5. Perform analysis by clicking Perform
Analysis or using the Main Menu, Analysis>Perform
Analysis.
6. When an analysis is completed, analyze the results using load cases
or load combinations with various post-processing functions from the Results
menu.
From the Main
Menu select Load > Response Spectrum Analysis Data > Response
Spectrum Load Cases.
Select Response
Spectrum Analysis > Response Spectrum Load Cases in the
Menu tab of the Tree Menu.
Load Case Name
Enter the name of the response spectrum
analysis case. The name is used for load combinations. (Refer to "Combinations")
Direction
X-Y:
Apply the response spectrum loads in the horizontal directions (directions
parallel to GCS X-Y plane) of the structure.
Z:
Apply the response spectrum loads in the vertical direction (GCS Z-direction)
of the structure.
Revision of Gen 2010
Auto-Search Angle
Select this option to automatically
take the excitation angle of response spectrum as the major-axis direction
of a building.
Major
: Major-axis direction
Ortho
: Major-axis direction + 90˚
Note
"Major" and "Ortho"
must be defined in the identical Response Spectrum function. For example,
if we define"RX" load case as "Major", "RY"
load case must be defined as "Ortho". After performing the Response
Spectrum Analysis, excitation angle of the structure will be automatically
entered in the "Excitation Angle" field.
Excitation Angle
When the seismic excitation direction is
parallel to the X-Y plane (Direction='X-Y'), the sign of the seismic loading
angle [Degree] is referenced to the Z-axis using the right hand rule.
The angle is zero at the GCS X-axis.
Scale Factor
Scale factor for the entered response spectrum
excitation
Period Modification Factor
A multiplier factor for periods calculated
by eigenvalue analysis.
Non-structural members are typically excluded
in the analytical model, but rather treated as loads. Such omission can
result in higher periods than actually are. This factor applies to all
the natural periods calculated by eigenvalue analysis for response spectrum
analysis. This functionality becomes useful when we wish to account for
stiffness contribution of non-structural elements in which case we may
wish to reduce the calculated periods.
Note
This factor applies to all the natural periods calculated by eigenvalue
analysis for response spectrum analysis. This functionality becomes useful
for example when we wish to account for stiffness contribution of non-structural
elements in which case we may wish to reduce the calculated periods.
Modal Combination
Control
Enter the method of mode combination and
specify whether to restore the signs of response spectrum analysis results.
MIDAS/Gen allows the user to select the modes for a modal combination
so that the major modes of a structure can be combined. [Details...]
Modal
Combination Type: Set the method of combining modes in the response
spectrum analysis.
• SRSS: The Square Root of Sum of
the Squares
SRSS method, which is
most commonly used, renders close approximations of design response for
a structure exhibiting well-distributed natural frequencies. However,
it tends to overestimate or underestimate the combination for a structural
system with close natural frequencies, which can be found in a multi-span
bridge with continuous short spans. Another drawback is that it looses
signs in the process of combination
• CQC: Complete Quadratic Combination
Where
: the
representative maximum value for a particular response
:
the peak value of the particular response for the i-th mode
:
the ratio of the natural frequency of the i-th mode to that of the j-th
mode
:
damping ratio
CQC method considers
the probabilistic correlation between modes for a structural system with
close natural frequencies, which can be found in a multi-span bridge with
continuous short spans. By applying the correlation factor in combination
using close natural frequency ratios, the overestimating or underestimating
problem can be resolved. As shown in the equation above, the correlation
factor will become 1 irrespective of the damping ratio when i=j, and it
will become identical to SRSS method when the damping ratio is 0.
• ABS: ABsolute Sum
ABS method renders the
largest responses among different combination methods. The signs are neglected
by the use of absolute values. It tends to overestimate the response results.
When a specific ratio such as the 100:30 rule, etc. is applied after combining
the analysis results in each direction considering the directionality
of earthquake, the maximum response is obtained by summing the absolute
results in three directions.
• Linear: Linear Sum
In linear method, the
user chooses specific modes and enters the Mode Shape Factors directly,
which are then linearly combined. The signs are preserved. It is used
to check the effects of a specific mode or compare responses by modes.
Add
signs(+, -) to the Results
Specify
whether to restore the signs deleted during the mode combination and specify
the restoration method.
•Along
the Major Mode Direction: Restore the signs
according to the signs(+, -) of the principal mode for
every loading direction.
•Along
the Absolute Maximum Value: Restore
the signs according to the signs of the absolute maximum values of the modal results.
