Harmonic Analysis Example

Harmonic Analysis Example
The purpose of the following example system is to demonstrate the procedure required to
perform a harmonic analysis for a system subjected to harmonic loads.
Harmonic loads are periodic loads generated by reciprocating equipment or by flow generated
vortices near closed tee branches or partially open valves. The periodic loads could have any
shape. They have to be decomposed into a set of harmonics for analysis purposes. For example
when a reciprocating compressor is operating it generates non-sinusoidal periodic pressure
pulses for every revolution of the crank. These pulses generate unbalanced forces on the piping
system. The unbalanced forces are more significant at locations where there is a change in pipe
direction and the pressure at one end is out of phase with the pressure at the other end. The
periodic forces can be decomposed into a set of harmonics or frequencies, each with different
amplitude and phase. These harmonic loads can then be entered into AutoPIPE to perform
harmonic load analysis.
Choose from the following list of topics:
Problem Definition
Definition of the Harmonic Analysis Example in AutoPIPE
AutoPIPE Harmonic Analysis Report
Problem Definition: Harmonic Analysis

The suction side of a natural gas supply system with a reciprocating compressor is shown below.
Two 6" suction lines are connected to the reciprocating compressor assembly. The reciprocating
compressor assembly consists of 22" suction and discharge bottles, 8 " suction and discharge
nozzles and 16" compressor cylinder assembly. The pressure at the suction bottle is 400 psi
which is increased to 650 psi at the discharge bottle. Acoustic shaking forces which are periodic
in nature are produced by the operation of the compressor. If the frequency, phase and magnitude
of these shaking forces are known , the harmonic analysis utility of AutoPIPE can be used to
perform the harmonic analysis. Up to 10 harmonic load cases H1, H2, H3 ... H10 can be created.
The acoustic shaking forces can be calculated using any acoustic simulation program or can be
obtained from some industry guidelines (e.g. compressors manufacturers guidelines). The
program PULS, another product of Bentley, can generate these forces in the form that can be
used directly in AutoPIPE.
For this example, the acoustic shaking forces are computed using PULS. There were two critical
speeds, 276 rpm and 280 rpm of the compressor that generated high shaking forces. To simplify
this example only the 2 most critical harmonics associated with each speed are used in the
harmonic load analysis. Since the compressor operates at a single speed, two harmonic load
cases are considered in the analysis, one for each critical speed. A further simplification is to
consider only two shaking forces.
1. Shaking force applied at point A5 due to unbalanced pressure at the suction bottle (A5A6).
2. Shaking force applied at point A81 due to unbalanced pressure in the 6" suction line
between elbows A8 &A9. (A81 is the mid point of segment between A8 & A9).
Reciprocating Compressor Example
Note: For this example the flexibility of the nozzles has been ignored. The Figure below
shows a suggested modeling approach for considering the flexibility of nozzles in the
analysis. At the end of 8" nozzle pipe define a Nozzle element. AutoPIPE will
automatically calculate the nozzle flexibility by taking into account the suction or
discharge bottle dimensions. But these flexibility values are at the Bottle-Nozzle
interface. To transfer the effect to the center of bottle a rigid pipe element can be attached
between the nozzle and the center of the bottle.
Suggested Model of Nozzle/Bottle Interface
Definition of the Harmonic Analysis Example

This section illustrates the steps required to define and perform a Harmonic force analysis in
AutoPIPE. Follow the text and enter data into the dialog fields exactly as shown and described in
each of the following steps. The steps shown are configured for AutoPIPE for Windows.
1. Open AutoPIPE then select File/Open
and load the harmonic analysis file HRMEXP.
A working model of a typical system with a reciprocating compressor is shown below.
2. Select Load/Harmonic to display the Harmonic Load dialog. Input RPM276 in the
"Harmonic Load case name" field) to define a load case with a critical speed of 276
RPM. Next, enter the "Damping" ratio 0.02. Complete the remaining fields based on the
dialog shown below, then press OK. AutoPIPE automatically stores the data in ASCII
formatted file, RPM276.HMF.
3. Select Load/Harmonic to create a second harmonic load case, RPM280, which corresponds
to a critical speed of 280 RPM. Enter the values shown below.
4. Select Load/Dynamic Analysis/Modal Tab to display the Modal Analysis dialog. Input 12
in the "Maximum number of modes" field. (note that this number may have to be
increased if the cutoff frequency is not reached). Enter a "Cutoff frequency" of 100 Hz
(note that for larger piping systems, higher modes may be present). Use the default of
None in the "Pressure stiffening case" field, then enable the "Include contents" option.
When all fields are complete, press OK. Note: A dialog will appear asking "Do you want
to analyze the model?" Press the Yes button. The "Modal" option should be enabled,
while the others are disabled. Press the OK button.
Note: The modal analysis must always be run before a Harmonic analysis.
5. Select Load/Dynamic Analysis/Modal Tab to display the Harmonic Analysis dialog .
After completing the steps above, case no. 1 and 2 are automatically configured. Case
no. 1 = RPM276 (or select from the list) in the H1 "Data set" field, then select the RMS
combination method to be employed for combining the response of individual harmonics
to compute the final response. Leave the ZPA (Zero Period Acceleration) and Miss
(Missing mass ) correction fields blank. Next confirm case no. 2 settings; specifying the
RPM280 "Data set" corresponding to load case H2, and selecting an RMS combination
method. Press OK. Note: A dialog will appear asking, "Do you want to analyze the
model?" Press the Yes button. The "Modal" and "Harmonic" options should be enabled,
while all other options are disabled. Press the OK button.
Note: The Rms method is selected for combining the response of individual harmonics
because it is unlikely that the peak response of each harmonic will occur at the same
time. Therefore, statistically the Rms method will give the best results. However, in this
case the displaced shape of the system is not realistic because all the computed
displacements will have a positive sign.
6. Select Result/Code Compliance . When the Code Stresses dialog appears, select Ratio in
the "[S]tress/[R]atio/[N]one" field and All in the "Combination" field, then press OK. The
code compliance stress ratio profile is displayed as shown below.
7. Press Quit to return to the Main Menu.

