CAESAR II Statics Training
CAESAR II Version 2011 - Statics Training
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CAESAR II Statics Training
Introduction
Contents
Introduction ..................................................................................................................... 6
Interface .............................................................................................................................................. 6
Default Data Directory .................................................................................................................... 6
Units .................................................................................................................................................... 7
Create Custom Units File................................................................................................................. 7
F = Kx Example .................................................................................................................................... 9
Model Input .................................................................................................................................. 12
Load Case Editor............................................................................................................................ 16
Hand Calculation ........................................................................................................................... 18
Output Processor .......................................................................................................................... 19
Axial ............................................................................................................................................... 21
Theory and Development of Pipe Stress Requirements ................................................... 25
Basic Stress Concepts ........................................................................................................................ 25
Example ......................................................................................................................................... 30
3D State of Stress in the Pipe Wall.................................................................................................... 33
Failure Theories................................................................................................................................. 36
Maximum Stress Intensity Criterion ................................................................................................. 38
Code Stress Equations....................................................................................................................... 40
B31.1 Power Piping ....................................................................................................................... 40
Pipe 1 ............................................................................................................................. 42
Input Model ...................................................................................................................................... 43
Error Checking ................................................................................................................................... 52
Review Load Cases ............................................................................................................................ 54
Review Results .................................................................................................................................. 55
Supt 01 ........................................................................................................................... 64
Locating Supports ............................................................................................................................. 65
Adding Supports to Model ............................................................................................................ 69
Analyse .............................................................................................................................................. 75
Fix Model........................................................................................................................................... 80
Place Spring Hangers..................................................................................................................... 87
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CAESAR II Statics Training
Introduction
Turbo ............................................................................................................................. 92
Model Inlet ........................................................................................................................................ 93
Combine Models ............................................................................................................................... 98
NEMA SM23 .................................................................................................................................... 100
Manifold ...................................................................................................................... 111
API 610 Analysis .............................................................................................................................. 120
Tutor ............................................................................................................................ 128
Boundary Conditions................................................................................................................... 130
API 610 Analysis .............................................................................................................................. 136
Fix Model – Part 1 ........................................................................................................................... 139
Include WRC 297 flexibilities....................................................................................................... 139
Review Results ............................................................................................................................ 141
Fix Model – Part 2 ........................................................................................................................... 143
Build Steel Structure ................................................................................................................... 144
Combine Pipe and Steel models ................................................................................................. 154
Review Results ............................................................................................................................ 157
Fix Model – Part 3 ........................................................................................................................... 158
Loop Optimisation Wizard .......................................................................................................... 161
Fix Model – Part 4 ........................................................................................................................... 166
Model the Expansion Joint Assembly ......................................................................................... 170
Document the Analysis ................................................................................................................... 174
Custom Reports........................................................................................................................... 174
Filters........................................................................................................................................... 178
Generate Report ......................................................................................................................... 179
ISOGEN Stress Isometrics ............................................................................................................ 182
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CAESAR II Statics Training
Introduction
Cool H20 – FRP Piping.................................................................................................... 194
Basics of Fibreglass Piping Analysis ................................................................................................. 195
CAESAR II’s Orthotropic Model for Piping Systems ........................................................................ 198
Requirements of the ISO 14692 Code............................................................................................. 199
Allowable Stress Data for this Model.............................................................................................. 202
Configuration Options for FRP Piping: ............................................................................................ 204
Model the system ........................................................................................................................... 206
Load Case Setup .............................................................................................................................. 213
Review Results ................................................................................................................................ 213
Solving Expansion Problems ........................................................................................................... 214
Static Seismic Using the ASCE 7-05: ................................................................................................ 214
Inertial Loads ............................................................................................................................... 214
Seismic Data Input ...................................................................................................................... 219
Load Case Setup .......................................................................................................................... 223
Review Results ............................................................................................................................ 225
Gas Transmission Pipeline - Buried Pipe ........................................................................ 228
B31.8 Design Code .......................................................................................................................... 229
Modelling the system ..................................................................................................................... 229
Material Database........................................................................................................................... 234
Buried Pipe Modeller ...................................................................................................................... 237
Restraint Parameters .................................................................................................................. 237
American Lifelines Alliance Clay Model ...................................................................................... 238
American Lifelines Alliance sand model: .................................................................................... 240
Meshing Parameters ................................................................................................................... 241
Virtual Anchor Length (VAL):....................................................................................................... 243
Bury Pipe ..................................................................................................................................... 244
Load Case Setup .............................................................................................................................. 249
Results Review ................................................................................................................................ 250
Fatigue ............................................................................................................................................ 251
Setting up the Fatigue Load cases............................................................................................... 251
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CAESAR II Statics Training
Introduction
Riser ............................................................................................................................. 254
Modelling ........................................................................................................................................ 255
Injection Line ............................................................................................................................... 256
Product Line ................................................................................................................................ 260
Jacket .............................................................................................................................................. 261
Hydrodynamic Theory..................................................................................................................... 264
B31.4 Code Requirements .............................................................................................................. 265
Hydrodynamic Input ....................................................................................................................... 266
Wave Solution ................................................................................................................................. 267
Hydrodynamic Coefficients ......................................................................................................... 272
Wind Loading .................................................................................................................................. 274
Load Case Setup .............................................................................................................................. 277
Analysis ........................................................................................................................................... 278
SUPT01 – Water Hammer ............................................................................................. 280
Edit the Model ................................................................................................................................ 281
Determine the Load ........................................................................................................................ 282
Define the Occasion Load ........................................................................................................... 283
Load Case Setup .............................................................................................................................. 283
Check the Results ............................................................................................................................ 284
Reset the Load Cases ...................................................................................................................... 284
Check Results .................................................................................................................................. 285
Correct model ................................................................................................................................. 286
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CAESAR II Statics Training
Introduction
Introduction
CAESAR II is pipe stress analysis software which uses beam theory to evaluate piping systems to
numerous international standards. CAESAR II is not Finite Element Analysis (FEA) software, but
instead uses a stick model built up of elements connected by nodes.
This course will introduce CAESAR II and demonstrate various modelling and analysis methods in
order to evaluate and correct piping systems.
Interface
When starting CAESAR II, the Main Window appears. This is the window where all tasks are started
from. This includes opening/creating an input file, reviewing Load Cases, reviewing results or
accessing any auxiliary modules such as WRC 107/297 processor or the ISOGEN stress isometrics
module. All modules open up in their own separate window.
When opening a new file, the file will open, but you will return to the Main Window. You can then
choose to go to the Input processor, Output processor or the results for this file.
These modules (and other auxiliary modules) and their interfaces will be introduced as they occur
throughout the training.
Default Data Directory
CAESAR II has the option to specify the default working directory – that is all files working with will
be saved/opened from this default location. Of course it is still possible to navigate using windows
explorer functions, this setting is just the default location when selecting New/Open.
Select File > Set Default Data Directory from the CAESAR II Main window
Click on the ellipsis button at the end of the text field and browse to E:\Training\CAESAR II\Exercises
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CAESAR II Statics Training
Introduction
Units
CAESAR II performs all internal calculations in English units. To enable the entry and review of data in
alternative units (such as SI), units files are used by CAESAR II. These units files simply convert the
internal CAESAR II English units to the user’s preferred unit. Each CAESAR II file (referred to as a “Job
File”) uses a particular units file which is specified on creation of the job. Files can be converted
from one units file to another if required. The units files have the extension *.FIL and are located in
the CAESAR II System directory, or in the same directory as the job file. The file to use is specified in
the Configuration file.
Create Custom Units File
Throughout this course, we wish to use specific units for various parameters such as Pressure,
Density etc. As such we require a units file which is different to the supplied default files. So we will
create our own CAESAR II units file.
Select Tool > Make Units Files from the Main Window
This allows the creation of new units files, or the review of existing units files, useful if you receive a
units file from a colleague and wish to check the units in use in the file.
Choose to Create New Units File and for the template file to use as a start point, select *MM.FIL.
Give the new file a name and click View/Edit file.
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CAESAR II Statics Training
Introduction
In the Units File dialogue box, change the following units from the MM defaults:
Stress

Pressure

Elastic Modulus 
Pipe Density 
Insul. Density 
Fluid density 
Transl. Stiffness 
Uniform Load 
N/sq.mm.
bars
N/sq.mm.
kg/cu.m.
kg/cu.m.
kg/cu.m.
N/mm
N/mm
Ensure Nominals is set to ON. This allows the entry of pipe nominal sizes and schedules into the
input, which will be converted to actual diameters and wall thicknesses (e.g. enter 4 into the
diameter field and CAESAR II will convert this to 114.3mm).
Give the file a label as well to easily identify the file.
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CAESAR II Statics Training
Introduction
F = Kx Example
As CAESAR II uses a stick model, and beam theory, it is easy to prove this using a simple cantilever
example. This example will introduce the basic modelling methods in CAESAR II and introduce the
Input Spread Sheet, Load Case editor and the Output Processor. In addition, we can check the
CAESAR II results against some simple hand calculations.
CAESAR II calculates forces using
. Using the example below, we will create a simple
cantilever model, fixed at one end, and apply a displacement of 2mm at the other end. We can then
calculate the force required to generate this 2mm displacement – and see this in the results.
First we will create the model in CAESAR II.
Create a new file in CAESAR II, called FKLateral
After creating the new job file, the first time it has opened, the units will be displayed to the user for
confirmation. You will notice that the units file displayed here for our file is English (CAESAR II
default units) not the units file we have just created. By default, CAESAR II uses the units file set in
the Configuration/Setup as the default file for new jobs (and also as the units to use to display the
output results).
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CAESAR II Statics Training
Introduction
Click OK on the units review screen and the input spread sheet will open. To confirm/check the
units, hover over any field in the input – the units used in this field will be displayed in the tooltips.
For example, we changed the pressure units to bars, but the pressure field displays the units as
lb./sq.in.
Close the input screen – we will change the units and return to the input with the correct units
displayed.
In the CAESAR II main window select Tools > Configure/Setup
In the window which appears, select Database Definitions from the categories tree on the left.
Now change the Units File Name setting to the units file just created.
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CAESAR II Statics Training
Introduction
Save and exit.
Return to the Piping Input. Again, the units file to be used will be displayed – this should now be
your custom units file.
Verify that the correct units are in use via the tooltips
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CAESAR II Statics Training
Introduction
Model Input
We will now create the simple cantilever model and apply a 2mm displacement at the free end.
The model will be as follows:
One element 10m in length going from node 10 to node 20 in the X direction, anchored at one end.
8” pipe with Standard wall thickness.
The input spread sheet will have defaulted to nodes 10 to 20, so simply enter 10000 in the DX field.
We are in mm units already.
Enter the pipe diameter and wall thickness – this is 8” NS and STD wall thickness. As we have
“nominals” set to ON, simply type in 8 in the diameter and hit enter. The actual OD for 8” pipe will
be inserted. Repeat for the wall thickness, simply type in “S” and press enter.
Now we must fill in the pipe properties. We need to know the material properties to carry out the
analysis. Select A106 – B from the list of materials. Notice that all materials have a number to
identify it, you can simply type in the material number here - in the case of A106-B this is 106.
Selecting the material will fill in the Elastic modulus and Poisson ratio and various material
allowables under the Allowable Stress area, depending on the design code selected (B31.3 default).
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CAESAR II Statics Training
Introduction
That is our pipe itself. We now need to anchor it at one end (node 10) and apply a displacement at
the other end (node 20).
Place the anchor by double clicking the Restraints check box. All the check boxes shown in the
middle column on the spread sheet must be double clicked to check/uncheck.
To define a restraint you must specify a minimum of the node that the restraint will be attached to,
plus the type of restraint. Press F1 for more information on the different restraint types. We need
an anchor, so select ANC and locate it at node 10.
Now we will apply the 2mm displacement at the opposite end. Double click the Displacements
check box to apply a displacement.
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CAESAR II Statics Training
Introduction
Specify the displacement at node 20, and specify a 2mm displacement downwards in the Y direction
– i.e. enter -2 in the DY row.
Leave the remaining rows empty – do not specify 0. Specifying 0 fixes the node in the specified
direction. Entering 0 in each row would be the same as an anchor. Leaving the values blank leaves
the remaining directions free.
Finally to complete the analysis we must specify a design temperature and pressure. In our case
these are not really relevant as we are only concerned with displacement, so just enter 21°C in T1
and 1bar in P1 fields.
The file can now be analysed.
Before analysis the input must be error checked in order to identify any issues which may prevent
the analysis running (such as specifying both an anchor and an applied displacement at the same
point), or anything which may provide incorrect results (such as Stress Intensification factors not
present at a geometric intersection).
Run the error checker to check the model.
You should see only one note in the error checker report – the C of G. This can be useful for
identifying problems such as incorrect densities applied – giving an incorrect weight for example.
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CAESAR II Statics Training
Introduction
If you receive anything other than this C of G, review the model for any issues. A common error on
this exercise is the following:
This indicates that the displacement and the anchor have been specified at the same location. Check
that the Anchor is specified at Node 10 and the displacement is specified at Node 20.
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CAESAR II Statics Training
Introduction
Load Case Editor
Once the error check is successful, we can create load cases to analyse the system. Access the load
case editor. This button is only available after a successful error check.
The load case editor will be shown.
The default load cases are the Operating, Sustained and Expansion cases, as required by the design
codes such as B31.3. Remove all these load cases, as we are only concerned with the displacement.
Add one new row.
Into the load case we can add any of the loads defined in the input into the load case. As we are
only concerned with the displacement, drag in D1 – Displacement Case #1 into the L1 row.
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CAESAR II Statics Training
Introduction
Also select the stress type as SUS(tained).
The analysis will now take into account only the displacement reaction.
Before we analyse the piping system, let us first perform the hand calculation in order to check.
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CAESAR II Statics Training
Introduction
Hand Calculation
As we know,
The stiffness K is
; Where D = Pipe OD and d = Pipe ID
E being Modulus of Elasticity and L being the length.
So if we wish to know what force is required to displace the cantilever 2mm, we can calculate this
quite easily.
So for a 2mm displacement, the force required is
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CAESAR II Statics Training
Introduction
Output Processor
Back in CAESAR II, run the analysis by clicking on the “Running Man” icon from within the load case
editor.
You will see the following message explaining that certain loads have been defined in the model but
are not included in any of the load cases to be analysed – this is OK in our case, but can serve as a
useful warning if you have may loads/load cases defined. Select OK as is…Continue and click OK to
analyse.
Once the analysis is complete, the Output Processor will be shown. We can view various results for
any load case from here, plus general model reports such as the Input Echo. These reports can be
viewed on screen, or output to Word/Excel/Text or straight to a printer.
In addition Custom report templates can be created, and any available report can be selected and
added to the Output viewer Wizard, and exported/viewed to create/view a comprehensive report
very quickly.
For now we will just check the displacement at node 20 to verify that it is 2mm, and the force at
node 20 to check against out hand calculation.
Select the load case (SUS) D1 and the Displacements standard report and click to show on screen:
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CAESAR II Statics Training
Introduction
The DY at Node 20 is -2mm, as we specified.
Now to check the force at node 20; view the Global Element Forces report.
37 N as we calculated.
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CAESAR II Statics Training
Introduction
Axial
We can repeat this exercise for axial forces. This is a simple change in the model changing the
displacement from the Y to the X direction.
The analysis can be quickly re-run in cases where a change such as this has been made by using the
Batch Run “Double Running Man” icon. This will run the error checker followed immediately by the
analysis (providing there are no Errors).
The force should be as follows:
We are still using F = Kx, but we are using the Axial stiffness.
Therefore:
110,021 N/mm
So for an axial extension of 2mm, the force required is
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CAESAR II Statics Training
Introduction
The CAESAR II results, Global Element forces report should verify this:
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CAESAR II Statics Training
Introduction
The forces calculated such as in the previous example produce bending moments throughout the
piping system. Bending moment is produced when a Force is applied at a distance – MB = F x L
Once the bending moment has been calculated, beam theory is used in order to calculate the stress
at this point.
rearranges to
is the section modulus Z. So this reduces further to
The stresses are calculated using this basic theory and compared to the allowable stresses in the
design codes. CAESAR II has many design codes available, all of which have evolved separately over
time, thus the way the stresses are calculated for each specific code are slightly different. However,
looking at one of the most common piping codes – B31.3 – it can be seen that the equations used
are based on the basic bending as detailed above.
B31.3 Chemical Plant and Petroleum Refinery Piping
Sustained:
Expansion:
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CAESAR II Statics Training
Introduction
As can be seen, the equations essentially use bending stress M/Z. The equations are a little more
complicated than the basic cantilever example for the following reasons:




To address piping systems in 3 dimensions
To address areas in a piping system where particular geometry/components, such as at a
branch connection or a bend, can increase the stress, and therefore the likelihood of failure.
At these points, the stress is increased by a Stress Intensification Factor (SIF) known as i. The
design codes contain formulae to calculate these SIFs.
Stresses can also be caused by Pressure and Axial Forces
The Stresses are categorised into Sustained, Expansion and Occasional, as detailed below.
Sustained Stress: This is primary stresses caused by primary loadings such as the weight and
pressure of the piping system.
Expansion Stress: Expansion stresses are secondary stresses caused by secondary loadings such as
the thermal expansion and applied displacements.
Occasional Stress: Combines sustained stresses with those produced by an occasional loading such
as earthquake of relief valve operation. As these are occasional loads, the allowable can be
increased by a scalability factor, k. k is usually dependant of the duration or frequency of the
occasional load.
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Theory and Development of Pipe Stress Requirements
Basic Stress Concepts
Normal Stresses: Normal stresses are those acting in a direction normal to the face of the crystal
structure of the material, and may either be tensile or compressive in nature. In fact in piping,
normal stresses tend more to be in tension due to the predominant nature of internal pressure as a
load case. Normal stresses may be applied in more than one direction, and may develop from a
number of different types of loads. For a piping system these are:
Longitudinal Stress: Longitudinal or axial stress is the normal stress acting along the axis of the pipe.
This may be caused by an internal force acting axially in the pipe.
Where:
Longitudinal Stress
Internal axial force acting on cross section
Cross sectional area of pipe
(
)
Outer diameter
Inner diameter
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
A specific instance of longitudinal stress is that due to internal pressure:
⁄
Design pressure
Internal area of pipe
⁄
Replacing the terms for the internal and metal areas of the pipe, the previous equation may be
written as
⁄
Or:
⁄
For convenience the longitudinal pressure stress is often conservatively approximated as
Bending Stress: Another component of axial normal stress is bending stress. Bending stress is zero
at the neutral axis of the pipe and varies linearly across the cross-section from the maximum
compressive outer fibre to the maximum tensile outer fibre. Calculating the stress as linearly
proportional to the distance from the neutral axis:
⁄
Where:
Bending moment acting on cross section
Distance of point of interest from neutral axis of cross section
Moment of inertial of cross section
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
The maximum bending stress occurs where c is highest – the maximum value c can be is equal to the
radius of the pipe.
⁄
=
Where:
Outer radius of pipe.
Section modulus of pipe
Summing all components of longitudinal normal stress (for axial and bending):
Hoop Stress: Hoop stress is another of the normal stresses present in the pipe and is caused by
internal pressure. This stress acts in a direction parallel to the pipe circumference.
The magnitude of the hoop stress varies through the pipe wall and can be calculated by Lame’s
equation as:
(
)
Where:
Hoop stress due to pressure
Inner radius of pipe
Outer Radius of pipe
Radial position where stress is being considered
The hoop stress can be approximated conservatively for thin-wall cylinders by assuming that the
pressure force applied over an arbitrary length of pipe, l is resisted uniformly by the pipe wall over
that same arbitrary length.
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Or conservatively
Radial Stress: Radial Stress is the third normal stress present in the pipe wall. It acts in the third
orthogonal direction – parallel to the pipe radius. Radial stress is caused by internal pressure and
varies between a stress equal to the internal pressure at the pipe’s inner surface, and a stress equal
the atmospheric pressure at the pipe’s external surface. Assuming that there is no external
pressure, radial stress is calculated as:
Where
Radial stress due to pressure
Note that radial stress is zero at the outer radius of the pipe, where the bending stresses are
maximised. For this reason, this stress component has traditionally been ignored during the stress
calculations.
Shear Stresses: Shear Stresses are applied in a direction parallel to the face of the plane of the
crystal structure of the material and tend to cause adjacent planes of the crystal to slip against each
other. Shear stresses may be caused by more than one type of applied load. For example, shear
stress may be caused by shear forces acting on the cross section.
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Where:
Maximum shear stress
shear force
shear form factor. Dimensionless quantity (1.333 for solid circular section)
These shear stresses are distributed such that they are at the maximum at the neutral axis of the
pipe and zero at the maximum distance from the neutral axis. Since this is the opposite of the case
with bending stresses and since these Shear stresses are usually small, shear stresses due to forces
are traditionally neglected during pipe stress analysis.
Shear Stresses may also be caused by torsional loads.
⁄
Where:
Internal torsional moment acting on cross-section
distance of point of interest from torsional centre (intersection of neutral axes) or cross section
torsional resistance of cross section
(
)
Maximum torsional stress occurs where c is maximised. Again at the outer radius.
⁄
Summing the individual components of the shear stress, the maximum shear stress acting on the
pipe cross section is:
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
As noted above, a number of the stress components described above have been neglected for
convenience during calculation of pipe stresses. Most piping codes require stresses to be calculated
using some form of the following equations:
Longitudinal Stress:
Shear Stress:
Hoop Stress:
Example
This example calculation illustrates for a 6” nominal diameter, standard schedule pipe (assuming the
piping loads are known):
Cross sectional properties
Outside diameter
Mean thickness
Inside diameter
154.076mm
Cross sectional Area
–
(
–
(
Moment of Inertia
–
(
)
)
–
(
Section Modulus
)
)
⁄
⁄
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Piping loads
Bending Moment
Axial Force
Internal Pressure
Torsional Moment
Stresses
Longitudinal Stress
Shear Stress
Hoop Stress
Bending Component of
Longitudinal stress
is the radius where the stress is being considered. This will be at a
maximum value at the outer surface where
⁄
(
)
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Torsional Stress
The maximum torsional stress occurs at the outer radius where
again
– at the outer surface
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
3D State of Stress in the Pipe Wall
During operation, pipes are subject to all these types of stresses. Examining a small cube of metal
form the most highly stressed point of the pipe wall, the stresses are distributed as so:
There are an infinite number of orientations in which this cube could have been selected, each with
a different combination of normal and shear stresses on the faces. For example, there is one
orientation of the orthogonal stress axes for which one normal stress is maximised and another for
which one normal stress is minimised – in both cases; all shear stress components are zero. In
orientation in which the shear stress is zero, the resulting normal components of the stress are
termed the principal stresses. For 3-dimensional analyses, there are three of them and they are
designated S1 (the maximum), S2 and S3 (the minimum). Note that regardless of the orientation of
the stress axes, the sum of the orthogonal stress components is always equal, i.e.:
The converse of these orientations is that in which the shear stress component is maximised (there
is also an orientation in which the shear stress is minimised, but this is ignored since the magnitudes
of the minimum and maximum shear stresses are the same); this is appropriately called the
orientation of maximum shear stress. The maximum shear stress in a three dimensional state of
stress is equal to ½ the difference between the largest and smallest of the principal stresses (S1 and
S3).
The values of the principal and maximum shear stress can be determined through the use of Mohr’s
circle. The Mohr’s circle analysis can be simplified by neglecting the radial stress component,
therefore considering a less complex (i.e. 2D) state of stress. A Mohr’s circle can be developed by
plotting the normal vs. shear stresses for the two known orientations (i.e. longitudinal stress vs.
shear and hoop stress vs. shear), and constructing a circle through the two points. The infinite
combinations of normal and shear stresses around the circle represent the combinations present in
the infinite number of possible orientations of the local stress axes.
A differential element at the outer radius of the pipe (where bending and torsional stresses are
maximised and the radial normal and force-induced shear stresses are usually zero) is subject to 2D
plane stress and thus the principal stress terms can be computed from the following Mohr’s circle:
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
The centre of the circle is at
and the radius is equal to(*
+
)
. Therefore
the principal stresses S1 and S2 are equal to the centre of the circle, plus or minus the radius
respectively. The principal stresses are calculated as:
*(
)
+
*(
)
+
and
As noted above, the maximum shear stress present in any orientation is equal to
Continuing our example:
Mohr’s Circle of Stress
Centre of circle
Radius of Circle
√(
√(
)
)
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Maximum Principal Stress S1
√(
√(
)
)
Or from the Mohr’s circle above, S1 = 78.07 + 50.59 = 128.66 MPa
Maximum Principal Stresses S2 and S3
√(
√(
)
)
Or from the Mohr’s circle, S2 = 78.07 – 50.59 = 27.48 MPa
S3 = S2
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Failure Theories
The calculated stresses are not much use on their own, until they are compared to material
allowables. Material allowable stresses are related to strengths as determined by material uniaxial
tests, therefore calculated stresses must also be related to the uniaxial tensile test. This relationship
can be developed by looking at available failure theories.
There are three generally accepted failure theories which may be used to predict the onset of
yielding in a material:



Octahedral Shear or Von Mises theory
Maximum Shear or Tresca Theory
Maximum Stress or Rankine Theory
These theories relate failure in an arbitrary 3D stress state in a material to failure in the stress state
found in a uniaxial tensile test specimen, since it is that test that is most commonly used to
determine the allowable strength of commonly used materials. Failure of a uniaxial tensile test
specimen is deemed to occur when plastic deformation occurs, i.e. when the specimen yields; that
is, release of the load does not result in the specimen returning to its original state.
The three failure theories state:
Von Mises:
“Failure occurs when the octahedral shear stress in a body is equal to the octahedral
shear stress at yield in a uniaxial tension test”
The octahedral shear stress is calculated as:
√
In a uniaxial tensile test specimen at the point of yield:
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Therefore the octahedral shear stress in a uniaxial tensile test specimen at failure is calculated as:
√(
)
(
)
√
Therefore under the Von Mises theory:
Plastic deformation occurs in a 3-Dimensional
stress state whenever the octahedral shear stress
𝑆𝑦𝑖𝑒𝑙𝑑
exceeds √
Tresca:
“Failure occurs when the maximum shear stress in a body is equal to the maximum
shear stress at yield in a uniaxial tension test.