Note
In
general, structural characteristics can be reflected properly by using
the "Along the Major Mode Direction" option and using the sign
of the major mode that greatly contributes to the structural behavior.
However, when torsion is considerable due to the structural irregularity,
or the modes are closely spaced and the major mode is not very distinctive,
the "Along the Major Mode Direction" option can partially distort
the structural behavior. In such a case, it is desirable to opt for "Along
the Absolute Maximum Value"option.
Select Mode Shapes
Select modes for modal combination. Using
the “Select Mode Shapes” option, linearly combine the modes
while entering the Mode Shape Factors directly.
Spectrum
Functions
Select pre-defined design spectrum functions,
which will be used to define a number of response spectrum load cases.
A same spectrum from a code may result in a number of spectrum functions
depending on the damping ratio. Therefore, this becomes useful when the
user wishes to define a number of spectrum functions based on different
damping values in a structure.
Function Name
Select a spectrum function name. If spectral
functions have not been defined, click the button located
at the bottom of the dialog box to define spectrums. (Refer to "Response Spectrum Functions")
1. Select a number of spectrums in Spectrum
Functions list. Spectrum Function is defined in Response Spectrum Function.
Note
In
case a single spectrum is selected, Damping Ratios for each mode are not
calculated, and an identical Damping Ratio is applied to all the modes.
2. Check on "Apply Damping Method"
and select Damping Method. Default is Modal.
3. Check if Interpolation of Spectral Data
is selected. Default is Logarithm.
Application
Principles
1. Calculation is carried out by the interpolation
of spectrum data applied by the Damping Ratios corresponding to modes.
2. If the calculated values deviate from
the range of the maximum and minimum values of the selected spectrum,
the maximum or minimum value of the spectrum will be applied.
3. If the calculated values exist in the
range of the maximum and minimum values of the spectrum selected with
a damping ratio for a mode, modal spectrum is internally generated for
the mode by interpolation of spectrum data.
Procedure
for Interpolation of Spectrum
Select multiple spectrums defined in Spectrum
Function and calculate the Damping Ratios for each mode according to the
selected method in Apply Damping Method of Response Spectrum Load Cases
after which spectrum data for each mode is generated.
Example
In case "Damping Method = Modal",
the method of generating spectrums by modes on the basis of the figure
above is outlined below.
1. Mode 1: The user specified Damping Ratio=0.01
is greater than the maximum spectrum with 0.02. So the spectrum with the
damping ratio of 0.02 is created.
2. Mode 2: Spectrum with the damping ratio
of 0.05 defined in Spectrum Function is directly used without any interpolation.
3. Mode 3: The user specified Damping Ratio=0.07
is within the damping ratios 0.05 ~ 0.10. The spectrum with the damping
ratio of 0.07 is generated by the interpolation of the spectrum data.
4. Mode 4:. Spectrum with the damping ratio
of 0.10 defined in Spectrum Function is directly used without any interpolation.
5. Mode 5: The user specified Damping Ratio=0.15
is less than the minimum spectrum with 0.10. So the spectrum with the
damping ratio of 0.10 is created.
Note
In case of Mass & Stiffness Proportional
Damping and Strain Energy Proportional Damping, damping ratio for each
mode is automatically calculated, which is then used to generate the spectrum
data by modes in the same manner as above. If Strain Energy Prop. is used
to calculate damping ratios, the "Calculate Only When Used"
option needs to be checked off at the lower part of the Model > Property
> Group Damping dialog box.
1. Select a single spectrum from the Spectrum
Functions of Response Spectrum Load Cases.
Note
When
the user selects multiple spectrum functions, the Correction equation
is not applicable since spectrum functions are generated by interpolation
of spectrum data based on damping ratios.
2. Check on “Apply Damping Method”
and “Correction by Damping Ratio”.
3. Check to see Interpolation of Spectral
Data is selected. Default is Logarithm.
Note
In case a single spectrum is selected,
Interpolation of Spectral Data will not be used since modal damping ratios
are calculated by modes by the method below.
Application
Principles
1. 1. Calculate damping ratios for each
mode.
2. 2. The equation calculated here is applicable
only for a spectrum with the damping ratio of 0.05. So it cannot be used
for other spectrums with different damping ratios.
Procedure
for Spectral Data Correction
As shown in the figure below, damping ratios
by modes are obtained and spectral data is generated, using the Spectrum
Function (Damping Ratio = 0.05).
