1. Geothermal
Engineering
Design
PIPING DESIGN CONCEPT

2. Piping Design Concept
• Piping Stress Analysis
What is Stress Analysis?
Stress analysis is an engineering discipline that determines the stress in materials and structures subjected to static or
dynamic forces or loads.
The aim of the analysis is usually to determine whether the element or collection of elements, usually referred to us structure,
can safely withstand the specified forces. This is achieved when the determined stress from the applied force(s) is less than
the allowable tensile strength, allowable compressive strength or fatigue strength the material is known to be able to
withstand, though a factor of safety is applied to the design.
Why do we perform Pipe Stress Analysis?
There are a number of reasons for performing stress analysis on a piping system. A few of these follow:
1. In order to keep stresses in the pipe and fittings within the code allowable levels.
2. In order to keep nozzle loadings on attached equipment within allowable of the manufacturers or recognized standards.
(like the separator vessel nozzles).
3. In order to keep vessel stresses at piping connections within allowable.
4. In order to calculate design loads for sizing supports and restraints.
5. In order to determine piping displacements for interference checks.
6. In order to optimize piping design.
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3. Piping Design Concept
• 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 be either tensile or compressive in nature. Normal stresses may be applied in more than one
direction, and may develop from a number of different types of loads.
Longitudinal Stress - Longitudinal or axial stress is the normal stress acting parallel to the longitudinal axis of the pipe. This
may be caused by an internal force acting axially within the pipe.
SL = Fax / Am
Where:
SL = Longitudinal Stress, psi
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Fax = internal axial force acting on cross-section, lbs
Am = metal cross-sectional area of pipe, in²
= ╥ (do² - di²) / 4
= ╥dm t
do = outer diameter, in
di = inside diameter. In
dm = mean diameter, = (do+di)/2
A specific instance of longitudinal stress is that due to internal pressure:
SL = P Ai / Am
Where:
P = design pressure, psig
Ai = internal area of pipe, in²
= ╥di²/4
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Thus:
SL = Pdi² / (do² - di²) or Pdi²/4dmt
For convenience, longitudinal stress is often approximated as:
SL = Pdo/4t
Another component of the axial normal stress is the bending stress. Bending stress is zero at the neutral axis of the pipe and
varies linearly across the pipe’s cross-section from the maximum compressive outer to the maximum tensile outer fiber.
Calculating the stress as linearly proportional to the distance from the neutral axis:
SL = Mb c / I Where: Mb = bending moment acting on cross-section, in-lb
c = distance of point of interest from neutral axis
of cross-section, in.
I = moment of inertia
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Where: I = ╥ (do4 – di4) / 64
Note that the maximum bending stress will occur where c is the largest in our pipe it will happen where c = the radius of the pipe.
Smax = Mb Ro / I or Mb / Z
Where: Ro = outer radius of the pipe, in.
Z = section modulus of pipe, in3
= I / Ro
Summing all the components of the longitudinal normal stress: SL = Fax/Am + Pdo/4t + Mb/Z
Hoop Stress - There are other normal stress present in the pipe, applied in directions orthogonal to the axial direction. One of
these stresses, caused by internal pressure, is called the hoop stress. This stress acts in a direction parallel to the pipe
circumference.
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The magnitude of the hoop stress varies through the pipe wall and can be calculated by Lame’s equation as:
SH = P(ri² + ri² ro² / r²) / (ro² - ri²)
Where:
SH = hoop stress, psi
ri = inner radius of the pipe, in.
ro = outer radius of the pipe, in.
r = radial position where stress is being considered, in
The hoop stress can be conservatively approximated for thin-wall cylinders, by assuming that the pressure force, applied
over an arbitrary length of pipe, l (F=Pdi l), is resisted uniformly by the pipe wall over that same arbitrary length (Am=2tl), or:
SH = P di l / 2tl or
= P di/2t or conservatively:
SH = Pdo/2t
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. Radius stress, which is caused by internal pressure, varies between a stress equal to the
internal pressure at the pipe’s inner surface and a stress equal to atmospheric pressure at the pipe’s external surface.
Assuming there is no external pressure, radial stress may be calculated as:
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SR = P(ri² - ri² ro² / r²) / (ro² - ri²)
Where:
SR = radial stress due to pressure, psi
Note that radial stress is zero at the outer radius of the pipe, where the bending stresses are maximized. For this reason, this
stress component has traditionally ignored during the stress calculations.
Shear Stress - 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.
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9. Piping Design Concept
Shear stresses caused by shear forces acting on the cross-section:
max = V Q / Am
Where:
max = maximum shear stress, psi.
V = shear force. Lb
Q = shear form factor, dimensionless (1.333 for solid circular section)
These shear stresses are distributed such that they are maximum at the neutral axis of the pipe and zero at the maximum
distance from the neutral axis. Since this is opposite of the case with bending stresses, and since this stresses are usually
small, shear stresses due to forces are traditionally neglected during pipe stress analysis.