The maximum shear stress is calculated as:
In a uniaxial tensile test specimen at the point of yield:
Therefore
Therefore, under Tresca theory
Plastic deformation occurs in a 3-Dimensional
stress state whenever the maximum shear stress
exceeds
𝑆𝑦𝑖𝑒𝑙𝑑
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Rankine:
“Failure occurs when the maximum tensile stress in a body is equal to the
maximum tensile stress at yield in a uniaxial tension test”
The maximum tensile stress is the largest, positive principal stress, S1 (by definition, S1 is always the
largest of the principal stresses.)
In a uniaxial tensile test specimen at the point of yield:
Therefore, under Rankine theory:
Plastic deformation occurs in a 3-Dimensional
stress state whenever the maximum shear stress
exceeds 𝑆𝑦𝑖𝑒𝑙𝑑
Maximum Stress Intensity Criterion
Most of the piping codes use a slight modification of the maximum shear stress theory for flexibility
related failures. Repeating, the maximum shear stress theory predicts that failure occurs when the
maximum shear stress in a body equals
, the maximum shear stress existing at failure during
the uniaxial tensile test. Recapping, the maximum shear stress in a body is given by:
For a differential element at the outer surface of the pipe, the principal stresses were computed
earlier as:
√(
)
√(
)
As seen previously, the maximum shear stress theory states that during the uniaxial tensile test the
maximum shear stress at failure is equal to one-half of the yield stress, so the following requirement
is necessary:
√
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Multiplying both sides by 2 creates the stress intensity, which is an artificial parameter defined
simply as twice the maximum shear stress. Therefore the Maximum Stress Intensity Criterion, as
adopted by most piping codes, dictates the following requirement:
√
Note that when calculating only the varying stresses for fatigue evaluation purposes, the pressure
components drop out of the equation. If an allowable stress based upon a suitable factor of safety is
used, the Maximum Stress Intensity criterion yields an expression very similar to that specified by
the B31.3 code:
√
Where:
longitudinal normal stress due to bending
shear stress due to torsion
allowable stress for loading case
Continuing our example for the 6” diameter, standard wall pipe, in which longitudinal, shear and
hoop stresses were calculated:
Assuming that the yield stress of the pipe material is 206 MPa (30,000 psi) at operating temperature,
and a factor of safely of 2/3 is to be used, the following calculations must be made:
√
√
The 101.185 MPa is the calculated stress intensity in the pipe wall, while the 137.33 MPa is the
allowable stress intensity for the material at the specified temperature. In this case, the pipe would
appear to be safely loaded under these conditions.
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Code Stress Equations
The piping code stress equations are a direct outgrowth of the theoretical and investigative work
discussed above, with specific limitations established by Markl in his 1955 paper. The stress
equations were quite similar throughout the piping codes (i.e. between B31.1 and B31.3) until the
winter of 1974 when the power codes having observed that Markl was incorrect in neglecting
intensification of the torsional moment in a manner analogous to the bending component,
combined the bending and torsional stress terms, thus intensifying torsion.
It should be noted that the piping codes calculate exactly the stress intensity (twice the maximum
shear stress) only for the expansion stress, since this load case contains no hoop or radial
components and thus becomes an easy calculation. Including hoop and radial stresses (present in
sustained loadings only) in the stress intensity calculation makes the calculation much more difficult.
When considering the hoop and radial stresses, it is no longer clear which of the principal stresses is
largest and which is the smallest. Additionally the subtraction of S1 – S3 does not produce a simple
expression for the stress intensity. As it turns out the inclusion of the pressure term can be
simplified by adding only the longitudinal component of the pressure stress directly to the stress
intensity produced moment loading only. This provides an equally easy to use equation and
sacrifices little as far as accuracy is concerned.
The explicit stress requirements for the B31.1 piping code addressed by CAESAR II follows. Note that
most codes allow for the exact expression for pressure stress
to be using in place of
in
the sustained stress calculations.
Note also that there are many additional piping codes addressed by CAESAR II.
B31.1 Power Piping
The B31.1 code requires that the engineer calculate sustained, expansion and occasional stresses,
exactly defined as below:
Sustained
Where:
= sustained stress
= intensification factor
= resultant moment due to sustained (primary) loads
√
= basic allowable material stress at the hot (operating) temperature, as per Appendix A of
B31.1 Code. Sh is roughly defined as the minimum of:
1. ¼ of the ultimate tensile strength of the material at operating temperature
2. ¼ of the ultimate tensile strength of the material at room temperature
3. 5/8 of the yield strength of the material at operating temperature (90% of the
yield stress for austenitic stainless steels)
4. 5/8 of the yield strength of the material at room temperature (90% of the yield
stress for austenitic stainless steels)
5. 100% of the average stress for a 0.01% creep rate per 1000 hours
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CAESAR II Statics Training
Theory and Development of Pipe Stress Requirements
Expansion
Where:
= expansion stress range
= resultant range of moments due to expansion (secondary) loads
=√
= Allowable expansion stress
= basic allowable material stress at the cold (installation) temperature, as per Appendix A of
B31.1 Code
Occasional:
Where:
= Occasional Stresses
= resultant moment due to occasional loads
=√
= occasional load factor
= 1.2 for loads occurring less than 1% of the time
= 1.15 for loads occurring less than 10% of the time.
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CAESAR II Statics Training
Pipe 1
Pipe 1
This exercise will provide further practise with the piping input, and introduce alternative editing
tools which may increase productivity in creating models. We will also investigate and review the
results to see what to look for and see how the piping system is behaving, and how to correct any
issues which may arise during the design.
The first stage of this exercise is to input the model. The model is below; you will also have the same
isometric printed on a separate hand-out in a larger format.
As before with the cantilever example, the model will be input using the node numbering system.
Each section between two nodes is called an element. i.e. node 10 to node 20 are linked together by
an element, referred to by ‘element 10 to 20’. Prior to entering geometry, it can be very useful and
is a good idea to mark up the isometric drawing with the intended node number sequence.
We will use a slightly different method of inputting the data, which will allow us to maximise the
graphics area during input. In the main “Classic Piping Input”, on each area, notice the “>>” symbol
in the top right corner:
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CAESAR II Statics Training
Pipe 1
Double click this symbol to “tear off” the particular section of the input spread sheet. This will allow
the Classic window to be minimised for the most part thus maximising the graphics.
Tear off the Node Numbers, Dimension Deltas and Pipe Sizes areas. As the material temperatures
and pressures do not change throughout the model we can enter these on the first element and
then we will not need them again.
Input Model
Enter A106-B as the material, 330°C as the temperature and 17 bars as the pressure
In this model we also require insulation; 65mm thick Calcium Silicate.
The rest of the information we will need to enter for our model can be done via the three windows
we have “torn off”. Minimise the Classic piping input (of course this can always be maximised at any
point if needed).
Finally we can enter the pipe size and schedule, along with the densities and corrosion allowance, as
per the isometric.
The fluid density can be entered as 0.72SG and CAESAR II will convert this specific gravity to the
correct units. As before the pipe size can be entered as 10 for 10” and S for STD schedule piping.
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CAESAR II Statics Training
Pipe 1
We will begin at the bottom “right” pipe where it is connected to a pump. This will be node 10.
Note that this is an anchor, a fixed point in our system. Element 10 to 20 is 400mm in length, in the -Z direction. Enter DZ as -400mm
Node 10 is also fixed so we need to specify an anchor. Use the toolbar on the left hand side of the
graphics window (default location) to specify a restraint.
The Auxiliary Data – Restraints window will appear. Specify that the anchor is at node 10. The
auxiliary data window can now be closed.
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CAESAR II Statics Training
Pipe 1
Our first element is complete, and should look like the one below:
Use the Continue button to create a new element:
This next element is a 300# flanged gate valve. We could enter this in a number of ways. The valve
will be rigid relative to the surrounding piping, so must be specified as a “rigid element” with a
weight. This can be done either as 3 separate elements (flange – valve – flange), or as one overall
element with the total length and combined weight specified. This can be done manually or by using
the valve flange database to obtain the length/weight automatically from CAESAR II’s catalogue,
which we will do. Select the Valve flange database button and select a gate valve with flanged ends,
class 300.
The Flange – Valve – Flange check box can be used to split the component into 3 elements
ifrequired.
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CAESAR II Statics Training
Pipe 1
The element will appear in node 20 to 30.
The correct length will be inserted (and the element will continue in the same direction as the
previous element). Also note that the Rigid check box is checked and the rigid weight has been
entered with the relevant weight for a 300# gate valve and flanges. (Hover briefly over the Classic
piping input where it is docked).
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CAESAR II Statics Training
Pipe 1
Continue to the next element
.
Enter the DZ as -825mm. This element also leads into a bend, so press the Bend button on the right
hand toolbar. If using the classic piping input we could check the bend check box to achieve the
same result.
The bend auxiliary data window will appear.
The default bend type is a long radius (1.5D) bend This radius can be changed. Common bend radii
are available in the drop down, alternatively any radius required can simply be typed in here.
In addition, further data can also be entered such as if the bend is flanged or mitred etc. Accept the
default long radius bend.
The graphics will not display the bend yet, as there is no following element.
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CAESAR II Statics Training
Pipe 1
Continue to the next element
.
This time we are now continuing in the –X direction. DX is -1050. The bend will now be visible in the
graphics.
Continue to the next element
.
This element is a 10”x12” concentric reducer and is 203mm in length. Enter DX as -203mm and
specify that this is a reducer.
The Reducer Auxiliary will appear and we can specify further data, including the second end size. A s
before, entering a nominal size in here will be converted to the actual OD. Enter 12 in the diameter
2 and S in the thickness 2 fields, which will be converted to the actual values.
Continue to the next element
.
Finally continue from the end of the reducer to the centre of the tee, 254mm as shown on the
isometric. DX is -254mm
The model at this point should now resemble the image below, note the node numbers in the image:
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CAESAR II Statics Training
Pipe 1
We can now take advantage of the fact that the model is symmetrical and use the functions in
CAESAR II to mirror the piping to create the opposite leg.
Use the Select group function to activate the graphical selection mode and draw a window around
the model.
All elements will turn yellow to indicate that they are currently selected. Ensure all components are
selected.
The Duplicate function can be used to copy, and mirror if required, selected elements.
Duplicate the selected elements and choose to mirror about the Y-Z plane.
We also need to increment the node numbers so that we do not have duplicate nodes.
Currently our model goes from node 10 through to node 70.
If we increase the node numbers by 70, node 10 will become node 80, 20 becomes 90 and so on.
Therefore the second leg will be node 80 through to node 140. The only issue with this is that there
are no common nodes, so the piping will not actually be connected. This can easily be fixed by
chaging node 140 (the centre of the tee on the second leg) to become node 70 (the node at the
centre of the tee on the first leg). This will connect up the piping at the common node, 70 – the
centre of the tee.
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CAESAR II Statics Training
Pipe 1
Click OK and the pipe will be duplicated, but as already stated there is no common node so CAESAR II
does not know where to place the pipe. As such it locates it at the origin. The resulting model looks
like the following.
All we need to do is connect element 130 – 140 to element 60 – 70. This can be done by changing
140 to become node 70. Select element 140. There are various ways of doing this – either double
click in the graphics area, or user the navigation buttons to navigate to the correct element (as this is
the last element the end button will quickly take you to the correct element).
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CAESAR II Statics Training
Pipe 1
The Edit Node numbers window should now read 13 to 140 and the element will be highlighted in
the model.
Simply change the “To” node from 140 to 70. The model will now be connected as should look like
the one below:
We can now complete the model by adding the vertical leg and connection to the vessel.
Skip to the last element. This can be done by again using the Last Element navigation button or
using the Ctrl + End buttons on the keyboard.
Click “Continue” to move to the next element
need to change this to 70 to 140.
. The node numbers will default to 70 to 80. We
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CAESAR II Statics Training
Pipe 1
This element is the vertical leg, and is 7m in the Y direction. DY is therefore 7000. This also leads
into a bend so select the Bend icon as well.
.
Click “continue” and place the final element 140 to 150 in the –Z direction, 2000mm. The final
element connects to the vessel, so we will place an anchor at this point. Click the retsraint button
and specify an anchor at node 150
Notice in the isometric that at the vessel connection, there are DY and DZ displacements. These are
due to the thermal expansion of the vessel.
Select the Displacements button and enter in the required values 3mm in DZ and 12mm in DY.
Error Checking
The model is now complete, so run the error checker.
We will receive a fatal error and three warnings. We must correct the errors before we can analyse
the model. The warnings may be acceptable but we should check to confirm that the input is as
intended.
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CAESAR II Statics Training
Pipe 1
So our error is mentioning that we have both an anchor and displacements speciified at node 150.
This cannot be possible as the anchor fixes the point, but the displacements move the same point.
We cannot have both at the same time. Remove the anchor and edit the displacements.
Double click the error message to go straight to the area of concern. Now click the restraints button
to remove restraints. Click OK in the message which appears. Now edit the displacements and fill in
0 in all other field (DX,RX,RY,RZ). A displacement of zero will fix the node in that direction, so now
our node is fixed in all directions, except for DY and DZ where the relevant displacements are
applied.
Re run the error checker and investigate the warnings. The second two warnings are regarding the
reducer alpha angle which is not specified. CAESAR II is therefore using a default computed value.
This is acceptable here for us.
The first warning is stating that there is a geomtric intersectaion at node 70 (the tee) but we have
not specified a type of tee, and therefore a SIF. This can sometimes be correct but is most often the
result of an oversight, as in this case. Return to the input and locate node 70. The Find tool can be
used to do this:
The Zoom to Node if found check box will also zoom into that node/element if it is found, useful on
larger models.
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CAESAR II Statics Training
Pipe 1
On node 70 use the SIFs/Tees button to specify a SIF at this point. This only needs to be done on one
of the elements connecting to node 70, it is not necessary to do this on all three.
Select an unreinforced tee.
Re-run the error checker. All should now be OK, only the reducer alpha warnings will remain, plus
the C of G report.
Review Load Cases
Access the load case editor
Recall from earlier the design code (we are using B31.3) addresses the stresses produced by the
various loads. In our model we have the following loads applied:
 Weight
 Pressure
 Temperature
 Displacement
B31.3 requires that two checks are performed – Sustained and Expansion
Sustained – Weight and Pressure
Expansion – Temperature and Displacement
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CAESAR II Statics Training
Pipe 1
These load cases are defined by CAESAR II as the default (recommended) load cases, shown in rows
L2 and L3.
Row L1 is an operating case (OPE) and is the “Hot” case consisting of the ‘real world’ loads. This case
is not required by B31.3 (although some codes do require this case also). However as this case is a
“real world” scenario it is used to estalish restraint loads and loads on equipment conections. In
addition, it is used to derive the Expansion case. The expansion case is the algebraic difference
between L1 and L2 (L1 – L2).
Accept these load cases and run the analysis by clicking the “Running Man” icon.
Review Results
After the analysis has run, the output processor will appear. The first thing to notice is that the EXP
case is coloured red. This indicates that this case has failed to code stress check. That is, the
computed stresses in the system at some point are greater than the allowables published in the
code.
We need to fix this.
Select the Expansion case and view the results for the Stresses report.
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CAESAR II Statics Training
Pipe 1
The report shows that the code stress check failed and highlights in red where the check failed.
Double clikcing on any column will order the report by that coluumn. Double click on the Code
Stress column header to order by highest stress.
The overstress points are at nodes 70, 10 and 80.
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CAESAR II Statics Training
Pipe 1
First we will check node 70. This is the tee. Look at the SIFs here. The in-plane SIF is 4.625 and the
Out-Plane is 5.833. The stresses at this point are therefore being multipled by 4 and 5 times. If we
can reduce these SIFs then the stress will reduce and can easily be reduced below the code
allowable.
Return to the input and return back to node 70. Pick the Intersection SIF scratchpad and choose
node 70.
Change the unreinforced tee to a reinforced tee. Specify a pad thickness of 10mm
Click the Recalculate button and notice the SIFs reduce dramatically. Now the stresses will be
multplied by 2.887 and 2.415 rather than 4 and 5.
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CAESAR II Statics Training
Pipe 1
Re-run the analysis using the batch run feature. The Expansion case is still shown in red, indicating
the system is still overstressed. But check the Stress report for the Expansion case and notice that
only nodes 10 and 80 are overstressed.
So what is happening at nodes 10 and 80?
Nodes 10 and 80 are the initial anchor locations, so we need to find out what is causing the
overstress. This is in the expansion case, so if we recall the code equation for the expansion case:
From this equation it can be seen that the dominant factor in the code equation is the bending
moment – it is the only factor in the expansion case. So which bending moment is this, Mi, Mo or Mt?
Mt is torsion, Mz and Mi and Mo are inplane and outplane – so vary dependant on the location. What
we can see from the results though, is which bending moment is the highest in terms of our axes.
View the Expansion case, Restraint Summary report.
We can see from this report that at nodes 10 and 80, the highest bending moment is the MY
moment, at 116 kN.m. The MX is also rather high at 88 kN.m.
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CAESAR II Statics Training
Pipe 1
So we know what is causing the overstress, but how do we correct this and reduce the bending
moment (and therefore the stress)?
Let us look at the 3D plot to view what is causing the bending moment.
Close the report and view the 3D plot
In the 3D plot window which appears, ensure that the Load case we are viewing is the expansion
case and select to Show the deflected shape. You may need to Adjust the deflection scale to get a
more exaggerated deflected shape.
View the pipe from the bottom, using the standard views available
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CAESAR II Statics Training
Pipe 1
We are looking upwards at the pipe from below. The Y axis is pointing upwards (away from us). The
pipe is undergoing thermal expansion and causing the pipe to bend at the anchor points.
Looking at the model from the side view will also explain the MX moment. As can be seen, the riser
is expanding causing the MX bending moment.
If we could add some flexibility in to the area where the pipe is expanding we can absorb some of
this expansion, and so reduce the bending moment. We have the top leg which is flexible, but the
bottom leg is not flexible enough.
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CAESAR II Statics Training
Pipe 1
If we can transfer some of the flexibility in A to B then we may solve the problem.
To do this, increase the length of B by 1m and so consequently reduce the length of A by 1m. This
should give us more flexibility at the bottom, hopefully without removing too much flexibility at the
top.
Return to the input and select element 30 to 40. The DZ value here is 825mm. Edit this to 1825mm.
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CAESAR II Statics Training
Pipe 1
Repeat for element 100 to 110.
We will have to also consequently reduce the length of 140 to 150 by the same amount (1m).
Change this from 2000mm to 1000mm.
The model should now look like the one below.
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CAESAR II Statics Training
Pipe 1
Re run the analysis and check the results. The expansion case is now no longer coloured red and the
highest code stress is 91% of the allowable at node 10. We have successfully reduced the stresses
and the model now passes the code stress checks.
Verify the sustained stress report that this is still acceptable – it should be around 37% of the
allowable.
Our model is now compliant with B31.3.
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CAESAR II Statics Training
Supt 01
Supt 01
This exercise is designed to demonstrate adding supports in CAESAR II and demonstrate the
Operating case and Restraint load reports and give an indication of what the results mean on the
restraint load report, along with a short example on how to combat issues with supports, such as
“lift off”.
The model shown above will also be in your hand-out. Model the piping system as per this
isometric. Anchor at nodes 10 and 90.
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CAESAR II Statics Training
Supt 01
Locating Supports
The system is anchored at the termination points (nodes 10 and 90), but we also need to support the
weight of the piping system as well.
If both supports are pinned (free to rotate), standard beam theory states that the max moment is at
the centre of the span, l.
This moment is:
If both ends are fixed then the max moment is at the end of the span
This has a value of
Where
As piping systems are neither one nor the other and tend to be somewhere in the middle, a
compromise therefore is reached with an approximation thus;
Taking into account the maximum moment could be somewhere between the ends and the centre –
i.e. anywhere along the span.
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CAESAR II Statics Training
Supt 01
This deals with continuous runs of pipe, however there are of course concentrated loads sometimes
in the piping system, such as valves, flanges etc. The effects of these items on the pipe stresses can
be estimated as well. For pinned connections, the maximum moment is located at the point of
loading (P).
This maximum moment has a value of
Where a = longer portion of span
b = shorter portion of span
For fixed connections:
He maximum moment here is located at the end nearer the load, and has a value of
In either case (or in some case in between) the additional stress (M/Z) due to the concentrated loads
should be added to the stress from the uniform load in order to determine the total stress.
Examining the formulas above, it can be seen that as the shorter span (b) approaches zero in length,
the moment, and therefore the stresses approach zero as well.
So, if supports are located as close as possible to concentrated loads, the effects of these loads are
reduced as much as possible.
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CAESAR II Statics Training
Supt 01
The information on the preceding pages provides a simple rule of thumb to design for weight
loading.
First support all concentrated loads in the system as closely as possible, reducing the stresses due to
those loads to as close to zero as possible.
Next, we can use
Along with
If we knew the allowable stress, we could then use this information to determine a maximum
allowable length of pipe – i.e. a distance between supports.
Rearranging the equations above, we can obtain
√
As this calculation will need to be done often, in order to save time calculating
the Manufacturer
Standardisation Society of the Valve and Fitting Industry has calculated allowable piping spans for
various configurations. These standard spans have been published and are shown on the next page.
These spans assume:







The pipe is standard wall with insulation
Maximum moment is Mmax = wl2/10
No concentrated loads are present
There are no changes in direction
Maximum allowable stress is taken to be approx. 10 MPa
Max deflection is approx. 2.5mm
SIFs are not taken into account
It is rare that piping systems are only horizontal runs with no changes in direction etc.; therefore a
caveat is taken in that changes in direction reduce the allowable span to ¾ of the standard span.
In addition, the standard span does not apply to risers, since no moment (thus no stress) develops,
regardless of length. However it is preferable to locate supports above the centre of gravity of the
riser to prevent toppling.
These rules here are simply rules of thumb and can provide a good start point for support locations.
Of course, supports should be located with practical considerations taken into account (locations of
building steel/pipe racks etc.).
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CAESAR II Statics Training
Supt 01
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CAESAR II Statics Training
Supt 01
Adding Supports to Model
Let us now return to our model SUPT01.
As there is an anchor at node 10, the valve here is supported.
The valve at 60-70 requires supporting. We will create a new node on element 50 to 60, called 57,
and locate a +Y support here.
Use the Break command to split the element into two. First select element 50 to 60 and choose the
break command.
We will locate this support close to the valve (node 60). Specify to break the pipe and insert the new
node, number 57, 150mm from node 60:
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The element will be broken and a new node inserted close to the valve. Locate a +Y support at this
node 57.
The +Y support will support the pipe from below, and will allow movement in the +Y direction.
All the concentrated loads are now supported.
We can return and run through the piping system, placing supports as per the standard span.
Check the table on page 48 to determine the maximum span for 12” pipe carrying water
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The table on page 48 indicates that the maximum span for 12” pipe in water service is 7m. As
discussed previously, for horizontal changes in direction, the support span is amended to ¾ of the
standard span. 0.75 x 7 = 5.25m
The valve is supported at node 10. After node 10 the piping continues horizontally with a bend. The
maximum span therefore is 5.25m. This places our support round the bend.
The piping after the bend is 13715mm before the riser. This can almost be split in two exactly with
our 7m span spacing. Remember that the standard span does not apply to risers, and as mentioned
before we will support the riser from the top, rather than trying to balance it from the bottom. As
such we can locate a support near the middle of the 13715mm run, and one close to the bend (node
30).
Break element 30 to 40 and locate a new node number 33. Locate this 600mm from node 30.
It is possible to add a support in at the new node location. We wish to add a +Y support at node 33,
exactly the same support configuration as at node 57. So typing in 57 in the “Get Support from
Node” field will place the same support as at 57 at our new node 33.
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Repeat and break element 33-40. Break this 7000mm from node 33. Call the new node 37. Place
the same +Y support from 33 (or 57) at this point too.
Continue on after the riser. There is already a restraint next to the valve, so we have fulfilled the
minimum span up to the valve. After the valve we have horizontal pipe with a bend again.
Therefore our maximum span is 5.25m. The length of pipe is 4115mm and then 3640mm after the
bend. There is an anchor at the end, so we just need one more support between the valve and the
anchor at the end of the pipe.
Locate this support on element 70 to 80, close to the bend at node 80. Locate this 600mm from the
bend.
Break element 70 to 80 and create a new node 77, 600mm from node 80 and with a +Y support the
same as before.
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Finally the piping riser needs to be supported. The length of horizontal run at the top and bottom of
the riser is less than our span of 7000mm. There is no bending in the riser so in theory we can place
a single restraint near the top of the riser.
Break element 40-50 and locate a +Y restraint 600mm from the tangent intersection point of the
bend. Note that, although this support should satisfy our bending requirements on the horizontal
sections, it may have a very large load since it will also support the whole of the riser.
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The support located in the riser may be difficult to see, as it is probably hidden by the piping. To
view the support either the size of the restraint symbol can be increased, or the pipe can be set to
translucent mode.
The system is now supported as per the maximum span requirements. We can be sure that the
sustained stress case therefore is acceptable, and should be in the order of approximately 10MPa.
Error Check the model.
You should receive only the Centre of Gravity report, and no errors or warnings.
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Analyse
Access the Static load cases create only a single load case with weight only. We wish to check the
support locations we have just placed are below the acceptable limits
Run the analysis.
View the Sustained Stresses report.
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The highest stress level is 10.7MPa, which is almost exactly at the allowable from the standard span
limit (this limit is based on an allowable of 1500 psi ~10.3MPa). The system is supported from a
purely weight induced stress perspective.
We can also now view the restraint loads to see how the weight loads are distributed. View the
Restraint Summary report.
