, select the Geometry tab, as shown in Figure 5. On this tab,
click the Z-axis Vertical check box, as shown in the figure below.
Figure 5 - Geometry Configuration
After the Z axis Vertical check box is selected, the CAESAR II global coordinate system is
in accordance with the right half of Figure 1. This configuration affects all new jobs created in
this data directory. Existing jobs with the Y-axis vertical are not affected by this configuration
change.
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The second method to obtain a global coordinate system with the Z-axis vertical is to switch
coordinate systems from within the input for the specific job at hand. This can be
accomplished from the Special Execution Parameters dialog box of the piping input
processor. This dialog box is shown below in Figure 6.
Figure 6 - Special Execution Parameters Dialog
Checking the Z Axis Vertical check box immediately changes the orientation of the global
coordinate system axis, with corresponding updates to the element delta dimensions.
However, the relative positions and lengths of the elements are not affected by this switch.
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Defining a Model
Using the CAESAR II default coordinate system (Y axis vertical), and assuming the
system shown below in Figure 7, the corresponding element definitions are given in Figure 8.
Figure 7 - Sample Piping Model
Figure 8 - Sample Piping Model Element Definitions
For this sample model, most of the element definitions are very simple:







The first element,
10-20, is defined as 5 ft. in the positive global X direction. This element starts at
the model origin.
The second element, 20-30, is defined as 5 ft. in the positive global Y direction.
This element
begins at the end of the first element, because both elements share node 20.
The third element, 30-40, is defined as 5 ft. in the negative global Z direction. Note in Figure
8 that the delta dimension for this element
is a negative number. This is necessary to define

the element in a negative direction.
The fourth element, 40-50, runs in both the positive global X and negative global Y
directions. This element slopes to the right and down, and is defined with delta dimensions
in both the DX and DY fields. Notice that these
 delta dimensions are equal in magnitude;
therefore this element slopes at 45 degrees.
Continuing the model, from node 50, along the same 45 degree slope can be rather tedious,
because most often only the overall element length is known, not its components in the global
directions. In CAESAR II this can be best accomplished by activating the Edit Deltas dialog box,
shown below in Figure 9. The Edit Deltas dialog box can be activated by clicking the Browse button
next to the DX field. Using this dialog box, you can enter the element length, and
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CAESAR II determines the appropriate components in the global directions, based on
the current direction cosines, which default to those of the preceding element.
Figure 9 - Edit Deltas Dialog Box
CAESAR II provides an additional coding tool, for longer runs of pipe with uniform node
spacing. Element Break enables you to break an element into equal length segments, given a
node number increment.
In the preceding example, the model is defined solely using delta dimensions. By
constructing the model in this fashion, it is assumed that the world coordinates of node 10 the
first node in the model are at (0., 0., 0.). This assumption is acceptable in all but one
instance, when environmental loads are applied to the model. In this instance, the elevation
of the model is critical to the determination of the environmental loads, and therefore must be
specified. In CAESAR II, the specification of the starting node of the model can be
accomplished using the Alt+G key combination, and all nodal coordinates are displayed as
absolute coordinates. Regardless of whether or not the global coordinates of the starting
node are specified, the relative geometry of the model will plot the same.
After a model has been defined, there are a number of operations that can be performed on
the entire system, or on any section of the system. These operations include:



Translating the model: translation can be accomplished by specifying the global coordinates
of the starting node of the model. If the model consists of disconnected
segments, CAESAR

II requests the coordinates of the starting node of each segment.
Rotating the model: by using the List processor or by clicking List Input
. The List
processor presents the model in a spreadsheet, format, as shown in Figure 8. Options in
this processor allow you to rotate the model about any of the three global axes, or a
specified amount. For example, if the model shown in Figures 7 and 8 is
rotated a negative 90 degrees about the global Y-axis, the result is as shown in Figure 10.
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