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Shear stresses caused by torsional loads:
max = MT c / R
Where :
MT = internal torsional momemt acting on cross-section, in-lb
c = distance point of point of interest from torsional center (intersection of neutral
axes) of cross-section, in
R = torsional resistance of cross-section, in4
= 2I
= p (do4 – di4) / 32
Maximum torsional stress occurs when c is maximized – at the outer radius:
max = MT Ro / 2 I = MT / 2 Z
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Summing the individual components of the shear stress, the maximum shear stress acting on the pipe cross-section is:
max = V Q / Am + MT / 2 Z
As noted above, a number of the stress components described above have been neglected for convenience during
calculation of pipe stresses. Most U.S. piping codes require stresses to be calculated using some form of the following
equations:
Longitudinal Stress: SL = Fax/Am + Pdo/4t + Mb/Z
Shear Stress: = MT / 2 Z
Hoop Stress: SH = Pdo/2t
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Example Stress Calculation:
For a 6 –inch nominal diameter, standard wall pipe (assuming the piping loads are known)
Cross-sectional properties:
do = 6.625 in. Z = 8.496 in3
di = 6.065 in. Am = 5.5813 in²
t = 0.280 in.
Piping loads:
Bending Moment (Mb) = 4247 ft-lb
Axial force (Fax) = 33488 lb
Pressure (P) = 600 psi
Torsional moment (MT) = 8495 ft-lb
Using the given equations:
SL = 4247 x 12/8.496 + 33488/5.5813 + 600 x 6.625/4 (0.280)
= 15547 psi
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= MT / 2 Z
= 8495 x 12/2(8.496)
= 5999 psi
SH = 600 x 6.625 / 2 (0.280)
= 7098 psi
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Since all the piping design and stress analysis are governed by standards and codes, the B31.1 Power Piping code requires
that sustained, expansion and occasional stresses be calculated exactly as defined below:
Please note that there are other codes that have particular calculation requirement for the pipe stresses but we will just focus
on B31.1 since it is the code that governs our geothermal piping system.
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• Designing for Sustained Loads – Pressure
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Minimum Wall Thickness Requirements (Also discussed by JF Peralta in his lecture)
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Note: For B31.1 the value of Y is 0.4
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• Designing for Sustained Loads – Pressure
Calculation of Weight Stesses
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• Designing for Expansion Loads
Magnitude of thermal load
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Guided Cantilever Method
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Use of Expansion Loops
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So far we have discussed many things about stresses; longitudinal, radial, shear, normal and etc. All of these are manually
calculated before using various tables, codes and references. Try to imagine how long a piping engineer can design and
calculate the stresses of an entire pipeline of the FCRS. May be it will take years. Now try imagining again if there will be a
revision in the design like for example a change in the pipe diameter or a change in the pipe route, it will take forever.
Lucky for our generation we already have computers. All the calculations now can be done using the computers and we
have several software in the market that specialize in piping stress analysis. In EDC we previously use TriFlex software, then
it was the known piping software. After the Triflex software which was develop by AAA Technology many piping stress
analysis software emerge in the market. One of these software was the CAESAR’s Stress Analysis software. CAESAR’S II
became globally known and many engineering and design firm started using it. EDC also uses CAESAR’s II, we started
using it in the late 90’s.
Before we discuss the “WHAT” and the “HOW” on CAESAR’s II or any other computer aided stress analysis let us go back
first go back to the work flow shown in part 1.
In part 1 we were able to have a basic knowledge the documents that we will need in piping layout. We need the P&ID, the
civil drawings and the mechanical equipment layout and other information. From these documents / drawings / diagrams we
were able to have a preliminary piping layout then followed by the preliminary flexibility check and support allocation.
Now that you have already your piping layout we will now proceed to stress analysis (CAESAR’s II)
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Piping Design Section Work Flow
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In Stress Analysis we will divide it into three parts; the pipe modeling, the stress analysis and the output.
Pipe Modeling
In pipe modeling you will have to prepare the input echo. It is in the input echo you will be needing to input all the data or
properties of the pipe line you are going to stress analyze. You will input the pipe size, pipe schedule or pipe thickness,
corrosion allowance (3mm for pipe and 5mm for bends), the pipe material, the weight factor of the fluid, the code that you will
use (B31.1 in our application), the pipe length or support to support distances or some other term is the pipe direction;
support to bend distances and the support type.
You can input the pipe direction in the XYZ direction. In our practice here in EDC we are using the left hand rule; the positive
X direction is your pointer which is always the along the axis of the pipe, the positive Z direction is your middle finger which is
always lateral to the pipe and lastly the positive Y direction is your thumb which is always normal to the pipe.
In modeling your pipe line you will need to put an identification to each point of the piping system (pipes and piping
components), we will call each point the NODE. We will use numbers for the nodes in your piping system, we use nodes with
an increment of 5 (for long piping system) or 10 (for shorter piping system). It is in each node that you will input the
necessary information (support type, length of pipe, etc).
It will be best demonstrated or explained if we will have an example.