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Again this look OK, all restraints are taking a downwards acting load (-FY), although the restraint at
node 43 is rather large compared to the others; 30,000N vs. less than half that for the remaining
supports.
These loads however are due to weight only. Let us run now the cases required by the piping code
B31.3. Return to the Static Load cases and select the recommended cases.
Run the analysis and view the sustained stresses. These will have increased slightly due to the fact
that we are now including the pressure term; however the stresses are still well within the
allowables determined by the code.
Similarly the Expansion Case stresses are also very low and well within the allowable – the system is
flexible unlike the PIPE1 example.
Now we can check the restraint loads in the real world operating case. Remember the Operating
case is not required by the code, but it does represent the actual loads in a “real world” scenario, for
the purpose of designing restraints.
View the Operating case Restraint Summary.
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The loads are different to before as we have included the effects of thermal expansion.
The load on node 77 is 0 (in the FY). This shows that this restraint is not taking any load. What is
happening here?
View the displacements report to see what is happening at this point.
At node 77 the pipe is moving upwards 2.3mm. Also notice that at node 50 (the bottom of the riser)
the pipe is moving down 26mm.
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Viewing the 3D Plot can confirm this:
View the deflected shape (you may wish to increase the deflection scale to exaggerate the deflected
shape)
The 3D plot shows that the thermal expansion is causing the riser to expand downwards at the
bottom (node 50). This in turn is causing the pipe to pivot at node 57 – giving the large operating
load at node 57. The pipe pivoting at 57 causes lift off at node 77 – so we see a 0 load.
The restraint at the top of the riser (at 43) is the datum point of expansion and so all the thermal
expansion is from this point. That is why there is no expansion at the top and a lot of expansion at
the bottom. We need to rectify this situation.
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Fix Model
As we know, the riser is expanding due to thermal expansion. The datum point for this expansion is
the support located at node 43, at the top of the riser, so all the expansion is going downwards –
causing the lift off issue. To rectify this we can attempt to move the datum point of the expansion,
so that the expansion is more evenly distributed.
Insert an additional restraint on the riser. Call this node number 45 and locate this restraint 6000mm
below node 43. Insert another +Y support at this location. This should have two effects:
1. Give a better distribution of
the weight loads of the riser
2. Cause less thermal expansion
downwards at node 50.
Re-run the analysis, the batch run command can be used as we have only made a small change by
adding a support.
Review the stresses is the SUS and EXP cases. These stresses should still be acceptable.
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Review the restraint report for the sustained and operating cases to see how the new restraint has
affected the results.
The sustained case shows that we have a better distribution of the weight of the pipe on the riser, as
the new restraint is taking some load. The load on node 43 at the top of the riser is now distributed
between 43 and 45 (43 has dropped from 30kN to 9kN).
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The operating case however still shows lift zero load at node 77, and now also zero load at node 43.
Checking the displacements also confirms this; there is still a positive displacement at nodes 77 and
now at 43. Node 50 is still moving downwards, although only 15mm now.
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We will attempt to further distribute the thermal expansion of the riser by adding a third restraint,
located near the bottom.
Break element 45-50 and create node 47. Locate node 47 6000mm below node 45 and locate a +Y
support at this point.
Rerun the analysis and check that the stress levels have not been adversely affected.
As before, view the SUS and OPE loads on the restraints to see how the new restraint has affected
the analysis.
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The sustained report shows that we have further improved the weight distribution among the
restraints.
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The Operating case now shows a negative load on restraint at node 77. There is no more lift off here
at 77. However the operating loads at node 43 and 45 are now zero. All the thermal expansion that
was going downwards with only the one restraint at the top of the riser has now been forced
upwards instead, causing the pipe to lift off at the top of the riser (43 and 45).
The displacements report confirms this
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The pipe is lifting off 22mm at the top of the riser.
The 3D plot can also confirm the situation:
So we have a situation where we are supporting the weight of the system adequately in the SUS load
case, but we have an issue with the thermal expansion. If we replace the rigid +Y restraints along
the riser with Variable Spring Hangers (VSH), these hangers should allow thermal growth whilst also
supporting the required weight for the SUS condition.
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Place Spring Hangers
Return to the input at locate element 40-43. Remove the restraint at node 43 by double clicking the
restraint check box.
Place a hanger here instead. Double click the Hangers check box
Select the Hanger table as Carpenter & Paterson. Carpenter & Paterson are a UK manufacturer
whose database of available spring hangers is programmed into CAESAR II. CAESAR II will
automatically calculate the required load and movement at the location, and then review the
database to select an appropriate spring for the calculated load and movements.
Notice that 2 hangers are located at this location also. The graphics will not change in CAESAR II, but
this will locate 2 hangers at this location, and the selected spring will be based upon this shared load.
Error check the model. You should now notice two further notes during the error check.
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The first not simply shows the number of hangers in the job, and how many of these hangers will be
designed by CAESAR II at run time.
The second message states that new load case combinations are required for the hanger design. A
load case for weight loads is required, so that CAESAR II knows how much weight the hanger(s) need
to support. Secondly, a hanger design operating case is required. This case determines the thermal
expansion at each restraint location to determine the movement at the spring hanger locations as
well. The values of weight from the previous weight load case are used. These two cases together
are used by CAESAR II’s spring selection algorithm to select the appropriate spring from the in-built
catalogue.
Access the load case editor to create these new load cases.
Click the Recommend button in the load case editor. CAESAR II knows that there are hangers
present that require designing, so will recommend the correct load cases for hanger design – cases 1
and 2.
Accept these cases. Note the stress type for these cases are HGR type. The results for these hanger
cases are supressed by default (theses are pre-analysis cases and the figures do not actually mean
anything other than for the spring hanger selection).
Case 1 W (HGR)
This case performs a Weight Analysis only with all support locations as rigid restraints. This tells the
spring selection algorithm how much weight needs to be supported at each location (usually in the
Operating condition)
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Case 2 W+T1+P1 (HGR)
The case uses the support weight values derived from case 1 as upward forces for an Expansion
analysis. That is, the values of W cancel each other out (support load versus actual weight), and the
system is then subject to temperature T1 in order to establish the thermal movement at each
restraint location. Given the Weight to be supported and the thermal movement at the same
location, the spring and its associated stiffness values can be selected and incorporated into the
subsequent load cases.
Run the analysis
CAESAR II will have selected and sized a spring hanger during the analysis. Check the Hanger Table
with text to view the hanger properties of the selected hanger.
As can be seen, CAESAR II has determined that the hanger will need to support a hot load (i.e. OPE)
of 6723N. There are two springs at this location, so this 6723N is the total load shared between two
supports (i.e. the total load is 6723N x 2).
CAESAR has taken these properties and browsed the inbuilt Carpenter & Paterson database and
selected a DV70 Size 11 spring.
Verify the sustained and expansion stresses – these should still be acceptable (13% and 19%).
Now check the OPE restraint loads.
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The hanger at node 43 is now taking load. This load is 13447N (which is 6723N x 2), however there is
still no load being taken at node 45.
Return to the input and replace the rigid +Y support at node 45 with a spring hanger. As before,
select the Carpenter & Paterson catalogue, and place 2 hangers at this location before re-running
the analysis.
As before the SUS and EXP stresses are acceptable.
The OPE case Restraint summary now shows that all the restraints are taking load. The new spring
hanger is taking some of the load of the riser – this is now distributed evenly.
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CAESAR II has again run the two hanger cases and used the results from these to select appropriate
hangers for placing at the two hanger locations. These can be seen from the Hanger Table with text.
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Turbo
Turbo
This exercise will build upon knowledge we have gained so far, and introduce the following new
features.
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Combining Pipe Models
Rigid Construction Elements
CNode Connections
NEMA SM23 Analysis
The model is shown above and is also supplied in the hand-out in a larger format. As can be seen,
this is an inlet and exhaust on a turbine. The turbine itself is anchored to the floor at the anchor
point specified.
To keep modelling simple, we can model the inlet and exhaust as two separate models. These two
models can be combined into a single model later – there is a common location at the turbine
anchor point.
We will model this common anchor point location as node number 5. However, we will come back
and model this point last.
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Model Inlet
Model the inlet pipework, on the first element; change 10 to 20 to 11 to 20. Begin at node 11, the
flange connection to the turbine nozzle, as shown below. Note that node 11 also has an anchor
attached.
Once the inlet piping is complete, return to the first element, 11 to 20. We will now insert an
element before 11 to 20, numbered 5 to 10. Node 5 will be the turbine anchor location. Node 10
will be connected to the anchor at node 11. We will connect these via CNode connections.
As there is an anchor at node 11, this node is fixed in all 6 degrees of freedom. However, the nozzle
connection on the turbine will undergo some movement due to the thermal expansion of the
turbine. Recall previously that we had a similar situation where displacements were specified to
account for a similar situation in PIPE 1 for the vessel thermal expansion. In this case, we do not
know what the thermal expansion is here so we cannot enter the displacements. To apply the
displacements to the nozzle point we will add in an element from the nozzle to the turbine base.
This will be a rigid element with zero weight, and it will have temperature applied (so it will undergo
thermal expansion). This element will also be anchored at the turbine base.
If however we specified this as 5-11 for example, nodes 5 and 11 are both anchored, so cannot move
and all that will happen is we will obtain large forces at nodes 5 and 11. We need a way of
connecting this rigid construction element to node 11 which will allow node 11 to move due to the
expansion of the construction element, but still be fixed as far as the rest of the piping is concerned.
This can be achieved in CAESAR II this using CNodes. A CNode will allow the anchor at node 11 to be
connected to another node “indirectly”. Essentially, both these points will be at the same location,
but CAESAR II will see these points as separate nodes. Therefore what will happen is that as element
5-10 expands, node 11 will act as an anchor, but as it is connected to node 10, node 11 will move to
wherever node 10 moves to, while still acting as an anchor.
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Nodes 10 and 11 are the same point in space.
Select element 11-20. First specify a CNode on the anchor at node 11; the CNode will be node 10.
Next use the Insert function to insert an element before this element.
Change the node numbers to 5 to 10
Fill in the DX, DY, DZ fields as shown on the isometric sketch
This is a rigid element, but leave the weight blank in this case. Also add an anchor at node 5.
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The zero weight rigid will be inserted and connected to node 11 as above. We now need to specify
the temperature for the rigid, as this will undergo thermal expansion.
Select element 5-10 and double click the “>>” on the temperature/pressure section to “tear off” the
Operating Conditions box. Uncheck the Propagate parameters box to ensure that the data entered
here is only entered on this one element, and not the whole model. Enter 200°C for T1 and make
sure that no pressure is specified.
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Check that this has been specified correctly, by using the Show Pressure graphical tool.
Display P1.
The rigid construction element should show as unspecified, and the rest of the model should show
as 12 bars.
The inlet is now complete.
Save the file and using the same concept, create a new job file for the exhaust.
Start the exhaust using nodes 1011 to 1020 for the first element.
Continue on. After the reducer, there is a bend. Place a length of pipe 350mm long in the Z
direction, adding a bend to this pipe. Place a corresponding pipe 350mm long in the Y direction
afterwards to complete the bend.
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Complete the rest of the exhaust.
Once finished, add one final element, inserted before 1011 to 1020 and numbered 5 to 1010. Set
the pressure for this element to blank, and ensure that only this element has no pressure.
Connect via a CNode of 1010 at the anchor at node 1011.
The exhaust is now also complete. Notice that we have a node numbered 5 in both our inlet and
exhaust models. This node is a common location in both files. As such we can combine the models
and they will be linked at node 5.
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Combine Models
Save the Turbine exhaust as Turbo_Combined.c2
Select the Include Piping Files button to bring in the Inlet piping to create one single model.
Browse for the inlet model and click OK.
The two models will be combined around node 5 – the common node in both files.
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Select an element in the inlet. Notice that it can be selected, but the input screen has all fields
disabled.
This is because currently the inlet is simply being “referenced” and not fully included. Return back to
the combine pipe models screen. As well as the File name field, there are three other columns.
RotY – allows the included file to be rotated by a specified angle about the Y axis.
Inc – allows the node numbers in the new file to be incremented by a certain value. i.e. if the file
included was 10-20, 20-30 etc., we could increment by 1000 so that the nodes would become 10101020, 1020-1030 etc.
The final column is Include Now? This column allows users to choosing whether to reference or
actually permanently include the file. This can be useful if checking that the file is correct before
including, so any changes required can be done in the original separate model.
If your model looks correct, change Include Now? to Y.
Selecting an element in the inlet side of the piping will now show all the fields to be enabled.
Error Check and analyse the model, use the recommended load cases.
The analysis results should show that the expansion and Sustained stresses are acceptable. Check
the OPE case and note the loads on the nozzles at nodes 11 and 1011.
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There is a reasonable force on these nozzles, as the anchor points are supporting some of the weight
of the pipe. We will now take these forces and check them against NEMA SM23 to analyse the
turbine to see if the loads on the nozzles are acceptable.
NEMA SM23
The National Electrical Manufacturers Association (NEMA) publishes and maintains a standard SM23
Steam Turbines for Mechanical Drive Service. This standard includes allowable loads that can be
applied safely to our turbine nozzles. CAESAR II incorporates this standard and a separate module
can be used to evaluate nozzles, using calculated loads from the piping analysis (as we have just
done).
Return to the CAESAR II main window. Select the Analysis menu and select the NEMA SM23 option
to load the module. You may need to use the to access the whole menu.
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Create a new file called pass1.
If you wish, give the equipment a short description.
Select the NEMA Input Data tab.
The first data to enter is the direction of the equipment centreline. This must be specified as the
direction Cosines.
The direction cosines are specified as the cosine of the angle of the centreline with the respective
axis. For example, if the centreline was as shown above, 60° from the Z axis and 30° from the Y axis,
the direction cosines would be:
Z = Cos 60° = 0.5
X = Cos 30° = 0.866
Our equipment centreline is along the Z axis, so the angle between the centreline and the Z axis is 0°
and the angle between the centreline and the X axis is 90°
Therefore the direction cosines are:
Z = Cos 0° = 1
X = Cos 90° = 0
Now we can define the nozzles. Click the Add Nozzle button
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The Node number is the corresponding node number which matches the node number in the
CAESAR II model. Specify the Inlet first – so this node number is 11.
This is the Inlet nozzle and is 4” diameter
The next box is the Distance from Resolution Point to Nozzle. NEMA SM23 is ambiguous about the
point of resolution of the combined forces and moments. Select one of the three fields and hit F1 to
bring up the help.
This point is the distance from the resolution point (face of the exhaust nozzle flange) to the nozzle
at node 11. This is as follows:
DX = +100 -150 = -50 mm
DY = -300 + 500 = +200 mm
DZ = +450 + 50 = 500 mm
The basic nozzle information is input. The final thing to do for this nozzle is to apply the loads on this
nozzle. We already have the loads in the CAESAR II job file that we have just analysed. So these
loads can be imported straight into NEMA SM23 module. Click the Select Loads Job and Load Case
button.
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Browse to the combined turbine model and select the operating case.
The loads will be imported from the job, these will be the loads at node 11 (as we specified the node
number as 11).
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The inlet nozzle is now complete. Select to add a new nozzle and enter the Exhaust nozzle details.
As before, import the loads from the OPE case in the combined job file.
Once complete, analyse the model using the “Running Man” icon.
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Another tab will now be present showing the results of the analysis. The analysis fails.
The Inlet and Exhaust both fail the analysis. A closer look at the results shows that the FY and MZ
moments are by far the leading causes of the failure. The FY is 214% of the allowable, while the MZ
is also 182%.
Save and Close the NEMA module and return to the piping input.
Looking at the input, it can be seen that the weight of the piping causing the FY will also clearly
result in the MZ moment being excessive – there is very little supporting the weight of the piping
other than the nozzles themselves. The only other supports are on the headers.
We need to support the weight of the pipe. Let us focus on the Exhaust first.
Let us support the weight of the pipe to reduce the FY component. Locate a Y support below the
elbow. This will be node 1039. We have not defined node 1039, only 1030 and 1040; so why 1039?
When building the model, it is built in the following way:
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Once a bend is inserted, CAESAR II moves node 1040 to the end of the bend, and inserts two
intermediate nodes:
These intermediate nodes are added by default at 0° around the bend, and at the mid-point of the
bend. This can be seen in the Bend auxiliary data (single click on the bend check box on element
1030 – 1040). M is used to designate the mid-point of the bend.
These nodes can be moved to the required location if needed for any reason by simply editing the
angle. But we just wish to add a +Y support under the mid-point of the bend, at node 1039.
Add a +Y at 1039.
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Re-run the analysis.
Check the SUS and expansion stresses, these should again be OK. Now review the OPE case restraint
summary to check if the load on node 1011 has reduced.
The loads on node 1011 are the same. The loads on 1039 are 0. This restraint is not taking any load
in the OPE case.
View the 3D plot to see the reason for this. View the deflected shape (you may need to increase the
deflection scale). From a left view, it can be seen that the expansion is causing the pipe to lift off the
support at node 1039.
The Operating/Displacements report confirms this, node 1039 is experiencing 0.614mm
displacement upwards – lift off.
The load on node 1011 has not changed. As such there is no need to run another NEMA analysis –
the results will be identical. Therefore, return to the input.
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Change the design by replacing the Y restraint with a spring hanger.
Select a Carpenter and Paterson spring hanger, and enter -500 in the Available Space field. The can
will be shown as below.
Re-run the error check and visit the Load cases window. We have added spring hanger into our
model, so we require` the hanger cases to determine the hanger size. Use the recommended load
cases again and analyse.
As before, the SUS and EXP cases are well within the code allowables. Check the restraint summary
for the OPE case.
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The spring hanger is taking some load now (4800N) and the load on the restraint at 1011 is much
reduced.
Return to the NEMA module and we will re-analyse with our new loads.
Save As… on the existing NEMA file, and select Nozzle 2 of 2 – the exhaust. The Inlet has not
changed so there is no need to re-import the inlet loads.
Refresh the loads from the current job to import the new changed data.
Once done, rerun the analysis. The exhaust now passes at 79% of the allowable.
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The Inlet of course still fails as we have not changed this.
Now let us reduce the load on the inlet. To do this, break element 40-50 with a new node number
42. This node should be 300m from node 40.
Locate a spring hanger at node 42. As before, select Carpenter & Paterson. Re-run the analysis and
check the OPE restraint summary. The load on node 11 will be reduced.
Return to the NEMA module and Save As… this file. Re-import the loads for the inlet nozzle and rerun the NEMA analysis.
The Inlet should now also pass.
The whole turbine passes
The piping system is acceptable in within the code allowables, and the loads on the turbine are also
within the allowables of NEMA SM23.
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This exercise demonstrates multiple load cases can be used along with multiple operating conditions
in order to evaluate various “what if” scenarios. In addition, the API 610 module is used to evaluate
loads on pumps.
Other features shown include naming nodes and naming load cases to make reviewing the results
easier.
The model below will also be on the hand-out. Notice that the three branch legs are virtually
identical. The input should be setup to take advantage of this trait through the use of the element
duplication facility.
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Begin at node 10 and model all the way to the end anchor as shown. Note that the bend has not yet
been specified at node 70.
Use the duplicate feature to create the remaining two legs for Pumps B and C. Increase the nodes
by 1000 each time.
You will not see the new elements initially, as they will be in the same location as run 10 to 70. Find
elements 1060-1070 and change to 1060-90. Also do the same for 2060-2070 and change to 2060100
The elements will all now be connected. Finish by specifying the bend at node 70.
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Now that the model is complete, we can enter the loading information. The hangers are to be
designed with the entire system hot. Then, each branch line must in turn be run at ambient with the
remainder of the system hot. These four conditions can be evaluated in a single run, using four
different temperature and displacement vectors.
First we will label the pump locations so that we can easier review these locations in the results.
Select element 10-20 and double click the Name check box.
Specify that the from Node (node 10) is labelled as Pump A
Repeat this for Pumps B and C
Next we wish to reduce the loads on the pumps by having the hanger support the riser weight. The
hanger algorithm works by distributing the weight evenly among all supports. If we free the pump in
the Y direction at node 10, this will ensure that the weight is not distributed at this point – and so is
supported by the hanger. Do this by specifying the Hanger as follows:
Repeat this for Pumps B and C.
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Now we need to specify the loading conditions, as mentioned before, we wish to evaluate the
system in four conditions. We can do this by specifying four different temperature/pressure cases,
and four different displacement vectors at the pumps.
All pumps on
Pump A idle
Pump B idle
Pump C idle
T1
T2
T3
T4
P1
P2
P3
P4
D1
D2
D3
D4
Enter the temperatures as follows. The element listing displays the value in red whenever it changes
from the previous value.
Use the graphics to verify that the temperatures are correct. Note that the temperatures do not
simply stop being 120°C and suddenly drop to ambient. The way we have entered the temperatures
give a basic approximation of a temperature gradient.
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T1 – All same temperature
T2 – Pump A idle
T3 – Pump B idle
T4 – Pump C idle
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Perform a similar task with the pressure. Only this time the pressure will drop from 20 bars to 0
after the valve. It is at fill pressure right up to the valve, then it will drop.
Enter the pressures as shown below:
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Again the graphics can be used to verify the correct pressure has been specified
P1 – All same pressure
P2 – Pump A idle
P3 – Pump B idle
P4 – Pump C idle
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Finally we need to specify the pump nozzle displacement. The pump discharge nozzle vertical
growth is 0.75mm, when the pump is running. Therefore we also need 4 displacements at each
pump. Enter the displacements as in the table below. An example for Pump A is shown in the
screenshot afterwards.
D1
D2
D3
D4
Pump A
0.75
0
0.75
0.75
Pump B
0.75
0.75
0
0.75
Pump C
0.75
0.75
0.75
0
The model is now complete. Run the error checker. You should receive 3 notes – two on the hanger
design, plus the C of G report.
Correct any errors or warnings you may receive.
Access the Static Load cases. We require a number of load cases now – one each for SUS, OPE and
EXP for each of our situations, i.e. 12 cases. Plus we require the hanger design cases. The hangers
should be designed for the system when all pumps are hot.
The recommended cases should satisfy these requirements.
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As we have a number of load cases now, it is becoming a little confusing to work out each time
which combination of loads is which case. To make this easier, we will rename the load cases.
Access the Load Case Options tab and rename the load cases to reflect the situation.
Run the analysis
The list of load cases will still be the CAESAR II Load Case name. To change this, go to Options > Load
Case Name and select User Defined Loadcase Name instead
In addition, to make it easier to identify the pumps, choose to display the Node Name in the reports
as well as the number. Again, this is accessible via Options menu > Node Name
Verify that the system is within the allowables for B31.3 in all situations, both EXP and SUS.
Also check the OPE loads on the pump nozzle connection.
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API 610 Analysis
The model is complete and satisfies the requirements of B31.3. We can now evaluate the pump
nozzles to ensure that the nozzle connections satisfy the requirements of API 610 for the pump.
A total of 12 API-610 evaluations must be made in order to find the worst case scenario. These
scenarios are shown below:
Pump A – All pumps on
Pump A – Pump A idle
Pump A - Pump B idle
Pump A - Pump C idle
Pump B – All pumps on
Pump B - Pump A idle
Pump B - Pump B idle
Pump B - Pump C idle
Pump C – All pumps on
Pump C - Pump A idle
Pump C - Pump B idle
Pump C - Pump C idle
Access the API-610 module from the CAESAR II main window and create a new file for the first
iteration – Pump A with all pumps activated.
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Move to the Input Data tab to specify the data for the pump. Note the API coordinate system is
different from the CAESAR II coordinate system, hence API My aligns with CAESAR II Mz. We are
also only concerned with the Discharge nozzle; as such we do not need to enter any data into the
Suction Nozzle tab or fields.
We wish to evaluate the discharge nozzle. This is pump A, so the nozzle is node 10. Fill in the
correct data for Node 10.
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Now we need to specify the loads on the discharge nozzle. As before, these loads can be imported
from the analysis just done.
Select Load Case 3 – Operating case for all pumps active.
Also, for the analysis, we will assume that the distance from the centreline to the nozzle is zero.
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All the data has been input, so the analysis can now be run.
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The results show that Pump A is OK for this condition. However, to determine the worst case, we
must perform the other eleven evaluations.
Repeat the above task for all the remaining pumps.
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After completing all twelve iterations, you should notice that one of the iterations fails. This is Pump
C with Leg B Idle.
From these results, it can be seen that the local Y moment is failing, and is 262% of the allowable. As
mentioned previously, the API-610 coordinate system is different to the CAESAR II local coordinate
system. The local MY translates to the MZ in CAESAR II.
Return to the piping static output and review the results. View the restraint summary for all the
Operating cases.
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The MZ for Pump C in case 5 is the highest of any MZ moments – confirming the findings of the API
610 analysis.
View the 3D plot and view the deflected shape for Operating case with Pump B idle.
The datum for the thermal expansion is the line stop at node 80. The expansion at the leg for pump
C is the greatest, and so is causing the higher moment at this point. Similar to the exercise SUPT01,
if we can adjust the datum for thermal expansion, we should be able to reduce the amount of
expansion which is causing the moment on Pump C.
This can be done by moving the line stop from node 80 to node 110.
Remove the Z restraint at node 80 and add a new Z restraint at node 110, then re-run the analysis.
Notice now that the restraint summary shows that Pump C has a much lower MZ now. The loads
have been more evenly distributed (Pumps A and B have slightly greater loads, but these pumps
were OK anyway).
Return to the API 610 module and open the file which failed previously -
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Select the Discharge nozzle tab. The loads on this pump have changed, so we will have to import
these new loads.
Use the Refresh Loads from Current Job button to bring in the new loads and re-run the analysis.
This time the pump should pass – as we have reduced the loads sufficiently
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This exercise will develop various sequences of “run – evaluate – modify” workflow to determine the
acceptability of the system. Each of the evaluations of the system will develop another aspect of
CAESAR II.
Once the system is acceptable, we will generate a custom report and stress isometrics.