8. Select Result/Output Report , then enable the Displacement, Restraint, Code compliance,
Frequency, and Analysis summary options as shown below. Press OK to generate the
report.
This concludes the modeling of the Harmonic Analysis example. The result file you have just
created should match the results shown in the next section. It can be noted from the results file
that the analysis summary report gives the description of the harmonic load cases analyzed. It is
recommended to check this description to make sure that the data has been read by AutoPIPE
correctly. The displacement report indicates that the maximum displacement and rotation occurs
in the suction line at elbows A8 and A9. From the code compliance report it can be noted that the
maximum stressed point is A7.
Press here to view the AutoPIPE Harmonic Analysis Report.
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
09/17/2008 RECIPROCATING COMPRESSOR EXAMPLE
BENTLEY
09:40 AM
AutoPIPE Advanced 9.10
MODEL PAGE
1
-----------------------------------------------------------------------------------------------------------------------------------
*
***
**
** **
******
**
**
**
** **
*****
*********
**
** ** **
**
**
** **
** ** **
**
**
** *****
**
*****
*******
**
**
**
**
*******
**
**
**
**
**
**
**
**
**
**
*******
**
**
**
**
*******
**
**
**
*******
**
**
*****
**
**
*******
Pipe Stress Analysis and Design Program

Version: 09.01.00.25
Edition: Advanced
Developed and Maintained by
BENTLEY SYSTEMS, INCORPORATED
1600 Riviera Ave., Suite 300
Walnut Creek, CA 94596
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
2
-----------------------------------------------------------------------------------------------------------------------------------
************************************************************
**
**
**
AUTOPIPE SYSTEM INFORMATION
**
**
**
************************************************************
SYSTEM NAME : HRMEXP
PROJECT ID
: RECIPROCATING COMPRESSOR EXAMPLE
PREPARED BY
: ______________________________
NZ
CHECKED BY
: ______________________________
KR
1ST APPROVER : ______________________________
2ND APPROVER : ______________________________
PIPING CODE
: ASME B31.3
YEAR
: 2006
VERTICAL AXIS
: Y
AMBIENT TEMPERATURE
COMPONENT LIBRARY
: AUTOPIPE
MATERIAL LIBRARY
: AUTOB313
MODEL REVISION NUMBER
70.0 deg F
88
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
3
----------------------------------------------------------------------------------------------------------------------------------P O I N T
D A T A
L I S T I N G
POINT
---------OFFSETS (ft
)-------NAME TYPE
X
Y
Z
----- ---- ---------- ---------- ------------------------------------------*** SEGMENT A
A5
Run
0
0
0
A4
Tee
0
0
-2.75
A6
Redu
0
0
-2.50
A0
Run
0
0
-0.50
A7
Tee
0
0
-1.75
A01
Run
0
0
-1.75
A8
Bend
0
0
-12.25
A81
A9
Run
Bend
A10
Run
*** SEGMENT B
A7
Tee
B11
Valv
7.50
7.50
0
0
0
-9.20
0
0
DESCRIPTION
PIPE ID = 22XS
SIF = 1.00
PIPE ID = 6STD
Long Elbow, Radius = 9.00 inch
Bend angle change = 90.00 deg
End flanges = 0, Flex = Auto
SIF - In 2.27, Out = 1.89
0
0 Long Elbow, Radius = 9.00 inch
SIF - In 2.27, Out = 1.89
-10.00
-7.50 PIPE ID = 6STD
0 NS
, Rating
Valve Weight =
Surface factor =
Weld neck, SIF =
= 400
460 lb
5.50
1.00
B12
B13
Run
Bend
-1.63
-10.00
0
0
0
SIF - In 2.27, Out = 1.89
B14
Bend
5.00

SIF - In 2.27, Out = 1.89
B15
Run
-14.00
*** SEGMENT C
A4
Tee
C2
Tee
C02
Tee
0
0
0
0
-2.50
-2.50
-2.75 PIPE ID = 8XS

0
0
*** SEGMENT D
D00
Run
D01
Run
C02
Tee
D03
Run
D04
Run
0
0
0
0
0
-5.00
0
0
0
0
0 PIPE ID = 22XS
-1.00
-1.75
-1.75
-1.00
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
4
----------------------------------------------------------------------------------------------------------------------------------P O I N T
D A T A
L I S T I N G
POINT
---------OFFSETS (ft
)-------NAME TYPE
X
Y
Z
DESCRIPTION
----- ---- ---------- ---------- ------------------------------------------*** SEGMENT E
E00
Run
1.50
-2.50
-2.75 PIPE ID = 16XS
C2
Tee
-1.50
0
0
E01
Run
-4.00
0
0
Weight of Empty Pipes + Weight of Contents = Total Weight of System

