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Chapter X Dynamic Input and Analysis
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BAB X
DYNAMIC INPUT &ANALYSIS
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10.1. The Dynamic Capability :
1. Natural Frequency Calculation
2. Harmonic Analysis
3. Response Spectrum Analysis
4. Time History Analysis
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1. Natural Frequency Calculation
1. Natural Frequency Information can
indicate the tendency of the piping system
to response the dynamic loads2.A systems modal natural frequency
should not to be close to the equipment
operating frequency
3. Higher natural frequency usually cause
less trouble than low natural frequency
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Basic DynamicEquation
Eigensolver
- Natural Frequency
- Modes of Vibration
MODAL ANALYSIS
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If Sturm Sequence Check is failed, the user may
either return to the dynamic input or continue with
the spectral analysis
Sturm Sequence Check
used to confirm no mode
were skipped
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2. Harmonic Analysis
1. Fluid pulsating in reciprocating pump line or
vibration due to rotating equipment
2. The loads are modeled as concentrated force ordisplacement at one or more points in the system
3. Harmonic response represent the maximum
dynamic amplitude the piping system
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For each forcing frequency listed in the dynamic input,
CAESAR II performs a separate analysis. These analysis
are similar to static analysis and take the same amountof time to complete.
At the completion of each solution the forcing frequency,
its largest calculate deflection, and the phase angle
associated with it are listed on the screen. The rootresults for each frequency, and the system deflection, are
saved for further processing.
When all frequencies are analysis, CAESAR II presents
the frequencies on the screen and allow the user toselect those whose needs for further analysis. This
choice can be made after checking deflection at pertinent
node for those frequency
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Selection of Phase Angles
- For all phased harmonic analysis, the user is given the choice ofselecting from 18 separate phase angles solution for each
excitation frequency. Each separate phase angle solution
represents a point in time during one complete cycle of the
system response.
- The primary difference between the solution with and without
phase angle is when the phase angles are entered, there is no
way of knowing beforehand just when the maximum stress, force,
and displacement are going to occur during the cycles.
- For these reason, the displacements and stresses are oftenchecked for a number of points during the cycles for each
excitation frequency.
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3. Response Spectrum Analysis
1. The response spectrum method allows an impulse type
transient event to be characterized by response vs.
frequency spectra
2. Each mode of vibrating of the piping system is related toone response on the spectrum
3. The modal are summed together to produce the total
system response
4. The stresses for these analysis, summed with the
sustained stresses, should be compare to the occasional
stress allowable defined by the piping code
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The spectrum analysis procedure can be broken
down into three tasks :
1. Calculate the systems natural frequencies, modeshapes, and mass participation factors.
2. Using the system frequencies, pull thecorresponding response amplitude from the
spectrum table, and calculate the system responsefor each mode of vibration.
3. Combine the modal responses and directionalcomponents of the shock.
After the natural frequencies are calculated, systems
displacement, forces, moments, and stresses are
calculate on the modal level and combined
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4. Time History Analysis Is used to solve (by numeric integration) the dynamic equation of
motion to simulate the system response throughout the load
duration
It can solve any type of dynamic loading.
The modal time history analysis follows steps similar to aspectrum analysis.
The modes of vibration of the system are computed, the equation
of motion is solved through numerical integration techniques for
each mode, at a number of successive time steps, with the modal
results being summed, yielding system response at each time
steps.
The output processor displays one load cases with the maximum
loads developed throughout the load application.
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10.2. Model Modification for Dynamic Analysis
The dynamic technique employ by CAESAR
II require strict linearity in the piping and
structural system
Dynamic response associated with nonlinear
effect are not addressed
Non-linear problem (ex: slapping and friction
problem) must be linearized for use in
dynamic analysis
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If requested,
CAESAR II
canapproximate
the friction
resistance to
movement in
the dynamic
model by
including
spring
stiffnessnormal to the
restrain line
action.
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10.3. Major Steps in Dynamic Input
Developing dynamic input for CAESAR II
comprises four basic steps :
1. Specifying the loads
2. Modifying the mass and stiffness model
3. Setting the parameters that control the analysis4. Starting and errors checking the analysis
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Entering the Dynamic
Analysis Input Menu
10.4. Overview The Dynamic Input Processor
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Available Commands During Dynamic Input
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10.5. Input Overview Based on
Analysis Input ProcessorLump Mass
Snubbers
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Control Parameter
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Advanced
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10.6. H a r m o n i c
1. Specifying The Loads
Excitation Frequency
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Harmonic Forces
Harmonic Displacements
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2. Modifying Mass and Stiffness Model
Lumped mass and snubbers are modified in the same way
as described formodal analysis
3. Control ParameterThese parameter described how the analysis will be conducted.
Undamped harmonic analysis may be done by setting damping to 0.0
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10.7. Earthquake loads
Define by defining one or more response spectra and applyingthem in a specified direction over part or all of the pipingsystem.
Spectrum Definition Command
Describe the type of data in the spectrum
- period/frequency vs. force multiplier- period/frequency vs. acceleration
- period/frequency vs. velocity or
- period/frequency vs. displacement
as well as the interpolation method for each axis.