System parameters
Pipe: 8” diameter, standard wall, ASTM A-53 Gr. B
Analysis temperature: 315°C
Analysis pressure: 2 bar
Corrosion allowance: 0.8 mm
Insulation: 75 mm CaSi
Fluid: 0.8SG
Pipe Specification: 150 pound class components
Design Code: B31.3
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Node 10 is connected to a Pump and node 110 is connected to a vessel Nozzle. Their details are as
follows:
Pump Details:
10 inch end suction, 8 inch top discharge
Suction is -380 mm in X from pump centre
Discharge is 500 mm above and 300 mm in Z from pump centre
Piping load on suction nozzle given as: (4450,-3550,-5340) N and
(-4070,-3390,2170) N-m
Nozzle Details:
Fixed end is preceded by a long weld neck flange in the -Z direction:
OD=247.65, wt=22.225, length=300 mm, weight=458 N
and a standard, 8 inch weld neck flange and gasket
Model the system as shown in the isometric. When modelling the bypass loop, the Close Loop
command can be used if required to connect node 150 to 60. Change the node numbers to 150 and
60 and click the close loop button. CAESAR II will add in an element of the required length
automatically.
The completed model will look as the one below.
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Boundary Conditions
We now need to specify the boundary conditions for the analysis. The piping is connected to a pump
and a vessel at the termination points, so we can apply the effects of these to the relevant nodes.
Pump Connection – Node 10
The discharge is 500mm above (Y) and 300mm in Z from pump centre
We have two options for the approach here.
1.
Calculate the thermal growth of discharge nozzle from pump base point.
Alpha= 0.003832 mm/mm
Displacements therefore:
X=0
Y = 500 x 0.003832 = 1.916 mm
Z = 300 x 0.003832 = 1.1496 mm
No rotational displacements
2. Add a construction element between the nozzle node (10) and the pump base with
appropriate material and temperature.
For this exercise, specify the displacement set for node 10 as above.
Vessel Connection – Node 110
As before we have the same two approaches; provide the thermal growth of the nozzle, or model
the vessel. The thermal growth of the vessel is
X=0
Y = 8.43
Z = -2.87
RX = 0
RY = 0
RZ = 0
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Support Riser
We wish to unload the pump discharge nozzle as much as possible, and also support the thermal
growth of the riser. To do this we will locate a spring hanger near the elbow (node 70).
Place a Carpenter & Paterson hanger at node 70
Support Horizontal Runs
The suggested maximum support spacing for 8” water filled pipe is 5.8m for horizontal straight runs.
75% of that spacing for horizontal spans including changes in direction would therefore be 4.35m.
This will support the pipe weight and so account for the SUS case. Since we will check these
SUStained stresses (and since the fluid weight is less than water-filled) we can exceed the suggested
spacing.
Locate a restraint on each horizontal 8” run using the Break function.
70-80 add node 75, located 1200mm before node 80
80-90 add node 85, located 3000mm after node 80
Add the following restraints:
Node 75
1x (double acting) Y restraint, with a friction coefficient of 0.3
1x guide with a gap of 8mm, again with friction
Node 85
1x (double acting) Y restraint, with a friction coefficient of 0.3
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The model is now complete. Error Check the model and run the Recommended load cases.
Immediately it can be seen that there is an issue with the EXP case. Check the stresses for both the
EXP and SUS cases.
The SUS case is OK
The EXP case however is an issue:
The only issue is at node 30, where the stress is 130% of the allowable.
Node 30 is the Tee connecting the bypass.
One of the easiest fixes for an overstressed component is to replace it with a stronger component.
Component strength is indicated by the stress intensification factor (SIF). Here, the stub-in branches
are overstressed. Their in-plane SIF is 3.96 and their out-plane SIF is 4.95. Adding a pad to these
tees will strengthen them. Check the effect of adding a pad by using the Tee SIF Scratchpad. Change
the unreinforced tee to a reinforced tee with a 9mm pad. Using the Recalculate button will show
that the SIFs have been reduced to 2.04 and 2.38 for in-plane and out-plane respectively.
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Accept these changes and apply to node 30.
Re-run the analysis and review the results.
The expansion case is now ~75% rather than 130%.
The SUS case is still 14%.
Hanger Sizing
Review the Hanger table with text. A Carpenter & Paterson DV70 spring is selected.
Hot Load 1355N, deflection 17mmm cold load 1544N. We need to now see if this is appropriate.
View the Restraint summary for the OPErating and installed (SUS) cases.
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Look at the operating load and installed load on the pump discharge nozzle (node 10). Typically,
with a spring hanger above the pump, the pump will see a positive (up) load in the cold state and a
negative (down) load in the hot state. Here, the piping pushes down on the pump in both states.
This spring is undersized. Why? The calculated load carried by the spring is based on the overall
distribution of weight between all vertical supports. The interaction of the pump nozzle (anchor),
the spring and the other Y supports has very little load “assigned” to the hanger location. More
weight is carried by the pump rather than the spring hanger.
Deadweight that is resting on the pump must now be transferred to the hanger. The easy way to do
this is to remove the load-carrying capability of the pump in the initial weight analysis when the
hanger load is first calculated. To do this, CAESAR II allows the restraint to be “freed” – effectively
removing this node from the hanger sizing calculation, so the load is distributed amongst the
remaining support locations.
Return to the input and on the hanger; free the restraint at node 10 in the Y axis:
Now reanalyse the system.
Review the results again.
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The EXPansion stress results are unaffected by this hanger change. The maximum SUS stress ratio is
also still around 14%.
Review the hanger table with text.
A Carpenter & Paterson DV70 has been selected again, but the hot load has increased to 7000N and
the installed load has increased to 8000N.
Review the restraint summary report to view the pump load (node 10).
The resized spring now pulls up on the pump in the cold position and unloads as the system heats
up. (The riser growth drops the load supplied by the spring.) This spring is much better than in the
first iteration; however it could be improved even more. The hanger data input provides for the
specification of the hanger operating (hot) load:
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Pump Load
Review the restraint summary report for the OPE and SUS (installed) cases. The loads shown for the
pump are a little high in some directions – MX is almost 30000N. However no indication is given that
these loads are excessive.
American Petroleum Institute Standard 610 (API 610) sets maximum nozzle loads for pedestal
supported pumps. CAESAR II provides this calculation. Run this analysis with the pump data
provided above and using the discharge loads from this analysis. Since both suction and discharge
nozzles are evaluated together, the Table 4 limits in API 610 can be doubled (see API 610 Annex F).
API 610 Analysis
Access the API 610 module from the Analysis menu on the main window.
Create a new file and input the pump data.
The pump centreline can be seen to be in along the X axis, therefore the angle between X axis and
pump Centreline is 0°. The angle between the Z axis and the pump centreline is 90°. The direction
cosines are therefore
X Cosine = cos 0 = 1
Z Cosine = cos 90 = 0
The Base point node number can be any arbitrary node number. This node number does not have to
appear in any of the piping model, but is used by API 610 as a point of reference about which to sum
moments.
The suction Nozzle is not defined in the piping model as we are given the loads so can input these.
We also know that this is a 10” End type suction nozzle.
The discharge nozzle is in our piping model, and is node 10. This is an 8” Top type suction nozzle.
As mentioned, since both suction and discharge nozzles are evaluated together, the Table 4 limits in
API 610 can be doubled.
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The suction nozzle loads and location have already been given:
Suction is -380 mm in X from pump centre.
Piping load on suction nozzle given as: (4450,-3550,-5340) N and (-4070,-3390,2170) N-m
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The pump discharge nozzle is located 500 mm above (Y) and 300 mm in Z from pump centre.
The loads on the discharge nozzle can be imported from the piping model. This will be the OPE case.
Now analyse the pump.
The suction nozzle passes OK. But the discharge nozzle fails.
The load in the local Y direction (global Z) is excessive as are all three moment terms. The worst
component is the local My (global Mz) which is almost 10 times the Table 4 limit.
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Fix Model – Part 1
We need to know what is causing this large load. Return to the piping model and again view the
results. Review the Restraint summary for the OPE and SUS (installed) cases.
The large loads are present in operation but not at “installation”. Therefore these excessive loads
are caused by the thermal expansion of the system. To reduce these loads we need to increase
system flexibility. There are two options to do this.
1.
2.
Model existing flexibility not currently in the model
Modifying the piping and/or support layout.
The most inexpensive modification would be to provide more modelling detail – modelling flexibility
in the system that is not currently included. Welding Research Council Bulleting 297 provides
flexibilities for cylinder – cylinder intersections. These flexibilities may be applicable to the vessel
connection at node 110.
Include WRC 297 flexibilities
The vessel nozzle/connection is as follows:








Vertical vessel constructed of SA-516 Gr. 70
OD = 1500mm (D), wall = 4.75mm (T)
Nozzle is 2200mm above skirt
Skirt is 3000mm above foundation
The long weld neck flange serves as the nozzle
OD=247.65mm (d), wall=22.225mm (t)
Nozzle pad is 4.75mm thick and 100mm wide
A tray is within 600 mm of the nozzle and a stiffener ring is 1000 mm on the other
side
Firstly we must evaluate the vessel/nozzle to check that the WRC 297 approach is valid.
We have d and t (relating to the nozzle) and D and T (relating to the vessel) described as above.
Below, T is the vessel thickness plus the pad thickness.
According to WRC 297:
⁄
⁄
⁄
⁄

⁄

⁄

We will use this data even though it is outside the acceptable range
Apply the nozzle flexibility and complete the vessel/nozzle data in the Nozzles input.
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The nozzle node is at 110 (recall that the nozzle is represented by the long weld neck). A valid nozzle
node has only a single element connecting to it (i.e. must have a free end) and also a nozzle node is
not restrained nor does it have any displacements specified. We have displacements applied at
node 110, for the vessel thermal growth. To rectify this we will specify a vessel node and apply the
displacements to the vessel node.
The vessel node is optional and works in a similar way to CNode described earlier. Give the vessel
node a unique number. In this case ours will be 1500. In addition, change the node the
displacements are acting on to 1500 as well.
Fill in the remaining vessel data, including the direction cosine – the vessel is vertical (Y) so the Y
direction cosine is 1.
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This models the nozzle flexibility by inserting a zero length spring which is inserted between the long
weld neck flange (100-110) and the displacements representing the vessel thermal growth – which
we have now reassigned to node 1500.
Run the error checker. The WRC nozzle flexibilities will be calculated and included in the notes.
The nozzle provides limited axial flexibility, but the longitudinal and circumferential bending
flexibilities appear significant.
Re-analyse the system and again review the results.
Review Results
These changes have not had any effect on the SUS case, and the EXP case is still below the allowable,
in fact the highest stress has now dropped slightly - as we have added more flexibility in the model.
The selected spring hanger is still a Carpenter & Paterson DV70, but the hot load has increased by
around 40N.
However, we were previously concerned with the pump loads. Review the OPE case restraint
summary. The loads on the pump (node 10) have now decreased.
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Run these new loads through the API 610 processor. Use the “Refresh Loads from Current Job”
button to bring in the new loads.
The values have decreased slightly, but still the discharge nozzle fails.
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Fix Model – Part 2
Return to the piping results and review the OPE restraint summary once again.
There is a rather large load on the guide (Z restraint) at node 75.
The thermal growth of the long Z run from 80-90 loads the guide and pushes the elbow at node 70 in
the positive Z direction. This thermal growth increases both the pump load in Z and the bending
moment about X. Is the structure guiding the pipe as rigid as the CAESAR II model says it is? If the
guide has lower stiffness, the pump loads may reduce within their allowed limits. There may be
reason, then, to model the structural steel that is interacting with this piping system.
There are two structures – a frame under Node 75 and a T pole under Node 85. These structures will
be included in the analysis.
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Build Steel Structure
CAESAR II includes a structural modeller. This module can be used as just described, to model steel
structures to support the piping in order to include the flexibility in the supports, as opposed to fully
rigid supports.
Return to the CAESAR II main window and create a new file. Specify this as structural input.
The structural wizard will guide you through the process of setting up the structural file.
First the units to be used must be specified. Ensure that the Training units (TRAIN.FIL) are selected
here. Click Next
On next screen, the vertical axis should be selected for the model, either the Y or Z axis can be set to
vertical. Select the Y axis as vertical and click Next
The following screen is to specify the material and material properties.
Any number of materials can be specified, each identified by a Material ID. For each material ID the
material properties can be specified. Within the steel modeller, each steel member is assigned a
material ID. Accept the defaults for material ID number one and click Next.
(The units are those from the specified *.FIL from the first step).
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The following screen is to specify the steel members to be used in the structural model. Each steel
member is identified by a section ID and can be either selected from an included database of
sections, or can be User defined.
In the structural modeller, each element can be assigned a section ID as well as a material ID.
We will use I-Beams in our model and will select from the built in database. Choose the Select
Section ID button and select the following I-Beams
Section ID 1:
Section ID 2:
W8 x 31
W6 x 20
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The final stage of the structural modeller wizard is to specify the method of element definition.
There are two options for this.
Method One - “EDIM” method, which is similar in concept to how piping elements are defined – a
start node and an end node are specified, along with the distance between the two to define the
structural elements.
Method Two – Node/Element method is a slightly different concept. Nodes are added and are
located at points in 3D space. Elements are then defined and users specify the nodes which each
element connects.
Select Method one and click Finish.
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The steel modeller will now appear with the options selected in the wizard added to the “Card
Stack”.
The Card Stack is a logical list view of the structural model where all parameters are listed and can
be edited.
Now we will define the structure. As we have used the wizard to define the material and section IDs,
the next items we can define are the elements themselves. Use the EDim button to add a new entry
to the card stack.
From the sketch we can see that starting at node 2000, there are two vertical steel members, both
2500mm in length. These two members can actually be defined in one entry into the card stack as
they are identical.
Expand the new row in the Card Stack and first enter the From and To node numbers as 2000 and
2010. Also enter dy as 2500. Specify the section ID and Material ID for this section also. Section ID
is 1 and Material ID, as there is only 1 is 1. We now have one element, from Node 2000 to 2010,
2500mm in length in the vertical (+Y) direction.
The inc, incTo and last fields can be used to duplicate this element quickly without adding a new
entry into the card stack. The inc field will increment the “From” node, starting with the original
“From” node. i.e. if we enter 10, the “From” node on the second element will be 2000 +10 = 2010.
So in this case would connect to the first element. The incTo is the same concept, but using the “To”
node. The last field is simply the “to” node on the last element to be defined.
Enter inc and incTo as 10 and the last “To” node will be 2020.
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Continue and add a second Edim to the card stack. Define element 2010 – 2012. This time the
section ID 2 will be used.
The model so far should look like the following
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Continue with 2002 – 2012. Again, this entry in the card stack will define multiple elements
Add the finial members on the top. As these are not identical, they must be defined as separate
entries in the card stack.
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The final step is to anchor the steel at the base. Use the Fix icon to add a “Fix” entry into the Card
Stack, and fix at node 2000 and 2002. Fix in all degrees of freedom.
The completed frame should look like the following.
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Save the frame. On saving the structural modeller will check the file. The following dialogue will
appear. Ensure that all three check boxes are checked.
Now create a new structural file for the T-post.
As before, follow the new structural file wizard. The T Pole is similar to the Frame in that it is the
same material and the same two steel sections used – W8 x 31 and W6 x 20.
After completing the wizard, the Card Stack should again display as before with the same starting
entries.
The first thing to note about the T Pole is that it is rotated 90°. Add in a rotation angle of 90°
Continue and add in the elements
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1000 – 1005
The remaining horizontal elements will not be rotated 90°, so add in another Angle and set this to 0
The remaining horizontal elements will also all be Section ID 2. To save having to specify Section ID 2
for all elements, a default Section ID can be set.
Set this default section ID to 2.
Continue and add the remaining elements as follows
From
1005
1005
1015
To
1010
1015
1020
DX
-600
300
300
Finish off by fixing node 1000.
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The completed T Pole should look like the following
Save the T Pole and again ensure that all three check boxes are checked.
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Combine Pipe and Steel models
Return to the piping input. We will now include the Steel models in the Pipe model. Select the
“Include Structural Files” button and browse to locate the two files just created.
After Clicking OK the steel members will be included in the pipe file, however as there are no
common node points between the pipe and steel, the structural members are simply located at the
origin. We now need to move these structural files into the correct location.
A quick review of the pipe and steel model node numbers shows that pipe node number 75 will be
connected to steel node number 2021 and pipe node 85 will be connected to steel node 1015.
However the centrelines of the steel and pipe are not in contact, rather the bottom of the pipe is
resting on the top of the structure. The pipe and steel can be connected either way; connecting the
bottom of pipe with top of steel will be a more visually pleasing model, and in some cases (e.g.
where friction or a guide is included on larger diameter pipe) the proper contact point will affect the
results.
A dummy rigid element will be built at both support points to offset the pipe above the steel. First
locate element 70-75. INSERT a new element AFTER this element. The new element will be from 75
to 1075 and the distance between these nodes will be -210 mm in Y. Make this a weightless, rigid
element.
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Now return to the element 70-75 and redefine the restraint at node 75 by changing the Node to
1075 and define a CNode (connecting node) of 2021. Now that the pipe to 1075 is in Y, the Guide
must be replaced with a Z restraint (a Guide makes both X & Z on a Y pipe). Be sure to do this for all
restraints at this point.
The frame will now be moved to connect to node 1075.
Repeat this procedure for the restraint at 85, creating a new element 85-1085 and connecting 1085
to 1015.
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The completed model will show the steel structures supporting the pipe as below.
Re Analyse the system.
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Review Results
The SUS case has increased very slightly, but the EXP case has dropped down to 38%. This is because
further flexibility has been added to the system. Specifically the stiffness at node 75 which was a
rigid guide now matches the frame stiffness. The OPE displacements report shows that the 8mm
gap on the Guide (now the Z restraint) is closed, but then the guide itself shifts another 8mm in the Z
direction, rather than being stationary as a rigid. Note the displacements on nodes 1075 and 2021.
The restraint summary for the OPE case shows a significant reduction on the operating loads on the
pump nozzle.
As before, run these new loads through the API 610 processor (use Refresh Loads button to bring in
the new loads).
The discharge nozzle now shows that only the moment about the Y axis (global Z) exceeds the
allowable limit.
Adding the steel effectively increased the guide’s gap. This greatly reduced the pivot action and the
resulting pump load.
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Fix Model – Part 3
The only issue with the model now is that the local Y moment, global Z moment on the pump
discharge nozzle (node 10) is excessive. Without changing the position of the pump or vessel nozzle,
or changing the thermal strain, the only way to reduce these loads is to add flexibility to the layout.
There is no inherent flexibility that was excluded from the model so an expansion loop will be
introduced.
How big a loop is required and where should it be placed?
Expansion loop legs should be perpendicular to the thermal growth causing the load. We will focus
on the Z axis bending moment. This bending moment is being caused by the +X force – the thermal
growth in the X direction (element 70-75).
Therefore the loop can be added in the Y or Z direction (perpendicular to X). Which is the best loop
layout?
Layout A - A loop in the Z direction at the end of the X run (node 80)
Layout B – A loop in the Y direction at the end of the X run (node 80)
Layout C – A Y loop on the opposite end of the X run (node 70)
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⁄
∑
The bending stress at the nozzle is estimated using
= stress range in leg j (leg j is orthogonal to the direction of thermal growth to be absorbed)
= Length of leg j
= length of leg i (leg i represents each leg helping to absorb the thermal growth)
We know that
∑
So let 6EIΔ = K
Therefore solving for K using the current M (MZ Bending moment which is 5139 Nm) and Li and Lj
Lj = 4200mm
Li = L1 6205mm & L2 4200mm
∑
(∑
)
Keeping K as a constant, we can attempt to reduce M. To do this we will increase the length of the
leg in the three layouts mentioned previously and recalculate M
The following table and graph summarises this.
Added Loop
Leg (m)
In Z
(Layout A)
0
1
2
3
4
5
5.153
3.591
2.542
1.831
1.343
1.004
In Y
(Layout B)
5.153
5.120
4.902
4.395
3.657
2.865
Riser
(Layout C)
5.153
5.248
4.907
4.326
3.686
3.092
Max Mz
(= 2 * Table 4)
3.525
3.525
3.525
3.525
3.525
3.525
Red = above max Mz
Green = below Max Mz
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Effect of Various Loops
on Pump Moment - Mz
Moment (KN-m)
6
Riser
(Layout
C)
4
In Y
(Layout
B)
In Z
(Layout
A)
2
Max Mz
(= 2 *
Table 4)
0
0
1
2
3
4
5
Added Loop Leg (m)
As can be seen, the most effective way of reducing the MZ moment is to use layout A – an expansion
loop along the Z axis. This increases Li which is cubed in the equation so will have a much larger
effect of the MZ Moment.
According to the calculation, slightly over 1m run in the Z direction is required, however this simple
equation does not take into account any rigid elements or elbows, nor does it consider any
intermediate supports such as the guide at node 75.
We could insert a loop of 1m in length and continue iterating the model until we find a suitable loop
length. However this can take time and finding an efficient loop design may involve several
iterations, even on a simple setup such as this. CAESAR II provides a Loop Optimisation Wizard to
automatically size and create an expansion loop to get the most efficient loop for the target data.
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Loop Optimisation Wizard
Return to the model and use File > Save As… to create a new iteration of the model with an
expansion loop. After performing the Save As… the analysis must be run once again because the
Loop Optimisation Wizard uses existing results in modifying the layout.
Run the analysis and return immediately back to the input. The Loop Optimisation Wizard button
will now be available (if this button is ever greyed out then there are no results available for use –
rerun the analysis).
Select element 75-80 as this is where the loop will be placed and click the Optimisation Wizard
button to access the wizard.
The Loop Design Wizard will appear and the data required can be input in order for CAESAR II can
design the expansion loop.
The wizard will create iterations of a loop setup in order to focus in on a specific Stress value or
Restraint load. We wish to reduce the Restraint Load on node 10 to below the allowable for API 610
table 4. We will reduce the load to 3300Nm (currently the load is around 5150Nm).
The loop will be located on what is currently the element 75 – 80. This will therefore be as in Loop
Layout A.
The final thing to define is the space allowed for locating the loop. A cube of space can be defined
which the loop will fit inside. The Wizard will create the largest loop possible in the available space,
and if this is below the specified target load, the wizard will continue iterating to create the most
efficient loop possible, as close as possible to the target value.
In the Loop Design Wizard, select the OPErating Load Case and choose the target data to be
Restraint Load.
As we already have element 75-80 selected, this element will be selected anyway.
The table will be filled in with the results data. Double Click in the MZ cell on the Node 10 row. This
will fill in the Node and Type fields. Enter 3300 as the data in the Load field.
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Specify the Loop Type as the centre loop type – this matches the type A that we have already
determined is the most efficient. The final option in the loop type section will allow the wizard to
evaluate all of the Loop Types and determine the most efficient. This takes longer as 8 loop types
are defined.
Also in the loop type section, change the Height to Width ratio to <none> to allow the height to vary
as needed.
Finally the space available for the loop must be specified. Click the Draw Cube button. A cube of
space will be shown in the model. Currently this will be facing the wrong way. Click and Drag the
point labelled PT3 to reposition the cube in the correct orientation. On doing this the “Major
Direction” field will change to –Z. Increase the size of the cube in the –Z direction to ensure that
there is enough room to design the loop.
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Once finished, click Design. The wizard will run through a number of iterations and converge on the
defined target value.
Once complete the loop will be added into the model automatically. A confirmation message of the
total length of pipe and number of bends is displayed
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The loop wizard has added an additional ~3070mm of pipe. Split between the two legs to the loop,
each leg is now ~1535mm longer. Our quick hand calculation indicated a length of just over 1m, but
as noted previously this did not take into account rigid elements or elbows, nor does it consider any
intermediate supports such as the guide at node 75. In addition, we used a target value slightly
lower than the Max Mz as in the hand calculation.
For simplicity, round up the length of each of the two new legs to 1600mm. With even more
flexibility, the MZ moment at node 10 will be lower still.
Re-run the analysis.
Code Checks:
SUS –Max stress is now 16% at node 68. Node 68 is the top of the riser. Recall how CAESAR II adds
intermediate node points around the bends as discussed in the TURBO example.
EXP – Max stress is 34% located at node 78. This node is the far end of the elbow at the start of the
long Z run
Hanger Sizing:
Carpenter & Paterson DV70 size 11 hanger is still selected. The hot load has decreased slightly.
Pump Load:
The loads on Node 10 look much better now:
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Re-run these loads through the API-610 processor once again
This time all loads pass on the discharge nozzle. The local My (global Mz) is now 1.85 times the
allowable (we have used the 2x table 4 approach) and so now passes.
We have reduced the load on the pump by adding flexibility into the system in the form of an
expansion loop. The addition of this loop required an extra 1.6metres of space. What if this space
was not available?
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Fix Model – Part 4
We will now return to the model without the expansion loop and once again attempt to reduce the
load on node 10, this time assuming that there is no space available for addition of an expansion
loop. In this case we will add in an expansion joint instead to add in flexibility.
Open TUTOR.c2 (the file before the expansion loop was added) and save as
Tutor_Expansion_Joint_Check.c2
We already know that the issue with the pump is the Mz moment. This moment as we have seen is
caused by the thermal growth of 70-75. This horizontal displacement at node 70 causes the bending
moment.
As such we wish to prevent this horizontal growth from being applied to node 10.
We will include an expansion joint to absorb this horizontal growth. Adding the expansion joint just
above the pump will best absorb this growth.
What type of joint should be used? As we are only trying to absorb movement by lateral deflection
only and there is no axial deflection or relative bending rotations at the joint ends, a tied expansion
joint will be suitable.
First of all we need to know the horizontal deflection that we have to absorb. We will use CAESAR II
to determine this by breaking the system above the pump and viewing the displacements report.
The value we obtain from this can be used to select the number of convolutions in the expansion
joint.
Select node 20 to 10 and change to 21 to 30
The system will now have two sub-systems sharing the same origin. We need to reconnect 20 and
21.
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Add a Y restraint at node 20 and specify node 21 as a CNode.