3869.7 lb
+
0.0 lb
=
3869.7 lb
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
5
----------------------------------------------------------------------------------------------------------------------------------C O M P O N E N T
D A T A
L I S T I N G
POINT ------COORDINATE(ft
)------ DATA
NAME
X
Y
Z
TYPE DESCRIPTION
----- --------- --------- --------- ----------------------------------------*** SEGMENT A
A5
A4
0.00
0.00
0.00
0.00
0.00
-2.75 TEE
A6
A0
A7
0.00
0.00
0.00
0.00
0.00
0.00
-5.25
-5.75
-7.50 TEE
A01
0.00
0.00
-9.25 GUIDE
0.00
0.00
0.75
7.50
14.25
15.00
15.00
15.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
*** SEGMENT B
A7
0.00
0.00
-7.50 TEE
B11
B11 M
B12
B13 N
-9.20
-10.01
-10.83
-20.08
0.00
0.00
0.00
0.00
-7.50
-7.50
-7.50
-7.50 GUIDE
B13
B13 F
B14 N
B14
B14 F
B15
-20.83
-20.83
-20.83
-20.83
-20.83
-20.83
0.00
0.75
4.25
5.00
5.00
5.00
*** SEGMENT C
A4
0.00
0.00
-2.75 TEE
A8
A8
A8
A81
A9
A9
A9
A10
N
F
N
F
-20.75
-21.50
-21.50
-21.50
-21.50
-21.50
-22.25
-31.50
-7.50
-7.50
-7.50
-7.50
-8.25
-21.50
B16.9 welding tee

SIF - In = 2.70, Out = 3.27
B16.9 welding tee
SIF - In = 1.85, Out = 2.14
ID : A01 1, Connected to Ground
Stiffness = .1000E+11 lb/in
TI
V-STOP ID : A81
1, Connected to Ground
TI
ANCHOR Rigid
Thermal movements : None
B16.9 welding tee
SIF - In = 1.85, Out = 2.14
ID : B13 N1, Connected to Ground

TI
TI
V-STOP ID : B14 F1, Connected to Ground
ANCHOR Rigid
C2
0.00
-2.50
-2.75 TEE
C02
0.00
-5.00
-2.75 TEE
*** SEGMENT D
D00
0.00
D01
0.00
-5.00
-5.00
0.00
-1.00 GUIDE
C02
0.00
-5.00
-2.75 TEE
D03
0.00
-5.00
-4.50 GUIDE
B16.9
SIF Other
SIF B16.9
SIF -
welding tee
In = 2.70, Out = 3.27
In = 1.00, Out = 1.00
welding tee
In = 2.70, Out = 3.27
ID : D01 1, Connected to Ground

B16.9 welding tee
SIF - In = 2.70, Out = 3.27
ID : D03 1, Connected to Ground
----------------------------------------------------------------------------------------------------------------------------------HRMEXP

BENTLEY
09:40 AM
MODEL PAGE
6
----------------------------------------------------------------------------------------------------------------------------------C O M P O N E N T
D A T A
L I S T I N G
POINT ------COORDINATE(ft
)------ DATA
NAME
X
Y
Z
TYPE DESCRIPTION
----- --------- --------- --------- ----------------------------------------D04
0.00
-5.00
-5.50
*** SEGMENT E
E00
1.50
C2
0.00
-2.50
-2.50
E01
-2.50
-4.00
-2.75
-2.75 TEE
Other
SIF - In = 1.00, Out = 1.00
-2.75 ANCHOR Rigid
Number of points in the system : 36

----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
7
----------------------------------------------------------------------------------------------------------------------------------P I P E
D A T A
L I S T I N G
Pipe ID/
Nom/ O.D. -----Thickness(inch)----E/
Composition
Material
Sch inch W.Th. Corr Mill Insu Ling
------------ ---- ----- ----- ---- ---- ---- ------- -------------------8"STD
8 8.625 0.322
0 0.04
0
0
1.00 Carbon Steel
A53-A
STD
1.00
Spec
Weight(lb/ft )
Grav
----
Pipe Other Total

----- ----- -----
28.52
21"XS
20 20.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
104
6"STD
6 6.625 0.280
1.00 Carbon Steel
A53-A
STD
1.00
0 0.04
18.95
0 28.52
104
0 18.95
8"XS
8 8.625 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
43.34
0 43.34
16"XXS
16 16.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
82.68
0 82.68
21INSTD
20 20.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
104
6INSTD
6 6.625 0.280
1.00 Carbon Steel
A53-A
STD
1.00
0 0.04
18.95
0 18.95
8INSTD
8 8.625 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
43.34
0 43.34
16INSTD
16 16.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
82.68
0 82.68
21XS
22 22.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
115
6STD
6 6.625 0.280
1.00 Carbon Steel
A53-A
STD
1.00
0 0.04
18.95
0 18.95
8XS
8 8.625 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
43.34
0 43.34
16XS
16 16.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
82.68
0 82.68
22XS
22 22.000 0.500
1.00 Carbon Steel
A53-A
XS
1.00
0 0.06
115
104
115
115
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
8
----------------------------------------------------------------------------------------------------------------------------------M A T E R I A L
D A T A
L I S T I N G
Material
Density Pois. Temper.
Modulus E6 psi
Expans. Composition
Name
Pipe ID lb/cu.ft Ratio deg F
Axial
Hoop
Shear
in/100ft
------------ -------- -------- ----- ------- -------- -------- --------------- ------------------A53-A
22XS
489.0 0.30
70.0
29.500
29.500
11.346
Carbon Steel
130.0
29.174
0.4569
A53-A
6STD
Carbon Steel
489.0
0.30
70.0
29.500
29.500
11.346
A53-A
8XS
Carbon Steel
489.0
0.30
70.0
29.500
29.500
11.346
A53-A
16XS
Carbon Steel
489.0
0.30
70.0
29.500
29.500
11.346
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE
9
----------------------------------------------------------------------------------------------------------------------------------M A T E R I A L
A L L O W A B L E
D A T A
Material
Temper. Allow.
Yield
Ultimate
Name
Pipe ID deg F
psi
psi
------------ -------- ------- -------- -------- -------A53-A
22XS
70.0 15997.7 30000.0 48000.0
70.0 16000.0 30000.0
130.0 16000.0 29250.0
A53-A
6STD
70.0
70.0
16000.0
16000.0
30000.0
30000.0
48000.0
L I S T I N G
A53-A
8XS
70.0
70.0
16000.0
16000.0
30000.0
30000.0
48000.0
A53-A
16XS
70.0
70.0
16000.0
16000.0
30000.0
30000.0
48000.0
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE 10
----------------------------------------------------------------------------------------------------------------------------------A U T O
Temperature
deg F
-----------70.00
130.00
W E L D
R E D U C T I O N
F A C T O R
D A T A
Weld Reduction Factor

