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# Response Spectrum Scale Factor

## Response Spectrum Scale Factor

(OP)
How do we define the "Scale Factor" in the Response Spectrum Case? I looked into the ETABS documentary and I found two different answers (one is saying to use gravitational acceleration (g) as the scale factor; and the other one is saying to use (I.g/R) and then adjust it based on the static base shear. I'm a little confused on how to apply this scale factor.

(1) What value of scale factor should be entered in the definition of a response spectrum load case?
Answer: When the response-spectrum curve is defined, acceleration is typically entered as a fraction of gravitational acceleration (9.81 m/sec2 or 32.2 ft/sec2). Scale factor should be specified such that its product with response-spectrum values generates the acceleration units desired.
For example, if acceleration for the response-spectrum function is plotted as a fraction of gravitational acceleration, and if length units are in feet, then U1, U2, and U3 should be scaled by 32.2 units.

(2) How is the response-spectrum scale specified?
Answer: 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 and the response spectra defined in either ASCE 7-05 Section 11.4.5 or 21.2 divided by the quantity R / I. The value for displacement and drift quantities shall be multiplied by the quantity Cd / I (ASCE 7-05, Section 12.9.2).
Therefore, the response-spectrum scale factor is I g / R, where g is acceleration due to gravity (386.4 in/sec2 for kip-in and 9.81 m/sec2 for kN-m). After analysis, users should review the base shear due to all modes, reported in the Response Spectrum Base Reaction Table. If the dynamic base shear reported is more than 85% of the static base shear, no further action is required. However, if dynamic base shear is less than 85% of the static base shear, then the scale factor should be adjusted such that the response-spectrum base shear matches 85% of the static base shear. In this case, the new scale factor would be (I g / R) * (0.85 * static base shear / response-spectrum base shear). Analysis should then be rerun with this scale factor specified in the response-spectrum case.

### RE: Response Spectrum Scale Factor

I would keep the scale factor the default regarding the units, and just instead scale the dynamic load up or down in load combinations to match the min 85% of static requirements.

----------------------------------------------------------------------

Why yes, I do in fact have no idea what I'm talking about

### RE: Response Spectrum Scale Factor

(OP)
Thank you Just Some Nerd. I found this article which provides two methods for determining and assigning the scale factor. I believe the second method is what you referred to.

https://www.thestructuralworld.com/2019/05/24/2-me...

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