We also need to prevent any rotation at this point as well. Specify three rotation restraints (RX., RY,
RZ) at node 21, CNode 20
Leave the transverse directions X & Z free to move. The system near the pump connection should
now look like the following:
Re-analyse the model once again.
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Using the EXP case Displacements report, we need to calculate the change in position between Node
20 and Node 21. Nodes 20 and 21 will move together in Y, RX, RY, RZ because of the Node/CNode
restraint definitions.
DX = 33.4mm
DZ = 11.446 – 1.150 = 10.3mm
This results in a relative horizontal displacement of 35mm.
This also shows a Mz moment of 4900Nm. This is quite a high load – as the system is completely
free to move in the X and Z direction, resulting in the largest displacement. If we were to introduce
some stiffness (as would be in the expansion joint itself) this displacement would decrease.
Using the Senior Flexonics/Pathway expansion Joint catalogue, we will select a 3.5kg/cm2 class 150,
8” expansion joint. The catalogue shows a 20 convolution expansion joint provides 38.8mm lateral
deflection. This satisfies our requirement. However this expansion joint also adds a lateral stiffness
of 6kg/mm or 58.7N/mm.
If we introduce this stiffness, the deflection would reduce. Reduced deflection drops the required
number of convolutions and, in turn, increases the stiffness between nodes 20 and 21.
This iterative process can continue until the deflection test fails or the pump load becomes too high.
Add the final two restraints (X and Z) between 20 and 21. Set stiffness to 58.7 N/mm
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Re running the analysis and viewing the EXP case displacements shows the new relative lateral
displacement of around 21mm.
The OPE restraint loads show that the MZ has now decreased drastically and is now around 25% of
the previous value.
However, the MY is excessive at over 6000Nm. This moment will also place torsion on the expansion
joint and this torsion may also be excessive.
If this observation did not stop the iteration, how would this process proceed?
•
Test 16 convolutions - 16 convolutions allow 24.8 mm lateral deflection and has K = 118
N/mm
•
Reset X and Z restraint stiffness to 118 and reanalyse
•
Check travel limits for the proposed joint and the load limits for the pump.
If 16 convolutions is OK and overall joint lateral translation drops, test a shorter (i.e., fewer
convolutions) joint.
In conclusion, because of the large global My on the pump and the torque on the expansion joint,
the proposed length and location of this joint should be reconsidered.
For the purposes of this exercise, analysis of a 20 convolution, tied expansion joint will be evaluated.
For this length, a tied universal joint would probably be preferred; consult manufacturer for other
options.
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Model the Expansion Joint Assembly
The flanged expansion joint would be located between the discharge nozzle and the existing weld
neck flange. To save time in this examination, the expansion joint will be placed between the flange
and pipe rather than between the nozzle and flange. The error introduced will be small.
Return to Tutor.c2 and rename as Tutor with Expansion Joint.c2
Select Element 20-30 and access the Expansion Joint Modeller.
Select to create an expansion joint with the following properties:
Pressure
Style
Convolution Material
# Convolutions
End Type
50 pound
Tied
304SS
20
Slip on (Both Ends)
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After clicking OK, CAESAR II will split the selected element to fit in the expansion joint. Which end of
the element to place the joint must be specified. We will split at the From end (Node 20).
The temperature of the element in question is 315°C. Apply this temperature to the joint, which will
subsequently cause the stiffness to be adjusted.
The expansion joint modeller will finally confirm the creation of all the elements to be used in
creation of the joint. The stiffnesses will also be displayed, along with the Allowed Movement.
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Click build and CAESAR II will attempt to define the expansion joint using the data supplied/obtained
from the catalogue.
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Re analyse the system.
Using the Expansion Case displacements, calculate the lateral deflection between nodes 21 and 22 –
the nodes on either end of the expansion joint.
DX = 20mm; DZ = approx. 12mm. The overall deflection is therefore around 23mm.
The Flexonics catalogue shows that this displacement is acceptable for a 20 convolution joint.
There is minimal Axial deflection (DY = approx. 0.3mm) and Angular Rotation (RX and RZ = 0mm).
Torsion in the joint is 0.3 degrees. The catalogue actually shows that this torsion is excessive.
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Document the Analysis
The analysis is now complete, and the model is acceptable. We will work with the model including
the expansion loop, rather than the expansion joint.
The stresses are all acceptable and well below the code allowables. The loads on the pump are also
all acceptable and below the allowables for API 610.
We can now document the analysis and produce a report which could be supplied to a client,
including a plot of the system and annotated stress isometrics.
Custom Reports
In addition to these, custom reports can also be created.
Custom reports are created using the Report template editor.
In the report template editor, a new report can be created by adding in all the columns you require.
Any column from any report section can be selected.
The following sections are available. The individual columns from these reports can be added in any
order as required.
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In addition to setting the column order, various other properties on each individual column can be
set. These properties are as follows:
As well as properties for each individual column, report wide settings can also be set.
The template can be either an individual report (one load case per report) or a summary report
(multiple load cases per report). Or a Code Compliance report (detailed information on calculated
values vs allowable) or a Nozzle check report (Displays nozzle loads if present).
We wish to create a custom report which shows the stresses in the EXP case and the SUS case similar
to the “Stresses” report. View this report for the EXP and SUS cases.
The issue here is that two reports are created, one for each case.
But we wish to view both cases in one report. This therefore would need to be a “Summary” report.
View the stress summary report for both of these cases.
This report displays the max stress for each case in one report, but does not display the stresses at
each node, like in the stresses report. We need a summary report which shows data at each node.
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Create this as a custom report. So that we can view sample data in the report, select the load cases
as well before accessing the report template editor.
First of all give the report a title “Stress Summary with Detail”. The report template preview will
update to show this. Also change the Report Type to Summary.
The report itself we wish to be shown in a nicer to read font that Courier. Select Calibri, 11pt text
and align the column text to the centre of the column to ensure everything stays inline.
Now we can add the following columns into the report, in the following order:
1. Bending Stress
2. Torsion Stress
3. SIF in Plane
4. SIF Out Plane
5. Code Stress
6. Allowable Stress
7. Ratio %
8. Piping Code
Enter in the column number next to each column required. Also tick the Show Piping Code check
box.
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The report preview should show a sample of the report.
Currently there is no summary table like in the Stress Summary report showing the max stresses.
Insert this into the report as well by checking the Show Highest Stresses check box.
Save the complete report.
Any custom reports created can be exported and then imported on any machine so that all users
have access to all reports.
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Filters
We have created a new customised report to show the data we are interested in. View this report
for both the SUS and EXP load cases.
The report will look as we expected and show all the data we require. However there is a lot of data
as we have all the stresses at all nodes, in two load cases. Reviewing the data shows that a number
of nodes have very low or even zero stress. We can filter this data out to display only stresses above
a certain value. Admittedly, our stresses are quite low throughout (highest is only 33.5%), but we
still are not concerned with stresses that are only a fraction of a per cent for example. As such we
will filter the data so that any stresses <5% will not be shown.
Close the report and access the Filters Dialog from the menu.
The filters dialog allows the data to be filtered on a combination of fields and values. The filters
work using Boolean algebra. As such, if multiple fields are required, you must select whether to
include an AND clause or an OR clause in the Filter options. Additionally, any values entered in the
filter can be either Absolute values – the modulus of the value is used (i.e. if “=500” is entered, -500
and 500 will be classed as matching the filter)) or Signed values (i.e. if “=500” is entered, -500 will
not be a match, but 500 will). The results can also be filtered on node numbers.
The filters can be combined by Fields and Classes. The Classes are the categories and are essentially
each tab in the filters dialog. The fields are the individual fields and are essentially each entry on
each tab. Any filters are only applied if the field filtered on is actually displayed in the report. So if a
restraint load filter of FY > 1000N was applied as a filter, this would not be applied to for example
the displacements report – FY is not displayed in the Displacements report.
Create a filter to display, as mentioned previously, all stresses greater than 5%.
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Click Apply and now review the Stress Summary With Detail custom report for the SUS and EXP
cases.
The report will not show every single element now, only those which have stresses higher than 5%.
Generate Report
As we have seen, there are many reports produced by the CAESAR II analysis. All these reports can
be viewed on screen as we have been doing, or alternatively each report can be sent to Microsoft
Word or Excel, or a text file.
We can produce a full report document of the type which could be submitted along with the analysis
for approval.
For our report we wish to include the following information.







Input Echo
Load Case Report
SUStained Stresses
EXPansion Stresses
OPE & SUS restraint loads
OPE displacements at all nodes
Hanger Table with text
This is a simple procedure and is simply a matter of selecting the reports to publish which contain
the data we require and including them in the “Output Viewer Wizard” section of the output
processor.
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Review each of the reports mentioned above in turn to verify that the data is suitable. Start with the
Input Echo.
The listing options window appears prior to the report being generated, where all input data can be
selected for inclusion in the input echo By default CAESAR II picks the most relevant data depending
on the model input – i.e. if WRC nozzle flexibilities are included, this is ticked, if there were no WRC
297 nozzle flexibilities, tis box would be un-ticked by default.
Select these defaults and click OK.
Review the Input echo to ensure that all data required is included.
Once happy with the contents of the input echo, close the report and click on the  Add button to
add into the Output Viewer list.
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Repeat this process for each of the reports shown, including for the SUS and EXP stresses; add in the
custom Stress Summary with Detail report.
Once complete all reports we wish to publish will be in the list. We will now send these to MS Word.
Ensure that the Send to MS Word radio button is selected and click Finish.
Word will load in the background and CAESAR II will publish all the selected data. The results will be
inserted as tables into the Word document.
Once complete, review the Word document. Formatting can be applied as usual within Word.
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ISOGEN Stress Isometrics
In addition to the Word Document report, stress isometrics can be generated and annotated with
input/output data to supplement the report.
Stress isometrics can be configured so that the output appears as the user requires, if you have
company/client standards for isometric drawings, these can be set up and configured using the
ISOGEN I-Configure module supplied with CAESAR II.
We will set up I-Configure to use one of the default styles. There are many switches which are
available to control the appearance and content of the isometrics. These switches are not covered
in this course. However, a number of Wizards are available for configuring common parameters.
I-Configure can be accessed from the CAESAR II main window, from the Tools menu.
The I-Configure window will currently be empty, as no styles will be set up.
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Most of the buttons on the toolbar along the top will be greyed out.
There will however be two buttons available; the first of which we are concerned with, in that this
button will be used to create a new Isometric directory. (The second button is simply to connect to
an existing isometric directory).
ISOGEN uses a specific file/folder structure, at the top is the isometric directory. Contained within
the isometric directory is a number of Project directories. Each isometric directory can contain
multiple project directories. Contained with a project directory can be many style directories. As
above, each project directory can contain multiple Style directories.
Within each style directory are a number of files, each of which contain various different data for the
appearance and content of the isometric output (including the format of the output - *.DWG, *.DXF
etc). These files are created by I-Configure. I-Configure reads an XML file on selecting the current
style containing all the settings and then writes these settings to various files which ISOGEN reads
when producing an output.
Choose to create a new Isometric Directory.
We will create a new folder on the E:\ drive in which all the ISOGEN data will be located.
Browse to E:\ and create a new folder called ISOGEN and set this as the Isometric directory.
An additional button is now available which allows us to create the project directory.
Within each project directory there must also be at least one style, so the template styles are
available to choose from.
Name the project TRNProject (spaces are not allowed) and select the Final Basic Style as the only
style to produce (Un-tick all other styles). Change the Name column to Stress-Iso as well.
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Before we produce isometrics, let’s check the output to see what an example isometric would look
like.
Before any style created in I-Configure can be used, it must be exported for use (as discussed above).
Select the Stress-Iso style and click Export Style.
Next we can process a sample file through ISOGEN to get a preview of what the output would look
like with our style. To do this, select the Preview Isogen Output button.
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A sample output will be produced. Select the Drawing preview.DXF and click View.
The resulting isometric will look like the one below. This is not quite what we want. We are
producing a stress isometric, so we do not need a Bill of Materials, and we also want a different
drawing border.
A sample drawing border already exists; we can use this sample border and turn the bill of materials
off.
Copy and paste the file from E:\Training\Masters\A2StressISOBorder.dxf into the isometric style
directory E:\ISOGEN\TRNPROJECT\Stress Iso.
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Within I-Configure, select the current style and in the bottom left pane, select the Overview tab.
Highlight the Drawing Frame entry in the tree. This will take you to the TemplateFile variable in the
table in the right pane. Double click this field and browse to the new file to be used as the border.
We have now specified our custom drawing frame, as we will not require a Bill of Materials on our
Isometrics, we have a little more space available for the isometric plot. Increase this space by
reducing the drawing margin. Currently the drawing margin on the right hand side is 202mm. The
left margin is only 10mm. Make these equal by changing the RightMargin to 10mm also. ISOGEN is
now allowed to use the space that was previously taken up by the BOM as extra space for the plot.
Finally we must now turn off the Bill of Materials. Still in the Overview tab, select the Material List =
True entry in the tree. Again, this will display the relevant variable in the right hand list. Change this
value to False.
Save the changes and Export the style once again so that we can see the results of these changes.
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This output looks acceptable. Save and close I-Configure and return to CAESAR II.
I-Configure is now set up and we can now use the ISOGEN module in CAESAR II to annotate and
produce stress isometrics.
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From the CAESAR II main window, access the ISOGEN isometrics module
CAESAR II will open the model for isometric production. Click OK to confirm and continue.
The model will be shown and can now be annotated
Annotating the model involves simply selecting which data to include in the annotations, and is
simply a matter of ticking the required data. All input data can in included as follows.
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All analysis data can also be included as well. For each load case run, the displacements, restraint
loads and stresses can be specified, as well as hanger data.
In addition to input and output data, custom annotations can be added to any node number or on
any element. Project attributes can also be specified and placed on the resulting isometric.
We will annotate our isometric with the following data:
Input:
Node numbers
Temperature T1
Pressure P1
Output:
SUS Max stress (node 68)
EXP Max stress (Node 78)
Nodal Annotations:
Node 10 – PUMP A CONNECTION
Node 110 – VESSEL D CONNECTION
Elemental Annotations:
Element 100 – 110 – LWN Flange as Nozzle
Project Attributes
Project Name
Project No
Client Name
Area
System
Prepared By
TRN
001
TRAINING
T1
TUTOR
<enter initials>
Select to Eit stress annotations to bring up the annotations panel.
From the panel select Input data and choose Node Numbers from the feature drop down list. We
wish to annotate all the node numbers. However, as we have discussed previously, CAESAR II
automatically splits bends and inserts intermediate nodes. We do not wish to annotate these
intermediate nodes. As such, select all nodes except the intermediate bend nodes. These bend
nodes should be as follows:
68
69
79
81
82
83
84
118
119
148
149
Select all nodes except those listed above. If you wish, return to the input and check which nodes
are the intermediate bend nodes on your model.
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Once completed, select Temperatures from the feature drop down and select T1. Do the same for
Pressure P1.
We can now specify the output data. Select Output tab and pick the SUS load case. Select the Stress
option. The highest stress for the SUS case is on the bend at the hanger (node 70) – the stress is
actually at node 68, but this is not selectable in the list. Node 60-70 is selectable and will annotate
correctly. Pick this node.
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Repeat for the stress in the EXP case. The max stress in the EXP case is at node 78
Next select the Nodal annotations. Annotate the two equipment connections as mentioned
previously.
Node 10 – PUMP A CONNECTION
Node 110 – VESSEL D CONNECTION
Perform a similar task for the elemental annotations, and annotate
Element 100 – 110 – LWN Flange as Nozzle
Finally enter the project attributes.
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Now we have completed the annotations, we can produce the drawings. Select Create Isometric
Drawing.
Select to Use Existing Style – as we have already created and configured our isometric style.
Browse to the Isometric ,Project and Stye directories as configured earlier
Once complete, click Create Drawing.
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After CAESAR II passes the information to ISOGEN, the data is processed and after a few seconds, a
drawing will be created.
Select the drawing created and click View.
The annotations and attributes specified will be inserted into the resulting isometric.
The isometric could do with a little tidying up – the attributes are not quite correctly positioned. The
colours could also do with some improvement – perhaps to make the restraints/hangers stand out
more. All this can be done via I-Configure if required.
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Cool H20 – FRP Piping
Cool H20 – FRP Piping
This job consists of an FRP cooling water header, which decreases from 1800mm diameter to
1500mm diameter to 1200mm diameter to 1050mm diameter as a succession of 750mm diameter
lines tap off it. Modelling this job provides the opportunity for the user to explore the capabilities
that CAESAR II offers for analysing FRP pipe. Additionally static seismic loads will be applied to this
system, illustrating methods using uniform loads and load combinations.
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Basics of Fibreglass Piping Analysis
Analysis of FRP materials is different to analysis of metallic materials, due to the orthotropic
properties of the FRP material.
Stress analysis of Fibre Reinforced Plastic 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.
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 fibres of a commercial
grade of glass (called 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.
Typically, on a micro level, the following failure modes are evaluated:
1) failure of the fibre
2) failure of the plastic matrix
3) failure of the fibre-matrix interface
Generally, the glass fibre is found to be much stronger in tension than is the matrix, so most tension
(along the axis of the fibre) is naturally taken by the fibre, rather than the matrix.
MICRO LEVEL GRP SAMPLE – SINGLE FIBRE EMBEDDED IN SQUARE
PROFILE OF MATRIX
Mini level analysis: 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 fibres
which may 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 element analysis inappropriate.
For mini-level analysis, a laminate layer is considered to act as a continuous material, with material
properties and failure modes estimated by averaging them over the assumed cross-sectional
distribution. The assumption regarding the distribution of the fibres can have a marked effect on the
determination of the material parameters; two of the most commonly postulated distributions are
the square and the hexagonal, with the latter generally considered to be a better representation of
randomly distributed fibres.
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Use of these parameters permits the development of the homogenous material models which
facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer. Typical
mini-level analysis shows that due to stress intensification and relative weakness of the matrix
relative to the glass fibres, laminate layers are typically very strong only in a single direction – i.e.,
the direction corresponding to the predominate alignment of the glass fibres.
STRESS INTENSIFICATION IN MATRIX CROSS SECTION
Macro level analysis: Where Mini level analysis provides the means of evaluation of individual
lamina 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 homogenous 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.
MACRO TO MICRO STRESS
CONVERSION
Since individual laminate layers are usually strong only in one direction, they are wound upon each
other at various angles to tailor the desired strength in various directions. Typically, for pipes, the
laminate layers would be arranged in such a way that their strength in the hoop direction is
approximately twice that in the axial direction.
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Total laminate properties may be estimated by summing the layer properties (adjusted for winding
angle) over all layers. For example:
||
(
)∑
||
Where:
||
= Longitudinal modulus of elasticity of laminate
= thickness of laminate
= transformation matrix orienting axes of layer k to longitudinal laminate
axis
= transformation matrix orienting axes of layer k to transverse laminate axis
= thickness of laminate layer k
Once composite properties are determined, the component stiffness parameters may be
determined as though it were made of homogenous material – i.e., based on component crosssectional and composite material properties, and interaction formulae for normal and shear stresses
can be developed.
COMBINED STRESSES σ AND τ AT FAILURE: ARALDITE CY232
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CAESAR II’s Orthotropic Model for Piping Systems
CAESAR II’s orthotropic material model is activated through the selection of Material 20 – FRP. The
orthotropic material model is indicated by the changing of two fields from their previous isotropic
values:
"Elastic Modulus (C)"  "Elastic Modulus/axial"
"Poisson’s Ratio"  "Ea/Eh*Vh/a".
These changes are necessary due to the fact that 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 with isotropic materials, the shear modulus does not follow the
relationship G = 1 / E (1-V) as for metals, so that value must be explicitly input as well.
In order 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 are 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):
⁄
Where:
⁄
= extension of piping element due to pressure
= longitudinal pressure stress in the piping element
= Modulus of elasticity in the axial direction
= Poisson’s ratio relating strain in the axial direction due to stress induced strain in
the hoop direction
= Hoop pressure stress in the piping element
= Modulus of elasticity in the hoop direction
= Length of piping element
This equation can be rearranged, to require only a single new parameter as:
(
Note that in theory, the single parameter (
(
⁄
⁄
))
) is identical to Va/h.
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Requirements of the ISO 14692 Code
In light of the isotropic nature of fiberglass reinforced plastic pipe, where hoop and axial strengths
are distinct, stress evaluation in ISO 14692 utilizes an idealized envelope of combinations of axial and
hoop stresses which cause the equivalent stress to reach failure. This curve represents the plot of:
(
)
(
)
*
+
Where:
= Allowable stress, axial
= Allowable stress, hoop
These terms are expressed in the ISO short term failure envelope:
ISO SHORT TERM FAILURE ENVELOPE
The (2:1) line indicates points where the hoop stress is twice the axial stress. This stress state occurs
in the wall of a pressurized, closed cylinder. The short term axial strength, σsa(2:1), and short term
hoop strength, σsh(2:1), occur where this (2:1) line intersects the failure envelope. By definition,
σsh(2:1)=2*σsa(2:1). A third strength is illustrated here – σsa(0:1) – this is the axial strength of the pipe
in the absence of pressure.
But there are several factors which reduce this short term strength in setting allowable (hoop and
axial) pipe stress:
•
•
•
Reduced long term strength of the component [fscale]
A design safety factor (based on load type) [f2]
Accommodation of specific load conditions (reduced strength associated with
temperature, chemical attack, and fatigue) [A1, A2, A3]
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This short term failure ellipse can be represented by a “fully measured envelope” shown below:
ISO FULLY MEASURED ENVELOPE
The line set intersecting the short term failure ellipse is a straight line representation of that ellipse –
labelled “short, ideal”. The manufacturer can establish σsh(2:1) from burst tests (and half of that is
σsa(2:1)) and can establish σsa(0:1) from tension tests. The next smaller line set, labelled “long, ideal”
reflects the long term strength of the pipe. This is the material limits usually provided by the
manufacturer. Using long term pressure testing, the manufacturer can project the “end of life”
strength of their components. The ISO Code reduces this material data by a system factor of safety.
This is the third line set, labelled “design” here. The limits used for piping evaluation are shown in
the smallest line set, “factored design”. Factored design limits account for those operating
conditions that reduce long term strength of the piping material.
Note also the (1:1) line in the figure above. This line represents the stress condition where the axial
stress equals the hoop stress. While having no engineering design significance, this line produces a
point on the failure ellipse where the axial limit will drop below σsa(2:1). The manufacturer may
provide σsa(1:1) (or the equal σsh(1:1)). If not the following simplification may be necessary:
ISO SIMPLIFIED ENVELOPE
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The dotted line set shows the simplified short term strength. This envelope would then be reduced
to a similar “factored (long term) design” envelope described above. This curve is also used in the
UKOOA Code.
ISO 14692 Annex D provides equations for effective hoop and axial stresses in piping component.
These effective stresses combine structural loads (due to weight, thermal strain, etc.) with pressure.
Safe design is assumed if both the hoop and axial stresses lie within the factored design boundaries.
CAESAR II analysis will evaluate both hoop and axial stress. The effective hoop stress must be less
than the factored design limit for hoop stress. The axial term will also be evaluated but, here, the
allowed axial stress is a function of the hoop stress. CAESAR II will report the stress term (hoop or
axial) that produces the largest stress/limit ratio.
The strength envelopes above are for straight pipe. Other piping components such as tees, bends
and joints do not have fully developed strength envelopes. Instead, manufacturers establish a
qualified stress, σqs, for these components.
(
)
(
)
(
)
Where:
= mean diameter of matching pipe
= reinforced pipe thickness of the matching pipe
= Qualified pressure of the fitting
This is a combination of equations (6) and (7) of the Code.
Qualified stress serves as the long term design hoop assigned to pipe. This qualified stress will be
adjusted by the same terms as pipe to develop a long term hoop design stress. The axial limit is
established through the biaxial stress ratio, r.
For pipe,
(
) (Equation (12) of the Code). The ISO Code assigns values for r for non-pipe
components in Table 4. Given r and the qualified stress, CAESAR II will calculate σsa(0:1) for the
component. CAESAR II requires qualified stress and biaxial stress ratio for bends and joints. Tees
have r=1 so only require a qualified stress. The stress envelope for a non-pipe component is a simple
rectangle bounded by a factored design hoop (or qualified) stress and an axial stress equal to r times
that hoop limit. Note that, for some piping components with relatively large axial strength, r can go
as large as 2 indicating that the component is just as strong axially as it is in hoop for any hoop
stress.
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Allowable Stress Data for this Model
As shown on the isometric, the material for this model is Wavin 55 material.
Pipe Data:
The value for long term hoop strength (shown as hl(2:1) in CAESAR II) may be obtained from vendor
data. In the case of the Wavin 55 material, it is available from the graph of the combined stress
failure envelope, as shown below. Note that the axes have been switched (axial stress on the
horizontal axis) on this graph relative to the traditional ISO envelope format, so the desired 2:1
position is now identified as R = 0.5. Likewise, the values in this graph include the service factor f2,
which can be eliminated by dividing the values on the outer curve by 0.67. This gives a f1 x LTHS
value of 125 N/mm2. An alternative means of getting this value is to find the value given by the
vendor for the long term Hydrostatic Design Basis; again, for this case 125 MPa. The long term axial
stress at maximum hoop stress, al(2:1), is, by definition, half of hl(2:1). The axial tension-only long
term strength is shown on the chart below as (41 MPa/0.67).
PIPES, WINDING ANGLE ω = 55°
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HYDROSTATIC PROPERTIES
Joint & Fitting Data:
Tees, bends and joints reference Qualified Stress instead of the pipe term hl(2:1). For this example,
these components have a lower “pressure rating” than the matching pipe. The Qualified Stress (Qs)
will also be set to 75 MPa. The axial stress limit for tees is constant but bends and joints may have a
varying axial stress limit measures by r, the ratio of two times al(0:1) divided by hl(2:1). For this
model, r is set to 2 for joints and 1.0 for bends. Bends also reference the hoop modulus of elasticity
which is entered here as the Eh/Ea ratio of 1.7
Other factors:
• A1 – factor for temperature
• A2 – factor for chemical resistance
• A3 – factor for cyclic service
• System Design Factor – this is a CAESAR II term that is combined with the CAESAR II Occasional
Load Factor (which is set or adjusted in the Load Case Options) to produce the “part factor for
loading”.