W
--------------------1.000
1.000
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
MODEL PAGE 11
----------------------------------------------------------------------------------------------------------------------------------OPERATING TEMPERATURE AND PRESSURE DATA
STRESSES IN psi
POINT
NAME CASE
---- ----
PRESS. TEMPER
psi
deg F
------ ------
EXPAN.
in/100ft
--------
MODULUS
E6 psi
-------
ALLOW
STRESS
------
YIELD
STRESS
------
*** SEGMENT A
A5
T1
440 70.00
0.000
A10
Same as previous point.
29.500
16000
30000
*** SEGMENT B
A7
T1
440 70.00
0.000
B15
29.500
16000
30000
*** SEGMENT C
A4
T1
440 70.00
0.000
C02
29.500
16000
30000
29.174
16000
29250
*** SEGMENT E
E00
T1
440 70.00
0.000
E01
29.500
16000
30000
u
*
*** SEGMENT D
D00
T1
695
130
0.457
D04
User-defined value
Non-code material for allowable stress;
Non-standard material for expansion and modulus
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
1
----------------------------------------------------------------------------------------------------------------------------------A N A L Y S I S
S U M M A R Y
Current model revision number : 88

Modal - Date and Time of analysis .............
Model Revision Number .................
Number of modes .......................
Cutoff frequency (Hz) .................
Weight of contents included ...........
Pressure stiffening case ..............
Water elevation for buoyancy loads ....
Hot modulus case used in analysis .....
Use corroded thickness in analysis ....
Rigid stiffness factor ................
Sep 17, 2008

9:40 AM
88
11
100.0
Yes
None
Not considered
0
No
1000.0
Harmonic - Date and Time of analysis .............

Model Revision Number .................
Number of load cases ..................
Load cases analyzed ...................
Date and time of modal analysis .......
Number of modes .......................
Cutoff frequency (Hz) .................
Model revision of modal analysis ......
Weight of contents included ...........
Pressure stiffening case ..............
Water elevation for buoyancy loads ....
Hot modulus case used in analysis .....
Use corroded thickness in analysis ....
Rigid stiffness factor ................
Sep 17, 2008

9:40 AM
88
2
H1 H2
Sep 17, 2008
9:40 AM
11
100.0
88
Yes
None
Not considered
0
No
1000.0
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
2
----------------------------------------------------------------------------------------------------------------------------------CODE COMPLIANCE COMBINATIONS
<Description>
Allowable
Combination
Category
Method
Case/Combination
Factor M/S K-Factor
(psi)
D/A/P
--------------------------------- -------- ----------------------------- --- --------- --------- ------Sus. + H1
Occasion
Abs sum H1
1.00
1.330 Automatic Y Y Y
Max Sus
1.00
Sus. + H2
1.330
1.00
Automatic
Occasion
Y Y Y
Abs sum
H2
Max Sus
1.00
Notes:
D/A/P: [D]efault/[A]uto-Update/[P]rint options (Y=Yes, N=No)
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
3
----------------------------------------------------------------------------------------------------------------------------------NON-CODE COMBINATIONS
<Description>
Combination
----------------------Harmonic 1
Method
Case/Combination
Factor D/A/P
-------- ------------------------ ------ ------Sum
H1
1.00 Y Y Y
Harmonic 2
Sum
Notes:
H2
1.00
Y Y Y
D/A/P: [D]efault/[A]uto-Update/[P]rint options (Y=Yes, N=No)

----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
4
-----------------------------------------------------------------------------------------------------------------------------------
CODE COMPLIANCE
Y - Factor ............................
Stress Range factor ...................
Design Pressure Factor ................
Minimum stress ratio used in reports...
Number of stress points per span ......
Include corrosion in stress calcs. ....
Include torsion in code stress ........
Include axial force in code stress ....
Include sustain load margin ...........
exceeded
Set sustained SIF=1 no bends ..........
Set sustained/occasional SIF = 1 ......
Set sustained/occasional SIF = 0.75i ..
Apply cold/hot modulus ratio ..........
Disable auto code combinations ........
Disable auto non-code combinations ....
No. of thermal ranges to report .......
Include Max Range combination .........
Total stress ..........................
Direct shear ..........................
Longitudinal pressure calculation .....
Use code case 178 .....................
Inc. Axial Str and Pcase in Sustained..
Use alternate occasional allowable ....
Apply circumferential weld W factor ...
0.40
1.00
1.00
0.00
0
Y
N
N
Only if allowable stress is
N
N
N
N
N
N
3
N
Octahedral
None
PD/4t
N
N
N
N
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
5
----------------------------------------------------------------------------------------------------------------------------------HARMONIC LOAD CASES :
---------------------
Number of load cases analysed :

