Response Spectrum Load Cases

Function

• Enter the load cases, spectrum functions and loading directions for response spectrum analysis.
• The procedure for response spectrum analysis in midas Civil is outlined below.

1. Enter mass data using various ways provided in the Main Menu, [Load] tab > [Type: Static Loads] > [Masses] group > [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] tab > [Perform] group > [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.

Call

From the mail menu, select [Load] tab > [Type : Dynamic Loads] > [Response Spectrum Data] group > [RS Load Cases]

Input

Load Case Name

Enter the name of the response spectrum analysis case. The name is used for load 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.

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.

Directional Combination (CQC3)

The CQC3 rule has been developed to estimate the peak value of the combined response due to simultaneous application of the principal components of ground motion. This rule gives the peak response as a function of the seismic incident angle.

rx: The peak response to a single component of ground motion applied along the structural axis x.

ry: The peak response to a single component of ground motion applied along the structural axis y.

γ: The ratio of the minor input spectrum to the major input spectrum.

The user defines only the ratio, γ, of the minor input spectrum to the major input spectrum, and the program finds the critical angle and provides the maximum responses for each component calculated using rx, ry, and rxy. It is not necessary to define the RS load cases for rx and ry.

rz: The peak response to vertical ground motion.

rz is not automatically taken into account in the results of CQC3. It can manually be combined in the load combination if necessary. 

rxy: the cross term between modal responses contributing to rx and ry that arises from correlation between ground motion components along the structural axes.

Ratio of minor to major spectrum : Enter the ratio of the minor input spectrum to the major input spectrum between 0 and 1.0.

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.

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.

Modal Combination Type

Set the method of combining modes in the response spectrum analysis.

SRSS (Squre Root of the Sum of the Sqares)

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

: Mode shape coefficient in the i-th mode.

: the ratio of the natural frequency at the i-th mode to the natural frequency at 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)

n 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 among all the modal results.

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

The spectrum data defined in the Response Spectrum Functions are listed. Check the function to be used in the corresponding load case.

In order to apply different damping ratios for each component of the structure, there should be spectrum data available for each mode corresponding to the respective damping ratios. Generally, multiple spectrum functions are defined for the same type of spectrum function, with only the damping ratios varying, allowing for different damping ratios for each function.

Defining spectrum data for every damping ratio is not an easy task. Therefore, it is common to define spectrum data for a few key damping ratios and interpolate between them for other damping ratios when needed.

If there is only one set of spectrum data available, it is not possible to obtain spectrum data for the remaining damping ratios using interpolation. In such cases, the "Correction by Damping Ratio" option is used. This method is typically based on the inverse relationship between damping ratio and spectrum data. The relationship between damping ratio and spectrum data is predefined by an equation or a formula, and this relationship is then utilized to obtain spectrum data for different damping ratios.

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

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

Apply Damping Method

Damping Method : Define the damping property of a structure.

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.

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

Add : to add a new damping ratio

Modify : to modify the existing damping ratio

Delete : 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.

Cal. 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 a corresponding damping ratio.  

Even if they belong to the same design criteria, the spectrum function can vary depending on the damping value. This functionality is used when multiple spectrum functions with different damping values are employed for a single structure.

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.

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

Description

Enter a short description

Operation

- Enter new or additional response spectrum analysis load cases

Enter the above entries and click Add.

- Modify previously entered response spectrum analysis load cases

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

- Delete previously entered response spectrum analysis load cases

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

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

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