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Configuration Options for FRP Piping:
In this example, the material has the properties of Wavin 55o winding FRP pipe. These parameters
are:
𝐸𝑎
𝑀𝑃𝑎
𝐸
𝑀𝑃𝑎 𝐸 ⁄𝐸𝑎
𝐸 ⁄𝐸𝑎 𝑉
⁄𝑎
𝐷𝑒𝑛𝑠𝑖𝑡𝑦
𝐶𝑇𝐸
𝑘𝑔 𝑚
𝑚𝑚⁄𝑚𝑚⁄°𝐶
𝑆 𝑒𝑎𝑟 𝑀𝑜𝑑𝑢𝑙𝑢𝑠
𝑀𝑃𝑎
𝐵𝑒𝑛𝑑 𝐿𝑎𝑚𝑖𝑛𝑎𝑡𝑒 𝑇𝑦𝑝𝑒
𝐶 𝑜𝑝𝑝𝑒𝑑 𝑆𝑡𝑟𝑎𝑛𝑑 𝑚𝑎𝑡 𝑤𝑖𝑡 𝑚𝑢𝑙𝑡𝑖
𝑓𝑖𝑙𝑎𝑚𝑒𝑛𝑡 𝑟𝑜𝑣𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛
CAESAR II’s material database is not currently configured for orthotropic materials such as FRP.
Therefore, CAESAR II’s orthotropic model must be triggered through use of Material 20 (FRP), with
the material parameters entered explicitly. These parameters include:
Axial Modulus of Elasticity (Ea)
The Ratio (Ea/Eh)Vh/a
Pipe Density
Coefficient of Thermal Expansion
Ratio of Shear Modulus (G) to Axial Modulus (Ea)
FRP Bend Laminate Type
(entered on spread sheet)
(entered on spread sheet)
(entered on spread sheet)
(entered on Special Execution Parameters)
(entered on Special Execution Parameters)
(entered on Special Execution Parameters)
This may become tedious, especially if the same type of FRP material is used frequently. In this case,
the appropriate material parameters may be entered in the CAESAR II Configure/Setup, to be used
automatically whenever Material 20 is used.
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These parameters are entered using the FRP PROPERTIES group in of Configure/Setup. The
configuration items are described below:
Axial Modulus of Elasticity: Self-explanatory; can be read from an FRP file.
Axial Strain : Hoop Stress (Ea/Eh*Vh/a): Ratio of the FRP axial modulus of elasticity to the hoop
modulus of elasticity, all multiplied by Poisson’s ratio for strain in longitudinal direction due to
stress-induced strain in circumferential direction; can be read from an FRP file.
FRP Alpha (x E-06): The coefficient of thermal expansion, length/length/degree, multiplied by
1,000,000; can be read from an FRP file.
FRP Density: Self-explanatory; can be read from an FRP file.
FRP Laminate Type: This item is considered when calculating SIFs and Flexibility Factors of bends
under the BS 7159 and UKOOA codes. Choices include:
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.
FRP Property Data File: Selecting an FRP type from one of the ones listed reads in much of the
associated material data.
Ratio Shear Mod : Elastic Mod: Ratio of the FRP shear modulus to the axial modulus of elasticity; can
be read from an FRP file.
The remaining settings are used with the other FRP codes BS 7159 and UKOOA and are unused for
ISO 14962. Their uses are discussed in the help file and are displayed on pressing F1 while on the
field.
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Model the system
When modelling using the orthotropic material, the very first thing that must be done, before even
creating a new file, is to enter the material properties in the configuration file (remember this can be
done by selecting an FRP data file). The once material 20 is selected within the job, these properties
will be used. Any changes made to the FRP properties in the configuration file will only take effect
when a new job is created.
On the CAESAR II main window, select Tools > Configure/Setup
Select the RP properties node and specify the properties of the FRP. This FRP is Wavin55 as
mentioned previously. Select this FRP property data file.
Confirm the choice
The FRP parameters will update to those set in the FRP data file.
Whilst in the configuration file, also specify a default friction coefficient of 0.15 to represent plastic
on steel/concrete.
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Once these FRP parameters have been set, only then can the job file be created. Create a new job
file called CoolH20.
Create the first element, 10 to 20. Note that this pipe is non-standard 1800mm diameter and also
has non-standard 46mm wall thickness.
The 1.5mm Corrosion layer should also be entered here. This layer will always be used in the weight
and thermal force calculations, but excluded from the pipe strength calculations.
Select the material number 20 – FRP.
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Upon selection of the material, the labels on the material properties change. Elastic Modulus (C)
becomes Elastic Modulus/axial and Poisson’s Ratio becomes Ea/Eh*Vh/a.
The values will be brought in from the FRP data file and will be as described above (as we chose the
Wavin55 FRP data file).
Also check the Special execution parameters for further FRP data. Again this should match the
correct data coming from the FRP data file.
Enter the temperature and pressure (50°C and 2 bars).
We must now also select the design code. Currently the code is the default - B31.3. Change this to
ISO 14692. Now we must enter the stress envelope for the FRP material. The entries are as
described previously. Recall the graph:
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(as mentioned before, the axes have been switched, so the 2:1 position is now identified by R = 0.5),
and also recall that mentioned previously the values on the graph include service factor f2, 0.67. This
factor also needs removing (i.e. divide all values by 0.67). the 0.67 value will be entered as the
system design factor.
As shown in the graph, the reading for the hoop stress is 84 N/mm2. Therefore the hl(2:1) value is:
By definition, long term axial stress at maximum hoop stress, al(2:1), is half of hl(2:1). Therefore:
The axial tension-only long term strength is shown on the chart above as 41 MPa. Therefore
The joint and fitting data is also discussed above. The Qualified stress Qs will be set to 75 MPa and
for bends r = 1.0 and for tees r = 2. Bends also reference the hoop modulus of elasticity which is
entered here as the Eh/Ea ratio of 1.7.
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A1, A2, & A3 bring in environmental effects to reduce the design stress to the factored design stress.
Thermal Factor (k) is the “mean temperature multiplier”, a factor by which the difference in
temperature between the fluid the environment is to be multiplied (since FRP has natural insulating
qualities). For liquids, the Code dictates a K value of 0.85; use 0.80 for vapour.
Note that we have not entered al(1:1) or hl(1:1) therefore the simplified envelope will be used.
Complete the first element by adding an anchor at node 10 and continue into the bend.
The bend is a mitred bend and has 2 mitre points. Note that the ISO Code ignores the number of
mitres when calculating the bend SIF and flexibility factor.
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In addition, there is also a +Y restraint on the start of the bend (node 18). Notice the friction factor
is included automatically when adding the restraint.
Continue to the next element.
The model so far should look like the one below:
Continue and complete the model. Note the following points:
•
•
The branch connection at node 40 (as well as all other branches) is a tee (SIF type 1).
Node 40 (along with nodes 60, 100, 120, 160, 180, 190, and 250) is supported by a +Y
(weight only) support (with friction coefficient of 0.15).
The restraint at node 50 (as well as those at nodes 90, 110, 150, and 170) is combination
guide and +Y (weight only) restraint (with friction coefficient of 0.15).
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•
Element 70-80 is a reducer (conical section). It can be modelled as such with the exiting
diameter and thickness set to 1500mm and 38mm.
Element 40-280 is a branch off of the 1800 mm line. Its diameter and thickness should be changed to
750 mm and 25 mm, respectively. (Offsets should be considered here as the actual flexible length of
straight pipe [before the bend] – 3600 mm – is much smaller than the modelled length – 4500 mm –
and therefore much stiffer. However, for this layout the effect is minimal [about 5% in terms of
stress] and excluded for simplicity.) The bend at node 280 has 4 mitre points.
After modelling the branch through node 300, that branch can be duplicated via the list processor 5
times (with the node increment set to 30, 60, 90, etc.). It is also necessary to change the branch
intersection nodes to 60 (from 70), 120 (from 130), and 180 (from 190).
The completed model should look as below.
Error Check the model
A warning relating to the fact that al(1:1) and hl(1:1) were not entered and so the simplified
envelope will be used is shown, as is a warning about SIFs on the intersections and that the reducer
Alpha was not entered so CAESAR II has calculated this value.
Accept these warnings and access the load case editor.
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Load Case Setup
ISO 14692 evaluates both hoop stress and axial stress in the installed and operating conditions and
also for any short duration (occasional) loads. The type of load will set the part factor, f2, used to set
the design stress limits. The System Design Factor specified in the input is multiplied by the CAESAR
II Occasional Load Factor in the Load Case Options tab to produce this f2. f2 = (System Design
Factor)*(Occasional Load Factor). The Code provides values for f2 in Table 3. Remember that the
System Design Factor in the CAESAR II input is set to 0.67.
Review Results
ISO 14692 Annex D provides a method for converting torsion and bending moments into hoop and
axial stress terms. These stresses, summed with their pressure counterparts, produce effective hoop
stress and effective axial stress. Terms common to B31 piping – flexibility factor and stress
intensification factor – are used here too. Stress evaluation will first compare effective hoop stress
to the factored design hoop stress. If this check fails, the hoop stress is reported, otherwise, CAESAR
II will continue with the axial check. The effective hoop stress is used with the design envelope to
pick up the factored design axial stress. The effective axial stress is then compared to the factored
design axial stress. If this check fails, the axial stress is reported, otherwise CAESAR II will print the
cause of the largest (stress/limit) ratio – either hoop or axial.
Running this analysis shows that this system stresses are satisfactory. Note the changing allowable
stress from node to node. CAESAR II prints a different allowable depending upon which stress
calculation controls – Hoop or Axial.
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Solving Expansion Problems
The philosophy behind solving expansion problems in a fiberglass piping application is different from
that in a steel piping application. For steel piping, the preferred hierarchy for solving such a problem
is 1) adding flexibility through loops and bends, 2) using expansion joints, and 3) using restraints to
re-direct growth to areas where it can be better handled. For fiberglass applications, due to the
relatively low modulus of elasticity of fiberglass, the lack of significant flexibility provided by FRP
bends, and the potential problems involved in the joining of FRP sections, the hierarchy is exactly the
opposite. The preferred method is to use axial restraint to force the thermal expansion into
compression (in this case, the line must be adequately guided); the next preference is to use
expansion joints; and the last resort is to use expansion loops.
Static Seismic Using the ASCE 7-05:
This cooling water system is located in a seismically active region, so it must also be designed to
withstand earthquake loads. For this analysis, the ASCE 7 Minimum Design Loads for Buildings and
Other Structures, 2005 Edition is in effect. We will assume that this installation is located in Site Class
D (Stiff soil profile), near Los Angeles, California. (For Site Class Definitions, refer to Table 11.4-1.)
The structure in which this system is operating has an average roof height of 12m. Section 13.3.2
discusses Seismic Relative Displacements to which piping must be designed. It states “The effects of
seismic relative displacements shall be considered in combination with displacements caused by
other loads as appropriate.” – meaning that they shall be treated as “secondary” loads, rather than
“primary” loads.
Inertial Loads
Section 1621.1.4 defines a horizontal seismic acceleration factor to be applied uniformly throughout
the structural mass. This acceleration factor, aH, is defined as:
(
[
But:
)
]
and
Where:
= Component amplification factor, from Table 13.6-1
= 2.5 for piping
= Design elastic response acceleration at short period, from Section 11.4.4
= Component response modification factor, from Table 13.6-1. Use 4.5 for pipes not
in accordance with B31, with bonded joints or use 12 for welded, steel B31 pipe.
= 4.5
= Component importance factor, from Section 13.1.3 (1.5 for life-safety
components, hazardous material containing, or piping is in a Category IV structure
(essential facility); 1.0 for all others).
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= 1.0
= Height in structure at point of attachment. Here, use the average of elevation of all
8 connections
= 6m
= Average roof height of structure
= 12m
Section 13.3.1 states that a vertical acceleration be considered as well. This acceleration factor, aV, is
defined as 20% of the Design elastic response acceleration at short period, or:
Determine SDS:
From section 11.4.4
Where
= Maximum considered earthquake spectral response accelerations for short period
adjusted for site class effects
And from section 11.4.3
Where:
= Site Coefficient defined in Table 11.4-1
= 1.0
= Mapped spectral accelerations for short periods, from Section 11.4.1
= 1.552 g (see below)
Maps of spectral acceleration are available from several sources (ASCE, IBC, NEHRP, and FEMA). Data
is also available on-line at http://earthquake.usgs.gov/hazards/ using the Java Ground Motion
Parameter Calculator (http://earthquake.usgs.gov/hazards/designmaps/javacalc.php). The location
of this piping system on the coast near Los Angeles is 33.9083 latitude and -118.41045 longitude.
Below is a screen capture from the USGS software. SS for the location of interest is shown;
SS=1.552g.
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Therefore:
So the appropriate seismic acceleration is:
(
[
)
]
](
[
)
Checking the limits on aH:


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Seismic load adjustment: The building codes are based on strength design where components (such
as reinforced concrete structures) are evaluated on their load-carrying capacity rather than stress.
Piping codes are based on allowable stress design and, while the calculated seismic load provides a
good estimate of the internal loads and deflections of the piping system, these seismic loads over
predict the resulting stress used here. Section 13.1.7 states “The earthquake loads determined in
accordance with Section 13.3.1 shall be multiplied by a factor of 0.7.”
Therefore the adjusted seismic loads for allowable stress design are:
Relative Seismic Displacements:
Section 1621.1.5 discusses the means of addressing relative displacements due to “story drift” – this
should be calculated via a structural analysis of the enclosing building. Assume this analysis yields
the following displacements (with attachment points near building columns, no vertical drift is
included):
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Node
10
18
40
50
60
90
100
110
120
150
160
170
180
190
240
270
300
330
360
390
420
450
Function
Anchor
+Y
+Y
X, +Y
+Y
X, +Y
+Y
X, +Y, Z
+Y
X, +Y
+Y
X, +Y
+Y
+Y
+Y
Anchor
Anchor
Anchor
Anchor
Anchor
Anchor
Anchor
Approx Elev (m)
4.6
4.6
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
28
0
7.3
7.3
7.3
7.3
7.3
7.3
X-Disp (mm)
26
26
16
16
16
16
16
16
16
16
16
16
16
16
16
0
42
42
42
42
42
42
Z-Disp (mm)
9
9
5
5
5
5
5
5
5
5
5
5
5
5
5
0
14
14
14
14
14
14
Note: Displacements need only be placed on +Y supports if friction loads are considered to be
significant.
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Seismic Data Input
We have already calculated the Seismic data and could build uniform loads to model the load in the
X Y and Z directions from what we have just calculated. Alternatively, CAESAR II includes a static
seismic wizard which can be used to perform all the calculations automatically, and build the
uniform loads and incorporate into the model.
We will use the static seismic wizard, and see that the values match up to our hand calculations.
The Static Seismic Wizard is available from the same toolbar as the Loop design wizard used
previously.
The static seismic wizard provides input for the various data we have discussed previously.
Recall the following values:
= Component amplification factor, from Table 13.6-1
= 2.5 for piping
= Component response modification factor, from Table 13.6-1. Use 4.5 for pipes not
in accordance with B31, with bonded joints or use 12 for welded, steel B31 pipe.
= 4.5
= Component importance factor, from Section 13.1.3 (1.5 for life-safety
components, hazardous material containing, or piping is in a Category IV structure
(essential facility); 1.0 for all others).
= 1.0
= Height in structure at point of attachment. Here, use the average of elevation of all
8 connections
= 6m
= Average roof height of structure
= 12m
In addition, we have the SS value obtained from the USGS utility = 1.552
Input the data into the Seismic Wizard
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On clicking OK, the values will be calculated for aH and aV as we have done manually above. These
will be included as Uniform Loads. (The uniform load will act on following elments until removed or
set to zero).
Note that the Uniform loads are also in g’s.
Next we also need to apply the displacements due to “Storey-shift” as detailed previously. These
displacements can be modeled as vector D1 (for X-direction) and vector D3 (for Z-direction). They
should be applied to CNODEs attached to the restraints (increment each restraint by 1000). To save
inputting effort, all restraints at a common level could be connected to a single CNODE. In this case,
displacements need only be entered at three locations.
Add the displacements only at nodes 10, 40 and 300.
Node 10
Node 40
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Node 300
We now have the restraints defined, but currently they are defined as displacements at nodes 1010,
1040 and 1300. These nodes do not exist in the model.
We will use these node numbers as cNodes and connect all the restraints to the relevant
displacement at the correct elevation. All restraint nodes at 4.6m elevation must be connected via
Cnode to displacement node 1010. (These are nodes 10 and 18).
Similarly, restraint nodes at 2.8m must connect to 1040 (Nodes 40 – 240) and nodes at 7.3m
elevation must be connected to 1300 (nodes 300 – 450).
This is easier to perform using the Restraint List view.
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You will notice that the graphic plot now looks a little odd. The reason for this is, that by default,
CAESAR II displays the system with Nodes and CNodes at the same point in space. This is fine for
connecting pipe nodes to structure CNodes (like in Tutor) or nozzle nodes to vessel/pump CNodes
(like in Turbo). But in this model, where several restraints reference the same CNode, the display
will still attempt to join all these Nodes and CNodes together, resulting in a ‘nonsense’ plot. To clean
up the plot and avoid the associated coordinate mismatch error during Error Check, change the
Configuration/Setup parameter “Connect Geometry through CNODEs” to False.
The plot will not update automatically, so must be done manually. Click the Reset plot button to
refresh the graphics.
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The plot will once again look correct.
Re-run the eror check – there should be no errors and no new warnings or messages.
Load Case Setup
Access the Load Case editor – you will receive a message stating that the individual loads for the job
have changed. This message is due to the fact we now have displacement loads in the model D1 and
D3 and the uniform loads U1, U2 and U3. These must be incorporated into our load cases. Section
1621.1.4 discusses the combination method for the various loading directions. It states that the load
along each horizontal axis shall be applied independently, but in conjunction with the vertical load.
Since ISO 14692 only looks at a single stress type (OPE), this leads to the following seismic load cases
(since boundary conditions are non-linear):
Note the +/- signs in the various cases
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Note that even though results only need be retained from two load cases (the last two), we are
electing to keep results from all load cases in order to help us “debug” in the event of an overstress.
Load Cases L10 and L11 are not combined algebraically, rather they are included to compare the
displacements, forces and stresses. Hence why they ar enot added or subtracted, just listed. We
wish to find the worst case load case, so we can get CAESAR II to compare the resluts from each load
case and report the maximum and minimum values.
Select the Load Case Options tab and select SignMin and SignMax for the Combination method for
L10 and L11.
SignMax compares the displacements, forces and stresses and uses the maximum force and
maximum stress value of the cases (i.e. sign is considered in the comparison). Displacements are the
maximum Signed valued of all displacements from each case included in the combination. Similarly
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for forces and stresses, these are the maximum Signed forces/stresses from each case included in
the combination.
SignMin is the opposite of this – the minimum signed values of the stresses/forces/displacements
are included.
Using SignMin and SignMax we can get the enveope of restraint loads for all cases.
Also for the static seismic cases, enter in the Occasional Load factor of 1.33.
Analyse the model.
Review Results
It can be seen straight away that there is an issue with Cases 4 and 5.
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Reviewing the Load Case 11 confirms that the maximum stress fails the code stress check, and is at
103.8% of the code allowable at node 180.
In order to solve this, it is necessary to know which of the seismic combination cases caused the
failure. We can see straight away that it is either case 4 or 5. Reviewing the code compliance report
for all cases 2 to 9 shows that cases 4 and 5 are very similar alhough case 5 is fractionally higher.
Cases 4 and 5 represent the-X,+Y and –X,-Y seismic loadings. Now we need to find out which
component of the seismic loadings caused the failure – the interial or the displacement. Stress due
to force-based load is a primary load, stress due to strain is a secondary load. Once we find out the
cause we can take the appropriate action to resolve the overstress situation.
An easy way to determine which is the worst cause is to run the components of the load case
individually to see wihich gives the greatest stress.
Return to the load case editor.
Load cases 4 and 5 both consist of W, D1, T1, P1, U1 and U2.
We know that W+D1+T1+P1 is not the cause as the OPE case is perfectly fine. So the culprit must be
one of eiether D1, U1 or U2. Therefore, create three new load cases and assign D1 ,U1 and U2
respectively to each load case.
After re-running the analysis review the code compliance report for the three new cases.
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This shows that clearly the D1 components is the largest contributer to the overstress, by a long way.
This is a secondary loading, so the solution is to add more flexibility. In this case the fix is actually
very simple and involves simply removing the guide just before node 180 located at node 170.
The system will now pass the stress check.
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Gas Transmission Pipeline - Buried Pipe
Gas Transmission Pipeline - Buried Pipe
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Gas Transmission Pipeline - Buried Pipe
This model of a gas transmission pipeline will introduce the buried pipe modeller, and also introduce
fatigue analysis. We will also explore the requirements of the B31.8 Design Code.
This job consists of a 36” header, an 8” branch, and a 2” bypass, in the vicinity of a natural gas
compressor station. The lines immediately go underground, from where they continue indefinitely
for a very long distance.
B31.8 Design Code
Gas transmission pipelines are covered by the B31.8 Code – Gas Transmission and Distribution Piping
Systems. The philosophy of this code is to use high strength steel and custom, optimized wall
thicknesses wherever possible, in order to minimize the amount of steel used in the long crosscountry pipelines. Stress analysis-wise, the code seeks to prevent yielding under any set of load
cases. This prevents catastrophic failure under primary loads, and prevents plastic deformation
under secondary loads. There are no requirements for reducing allowables for cyclic reduction
factors (i.e., fatigue requirements).
B31.8 is one of the few codes in which the OPErating case is a Code case and the EXPansion case is
not
Requirements of the different design codes are listed here in the table:-
OPE
SUS
EXP
B31.1
NO
YES
YES
B31.3
NO
YES
YES
B31.4
YES
YES
YES
B31.8
YES
YES
NO
B31.4 CH IX
YES
YES
NO
B31.8 CH VIII
YES
YES
NO
Modelling the system
Model the system as shown in the isometric sketches. The following issues are of specific interest
during the modelling phase.
Element 10-20 originates at (and is anchored at) the compressor connection, with a flange (250 mm
long, 5780 N weight). The pipeline is 36” diameter, with a non-standard 18 mm wall thickness.
Enter two temperatures to model the extremes of the operating range, which represents the
expectations due to winter lows and summer solar gain:
Ambient = 21 C (set in Config)
T1 = 50 C, T2 = -5 C above ground
ON THE FIRST ELEMENT
T1 = 30 C, T2 = 10 C underground
(we will use these temperatures later)
The material is API-5L X65 (material no 306), high strength steel. Its parameters can be found in the
CAESAR II material database.
The applicable code is B31.8
For natural gas, fluid density may be neglected.
The branch connection at node 30 (as well as all other branches) is a Weldolet (SIF type 5).
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The restraint at node 40 (as well as those at nodes 80, 110, 320, 360, 420, and 450) is a +Y (weight
only) restraint. Specify a coefficient of friction of 0.3 for steel-on-steel contact.
The bends at nodes 60 and 70 are 3-diameter bends (radius = 1370 mm).
Element 60-70 goes underground 685 mm below node 60. Therefore we will need a node to indicate
where the above ground/underground transition takes place. The entire element 60-70 can be
entered first, and then the Break command can be used to insert a node 65 one-third of the way
along the element length.
The element can be determined to be 5405 mm long (by clicking the local cosine “…” button) so onethird of that length is 1802.
The temperatures on 65-70 should be changed to T1 = 30 C, T2 = 10 C.
The valve at element 90 - 100 (as well as that at element 430-440) is supported within an accessible
valve pit (covered, but not buried). Node 75 (as well as nodes 115, 405, and 445) represents the
buried/non-buried transition, and will be used later.
Element 115-120 extends indefinitely, in a straight run, underground. Obviously, we need not model
it forever – at some point, the cumulative restraining effect of the soil acts as an anchor. We will
determine the required modelling length later; for now we can put in a dummy length of 10,000
mm.
The model of the main pipe will look like the one shown below:
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Now move on to the branch, starting with element 30-310. This is an 8” standard schedule pipe. The
temperatures on this element should be restored to T1 = 50 C, T2 = -5 C. The bends on this line are
standard Long Radius. This pipe is now A53 Gr B low carbon steel.
Element 30-310, modelled as is, is deceptively flexible, with a modelled length of 2440 mm, and an
actual length of 1980 mm (since the element really originates at the surface of the 36” header, not
at the centreline). So in reality, its flexibility should only be (1980/2440)3, or roughly 50%, of that
calculated. We could correct this by modelling a weightless rigid from the centreline of the header to
surface of the header (i.e., element 30-305), and then begin modelling the 8” line from that point
(i.e., element 305-310).
This approach has the following problems:
1. Placing the weldolet at node 30, causes no stress intensification on the 8” line (since there is
no stress calculated on the rigid, and no weldolet at node 305).
2. Alternatively placing the weldolet at node 305 intensifies the stress on the 8” line, but
doesn’t intensify the stress on the 36” line. Furthermore, the SIF would be both
miscalculated (since CAESAR II would think the header size would be that of the rigid
element) and misapplied (CAESAR II would not be able to determine in-plane from out-plane
since the SIF would be at applied to two co-linear elements).
One solution to this modelling dilemma is to use an OFFSET, in this case modelling a From Offset of
457 mm in the Z-direction. This internally models element 30-310 as a 457 mm long rigid element
connected to a 1980 mm pipe, and transfers all stress calculations out to the true start of the 2440
mm pipe. (Note Offsets may not be entered on bend elements, so in this case, it is first necessary to
break element 30-310 into two elements. Be careful that no elements, after applying Offsets, are
reduced to zero-length. So in this case, enter two elements, 30-305 (DZ = 1000 mm, From Offset Z =
457 mm) and 305-310 (DZ = 1440 mm, long radius bend).