Load case 1
H1
Data identifier : RPM276

Modal Combination method :
Captured modal mass (%) :
RMS
Added
102.81
missing mass (%) :
0.00
Missing mass : No
ZPA
: No
Number of Harmonics :
Point
Name
----A5
A81
A5
A81
Freq
Phase
(Hz.) (deg)
----- ----9.20 -28.70
9.20 90.41
18.40 -87.10
18.40 -81.20
2
Fx
(lb
)
-------0.00
307.50
0.00
826.70
Fy
(lb
)
-------0.00
0.00
0.00
0.00
Fz
(lb
)
-------93.37
0.00
5848.00
0.00
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
6
----------------------------------------------------------------------------------------------------------------------------------Load case 2
H2
Data identifier : RPM280

Modal Combination method :
Captured modal mass (%) :
RMS
Added
105.21
missing mass (%) :
0.00
Missing mass : No
ZPA
: No
Number of Harmonics :
Point
Name
----A5
A81
A5
Freq
Phase
(Hz.) (deg)
----- ----18.67-128.00
18.67-122.00
37.33 15.89
2
Fx
(lb
)
-------0.00
262.90
0.00
Fy
(lb
)
-------0.00
0.00
0.00
Fz
(lb
)
-------2129.00
0.00
1663.00
A81
37.33
14.17
4742.00
0.00
0.00
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
7
----------------------------------------------------------------------------------------------------------------------------------F R E Q U E N C I E S
Mode
Freq.
Period
Participation Factors
Captured Modal Mass
(Percent)
Number (Hertz) (Sec)
X
Y
Z
X
Y
Z
Average
------ ------- -------- ------- ------- ------- ------- ------- ------------1
3.585
7.9379
0.126
-1.04
0.02
-0.04
10.735
0.005
0.017
2
0.344
9.0889
0.110
-0.03
-0.32
0.05
0.007
1.004
0.022
3
5.752
10.8151
0.092
-0.06
-0.88
-0.97
0.030
7.759
9.466
4
5.722
11.2850
0.089
-0.07
0.90
-0.95
0.048
8.141
8.978
5
2.412
17.5490
0.057
0.83
0.14
0.09
6.959
0.197
0.080
6
2.829
19.6578
0.051
0.01
0.92
-0.04
0.001
8.471
0.016
7
2.987
28.2139
0.035
-0.07
0.01
0.95
0.043
0.002
8.918
8
13.000
40.7632
0.025
0.12
0.08
1.97
0.134
0.062
38.806
9
9.995
45.2558
0.022
1.71
-0.07
-0.28
29.162
0.046
0.778
10
3.807
59.8534
0.017
-1.05
0.04
0.21
10.951
0.017
0.454
11
3.537
63.6079
0.016
-0.32
0.16
-0.97
1.002
0.258
9.353
Total captured modal mass (%)
53.973
59.070
Total system weight =
25.961
76.886
3869.7 lb
Note: Participation factors and captured modal mass apply