Note
When
the user calculates damping ratios using Strain Energy Proportional Damping,
the "Calculate Only When Used" option needs to be checked off
at the bottom of the Group Damping dialog from the main menu, Model >
Property > Group Damping.
Apply Damping Method
Damping
Method : Define the damping property of a structure using multiple
design spectrums.
User defines the damping ratio for each
mode, and the modal response will be calculated based on the spectrum
function, which is modified by the user defined damping ratio.
Direct
Specification of Modal Damping: Specify
the damping ratio for each mode directly.
Damping
Ratio for All Modes: It applies to
every mode except the ones that user has directly specified. It applies
to all the modes other than the damping ratios assigned to specific modes
in the Modal Damping Overrides table below. When the entered damping ratio
is different from the user specified damping ratio in Response Spectrum
Functions, the previous spectrum data will be interpolated based on this
damping ratio.
Modal Damping Overrides:
User directly defines the damping ratio
for each mode.
Using the dynamic property and the modal
damping ratios of two modes, the damping matrix which is proportional
to Mass and Stiffness is generated.
This damping matrix evaluates the damping ratio for each mode, and the
response spectrum analysis is carried out while reflecting the modal damping ratio.
Mass and Stiffness Proportional
Damping Type:
Select if the damping matrix is proportional to Mass or to Stiffness.
Direct Specification:
User directly defines the proportional
coefficients for the checked Damping Type.
Calc. from Modal Damping: Using the modal damping ratios that the
user specified, it automatically calculates and inputs the proportional
coefficients.
Coefficients Calculation:
If either Mass or Stiffness proportional
is checked in Damping Type, modal damping ratio of only one mode can be
entered. If both are checked, modal damping ratios for two modes will
be specified.
Frequency[Hz]: Enter the frequency of the corresponding
mode to be assigned a damping ratio for calculating proportional coefficients.
Period [Sec]: Enter
the period of the corresponding mode to be assigned a damping ratio for
calculating proportional coefficients.
Damping Ratio: Enter the damping ratio corresponding to
the specified frequency or the period.
: It calculates the damping ratio based on
the entered proportional coefficient and the frequency or the period.
Since damping ratios for only two modes can be specified to reflect the
mass or stiffness proportional damping effect, this tool makes possible
to calculate damping ratios of other modes.
User evaluates the modal damping ratio according
to the damping ratio user-defined in Group Damping. The result modifies
the spectrum function and calculates the response.
When element damping by members and boundaries
defined in Group Damping is used, the damping matrices of most structures
become a non-classical damping type, which can not be separated by modes.
Therefore, in order to reflect the damping property of each element in
dynamic analysis, modal damping ratio is calculated on the basis of the
strain energy concept.
Correction
by Damping Ratio : When a single spectrum is selected, a modifying
equation is used to adjust the spectrum to apply to each mode having
Note
1
The modifying equation can not be used when multiple spectrums are selected
because the spectrums are interpolated based on the damping
ratios. A damping ratio can not go beyond the upper and lower bound damping
ratios of the spectrum.
Note
2
When combining modal responses, using Complete Quadratic Combination (CQC)
will reflect damping for each mode without the use of the
modifying equation. The combining method can be specified in Modal Combination
Control.
Interpolation of Spectral
Data
Select the method of interpolating the response spectrum load data.
Linear
: Linear interpolation method
Logarithm
: Log-scale interpolation method
Accidental Eccentricity
Select whether to include accidental eccentricity moments in the calculation
of response spectrum loads. Click to prompt the Accidental
Eccentricity for Response Spectrum Load dialog box.
Note
1
Using this functionality, we can check the analysis results from the auto-generated
load case (Es: Dynamic load case name), which reflects the accidental
eccentric moments.
Select a response spectrum analysis load
case from the list in the dialog box and click .
In addition to the spectrum functions and
the loading conditions of the response spectrum, access the following
functions to enter additional data required for a response spectrum analysis:
Perform
Analysis or using the Main Menu, Analysis>
Load Case Name
Revision of Gen 2010
: the
representative maximum value for a particular response 
:
the peak value of the particular response for the i-th mode
:
the ratio of the natural frequency of the i-th mode to that of the j-th
mode
:
damping ratio
button located
at the bottom of the dialog box to define spectrums. (Refer to "
: to modify the existing
damping ratio
: to remove the existing
damping ratio
to prompt the Accidental
Eccentricity for Response Spectrum Load dialog box.
Enter
new or additional response spectrum analysis load cases
.
.
