When using the mode superposition method to calculate seismic response, Chinese codes have explicit requirements for modal mass participation coefficients. Taking the ‘Code for Seismic Design of Buildings’ as an example, Section 5.2.2 commentary states:
To improve the analysis accuracy of tall and flexible buildings, the number of modes combined should be appropriately increased. The number of modes can generally be taken as the number required for the modal participation mass to reach 90% of the total mass.
For design software, mass participation coefficients can be easily obtained. However, for general-purpose finite element software, mass participation coefficients need to be manually extracted or viewed by the user, and cannot be directly viewed in post-processing. This article uses ANSYS software as an example to explain how to view modal mass participation coefficients.
Generally speaking, after performing a modal analysis, the conventional results are modal frequencies and corresponding mode shapes. By default, the model mass is normalized, and the maximum displacement value in the mode shape contour is not 1. If the user needs displacement normalization, simply set it with the following command:
MODOPT,,,,,,ONTo obtain the modal mass participation coefficient, you need to search in the solution information file or use the *get command for calculation.
Taking a frame structure modal analysis as an example, in the Output window solution information file, the following information is available:
In the above information, Modal Mass is the modal mass, and Kene represents kinetic energy. Their calculation formulas are respectively:
Effective Mass is the effective participation mass, which is the ratio of the modal participation coefficient to the modal mass. The calculation formula is:
Below Effective Mass, classifications are made by different directions. At the bottom, there is a total sum, where the ratio total is what we commonly refer to in engineering as the effective mass participation coefficient.
So how is this Ratio% obtained?
Ratio = the effective mass corresponding to the current mode order divided by the total structural mass.
Let’s verify below:
For convenience, only five modes were calculated. The structural mass statistics obtained from the solution information are as follows:
That is, the total structural mass is 2468.
The first five modes of the structure are as follows:
Taking the first mode in the Y direction as an example, its effective participation mass is 1982.
Ratio = 1982/2468 = 80.31%, which is consistent with the information listed in the figure.
Taking the second mode in the X direction as an example, its effective participation mass is 1206.
Ratio = 1206/2468 = 48.87%, which is consistent with the information listed in the figure.
For students using Workbench, click on Solution Information to view the corresponding values, as shown below:
Currently, ANSYS does not have a direct operation to extract mass participation coefficients, i.e., participation ratios. However, the following information can be obtained through the mode option of the *get command, and then manually calculated based on the ratio concept described above.
PFACT: Participation coefficients in each direction of the mode;
EFFM: Effective participation mass in each direction of the mode;
GENM: Modal mass
In addition to the above operations, users also need to extract the total structural mass to calculate the participation coefficient. Below is the command stream code, using the calculation of the mass participation coefficient in the X direction as an example, for reference:
/post1
!Get total structural mass
*get,Mass_Sum,elem,0,mtot,x
!Define total effective mass
Eff_Sum=0
!Get the number of solved modes
*get,freqnum,active,0,solu,ncmss
!Accumulate total effective mass from solved modes
*do,i,1,freqnum
!Get effective mass of each mode
*get,eff_freq,mode,i,effm,,direc,X
Eff_Sum=Eff_Sum+eff_freq
*enddo
!Calculate effective mass ratio
Eff_Ratio=Eff_Sum/Mass_Sum*100
*status,Eff_RatioThe final result is as follows:
It can be seen that the two are consistent, confirming the above method is correct. With the above code, you no longer need to review the solution information every time!
If you are using Workbench, you can easily insert the above command stream during the solution stage to obtain the results!
If you find this tip useful, welcome to share!
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