only to Response Spectrum and Earthquake Time History
load cases. Captured modal mass for other load
types can be found in the analysis summary sub-report.
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
8
----------------------------------------------------------------------------------------------------------------------------------D I S P L A C E M E N T S
Point
(deg )
name
Z
-----------
Load
combination
ROTATIONS
------
------
------
------
------
Harmonic 1
0.004
0.012
0.022
0.021
0.007
Harmonic 2
0.008
0.014
0.029
0.024
0.012
Harmonic 1
0.002
0.000
0.022
0.020
0.007
Harmonic 2
0.001
0.000
0.029
0.024
0.012
Harmonic 1
0.005
0.010
0.022
0.019
0.007
Harmonic 2
0.005
0.012
0.029
0.022
0.012
Harmonic 1
0.006
0.012
0.022
0.018
0.007
Harmonic 2
0.007
0.014
0.029
0.021
0.012
Harmonic 1
0.006
0.010
0.022
0.019
0.007
Harmonic 2
0.007
0.012
0.029
0.023
0.007
------------------------
*** Segment A
A5
0.005
TRANSLATIONS (in
begin ***
0.003
A4
0.005
0.003
A6
0.005
0.003
A0
0.005
0.003
A7
0.007
0.005
A01
0.009
0.005
A8 N
0.021
0.007
A8 F
0.025
0.009
A81
0.019
0.004
A9 N
0.034
0.015
A9 F
0.024
0.010
A10
0.000
0.000
Harmonic 1
0.000
0.000
0.022
0.028
0.030
Harmonic 2
0.000
0.000
0.030
0.030
0.022
Harmonic 1
0.196
0.030
0.023
0.016
0.093
Harmonic 2
0.049
0.009
0.030
0.015
0.023
Harmonic 1
0.209
0.027
0.023
0.017
0.054
Harmonic 2
0.053
0.008
0.025
0.013
0.038
Harmonic 1
0.208
0.000
0.053
0.021
0.010
Harmonic 2
0.053
0.000
0.023
0.010
0.013
Harmonic 1
0.208
0.042
0.014
0.024
0.060
Harmonic 2
0.053
0.017
0.005
0.009
0.028
Harmonic 1
0.192
0.043
0.000
0.031
0.130
Harmonic 2
0.048
0.017
0.000
0.012
0.036
Harmonic 1
0.000
0.000
0.000
0.000
0.000
Harmonic 2
0.000
0.000
0.000
0.000
0.000
Harmonic 1
0.006
0.010
0.022
0.019
0.007
Harmonic 2
0.007
0.012
0.029
0.023
0.007
Harmonic 1
0.006
0.005
0.014
0.012
0.011
Harmonic 2
0.008
0.001
0.003
0.014
0.016
Harmonic 1
0.006
0.005
0.015
0.012
0.011
Harmonic 2
0.008
0.001
0.004
0.014
0.016
*** Segment A
end
*** Segment B
begin ***
A7
0.007
0.005
B11
0.002
0.004
B11 M
0.002
0.004
***
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE
9
----------------------------------------------------------------------------------------------------------------------------------D I S P L A C E M E N T S
Point
(deg )
name
Z
----------B12
0.002
0.004
B13 N
0.002
0.001
B13 F
0.029
0.012
B14 N
0.035
0.015
B14 F
0.027
0.011
B15
0.000
0.000
Load
TRANSLATIONS (in
combination
ROTATIONS
------
------
------
------
------
Harmonic 1
0.006
0.005
0.016
0.012
0.011
Harmonic 2
0.008
0.002
0.006
0.014
0.016
Harmonic 1
0.006
0.000
0.000
0.004
0.013
Harmonic 2
0.008
0.000
0.000
0.005
0.011
Harmonic 1
0.006
0.001
0.001
0.004
0.008
Harmonic 2
0.007
0.000
0.001
0.003
0.009
Harmonic 1
0.027
0.001
0.001
0.001
0.003
Harmonic 2
0.007
0.000
0.000
0.000
0.006
Harmonic 1
0.031
0.000
0.000
0.006
0.010
Harmonic 2
0.009
0.000
0.000
0.002
0.003
Harmonic 1
0.000
0.000
0.000
0.000
0.000
Harmonic 2
0.000
0.000
0.000
0.000
0.000
0.002
0.000
0.022
0.020
0.007
------------------------
*** Segment B
end
*** Segment C
begin ***
A4
0.005
Harmonic 1
***
0.003
C2
0.001
0.000
C02
0.000
0.000
Harmonic 2
0.001
0.000
0.029
0.024
0.012
Harmonic 1
0.000
0.000
0.009
0.010
0.012
Harmonic 2
0.000
0.000
0.014
0.011
0.019
Harmonic 1
0.000
0.000
0.007
0.000
0.000
Harmonic 2
0.000
0.000
0.012
0.000
0.000
Harmonic 1
0.000
0.000
0.007
0.000
0.000
Harmonic 2
0.000
0.000
0.012
0.000
0.000
Harmonic 1
0.000
0.000
0.007
0.000
0.000
Harmonic 2
0.000
0.000
0.012
0.000
0.000
Harmonic 1
0.000
0.000
0.007
0.000
0.000
Harmonic 2
0.000
0.000
0.012
0.000
0.000
Harmonic 1
0.000
0.000
0.007
0.000
0.000
Harmonic 2
0.000
0.000
0.012
0.000
0.000
Harmonic 1
0.000
0.000
0.007
0.000
0.000
Harmonic 2
0.000
0.000
0.012
0.000
0.000
*** Segment C
end
*** Segment D
begin ***
D00
0.000
0.000
D01
0.000
0.000
C02
0.000
0.000
D03
0.000
0.000
D04
0.000
0.000
*** Segment D
end
***
***
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE 10
----------------------------------------------------------------------------------------------------------------------------------D I S P L A C E M E N T S
Point
(deg )
name
Z
-----------
Load
TRANSLATIONS (in
combination
ROTATIONS
------
------
------
------
------
Harmonic 1
0.000
0.000
0.013
0.010
0.012
Harmonic 2
0.000
0.000
0.020
0.011
0.019
Harmonic 1
0.000
0.000
0.009
0.010
0.012
Harmonic 2
0.000
0.000
0.014
0.011
0.019
Harmonic 1
0.000
0.000
0.000
0.000
0.000
Harmonic 2
0.000
0.000
0.000
0.000
0.000
------------------------
*** Segment E
E00
0.001
begin ***
0.000
C2
0.001
0.000
E01
0.000
0.000
*** Segment E
end
***
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE 11
----------------------------------------------------------------------------------------------------------------------------------R E S T R A I N T
Point
Load
(ft-lb )
name
combination
Z
Result
------ ----------------------------- ------A01
FORCES (lb
X
Harmonic 2
A81
0
V - Stop Tag No.: <None>

Harmonic 1
)
Z
MOMENTS
Result
------ ------ ------ ------ ------- -------
Guide
Tag No.: <None>
Harmonic 1
R E A C T I O N S
[ID: A01 1]
498
1133
1238
1169
1856
268
1441
[ID: A81 1]
0
268
Harmonic 2
0
A10
203
Anchor
Tag No.: <None>
Harmonic 1
3659
Harmonic 2
882
86
B13 N
Guide
Tag No.: <None>
Harmonic 1
Harmonic 2
B14 F
0
Harmonic 2
B15
158
64
Anchor
Tag No.: <None>
Harmonic 1
402
Harmonic 2
140
D01
Guide
Tag No.: <None>
Harmonic 1
Harmonic 2
D03
0
Harmonic 2
E01
393
432
127
468
90
25
477
752
3575
94
40
159
189
312
820
110
477
72
167
525
[ID: B13 N1]

0
464
Anchor
Tag No.: <None>
Harmonic 1
18733
Harmonic 2
27970
151
[ID: B14 F1]

0
525
0
186
186
43
19
31
56
85
359
18
20
29
121
693
778
431
[ID: D01 1]
384
577
612
Guide
Tag No.: <None>
Harmonic 1
127
V - Stop Tag No.: <None>

