First-Order Analysis Method 1

[Althalus]

AISC Appendix 7. Paragraph 7.3-1(b) gives a condition of using the first-order method: You have to compare the 2nd order drift to the first order drift.

I'm having trouble understanding why you'd go for the first-order method if you have to do the 2nd order method to verify that you don't have to use the 2nd order method.

What am I missing?

 

[JoshPlumSE]

I don't think you're missing anything. There is a logical gap here. You have to do a 2nd order analysis in order to know if the amplification is low enough that a 1st order analysis is permitted.

That being said, that's more of a technicality. In reality, you have a pretty good idea is the drift is going to be low. If so, then you can use your engineering judgment to say that 1st order analysis is allowed.

Also, you could do one of the hand calc methods:

B2, ASCE's Theta method, or ACI's Q method to get a good "ballpark" estimate of the 2nd order amplification. Heck you might even be required to do the Theta method by ASCE.

 

[OldDawgNewTricks]

You don't have to do a 2nd order analysis to satisfy 7.3.1.b. Per the User Note just below that sentence, you are allowed to estimate the ratio by using the Approximate Second-Order Analysis B2 multiplier in 8.2.2.