Response Spectrum Load Cases

 

 

 

Enter the load cases, spectrum functions and loading directions for response spectrum analysis.

 

The procedure for response spectrum analysis in midas Gen is outlined below.

 

1. Enter mass data using various ways provided in the Main Menu, Model>Masses.

 

2. Enter the number of modes and necessary data for eigenvalue analysis in Eigenvalue Analysis Control.

 

3. Define spectrum data to be applied in Response Spectrum Functions.

 

4. Set options related to response spectrum analysis in Response Spectrum Load Cases.

 

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 + 90вк

 

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")

• Generating spectrum data corresponding to damping ratios by modes using multiple Response Spectrum Functions

Input Data

 

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.

 

 

• Generating spectrum data corresponding to damping ratios by modes using a single Response Spectrum Function

 

Input Data

 

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.

• Direct Modal

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.

 

Mode: Mode Number

 

Damping Ratio: Damping ratio for each mode

 

 

: to add a new damping ratio

 

: to modify the existing damping ratio

 

: to remove the existing damping ratio

• Mass and Stiffness Proportional

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.

 

 

• Strain Energy Prop

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.

 

Note 2
The magnitudes of the applied accidental torsional moments can be checked in Results > Result Tables > Story Shear (Response Spectrum Analysis)

 

Note 3
This function becomes activated only when Model > Building > Story Data is defined.

 

 

Accidental Eccentricity for Response Spectrum Load dialog box

 

Eccentricity Data

 

Automatic

An eccentricity in terms of a percentage of plan dimensions is automatically considered.

 

User Defined

The user defines the eccentricities individually.

 

Revision of Gen 2010

 

Consider Eccentricity below G.L

 

Check on:  Eccentricity is considered for both above-ground and underground floors.

 

Check off: Eccentricity is considered only for above-ground floors.

 

Description

 

Enter a brief description.

 

 

Operations

 

 

Enter new or additional response spectrum analysis load cases

 

Enter the above entries and click .

 

 

Modify previously entered response spectrum analysis load cases

 

Select a response spectrum analysis load case from the list in the dialog box and click .

 

 

Delete previously entered response spectrum analysis load cases

 

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:

 

: Eigenvalue Analysis Control... is invoked to check dynamic properties of a structure

 

: Response Spectrum Functions... is invoked to define spectrums.