Harmonic 1
481
[ID: D03 1]
416
113
630
425
760
532
349
5078
5118
4835
18094
262
267
7519
7529
5500
27421
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE 12
----------------------------------------------------------------------------------------------------------------------------------ASME B31.3 (2006)
CODE COMPLIANCE
(Moments in ft-lb )
(Stress in psi
)
Point
Load
In-Pl. Out-Pl. Torsion
S.I.F
Eq. Load
Code
Code
name
combination
Moment Moment Moment In Out
no. type
Stress Allow.
------ ---------------------------- ------- ------- ---- ---- ---- --------- -----*** Segment A
A5
begin ***
Sus. + H1
1.00 1.00 (18)
OCC
Sus. + H2
1.00 1.00 (18)
OCC
- Sus. + H1
21277
Sus. + H2
21277
1040
54
2.70 3.27 (18)
OCC
1133
516
2.70 3.27 (18)
OCC
+ Sus. + H1
21277
Sus. + H2
1102 21277
4552
1235
2.70 3.27 (18)
OCC
5821
1286
2.70 3.27 (18)
OCC
A6
228
Sus. + H1
21277
Sus. + H2
21277
3326
519
1.00 1.00 (18)
OCC
4051
1274
1.00 1.00 (18)
OCC
Sus. + H1
21280
Sus. + H2
21280
2922
551
1.00 1.00 (18)
OCC
3525
1210
1.00 1.00 (18)
OCC
- Sus. + H1
21280
Sus. + H2
21280
1080
1376
1.85 2.14 (18)
OCC
942
1535
1.85 2.14 (18)
OCC
+ Sus. + H1
21280
Sus. + H2
21280
1169
1439
1.85 2.14 (18)
OCC
1861
1611
1.85 2.14 (18)
OCC
Sus. + H1
21280
Sus. + H2
21280
529
1590
1.00 1.00 (18)
OCC
795
202
1.00 1.00 (18)
OCC
N- Sus. + H1
21280
Sus. + H2
21280
133
490
1.00 1.00 (18)
OCC
68
171
1.00 1.00 (18)
OCC
21277
21277
A4
191
236
A4
876
287
A0
4200
5264
A7
5020
5244
A7
5309
6877
A01
2366
1159
A8
717
259
A8 N+ Sus. + H1
1607 21280
Sus. + H2
575 21280
490
133
2.27 1.89 (18)
OCC
171
68
2.27 1.89 (18)
OCC
A8 F- Sus. + H1
1732 21280
Sus. + H2
911 21280
538
74
2.27 1.89 (18)
OCC
282
51
2.27 1.89 (18)
OCC
F+ Sus. + H1
21280
Sus. + H2
21280
74
538
1.00 1.00 (18)
OCC
51
282
1.00 1.00 (18)
OCC
Sus. + H1
21280
Sus. + H2
21280
835
932
1.00 1.00 (18)
OCC
391
1033
1.00 1.00 (18)
OCC
A9 N- Sus. + H1
1449 21280
Sus. + H2
325 21280
175
1011
1.00 1.00 (18)
OCC
70
219
1.00 1.00 (18)
OCC
A9 N+ Sus. + H1
3268 21280
Sus. + H2
726 21280
1011
175
2.27 1.89 (18)
OCC
219
70
2.27 1.89 (18)
OCC
A9 F- Sus. + H1
2432 21280
Sus. + H2
388 21280
756
90
2.27 1.89 (18)
OCC
106
72
2.27 1.89 (18)
OCC
A8
767
404
A81
1767
1560
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE 13
----------------------------------------------------------------------------------------------------------------------------------ASME B31.3 (2006) CODE COMPLIANCE
(Moments in ft-lb )
(Stress in psi
)
S.I.F
Eq. Load
Point
Load
Code
Code
name
combination
Stress Allow.
------ --------------------------- -----A9 F+ Sus. + H1
1076 21280
Moment
Moment
Moment
In
Out
no. type
------- ------- ------- ---- ---- ---- ---90
756
1.00 1.00 (18)
OCC
Sus. + H2
21280
72
106
1.00 1.00 (18)
OCC
Sus. + H1
21280
Sus. + H2
21280
752
3575
1.00 1.00 (18)
OCC
312
820
1.00 1.00 (18)
OCC
Sus. + H1
21280
Sus. + H2
21280
701
92
1.85 2.14 (18)
OCC
942
114
1.85 2.14 (18)
OCC
B11
Sus. + H1
801 21280
Sus. + H2
658 21280
201
530
1.00 1.00 (18)
OCC
142
444
1.00 1.00 (18)
OCC
B12
Sus. + H1
981 21280
Sus. + H2
958 21280
228
656
1.00 1.00 (18)
OCC
182
653
1.00 1.00 (18)
OCC
B13 N- Sus. + H1
331 21280
Sus. + H2
158 21280
178
153
1.00 1.00 (18)
OCC
86
71
1.00 1.00 (18)
OCC
B13 N+ Sus. + H1
700 21280
Sus. + H2
334 21280
178
153
2.27 1.89 (18)
OCC
86
71
2.27 1.89 (18)
OCC
B13 F- Sus. + H1
1410 21280
Sus. + H2
660 21280
436
79
2.27 1.89 (18)
OCC
198
71
2.27 1.89 (18)
OCC
B13 F+ Sus. + H1
625 21280
Sus. + H2
296 21280
79
436
1.00 1.00 (18)
OCC
71
198
1.00 1.00 (18)
OCC
B14 N- Sus. + H1
283 21280
Sus. + H2
112 21280
184
78
1.00 1.00 (18)
OCC
75
25
1.00 1.00 (18)
OCC
B14 N+ Sus. + H1
625 21280
184
78
2.27 1.89 (18)
OCC
180
A10
5160
1239
*** Segment A
end
*** Segment B
begin ***
A7
1855
2488
***
Sus. + H2
21280
75
25
2.27 1.89 (18)
OCC
B14 F- Sus. + H1
785 21280
Sus. + H2
358 21280
173
209
2.27 1.89 (18)
OCC
58
115
2.27 1.89 (18)
OCC
B14 F+ Sus. + H1
383 21280
Sus. + H2
181 21280
173
209
1.00 1.00 (18)
OCC
58
115
1.00 1.00 (18)
OCC
B15
Sus. + H1
522 21280
Sus. + H2
176 21280
85
359
1.00 1.00 (18)
OCC
29
121
1.00 1.00 (18)
OCC
249
*** Segment B
end
***
*** Segment C
begin ***
----------------------------------------------------------------------------------------------------------------------------------HRMEXP
BENTLEY
09:40 AM
RESULT PAGE 14
----------------------------------------------------------------------------------------------------------------------------------ASME B31.3 (2006) CODE COMPLIANCE
(Moments in ft-lb )
(Stress in psi
)
S.I.F
Eq. Load
Point
Load
Code
Code
name
combination
Stress Allow.
------ --------------------------- -----A4
Sus. + H1
4405 21280
Sus. + H2
5875 21280
Moment
Moment
Moment
In
Out
no. type
------- ------- ------- ---- ---- ---- ---3513
155
2.70 3.27 (18)
OCC
4691
98
2.70 3.27 (18)
OCC
- Sus. + H1
21280
Sus. + H2
21280
1214
6800
1.00 1.00 (18)
OCC
694
8686
1.00 1.00 (18)
OCC
+ Sus. + H1
21280
Sus. + H2
1565 21280
183
1965
1.00 1.00 (18)
OCC
54
3197
1.00 1.00 (18)
OCC
C2
3381
4266
C2
966
C02
1135
907
2.70 3.27 (18)
OCC
345
2.70 3.27 (18)
OCC
D00
Sus. + H1
21277
Sus. + H2
0 21277
1.00 1.00 (18)
OCC
1.00 1.00 (18)
OCC
D01
Sus. + H1
21277
Sus. + H2
0 21277
1.00 1.00 (18)
OCC
1.00 1.00 (18)
OCC
C02 - Sus. + H1
237 21277
Sus. + H2
282 21277
1010
672
2.70 3.27 (18)
OCC
842
1070
2.70 3.27 (18)
OCC
C02 + Sus. + H1
165 21277
Sus. + H2
279 21277
198
727
2.70 3.27 (18)
OCC
744
1101
2.70 3.27 (18)
OCC
D03
Sus. + H1
21277
Sus. + H2
0 21277
1.00 1.00 (18)
OCC
1.00 1.00 (18)
OCC
D04
Sus. + H1
21277
Sus. + H2
0 21277
1.00 1.00 (18)
OCC
1.00 1.00 (18)
OCC
E00
Sus. + H1
21280
Sus. + H2
0 21280
1.00 1.00 (18)
OCC
1.00 1.00 (18)
OCC
C2
- Sus. + H1
22 21280
Sus. + H2
38 21280
165
1.00 1.00 (18)
OCC
293
1.00 1.00 (18)
OCC
432
Sus. + H1
21280
Sus. + H2
21280
*** Segment C
end
***
*** Segment D
begin ***
*** Segment D
end
*** Segment E
begin ***
***
C2
330
359
E01
2374
3597
+ Sus. + H1
21280
Sus. + H2
21280
1035
2295
1.00 1.00 (18)
OCC
641
2662
1.00 1.00 (18)
OCC
Sus. + H1
21280
Sus. + H2
21280
393
18094
1.00 1.00 (18)
OCC
432
27421
1.00 1.00 (18)
OCC
*** Segment E
end
***