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• Example: Pipe Diameter = 12”Ø Temperature = 183°c Pressure = 156 psig Class H
Pipe Schedule: 20
Pipe Layout
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• Manual Input Echo
Note: The manual input echo will be different in its presentation as compared to the input echo produced thru the software
10A NOD=10 S/20 T=183°c P=156 psig CA=0.125
20R X=6000 Y=0 Z=0 R/Y,Z
30R X=6000 Y=0 Z=0 R/Y,Z
40R X=6000 Y=0 Z=0 R/+Y
50B X=2000 Y=0 Z=0 CA=0.196
60R X=0 Y=0 Z=3000 R/+Y CA=0.125
70B X=0 Y=0 Z=3000 CA=0.196
80R X=3000 Y=0 Z=0 R/+Y CA=0.125
90B X=3000 Y=0 Z=0 CA=0.196
100R X=0 Y=0 Z= -3000 R/+Y CA=0.125
110B X=0 Y=0 Z= -3000 CA=0.196
120R X=2000 Y=0 Z=0 R/+Y CA=0.125
130R X=6000 Y=0 Z=0 R/Y,Z
140R X=6000 Y=0 Z=0 R/Y,Z
150R X=6000 Y=0 Z=0
150A
As you can notice in the given example of input echo the value of Y is always zero, this is because the pipe is flat (no change
in elevation). The letter after each node indicate what type of component that node will be (A=anchor; R=run; B=bend).
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The S/20 represent the pipe schedule but sometimes the schedule number of the pipe is not given, it is the pipe thickness
already that will be provided (refer to piping classification table provided in part 1). The R followed by a / and or X,Y,Z
represents the type of restraint or support will be used in that particular node.
For your Assignment 4 try preparing the input echo of the piping layout in your Assignment 2. You can submit your
assignment 4 on April 12 either by e-mail or after the classroom session (hard copy).
• After you have prepared your manual input echo, you can now model your piping layout in our CAESAR II.
One by one you will input necessary data for each node and all necessary pipe information.
• After your inputs you can check the graphic presentation of your pipe layout in the computer if it is the same with your piping
layout
• Now you have to set your load cases. The expansion, sustained and the occasional loads as shown on the figure on the next
slide.
Now you were able to model your piping layout (I hope successfully) and you are now ready for the stress analysis part.
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Click on the Edit Static Load Cases button (pyramid like button as shown)
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Your load case should be like this. L1 is the operational load, L2 is the sustained, L5&L6 are the occasional
loads (X&Z) and L7 is the expansion load.
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Stress Analysis
This is the part where the computer does his thing. It will calculate all the stresses that is required under the B31.1 code for
each node that you have input and compare it to the allowable stresses for that particular pipe material. The CAESAR’s II
can show you which part of your piping system has a high stress graphically whether it is expansion, sustained or occasional
stresses.
In this part the engineer will asses all the stresses that are above the allowable and adjust the degree of freedom of the pipe
for certain nodes. The engineer will balance the degree of freedom of the pipe and the stresses. The pipe line should not be
too rigid and also not to free. It is also here where the stress analyst will have to change some of the support type to attain
some degree of freedom of the pipe or the rigidness. In this portion the analyst can also check all the nozzle loadings if it
passes the manufacturer’s or codes requirement.
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After your inputs and setting up the load cases you can now start with the stress analysis by
clicking on the Batch Run button as shown
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This will appear after the analysis. Click on the load cases you want to check the compliance with the
code then click the code compliance on the next window and then click the view report button to view
the result.
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The report will look like the above. In here you will be notified if you have complied with the code
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In preparing for the input echo, click on the input echo on the third window as shown
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Then click the view report button as shown
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The input listing option will pop up. Click on the clear button because you don’t want the other details
except for the elements list
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The computer generated input echo will look like this
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Output
After your stress analysis you need to prepare your output. You will be needing these outputs for your support loadings, to
check on the displacement whether you will be needing pipe shoe and pipe support offsets and lastly for your record or file.
The computer generated Input Echo will also be part of your output. You will be needing this in case you will have some
changes in your piping layout or any revisions that may need for you to conduct stress analysis again and also for your file.
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In preparing for the support loading, select the load cases you want then select Restraint summary
Extended on the 2nd window in order to view and print the loading report for the supports
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Click on the view report (highlighted) in order for you to view and print report
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The Restraint Summary report will be like this
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In this report you will be given the forces, moments and the displacement for each support. These data will
then be given to the structural design section for the design of the supports
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• To have a hands on experience on stress analysis you can visit COADEinc and look for the CAESAR software and request
for a free trial version of the software. The trial version of the CAESAR II software has a limitation, the pipe size you can
stress analyze is up to 6 inch diameter only.
For you Assignment 5 : Model your pipe layout (assignment 2) in the computer, stress analyze and print the output.
You can submit your assignment 5 after the classroom session on April 12, the printed output together with the computer
generated Input Echo.
Source: COADE Piping Stress Analysis Seminar Notes
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