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Element 370-380 goes underground 685 mm below node 370, so we need a node to indicate where
the above ground/underground transition takes place. The entire element 370-380 can be entered
first, and then the Break command can be used to insert a node 375, 685 mm along the element
length. The temperatures at node 375 should be changed to T1 = 30C, T2 = 10C.
The valve at element 430-440 is supported within a valve pit. Nodes 405 and 445 represent the
buried/non-buried transition.
Element 445-450 (like element 115-120) extends indefinitely, in a straight run, underground. We will
determine the required modelling length later; and use a dummy length of 10,000 mm for now.
The completed model will look like the one shown below:
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Next model the bypass. Create this model in a new file before combining the two files.
Combine the models and run the error check.
Two errors will appear. Both errors relate to the temperature for case 2, at elements 10-20 and 30305. The temperature for case 2 at these locations is -5°C. The error message is showing that there
is no material data available for either of the two materials we have selected for a temperature this
low, in the B31.8 code.
We cannot analyse until this has been corrected. To correct, we can edit the material database to
include properties for the material down to the correct temperature.
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Material Database
Close the piping input to return to the main window. Access the material database form the Tools
menu.
Choose to edit a material
Search for material 102 (A53 B) (you can search on either term). Notice that there are a number of
entries for A53 B for the various different codes, including for B31.8. Select the B31.8 entry
The lowest temperature for which an expansion coefficient is entered is 0°C. The next row down is 73.3°C, which has no expansion coefficient. As our temperature in the model is -5°, we can see
where we have incomplete data. We could enter in the data here for the missing expansion
coefficient.
Alternatively, using engineering judgement, we can take the material properties for A53 B from
another code where the data is filled in sufficiently and use this in B31.8 code.
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Search again for the material A53 B. This time, select the All Codes data. This information is more
complete than the B31.8 specific data for A53 B.
If we are confident that this data will be suitable for B31.8 then we can use this data in place of the
default B31.8 data.
The material database is stored in two files. One file is CMAT.bin. This stores all the default data
and is read only. Any changes to the material are stored in a separate file called UMAT.UMD. This
file stores any material information which is different to that in CMAT.bin. CAESAR II then uses the
UMAT.UMD file first, and reads any further data from CMAT.bin.
Materials from CMAT.bin cannot be deleted, only those from UMAT.UMD.
If we save the A53 B B31.3 material data for use with B31.8, this will be written to the UMAT
database. The CMAT database will be still the same as it currently is, however the UMAT will be
read in preference to this, and it will act as though the data has been “overwritten”.
To make this change, simply select the Applicable piping code drop down, and change from B31.3 to
B31.8 and save the material.
Return to the input. You should see a warning stating that the properties for the material A53 B,
code B31.8 have changed in the material database, and given the option to use these new properties
or keep the existing. Select to update the material properties via the “No – Update” button.
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Select part of the bypass (or any part that is material A53 B that we have just changed) and double
click on the chevron in the temperature/pressure area. Notice that the expansion coefficient is now
filled in for both temperatures (whereas it was 0.000 for T2 previously).
Re-running the error check will show that the error is no longer present, for material A 53B but still
present for API-5L X65. We now need to update the material database for this material.
Repeat the exercise from before and update the material properties for API-5L X65.
Run the error check again – the material errors will no longer appear. The error checler should show
only the Centre of Gravity report.
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Gas Transmission Pipeline - Buried Pipe
Buried Pipe Modeller
The piping system beyond nodes 65 and 375 is mostly buried. The effect of this is
(1) It will be continually supported, causing the weight stresses to be negligible,
(2) It will be continually restrained against axial growth and bending by the adjacent soil.
The former effect can be best modelled by zeroing the density of any pipe, fluid, and insulation; the
latter can best be modelled by meshing the pipe and adding restraints, with mesh spacing, restraint
stiffness, etc. based upon the soil properties. CAESAR II provides an underground pipe modeller
which simplifies this process, performing the following functions:



Allows for the direct input of soil properties. These properties are used to generate first the
stiffnesses on a per length of pipe basis, and then the restraints that simulate the discrete
buried pipe restraint. (Note that any existing restraints in the underground area are deleted
during this process.) CAESAR II supports three different soil modellers – one based upon the
published work of Mr. L. C. Peng, plus two others (for clay and granular soils) from the
American Lifelines Alliance.
Automatically breaks down straight and curved lengths of pipe. CAESAR II uses a three Zone
concept to break down straight and curved sections. Those ends of pipe identified as
“transverse bearing lengths” are broken down into Zone 1 lengths (the smallest element
lengths selected to properly distribute the lateral forces to the soil). At distances far away
from Zone 1 are Zone 3 lengths (long lengths of pipe selected to transmit axial loads).
Between Zone 1 and Zone 3 is Zone 2 (transition lengths which vary linearly from the Zone 1
end to the Zone 3 end).
Allows for the direct input of user’s soil stiffnesses on a per-length of pipe basis. Input
parameters include axial, transverse, upward, and downward stiffnesses, as well as ultimate
loads. The user can specify user-defined stiffnesses separately, or in conjunction with
CAESAR II’s automatically generated soil stiffnesses.
Restraint Parameters
The Underground Pipe Modeller allows the use of any of three different soil modelling algorithms.
The first two are based upon the work of the American Lifelines Alliance, as published in their
document “Guidelines for the Design of Buried Steel Pipe”, dated July, 2001 (with addenda through
February 2005); this document offers different models for clay soils and granular (sand/gravel). The
third model is based on the soil restraint modelling algorithm presented by L.C. Peng in his two-part
paper entitled “Stress Analysis Methods for Underground Pipelines,” published in 1978 in Pipeline
Industry. Soil supports are modelled as bilinear restraints having an initial stiffness, an ultimate load,
and a yield stiffness. The yield stiffness is typically set close to zero, i.e. once the ultimate load on the
soil is reached there is no further increase in load even though the displacement may continue. The
basic ultimate loads that must be calculated to analyse buried pipe are the axial and three bearing
(transverse, upward, and downward) ultimate loads. (Note that for the Peng model, all three bearing
ultimate loads are considered to be identical.) Once the axial and bearing ultimate loads are known,
the stiffness in these directions can be determined by dividing the ultimate load by the yield
displacement. (Researchers have found that the yield displacement is typically related to the buried
depth, the pipe diameter, the soil type, and the load type.) The ultimate loads and stiffnesses
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computed are on a force per unit length of pipe basis; the restraint ultimate loads and stiffnesses are
then based upon tributary lengths of the adjacent piping elements.
The restraint equations use these soil properties to generate ultimate loads and stiffnesses using the
following equations.
Initial restraint stiffness is estimated by assuming that the Ultimate Load is developed over a “Yield
Displacement” (YD). Axial Stiffness (KAX) on a per-length of pipe basis:
Transverse stiffness (KTR) on a per-length of pipe basis:
American Lifelines Alliance Clay Model
Lateral Ultimate Load (FAX) per unit length
inches (stiff clay) or 0.4 inches (soft clay)
Where:
= Pipe diameter
= soil adhesion factor (dimensionless)
=
= soil cohesion representative of soil backfill
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Transverse Ultimate Load (FTR) per unit length
(
)
Where:
=
=
= 6.752
= 0.065
= -11.063
= 7.119
= height of soil cover (measured to centre of pipe, note CAESAR II requests distance
to top of pipe)
Downward Ultimate Load (FD), per unit length
Where:
= 5.14
= 1.0 (for clay)
= defective density of soil (taking buoyancy into account)
Upward Ultimate Load (FU), per unit length
Where:
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American Lifelines Alliance sand model:
Axial Ultimate Load (FAX), per unit length
Where:
= coefficient of pressure at rest (dimensionless) = 1 – sin φ
= interface angle of friction for pipe and soil = f φ
φ
= soil angle of internal friction, typical values are:
27 – 45° for sand
26 – 35° for silt
F = coating dependant factor (dimensionless), typical values are:
Pipe Coating
f
Concrete
1.0
Coal Tar
0.9
Rough Steel
0.8
Smooth Steel
0.7
Fusion Bonded Epoxy
0.6
Polyethylene
0.5
Transverse Ultimate Load (FTR), per unit length
(
)
Where:
=
A, B, C, D, E based on φ, according to the following table:
φ
20°
25°
A
2.399
3.332
B
0.439
0.839
C
-0.30
-0.090
D
1.059E-3
5.606E-3
E
-1.754E-5
-1.319E-4
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30°
35°
40°
45°
4.565
6.816
10.959
17.658
1.234
2.019
1.783
3.309
-0.089
-0.146
-0.045
-0.048
4.275E-3
7.651E-3
5.425E-3
6.44E-3
-9.159E-5
-1.683E-4
-1.153E-4
-1.299E-4
Downward Ultimate Load (FD), per unit length
Where:
=
=
= density of dry soil
Upward Ultimate Load (FU), per unit length
dense sand
loose sand
Where:
=
Meshing Parameters
Typical buried pipe displacements are considerably different than similar above ground
displacements. Buried pipe deforms laterally in areas immediately adjacent to changes in directions
(i.e. bends and tees); in areas far removed from bends and tees the deformation is primarily axial.
The optimal size of an element (i.e., the distance between a single FROM and a TO node) is very
dependent on which of these deformation patterns is to be modelled. Where the deformation is
“lateral” smaller elements are needed to properly distribute the forces from the pipe to the soil. The
length over which the pipe deflects laterally is termed the “lateral bearing length” (Lb) and can be
calculated by the equation:
(
)
Where:
= Pipe modulus of elasticity
= Pipe moment of inertia
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CAESAR II places three elements in the vicinity of a bearing span to properly model this load
distribution. The bearing span lengths in a piping system are called the Zone 1 lengths. The axial
displacement lengths in a piping system are called the Zone 3 lengths, and the intermediate lengths
in a piping system are called the Zone 2 lengths. Zone 3 element lengths (to properly transmit axial
loads) are computed by 100*Do , where Do is the outside diameter of the piping. The Zone 2 mesh is
comprised of elements that are 1.5 times the length of a Zone 1 element at its Zone 1 end, and that
are 50*Do long at the Zone 3 end. A typical piping system and how CAESAR II views this zone mesh
distribution is illustrated below:
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Virtual Anchor Length (VAL):
Since soil restraint capacity is a function of piping length, after a certain length, the soil restraints will
fully counteract the piping loads, acting as a “virtual anchor”. The piping need not be modelled
beyond this length. This length can be calculated as that length where the axial pipe force equals the
ultimate axial restraint load.
Axial pipe force consists of three types:
1. Thermal Load =
2. Poisson effect (longitudinal shrinkage due to hoop strain) =
3. Longitudinal pressure load =
Using the (ALA Sand Model), the Axial Ultimate Load (FAX) per unit length is:
The ultimate restraint load therefore is the VAL * Fax ,or:
*
Ultimate restraint load
+
*
+
Simplifying this gives:
[
(
)
] *
+
This value can be used to determine how long we must model elements 130-140 and 460-470 of the
GASTRANS model. This pipeline is in sandy soil – the soil parameters are as follows.
Soil Parameters
Soil Type
Coating Factor (rough steel)
Dry soil density, 𝑦
Effective Soil density, 𝑦′
Buried Depth, H
Angle of internal friction, φ
Coefficient of Pressure at rest, K0
Yield Displacement Factor, Axial dT
Yield Displacement Factor, Lat, dP (mult of D):
Yield Displacement Factor, Up, dQu (mult of H):
Yield Displacement Factor, Up, dQu (max mult of D):
Yield Displacement Factor, Down, dQd (mult of D):
Dense Sand
0.8
1909 kg/cm3
1190 kg/cm3
915mm (36” pipe)
610mm (8” pipe)
35°
0.426
2.5mm
0.1
0.01
0.1
0.1
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°
(coldest temp underground is 10 so delta from ambient of 21.11 is about 12 )
(36" pipe)
(8" pipe)
pipe) ,
Working this out give the following Virtual Anchor Lengths:
VAL36 = 206400mm
VAL8 = 127600mm
Unlike the perfectly rigid/perfectly plastic response due to friction alone, the CAESAR II soil modeller
inserts elastic/plastic springs to model some initial “give” in the soil. The program, therefore, may
require more pipe length to fully develop this virtual anchor along a straight run. Since an even
longer straight run is just as quick to enter and analyse, a more generous VAL length can always be
used in the model. For this example we will change the place-holder lengths originally entered for
elements 115-120 and 445- 450 to 300000mm and 200000mm, respectively.
Bury Pipe
We will now bury the pipe. Close the piping input and return to the main window. Access the
Buried pipe modeller
As soon as the buried pipe modeller is opened, the job file is saved as a copy with the same name
with suffix “B”
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In the underground modeller the soil underground conditions can be defined. This is done in two
parts:
1. Enter the soil model
2. Define where/how the system is buried
First let us define the soil model. We must define two soil models for our job – one for 915mm
depth, one for 610mm depth.
Access the soil model entry dialog.
We will use the American Lifelines Alliance Sand method. Notice that this is soil model number 2.
Soil model number 1 is reserved for a completely user defined stiffness which can be entered in the
main spread sheet.
Enter the soil properties as detailed above.
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Add a second soil model, model no 3 and enter the properties for the second model. Only the depth
op of pipe (H) is different.
Now that the soil models have been created, we must specify where/how the system is buried. This
is done in the main Buried Element description Spread sheet.
This spread sheet is used to indicate where the pipe is buried, under which soil type, which mesh
type should be used, as well as any user-defined stiffnesses. A critical part of the modelling of an
underground piping system is the proper definition of Zone 1 (or lateral) bearing regions. These
regions primarily occur:
•
•
•
On either side of a change in direction
For all pipes framing into an intersection
At points where the pipe enters or leaves the soil
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CAESAR II automatically puts a Zone 1 mesh gradient at each side of the pipe framing into an elbow,
it is the user’s responsibility to force it to do so in other areas. This is done using the FROM/TO end
mesh columns in the spread sheet. A tick in either of these columns places a “zone 1” mesh at the
corresponding element end (either From or To end). This should be done where the soil enters or
leaves the soil, in the vicinity of tees, or in “problem areas”.
The soil model number is used to specify whether the soil is buried
Complete the spread sheet using the following information.
The pipe enters the soil into soil model 2 at node 65, then leaves again at node 75. Enter soil model
2 on element 65-70. On the ‘from end’ of this element (i.e. node 65) place a Zone 1 mesh by
checking the box – this is where the pipe enters the soil. The soil model will propagate through the
spread sheet, so enter 0 on element 75-80 (the pipe is now in the valve pit, out of the soil). On the
previous element, place a zone 1 mesh on the from end (i.e. node 75) – where the pipe exits the soil.
Continuing on, the pipe re-enters the soil at node 115 through to the VAL at node 120.
Next moving on to the 8” pipe line, the pipe enters the soil at node 375, into soil model 3 and
remains in the soil until it exits at node 405 at the next valve pit. The one 1 meshes at the bends will
be automatically added, we only need to define these at the entry and exit points.
The pipe re-enters the soil at node 445 through to the VAL at node 450. Nodes 50 through to the
end are the bypass, and so are above ground.
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After completing the spread sheet, the model can be buried using the Convert Input function.
You will receive a warning during the conversion stating that any user defined intermediate nodes n
bends will be deleted – CAESAR II will re-specify these as per the soil meshing algorithm during
conversion. Accept this message.
The model will finish converting and will confirm that there were warnings – we only had the one
which is OK.
Clicking OK will close the buried pipe modeller. The currently selected c2 job file is now the buried
pipe model - GASTRANSB. This is identical to any other c2 job file, the only difference between this
model and the “unburied” model is the inclusion of a number of restraints with the correct stiffness
added as per the soil models input. Return to the piping input to view the updated buried model.
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Load Case Setup
In order to get the true Expansion Stress in a non-linear system, it is necessary to evaluate the
following load cases:
Extreme hot operating condition
Extreme cold operating condition
For this example, this can be implemented as:
W+P1+T1 (OPE) HOT
W+P1+T2 (OPE) COLD
W+P1 (SUS)
L1 - L2 (EXP)
L3 + L4 (OPE)
CAESAR II recommends the following set of load cases to perform these analyses.
This load case setup requires some minor modification. We need to add a third expansion check on
the stress range between operating case 1 and 2, along with a baseline for these expansion cases, of
the weight no contents of the pipe, which will be used rather than the sustained case. Add the
following load cases:
L3
L7
WNC
L1 – L2
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Also give the load cases meaningful names in the Load Case Options tab
We can now run the analysis
Results Review
The results show that there are failures in the expansion case 6. A review of the code compliance
report shows that the shakedown stresses on the weld-o-lets branch runs at 30 and 50 are
overstressed. The sustained stress is also quite high at these outlets. The range from operating case
1 to operating case 2 is insignificant.
Turning on the stress filter to display only nodes greater than 90 per cent of the allowable reduces
this report to only the branches at nodes 30 and 50:
Reducing these stresses will be left as a follow-up exercise. Now move on to the fatigue evaluation.
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Fatigue
Due to the danger of gas leaks, and the presence of cyclic loading (pressure fluctuations and solar
heat/cooling cycles) this system is being evaluated for fatigue failures. Since B31.8 does not offer any
specific guidance on fatigue analysis, our best course of action is to calculate the cyclic stresses
according to the Stress Intensity equation, and compare them to ASME Section VIII Division 2 fatigue
curves (Figure 5.110.1), using an appropriate factor of safety.
This system should be evaluated for the following load cases:
Design life: 40 years
Temperature variations:
Ambient temperature: 21C
Summer maximum temperature, above ground: 50C (for 40 years) (T1)
Summer maximum temperature, below ground: 30C (for 40 years) (T1)
Winter minimum temperature, above ground: -5C (for 40 years) (T2)
Winter minimum temperature, below ground: 10C (for 40 years) (T2)
Daily temperature variation, above ground: 20C from extreme (14,600 days) (T3=T1-Δ,
T4=T2+Δ)
Daily temperature variation, below ground: 10C from extreme (14,600 days) (T3=T1-Δ,
T4=T2+Δ)
Pressure variations:
Maximum pressure: 80 bar (P1)
Annual shutdown: 0 bar (40 times)
Minimum operating pressure: 63 bar, varies between 63 and 80 (1,000 occurrences) (P2)
Daily fluctuation: 5 bar drop (14,600 days) (P3=P1-Δ)
Setting up the Fatigue Load cases
Fatigue loads are incurred by transitioning between two or more different operating cases. It is
usually best to model the two extreme load cases, and set up all fatigue load cases to be a variation
from one of these. For example:
Operating Case A: Shutdown, winter minimum (extreme stress condition)
Operating Case B: Full pressure, summer maximum (extreme stress condition)
Operating Case C: Full pressure, winter minimum (enveloped in A-B cycle)
Operating Case D: Compressor operation, winter minimum
Operating Case E: Compressor operation, summer minimum fluctuation
Operating Case F: Pressure fluctuation, winter minimum
Operating Case G: Pressure fluctuation, summer minimum fluctuation
Operating Case H: Full pressure, winter maximum fluctuation
This translates into operating conditions of:
T1 = 50 AG, 30 BG (summer maximum)
T2 = -5 AG, 10 BG (winter minimum)
T3 = 30 AG, 20 BG (summer minimum)
T4 = 15 AG, 20 BG (winter maximum)
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P1 = 80 bar (maximum)
P2 = 63 bar (minimum pressure; compressor setting)
P3 = 75 bar (daily minimum)
Load Cases (including those required earlier):
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
W+T1+P1 (OPE) Hot operating, also Operating Case B
W+T2+P1 (OPE) Cold operating, Operating Case C
WNC (SUS) Shakedown Baseline
W+P1 (SUS) Sustained
W+T2 (OPE) Operating Case A
W+T2+P2 (OPE) Operating Case D
W+T3+P2 (OPE) Operating Case E
W+T2+P3 (OPE) Operating Case F
W+T3+P3 (OPE) Operating Case G
W+T4+P1 (OPE) Operating Case H
L1-L3 (EXP) Expansion Hot
L2-L3 (EXP) Expansion Cold
L1-L5 (FAT) 40 cycles (Algebraic) -- B-A (Summer MAX > Winter MIN)
L2-L6 (FAT) 500 cycles (Algebraic) – C-D (Winter MAX > Winter MIN (P1-P2))
L1-L7 (FAT) 500 cycles (Algebraic) -- B-E (Summer MAX > Summer MIN)
L2-L8 (FAT) 7300 cycles (Algebraic) – C-F
L1-L9 (FAT) 7300 cycles (Algebraic) – B-G
L10-L2 (FAT) 7300 cycles (Algebraic) – H-C
Before fatigue stresses can be checked, the allowable limits must be defined in the input. Return to
the first element and click on the Fatigue Curves button at the bottom of the Auxiliary Data Area for
Allowable Stress. Fatigue data may be typed in by hand but it may also be read from data files
supplied with CAESAR II or built and stored on the hard drive. Select the 5-110-1B.FAT file to use the
steel fatigue data for B31.8.
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Also enter in the correct temperatures and pressures as listed above, changing when the pipe is
below/above ground as necessary.
Once complete, create the load cases as described
Run the analysis.
After reanalyzing the system, select all fatigue loads and the cumulative usage report to evaluate the
system loads. It is apparent that fatigue stresses and their associated cycles are quite low. Only the
shakedown stresses at the weld-o-lets need be addressed.
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Riser
Riser
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Riser
This job is an offshore jacketed production riser. The job shows how to use the offshore capabilities
of CAESAR II. In addition to covering the hydrodynamic analysis techniques, this job also covers
model construction, element duplication, and problem resolution.
For this system, the piping details are defined in the table below
Item
Diameter
Thickness
Temperature
Pressure
Fluid
Riser Jacket
Product Core
Injection Core
18”
6”
4”
Standard
Standard
Standard
15°C
80°C
95°C
0 bar
5 bar
10 bar
0
0.85 SG
1.025 SG
Marine
Growth
50mm
0
0
The 4" injection line is used to inject water into the well to assist in product recovery. The oil is
recovered and pumped to the surface in the 6" product line. The 18" jacket pipe is used to house the
riser tubes, offering protection and support.
This system is installed in shallow water, and subjected to a specified wave train. The objective of
the analysis is to determine the loads and stresses on the system in accordance with ASME B31.4
Chapter IX.
The wave parameters are defined in the table below:
Item
Height
Period
Depth
Wave Theory
Value
5700mm
7.72 sec
9000mm
Stokes 5th
Modelling
The first thing you may notice on the sketch is that the node increment in this model is 5 rather than
10 as in all the previous models. As such we will adjust the node increment for this model. This
change affects this model only. Alternatively the configuration file can be changed if all models
should have a different node increment.
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Riser
This jacketed riser will be modelled in stages, where each stage represents a continuous run of
piping from the bottom to the surface. The two core pipes (6" and 4") are enclosed in the jacket pipe
(18"). The core pipes are positioned in the jacket through the use of internal spiders (braces). In
CAESAR II, these spiders can be modelled using dummy rigid elements, connected to the jacket
through the use of CNODES.
For the 4" pipe, these dummy rigid elements must be (114.3 mm / 2 + 25 mm = 85 mm), while for
the 6" pipe, the dummies are (168.275 mm / 2 + 25 mm = 110 mm). This will provide a clearance of
50 mm between the core pipes.
When constructing a model, the first element piping spread sheet is extremely important, since
much of its data is duplicated forward throughout the job.
Injection Line
Set the parameters as follows. Note the node numbering begins at 405 – 410. The “400” series
nodes will be for the 4” line
Material:
A 106 B
Diameter:
4” = 114.3mm
Wt/Sch:
S = 6.0198mm
Fluid Density: 1.025 SG = 1024.5 kg/m3
Temp 1:
95°C
Pressure 1:
10 bar
Design Code: B31.4 Chapter IX
Fac:
0.6
Fac is F1, Hoop Stress Design Factor, as per Table A402.3.5(a) of B31.4. Appropriate
values are 0.72 for Pipelines or 0.60 for Platform piping and Risers.
DZ = -1800mm
ANC at 405
Locate a bend at node 410. Specify a bend radius of 203mm
Finally, we need to reset the elevation of the system, so that node 405 lies on the sea
bottom. (This is important for the wave and wind loading later. While wave loading allows a
relative definition of position of the piping in the water, wind does not. Therefore, zero
elevation must be properly specified on the system so that the correct wind loads
calculated.) Use the global coordinate button to reset the origin, node 405, from (0,0,0) to
(0,-9000,0).
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Riser
Continue to the next element – 410 -415
This is 1500mm in the Y direction, and has two restraints at node 415, an X and a Z. Both the
restraints will have a CNODE to 414. Node 414 will be the spider connection as discussed above.
Continue to the next element. As the isometric shows, the riser continues in 1500mm sections, right
the way up to node 470 at the top. We can create this all in one element, and break to split up into
the 1500mm sections. Change the node numbers to 415 – 470. The pipe travels 16500mm in the Y
direction overall.
Now we can break this element with a node increment of 5. Use the break command as before, but
this time, select the Insert Multiple Nodes radio button.
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Riser
Enter in a node step of 5 – the Total Number and Length fields will be calculated automatically. Also
specify the support configuration as at node 415.
Checking the system coordinates in the list processor shows that node 440 is at the surface
(elevation 0), and there are 12 vertical elements - 6 above the surface and 6 below the surface.
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Riser
Add a bend at node 470 and change the radius to 203mm as before.
Return to element 410 – 415 (the bottom element on the riser) and add in a +Y support at node 415
with a CNODE to 414. This is done now because this vertical support should not be duplicated to all
the spider connections.
Complete the riser by adding in the final element (470 – 475). This is 1500mm in the –Z direction
and an anchor is located at node 475.
The injection line is now complete.
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Product Line
For the product line, duplicate the injection line, this is essentially duplicating the entire model at
this point. This duplication will use a node increment of 200, followed by a modification to the
temperature, pressure, diameter, thickness, and fluid specific gravity.