Harmonic Analysis Example

Uploaded by

Copyright:

Available Formats

Harmonic Analysis Example

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Harmonic Analysis Example

Uploaded by

Copyright:

Available Formats

Harmonic Analysis Example

Problem Definition: Harmonic Analysis

Reciprocating Compressor Example

Suggested Model of Nozzle/Bottle Interface

Definition of the Harmonic Analysis Example

and load the harmonic analysis file HRMEXP.

A working model of a typical system with a reciprocating compressor is shown below.

7. Press Quit to return to the Main Menu.

Pipe Stress Analysis and Design Program

SYSTEM NAME : HRMEXP

: RECIPROCATING COMPRESSOR EXAMPLE

1ST APPROVER : ______________________________

2ND APPROVER : ______________________________

MODEL REVISION NUMBER

0 Long Elbow, Radius = 9.00 inch

-2.75 PIPE ID = 8XS

Weight of Empty Pipes + Weight of Contents = Total Weight of System

B16.9 welding tee

ID : B13 N1, Connected to Ground

ID : D01 1, Connected to Ground

09/17/2008 RECIPROCATING COMPRESSOR EXAMPLE

Number of points in the system : 36

Pipe Other Total

Weld Reduction Factor

Current model revision number : 88

Sep 17, 2008

Harmonic - Date and Time of analysis .............

Sep 17, 2008

D/A/P: [D]efault/[A]uto-Update/[P]rint options (Y=Yes, N=No)

Number of load cases analysed :

Data identifier : RPM276

missing mass (%) :

Data identifier : RPM280

missing mass (%) :

Total captured modal mass (%)

Total system weight =

Note: Participation factors and captured modal mass apply

V - Stop Tag No.: <None>

------ ------ ------ ------ ------- -------

[ID: B13 N1]

[ID: B14 F1]

V - Stop Tag No.: <None>

1.00 1.00 (18)

1.00 1.00 (18)

2.70 3.27 (18)

2.70 3.27 (18)

2.70 3.27 (18)

2.70 3.27 (18)

1.00 1.00 (18)

1.00 1.00 (18)

1.00 1.00 (18)

1.00 1.00 (18)

1.85 2.14 (18)

1.85 2.14 (18)

1.85 2.14 (18)

1.85 2.14 (18)

1.00 1.00 (18)

1.00 1.00 (18)

1.00 1.00 (18)