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# Interpretation of ASCE 12.9.1 - Modal Response Parameters

## Interpretation of ASCE 12.9.1 - Modal Response Parameters

(OP)

#### Quote (ASCE 7-05 12.9.2)

The value for each force-related design parameter of interest, including story drifts, support forces, and individual member forces for each mode of response shall be computed using the properties of each mode of response shall be computed using the properties of each mode and response spectra defined in either Section 11.4.5 or 21.1 divided by the quantity R/I. The value for displacement and drift quantities shall be multiplied by the quantity Cd/I.

I want to clarify my understanding of this, as I am performing a response spectrum analysis. Using gravity = 9806 and R = 5, Cd = 5, I = 1 in ETABS scaling factor, which of the following options is correct.

1)
For member forces: 9806/(5/1) = 1961
Deformations/drifts: 9806 x (5/1) = 49030

OR

2)
For member forces: 9806/(5/1) = 1961
Deformations/drifts: 1961 x (5/1) = 9806

I feel like it should be option 2, as this would be the developed force assuming the structure remains elastic and we do not account for the allowance of plastic energy dissipation.

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

The member forces are arrived at by dividing by R/I. The dynamic displacements you get from the analysis using the forces that have been decreased by R are arrived at by multiplying those displacements by Cd/I. The 9806 is confusing in your question because it isn't a lateral force or displacement but rather it is noted as a gravity load?

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

Option 2 is correct. You are reducing forces to account for inelastic effects. But equal displacement principle says the inelastic system will displace to approximately the same as the elastic system. Hence, Cd ~= R and you scale the displacements back up.

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

I don't see how option #2 is correct by multiplying a force by Cd/I to get a deformation. And depending on the lateral system, there can be a significant difference between Cd and R.

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

hay, if you don't think its correct, could you please say why you think so? I was talking about scale factors for a response spectrum analysis (ie multiplying all response quantities by 1/R and then correcting displacements by multiplying by Cd).

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

I did say why I think option #2 is not correct.

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

But... option 2 is exactly what you're describing in your first post?

edit: I think maybe you're confused about 'g'? It's not a force, it's an acceleration.

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

The input criteria for the modal analysis is scaled by dividing g/(R/I). The output displacement/drift is multiplied by Cd/I.

### RE: Interpretation of ASCE 12.9.1 - Modal Response Parameters

Yes, I was confused as to what “gravity=9806” represented in the original post. I also now think the numbers are given in SI units. I agree with “g” being the seismic acceleration.

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