Select the entire model and duplicate as follows:
Change the properties of element 605-610 so that they are correct for the 6” line:
Diameter:
T1:
Fluid Density:
6”
80°C
0.85SG
Wt/Sch:
P1:
STD
5 bar
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Riser
Jacket
Important Notes When Duplicating Core / Jacket Piping
The diameter is changed after the duplication.
Typically, the core pipe uses long radius elbows, and the jacket uses short radius elbows.
This allows the radii of both the core and the jacket to be the same.
If the jacket contains fluid, its density must be computed such that the unit weight across the
entire jacket inner diameter yields the same weight as the real fluid in the annulus between
the jacket and core pipes.
Core pipes do not see environmental loads. This is important to check after building the
model.
Continue after the last element (670-675) and change the node numbers again. This time for the
18” pipe – so use node numbers 1810 to 1870.
This element is 18000mm long
Diameter:
T1:
P1
Fluid density:
Restraints:
18”
15°C
zero
zero
X
Y
Z
RY
Marine Growth:50mm
Next break this element, using the multiple break function again, and a node increment of 5. This
will split the element into 12 sections, each 1500mm in length.
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Riser
At node 1870, define a GUIDE restraint. With this element vertical, the program will create an X and
a Z restraint at node 1870.
The Wind/Wave settings will propgate through the model until changed or turned off, even though
on subsequent elements will not have the Wind/Wave check box ticked.
On element 1840-1845 (the first pipe out of the water and a t zero elevation), turn off the wave and
set a wind shape factor of 0.65. This is a typical value for cylindrical bodies.
The model at this point shows the three lines, but they are not properly located in space. A series of
construction elements will place these lines properly in space and also provide the right structural
connectivity. The idea here is to run a dummy rigid element from the restraint CNODEs of the
injection line, to the nodes on the jacket and, on to the restraint CNODEs of the product line.
Navigate to the end of the model and define a new element from 414 to 1815. This element will be
85mm long in the X direction, and will connect the restraint at 415 (with CNODE 414) to the jacket at
1815. Define this as a rigid element with zero weight.
Turn off the wind.
Follow with another dummy rigid element from 1815 to 614; 110 mm in X. This will join the product
line through the restraint at 615 with its CNODE at 614.
The graphics should now display the model correct.
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Using the Elements listing, duplicate these last two elements, with a node increment of 5 to place
the spider on the next restraint. Continue this duplication so that the spiders are placed all the way
up the riser.
Once complete, and all restraints along the riser are defined, run the error checker.
There will be a number of warnings concerning "zero weight" rigid elements and "four elements
framing into a node". These are all acceptable in this instance.
Note that the Centre of Gravity Report shows a combined weight of about 33,000 N. Recall that the
riser is supported only at its base, with a pin connection. In reality, risers are supported by top-side
tensioners, exerting a force sufficient to ensure the riser is always in tension. For this job, return to
the input and at node 1870 (the top of the riser), define a hanger to apply a constant vertical force of
45,000 N.
Re-run the error checker. The model should now be ready for analysis.
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Hydrodynamic Theory
A basic discussion of hydrodynamic theory can be found in the CAESAR II documentation (Technical
Reference Guide, Chapter 6). There are a variety of different wave theories, used to compute the
water particle velocities and accelerations resulting from a wave train. CAESAR II includes solutions
to the three most commonly used wave theories; Airy, Stokes 5th, and Stream Function. The latter
two theories are non-linear, but provide a better description of the water particle behaviour.
CAESAR II also includes modified versions of these three theories, which allow consideration of the
fluid above the mean sea level.
The basic procedure is to solve for the wave length, based on a selected wave theory. Once the wave
length is known, the velocities and accelerations can be determined at any position in the water
column. Based on these values, drag (Cd), inertia (Cm), and lift (Cl) coefficients are determined for
each pipe element. These coefficients, along with the velocity and acceleration are used to compute
the force applied to the piping elements, using Morrison's equation:
| |
Where:
= fluid density
= drag coefficient
= pipe diameter
= particle velocity
= inertial coefficient
= particle acceleration
The particle velocities and accelerations are vector quantities which 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 element’s axis. The lift force is defined as:
Where:
= fluid density
= lift coefficient
= pipe diameter
= particle velocity
The buoyancy force acts upward, and is equal to the weight of the fluid volume displaced by the
element. Once the force on a particular element is available, it is placed in the system load vector
just as any other load is. A standard finite element solution is performed on the system of equations
which describe the piping system.
For this particular model, a sample hand computation will be used to estimate the applied wave
load. This will be used as a verification of the loading, to ensure we are making the correct
assumptions and modelling correctly.
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B31.4 Code Requirements
The B31.4 piping code includes Chapter IX, for "Offshore Liquid Pipeline Systems". The scope of this
chapter states: "For the purposes of this Chapter, offshore pipeline systems include offshore liquid
pipelines, pipeline risers, offshore liquid pumping stations, pipeline appurtenances, pipe supports,
connectors, and other components as addressed specifically in the Code."
In Section A401.10.1, this Code states: "All parts of the offshore pipeline system shall be designed for
the most critical combinations of operational and environmental loads, acting concurrently, to which
the system may be subjected." This means that operating loads are to be combined with wind, wave,
and current!
In Section A402, this Code states that:
- Hoop Stress is limited as defined by:
Note that the pressure term used in the hoop stress equation is the difference between
internal and external pressure.
- Longitudinal Stress is limited as defined by:
The longitudinal stress is defined as the axial stress plus or minus the bending stress,
whichever results in the larger stress value.
- Combined Stress is limited as defined by:
Here, Scomb is defined by the Tresca Combined Stress Equation.
To satisfy these requirements, a single load case can be defined. This load case should include all
loads defined in the input (weight, pressure, temperature, wave, wind, etc). CAESAR II will compute
the above stresses for each element and report the maximum stress value with its corresponding
allowable. The factors F1, F2, and F3 are defined in the code in Table A402.3.5 (a) as:
Location
Pipeline
Riser
Hoop F1
0.72
0.60
Longitudinal F2
0.80
0.80
Combined F3
0.90
0.90
The B31.4 piping code states that the environmental loads used in the analysis correspond to the
"100 year" storm. This is equivalent to the largest storm that occurs every 100 years.
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Hydrodynamic Input
The hydrodynamic input specification in CAESAR II is relatively simple. Up to four different loading
conditions can be defined. These different conditions could be different waves, currents, or
directions. For each of these loading conditions the data is defined as shown below
This particular load definition is specifies only a wave. However, either a standard current profile or
a current table can also be defined. The particular wave used in this example is a well-publicised
wave, used as the example in the paper by Skjelbreia and Hendricson for the solution to Stokes 5th
Order Gravity Waves. Note this does not correspond to a "100 year storm". This wave is being used
because it has published results.
The wave data consists of the water depth (9 m), the wave height (5.7 m), the wave period (7.72
seconds). The wave kinematics factor is a factor used for Stream Function and Stokes 5th solutions
to account for the spreading of the wave energy in a real sea state. Values typically range from 0.85
to 1.0, and serve to reduce the particle velocities.
The "Phase Data" defines how the wave is imposed on the piping system. Since the wave moves over
the piping system, every element of the system is exposed to every phase of the wave. At one
particular position (phase) of the wave the piping system will experience the maximum
environmental load. Performing 360 solutions to find this maximum is not practical, given the other
factors involved (combination with current, non-uniform sea state, directionality, and spreading).
Typically drag governs the loading on (small) piping system, so the wave is positioned so that most of
the piping system sees a zero phase angle. Alternatively, the input can be set so that the entire
system sees a zero phase angle.
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Wave Solution
The hydrodynamic parameters as defined in the input are used by the Stokes 5th wave theory to
determine the water particle data. This solution can be evaluated numerically (by reviewing data
tables) or graphically (through the use of plots). A brief evaluation is shown below.
First, two dimensionless parameters are computed and used to determine the "suggested" wave
theory. This evaluation is performed by plotting these dimensionless parameters on a chart, found in
a number of publications. This chart, with the location of the specified wave for this job is shown in
the figure below. This chart (and the remainder of the wave solution) can be obtained using the
“Chart Current Results” button on the Load Case Editor.
For this particular wave, the chart shows that the recommended wave theory is Stream Function 9th
Order. (This job will still employ the Stokes 5th solution, for illustrative purposes.) Each region of the
chart corresponds to a different wave theory, as detailed in the key at the bottom.
The Drop down list at the top of the dialog box allows other graph representations to be shown.
Select the “Surface Elevation vs Phase” option
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This results in the following graph.
This figure shows that the wave crest is at a phase of zero, with the trough at a phase of 180
degrees, as expected. Notice also that the wave profile is not symmetric about the mean water level.
For this 5.7 m wave, the crest is 4 m above the still water level while the trough is 1.5 m below the
still water level. Only the Airy wave theory produces a symmetric wave profile.
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Changing the plot to "Horizontal Velocity versus Depth at Zero Phase" results in the figure shown
below. This figure shows that the velocity decreases with depth, as expected. Note however that
there is still an appreciable velocity, even at the bottom for this particular wave.
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Selecting the plot "Horizontal Velocity versus Phase at Zero Depth" results in the figure below. This
figure shows that velocities are positive in the wave crest, and negative in the wave trough, again as
expected. This is why there is a mean mass transport in the direction of the wave train.
Note that in this plot, the velocity in the trough is shown as zero. This is because the plot is showing
the data at a depth of zero, the still water level. In the trough region, the water is below this level. At
a lower depth, the velocities do go negative, which can be seen by reviewing the actual data tables.
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Selecting the plot "Horizontal Acceleration versus Phase at Zero Depth" results in the figure below.
This figure shows that the water particles are accelerating in front of the wave crest, and
decelerating behind the wave crest. Again, in the trough area, the plot shows values of zero because
the water level is below the "zero" elevation.
Plots such as these are typical of wave solutions. The wave solution produces data for the entire
water depth over the entire wave phase. Horizontal and vertical velocities and accelerations can be
studied as a function of depth or phase. In addition to plotting the data, the actual numerical values
can be reviewed by clicking the View Data Table button. This file is called <jobname>.WV1 and is a
text file – so opens in Notepad.
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At the top of this file, the wave length and speed are reported. (The corresponding values from
Skjelbreia and Hendricson's paper are 76.2 m (250.0 ft) and 9.87 m/sec (32.39 ft/sec). The difference
here is due to a correction to the Stokes solution published in 1985.) This set of tables shows the
free surface as a function of phase angle. If the water depth (9 m) is added to these values, the result
is the row of values labelled "Surface Elevation". The "Horizontal Velocity" table (for the Z direction)
is also shown. The first row (zero depth) and first column (zero phase) were used to produce the
velocity plots shown above.
Hydrodynamic Coefficients
The water particle data can be used directly in Morrison's equation to determine the force acting on
the pipe elements. However, in order to employ Morrison's equation, several hydrodynamic
coefficients must be determined. These coefficients are a function of the Reynold's and KeuleganCarpenter numbers, and are typically presented in graphical form, as shown in the figure below.
These coefficients have been determined through testing.
Cd versus Re and K
Cl versus Re and K
The Keulegan-Carpenter Number, K, is defined as
Where:
= maximum fluid particle velocity
= wave period
= characteristic diameter of the element
The Reynolds number Re is defined as
Where
= maximum fluid particle velocity
= characteristic diameter of the element
= kinematic viscosity of the fluid (1.17 mm2/sec for sea water).
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Note that these parameters depend on the water particle velocity as well as the diameter of the pipe
element. Therefore, these parameters typically vary over the piping model. For this reason, it is best
to leave the entry for these coefficients blank in the input. This will allow CAESAR II to determine the
coefficients on an element by element basis during the solution phase of the job.
A rough hand computation should be made to ensure that the applied environmental loads are as
expected. To assist in this check, a stand-alone load case with only wave loading will be setup to
check against these hand computations. The hand computations are shown below.
Wave Solution Data
Elevation
Velocity
Elevations are measured from the sea bottom
(m)
(m/sec)
0
2.3
All data for a phase angle of 0.0°
1.5
2.370
3
2.440
4.5
2.615
6
2.870
7.5
3.235
9
3.710
Hydrodynamic Coefficient Computation
Node
Elevation
(m)
Velocity
(mm/sec)
1810
0
2300
1815
1.5
2370
1820
3
2440
1825
4.5
2615
1830
6
2870
1835
7.5
3235
1840
9
3710
Element Force Computation
Element
1810-1815
1815-1820
1820-1825
1825-1830
1830-1835
1835-1840
Avg.
Velocity
(m/sec)
2.335
2.405
2.528
2.743
3.053
3.473
Acceleration
(m/sec2)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
KeuleganCarpenter
Number
31.87
32.84
33.81
36.23
39.76
44.82
51.40
Reynolds
Number
Cd
Cm
Cl
1.08 E +6
1.11 E +6
1.14 E +6
1.22 E +6
1.34 E +6
1.51 E +6
1.74 E +6
0.661
0.656
0.651
0.639
0.621
0.625
0.631
1.746
1.749
1.751
1.759
1.769
1.765
1.759
0.257
0.250
0.243
0.226
0.202
0.200
0.200
Avg. Cd
Avg. Cl
Diameter
(mm)
Density
(kg/cm3)
0.658
0.653
0.645
0.630
0.623
0.628
0.254
0.247
0.235
0.214
0.201
0.200
557.2
557.2
557.2
557.2
557.2
557.2
0.001025
0.001025
0.001025
0.001025
0.001025
0.001025
Drag
Force (Fd)
(N/mm)
1.025
1.079
1.176
1.353
1.658
2.163
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Lift Force
(Fl)
(N/mm)
0.395
0.408
0.428
0.460
0.534
0.689
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Element
1810-1815
1815-1820
1820-1825
1825-1830
1830-1835
1835-1840
Length
(mm)
1500.00
1500.00
1500.00
1500.00
1500.00
1500.00
Fd
(N)
1537.29
1618.83
1764.72
2029.74
2468.55
3244.27
Fl
(N)
592.13
611.34
642.70
689.51
801.55
1033.02
Total Drag force = 12681.40 N
Total Lift Force = 4370.25 N
Notice for these computations, that "average" values are being used for the element velocities and
hydrodynamic coefficients. The CAESAR II program actually computes the exact values at integration
points on each element, from which the "fixed end forces and moments" are determined.
Wind Loading
The default ASCE 95 wind loading procedures will be used on this riser. (This standard states that the
minimum wind pressure is 10 lb/sq.ft. or 0.479 KN/sq.m.) The basic procedure to compute the wind
load on each pipe element is as follows:
Obtain the wind speed (V). From ASCE 95, the Gulf Coast of the U.S. can experience winds of up to
225 km/hr (140 m/hr). API-RP2A recommends a wind velocity of 175 km/hr (109 m/hr) for the Gulf
of Mexico. Assume a wind speed of 55m/sec (123 m/hr) for this job.
Determine the applicable structural category from ASCE 95, Table 1.1. From this table, select
category II (2).
Determine the Importance Factor (I) from ASCE 95, Table 6.2. Based on the selected category, the
Importance factor is 1.0.
Determine the Exposure Category from ASCE 95, Section 6.5.3. For this job, select exposure category
D (flat, unobstructed terrain).
From ASCE 95, Commentary Section 6.5, determine Kz. This term varies by elevation and therefore
may vary from element to element. Constants used in the equations to determine Kz can be
obtained from Table C6-2, based on the exposure category.
Determine Kzt, which is the wind speed-up over hills. For this job, there are no hills, so Kzt is 1.0.
Based on these parameters, compute the velocity pressure as defined in ASCE 95, Section 6.5.1.
This is: qz = 0.613 * Kz * Kzt * V2 * I, where all terms are defined above. For this equation, V is
expressed in meters per second and qz in newton per square meter. (If V is in mph and qz in lbf/ft2,
the constant becomes 0.00256.)
Once qz is known, the force on the element can be determined from: F = qz * Gf * Cf * A, where:
- Gf is the gust response factor
- Cf is the shape factor for the element (defined in the piping input)
- A is the projected wind area of the element (including insulation if specified)
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The gust response factor Gf can be determined analytically as defined in the ASCE Commentary.
However, this procedure requires the first natural frequency of the piping system, which can be
obtained through a modal analysis. This dynamic procedure is not addressed in this seminar. If the
natural frequency input is left blank, CAESAR II will use a gust response factor of 0.85 as defined in
ASCE 95, Section 6.6.1.
For this system, the wind load can be defined for the analysis as shown below.
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For this system, the applied wind loads can be approximated as shown below.
Wind Solution Data (per ASCE 7)
Element
Mid-Point Alpha
elevation
(z)
(m)
1840-1845 0.75
11.50
1845-1850 2.25
11.50
1850-1855 3.75
11.50
1855-1860 5.25
11.50
1860-1865 6.75
11.50
1865-1870 8.25
11.50
( )
2/alp
ha
4.6/zg
213.36
213.36
213.36
213.36
213.36
213.36
0.174
0.174
0.174
0.174
0.174
0.174
0.0216
0.0216
0.0216
⁄
z/zg
Kz
0.513
0.513
0.513
0.525
0.548
0.568
0.0246
0.0316
0.0387
1.031
1.031
1.031
1.055
1.102
1.142
⁄
where x = max (4.6 or z)
Velocity Pressures
Element
Kz
1840-1845 1.031
1845-1850 1.031
1850-1855 1.031
1855-1860 1.055
1860-1865 1.102
1865-1870 1.142
V (m/s)
55
55
55
55
55
55
Wind Force
Element
1840-1845
1845-1850
1850-1855
1855-1860
1860-1865
1865-1870
G
0.85
0.85
0.85
0.85
0.85
0.85
qz
1912
1912
1912
1957
2044
2117
Zg
(m)
I
1
1
1
1
1
1
Cf
0.65
0.65
0.65
0.65
0.65
0.65
qz
1912
1912
1912
1957
2044
2117
Af (m2)
0.686
0.686
0.686
0.686
0.686
0.686
𝑞𝑧
𝐾𝑧
𝐾𝑧𝑡
𝐼
𝑉
𝑞𝑧
𝐺
𝐶𝑓
𝐾𝑧𝑡 = 1.0
Force (N)
725
725
725
741
775
802
𝐹𝑜𝑟𝑐𝑒
Total Applied Force = 4492 N
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Load Case Setup
The load cases required are as below:
We require for our code stress check, an operating case for each wind and wave direction. In this
case we have a Z direction wind load and wave load Therefore we will create cases for operating
conditions PLUS the wind and wave loads and MINUS the wind and wave loads
These load cases can be given more meaningful names in the Load Case options tab
The results for all load cases will be available at the output level, but for the "environmental only"
load cases, only displacements and forces will be presented by the output processor. Load cases #4
and #5 are the Code compliance cases necessary for the stress check. The output status for load case
#1 could have been set to "discard", since in this instance its results are not significant on their own.
However, it may be necessary to evaluate the results of this load case in the event of overloads or
over stressed elements. Therefore the output status is left as "keep".)
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Analysis
Once the load cases are defined (and the loading data has been checked), the analysis can proceed
as usual. At the output level, the results of the "environmental" load cases should be reviewed to
ensure they agree with the hand computations. For this job, the environmental loads act on the riser
body and are resolved about nodes 1810 and 1870. The restraint summary report details this loading
resolution.
For load cases #2 and #3, summing the FZ loads at nodes 405, 475, 605, 675, 1810 and 1870 yields
the applied environmental loads. These loads are summarised in the table below.
Applied Load Summation (from CAESAR II)
Node
405
475
605
675
1810
1870
Wave
Drag Fz (N)
539
380
1697
1145
6749
2030
Total Load: 12540
Lift Fx (N)
78
85
287
299
2769
810
Wind
Fz (N)
105
200
347
589
631
2620
4328
4492
These loads can be compared to the hand computed results of 12681 N, 4370 N , and 4492 N. This is
an acceptable comparison, given the approximations made in the hand computations.
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The code compliance report shows that there is a failure in one of the operating cases. This is
located around the bottom of the riser on the elbow. Reviewing the Stress Report shows that the
bending stress is dominating the behaviour of the system at these points.
One solution here is to reduce the thermal component of the stress by extending the bottom-side
piping, from 1800 mm to 3000 mm. This drops the stress level to 86.5% of the allowable.
(This job is not intended to be an example of good riser design. The riser tension was arbitrarily
selected to be simply larger than the "air weight" of the riser. Additional vertical supports may be
used along the length of the riser to assist in supporting the core piping. For larger (longer) risers,
external buoyancy chambers are used to offer additional vertical support along the riser body. None
of these concepts are addressed in this example.)
(Fatigue has not been addressed in this example, but is typically a required consideration. For this
job, the fatigue (FAT) case would be defined as "L4-L5" with a specified number of cycles and a
corresponding material fatigue curve.)
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SUPT01 – Water Hammer
SUPT01 – Water Hammer
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SUPT01 – Water Hammer
This exercise introduces the Occasional stress evaluation in B31.3. We will return to the model
produced previously SUPT01 and simulate a fluid hammer event acting when the valve slams shut.
This force will be applied to the model and defined as a shock load case and evaluated according to
the Occasional stress requirements of B31.3.
For Occasional stress evaluation, B31.3 requires:
Long. Sustained Stresses + Long. Occasional Stresses ≤ k Sh, where k = 1.33
In CAESAR II, this equates to a SCALAR summation of the SUS case with the OCC case, using the OCC
stress type.
Note: The OCC stress type serves two purposes: (1) it directs that stresses be calculated according to
the “occasional equation”, and (2) it activates (i.e., locks) any snubbers in the model.
Edit the Model
Open the file created previously SUPT01. Using File > Save As… create a new file called SUPT01 fluid
Hammer.c2
There are some slight changes to the support configuration in this file compared to our analysis done
previously.
Edit the support configuration as shown in the isometric sketch, and as detailed below.
Element 20-30
o Break this element
o Create a new node number 22, located 1400mm from node 20.
o Add a +Y restraint at node 22
Element 30-33
o Change the “to node” from 33 to 34
o Edit the length of this element and change to 6000mm
o Add a +Y restraint at node 34
Element 33-37
o
o
o
o
o
Change the “from node” from 33 to 34
Change the “to node” from 37 to 36
Edit the length of this element to be 6000mm
Remove the +Y restraint
Add a spring Hanger at node 36. Carpenter & Paterson hanger table
Element 37-40
o Change the “from node” from 37 to 36
o Edit the length of this element to 1715mm
Node 43
o
Remove the Spring hanger
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SUPT01 – Water Hammer
Element 50-57
o
o
o
o
Break this element
Create a new node number 55, located 3250mm from node 50
Remove the +Y support at node 57
Add a Carpenter Spring Hanger at node 55
Element 70-77
o Change the “to node” to be 72
o Edit the length to be 2000mm
o Edit the support node number to be 72
Element 77-80
o Change the from “node” to be 72
o Edit the length to be 2115mm
Element 80-90
o Break this element
o Create a new node number 85, located 1000mm from node 80
o Insert a +Y at this location
Determine the Load
Consider water hammer acting when the valve at node 70 slams shut. This creates an unbalanced
force due to the propagation of a pressure wave. The water hammer load can be estimated using
Joukowski’s equation:
Where:
D
t
= force acting on valve seat
= dynamic load factor (use 2.0)
= pressure change
=
= internal area of pipe (0.073 m2 for 12” std pipe)
= density of fluid (1000kg/m3 for water)
= speed of sound in the fluid (typ. 1000 – 2000 m/sec in water based on D/t)
= change of fluid velocity (typically 1.5 – 3m/sec for water)
= mean pipe diameter
= pipe wall thickness
Wave speed & pressure change for water in steel pipe (ΔP/ΔV= ρ·c):
D/t C (m/sec) ΔP/ΔV (bar/(m/sec))
20
1310
13.1
40
1210
12.1
60
1130
11.3
80
1065
10.65
Using D / t = 314 / 9.5 = 33, ΔP/ ΔV = approximately 12.45 bar / (m/sec); assume ΔV = 2 m/sec;
so:
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SUPT01 – Water Hammer
Define the Occasion Load
Model a Z-direction force at node 70, equal to 364,000 N, as calculated previously.
Load Case Setup
Build the shock load case(s). The hammer load may be reversing, so build both a +F1 case and a –F1
case. Then build a SCALAR combination case combining the SUS and OCC load cases:
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Check the Results
Immediately it can be seen that there are issues with the OCCasional load cases. What is causing
these issues?
Is this an accurate simulation? Viewing the restraint summary shows that the loads on the restraints
at nodes 22 and particularly 85 – both show zero load – an immediate uplift – for at least one of the
hammer cases. If a +Y restraint actually lifted off, it would first have to overcome the pre-existing
downward load present during the operating case. So what we have here is not an accurate
simulation
Reset the Load Cases
This points out the danger when modelling occasional loads on non-linear systems: load stepping
must be considered, i.e., first apply the operating loads, then apply the occasional loads, then isolate
the occasional loads by subtracting the former from the latter. This accurately models the effects of
the pre-existing restraint status. This can be done using the following load cases:
Remember to change the load case combination method to Scalar for the OCC load cases in the load
case options tab.
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SUPT01 – Water Hammer
Check Results
There are still issues in the OCC load cases, but
Note that even though the pipe lifts off of the restraint at node 22, the “occasional only” load, Load
Case 7, does overcome the pre-existing operating load first, for an accurate simulation of events:
The Code Compliance Evaluation shows that the system is still highly overstressed under this OCC
load. This problem can be resolved by adding restraint (since the water hammer is a primary load).
We can use a rigid Z-restraint to contain the water hammer if we can find a point in the vicinity of
the load (run 50-80) where the Z-operating displacement is negligible (so the previous expansion and
sustained analyses will be relatively unaffected). A good candidate is at node 78 as the OPErating
displacement report shows.
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SUPT01 – Water Hammer
Correct model
Return to the input and select element 72-80. Node 78 is on the 0 angle of the bend at the “to” end
of this element.
Place a Z restraint at this location
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SUPT01 – Water Hammer
With a Z-restraint at node 78, the stresses have decreased significantly
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