Response Spectrum Table Value
- can be entered directly
- built and store as a file for use by CAESAR II
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If not read in from a file, the data points for a user enter spectrum
may be entered by using the Tools-Spectrum Data Points
command, selecting the spectrum name and entering the data
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1. Spectrum Load Cases
Used to modify
the magnitude of
the shock
Define the
orientation of the
uniform inertialloading (X,Y,Z)
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2. Static/Dynamic Combination
Each shock case produce output report listing :
- displacements,
- forces,
- moments, and
- stresses
Most piping code combine the occasionaldynamic stresses with sustained staticstresses
It is the sustained plus occasional stresssum that is compared to the occasionalallowable stress
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Static
Load Case
Dynamic
Load Case
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3. Modifying Mass and Stiffness ModelLumped Mass and Snubers are modified in the same way as described
forModal Analysis
Theseparameter
described how
the analysis is
to be
conducted
4. Control Parameter
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10.8. Relief Loads
1. Specifying Loads
This method is set up to solve a relief valve loadingthrough Force Spectrum Methodology.
In other to analyze a piping system for a relief valveloading, its necessary to estimate the force-timeprofile for the loading
This must then be converted to a Force Multiplier(Dynamic Load Factor) spectrum
The applied force then must be applied in conjunctionwith this spectrum
C
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2. Relief Loads Synthesis
If the user does not know the characteristic of the relief valveload, the Relief Load Synthesis Command provided a
calculation scratch based upon a model of a relief valve
venting steam or liquid to atmosphere .
This utility can be used to estimate : relief valve thrust loads,
exits velocity, and
pressure
which can in turn be used to estimate the force vs. time profile
of the applied load.
Ch t X D i I t d A l i
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Ch t X D i I t d A l i
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3. Pulse Table/ DLF Spectrum Generation
Allow user to convert known Force-Time profile into
a Dynamic Load Factor Spectrum in order to solve
problem using spectrum methodology.
The user must designate a file name to which the
DLF spectrum is to be written, as well as the
maximum frequency to use, and the number data
point to generate.
Ch t X D i I t d A l i
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Chapter X Dynamic Input and Analysis
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4. Spectrum Definition
Response spectrum
table value can be
entered directly or built
and store as a file for
use by CAESAR II
such as those generated
through the DLF
Spectrum Generator
Chapter X Dynamic Input and Analysis
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5. Force Sets
Forces are
grouped into
numbered
forced setswhen :
- these forces
occur together,
or
- need to be
manipulated in
the analysis
together
Chapter X Dynamic Input and Analysis
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6. Spectrum/Load Cases
The Spectrum Load Cases for force spectrum runs must
ling a Force Multiplier spectrum to a force set
The Load CaseDefinition consists
of one or morelines on which :
- Spectrum
- Factor
(usually = 1)- Direction
- Force Set
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7. Control Parameter
- These parameter
described how the
analysis is to be
conducted- Particular
attention should
be paid to the
modal summationmethodology
Chapter X Dynamic Input and Analysis
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10.9. Water Hammer/ Slug Flow
1. Specifying The Load
This method of solving water hammer or slug
problem is the force spectrum method as used for
relieve valve loading, except the relieve loadsynthesizer is not necessary. The user estimates a
Force-Time profile, then turns it into a Force
Multiplier Spectrum, which is then linked to Force Set
in the load cases.
Chapter X Dynamic Input and Analysis
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This method is set up to solve a relief valveloading through Force Spectrum Methodology.
In other to analyze a piping system for a reliefvalve loading, its necessary to estimate the
force-time profile for the loading
This must then be converted to a ForceMultiplier (Dynamic Load Factor) spectrum
The applied force then must be applied inconjunction with this spectrum
Chapter X Dynamic Input and Analysis
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2. Pulse Table/DLF Spectrum Generation
Allow user to convert known Force-Time profileinto a Dynamic Load Factor Spectrum in order tosolve problem using spectrum methodology.
The user must designate a file name to which theDLF spectrum is to be written, as well as themaximum frequency to use, and the number data
point to generate.
Chapter X Dynamic Input and Analysis
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Chapter X Dynamic Input and Analysis
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3. Spectrum Definitions
Response spectrum
table value can be
entered directly or
built and store as afile for use by
CAESAR II such as
those generated
through the DLFSpectrum Generator
Chapter X Dynamic Input and Analysis
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p y p y
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4. Force Sets
Forces are grouped
into numberedforced sets when :
- these forces occur
together, or
- need to be
manipulated in the
analysis together
Chapter X Dynamic Input and Analysis
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p y p y
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5. Spectrum Load Cases
The Spectrum Load Cases for force spectrum runs must ling aForce Multiplier spectrum to a force set
The Load Case
Definition consists ofone or more lines onwhich :
- Spectrum
- Factor (usually = 1)- Direction
- Force Set
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p y p y
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6. Static/Dynamic Combinations
Each shock case produce output report listing :- displacements,
- forces,
- moments, and- stresses
- Most piping code combine the occasional
dynamic stresses with sustained static stresses- It is the sustained plus occasional stress sumthat is compared to the occasional allowablestress
Chapter X Dynamic Input and Analysis
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p y p y
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Static LoadCase
Dynamic Load
Case
Chapter X Dynamic Input and Analysis
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10.10. Time History
1. Specifying The Loads
Loading are specified in term of :
- Force-time profile
Used to specified the load timing
- Forces sets
Used to define the load direction and location
Either the force profile and force set can be used
to define the magnitude
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2. Time History Profile Definition
Time history profilemust be given :
- a name
- data definition(which must beForce vs. Time)
- interpolation
method
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3. Force Sets
Forces are groupedinto numbered
forced sets when :- these forces occur
together, or
- need to bemanipulated in theanalysis together
Chapter X Dynamic Input and Analysis
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4.Control Parameter
These parameter
described how theanalysis is to be
conducted