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# Response Spectrum Analysis - Scaling for building with non-orthogonal SFRS - NBCC 2015

## Response Spectrum Analysis - Scaling for building with non-orthogonal SFRS - NBCC 2015

(OP)
I have a building where approximately 50% of the structure is rotated 15 degrees.
I am using a response spectrum analysis in accordance with the National Building Code of Canada 2015.
The building is a structural steel, braced frame building.

Normally I would calculate the base shear using the static code method, then scale my RSA accordingly to be under the 2/3 cutoff, or 80% of the code base static shear, whichever is higher.

Due to the non-orthogonal layout, by base shear has an X and Y component for each response. To combat this, the code recommends that you lock the model to only allow X movement for the X base shear, and Y movement for the Y base shear. Then take the period and base shear from each locked model. We then determine the scaling factor and apply it to the main model.

This works fine, however i do have concerns.

For my locked model, i have a period of about 0.23 seconds in each direction. Code calculated period is 0.16 seconds. Great. I determine that the 2/3 cutoff applies and scale my response to 90% in my main model with both degrees of freedom active. (Note that i am still combining 30% of my X response with 100% of my Y response, and visa versa.)

Now here's the concern. When unlocked, my response in the x direction has a period of 0.37 seconds, and my Y response is 0.27 seconds.

Am I being unconservative by scaling down by 0.37 second response to 90%, and applying the 2/3 cutoff rule found in the Canadian code. Or is this the right approach?

### RE: Response Spectrum Analysis - Scaling for building with non-orthogonal SFRS - NBCC 2015

The suggested scaling procedure in the commentary always trips me up. As you note, by scaling the stiffer locked model to the min base shear, V, you end up with an analysis base shear in the unlocked model less than V.

I believe the commentary does acknowledge this, with the justification that the min base shear was always developed for a 2d simplified model, so the only way to have an 'apples to apples' comparison is through the locked model.

Could you explain where the 90% is coming from? Is that the ratio of scaled unlocked model base shear to the scaled locked model base shear?

-JA
try Calcs.app and let me know what you think

### RE: Response Spectrum Analysis - Scaling for building with non-orthogonal SFRS - NBCC 2015

(OP)

#### Quote (Sonofatkins)

Could you explain where the 90% is coming from? Is that the ratio of scaled unlocked model base shear to the scaled locked model base shear?

Apologies I didn't give any context.

My RSA shows a larger base shear than %80 of the static base shear from the code. Based on the period of the locked RSA, I was able to use NBCC 2015 Clause 4.1.8.12.(6) to apply the 2/3 cutoff and scale back my base shear in my model to 90%. This still results in a base shear that is higher than 80% static, but the results are much more reasonable than anything I could calculate by hand.

#### Quote (Sonofatkins)

I believe the commentary does acknowledge this, with the justification that the min base shear was always developed for a 2d simplified model, so the only way to have an 'apples to apples' comparison is through the locked model.

This actually makes a lot of sense, it just feels a little odd as you note. I appreciate the insight, as it does provide me with a little more comfort.

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