Notional Loads

[Althalus]

I've looked at the dozen or so threads on notional loads and I still need to ask this question to see if I'm reading everything right.

I'm looking at Eq A-7-2 (AISC 360-16). I'm guessing that the 2.1 was some form of factor of safety from AISC. (0.002 x 2.1 = 0.0042 which is the minimum per that equation). I can understand that.

It seems pretty straight forward. But somewhere along the line I picked up that there was a "maximum" of 0.005 for notional load. Yet, if I put in the maximum building deflection (which is also applied to drift) we get a maximum notional load of 0.019 (per A-7-2). And if we use it against the maximum permissible seismic drift of 0.025 for most steel structures, we get 0.084 as the notional load.

Those numbers are much higher than 0.005. So, am I reading this right?

 

[JoshPlumSE]

I'll actually dispute the basic premise of your question.... Your question is NOT actually about notional loads. Rather it is about the First Order Analysis Method of appendix 7.3.

It seems like I'm splitting hairs here and diving into semantics, that's somewhat true. However, there is a reason for it.

1) The intent of the Notional Loads (defined in chapter C) is to represent imperfections in the structure. The reason why we use 0.002*Alpha*Y is this represents a structure having an "out-of-plumbness" of H/500 (the maximum allowed by code). I'd refer to this as a the true intent of notional loads in AISC. In that sense, 0.005 would represent a notional load that corresponds to an out of plumbness of H/200.

2) When you get into appendix 7 an the "first order analysis method" the section on notional loads serves two purposes. It account for the initial "out-of-plumbness" the same way as it does in chapter C. But, it ALSO accounts for 2nd order effects.... i.e. P-Delta amplification of the initial out-of-plumbness.

Out-of-Plumbness is assumed to be L/500 as before.
P-Delta amplification is assumed to be 1.5. Why? Because if it were greater, then you are not permitted to use this 1st order analysis method. So, it is a conservative assumption.

To get to the 2.1 amplification, you can take a look at Appendix B of the AISC Design Guide on stability (DG -28). It's just a method of using the stiffness reductions, ASCE theta method and AISC B2 method to come up with an idea of what the final 2nd order amplification would be if the initial B2 value were 1.5.

 

[JoshPlumSE]

So, my point is that the 2.1 amplification factor has little to do with notional loads and much more to do with P-Delta approximations. And, the 0.005 notional load maximum (if it exists) would not apply to this "hybrid" notional load from appendix 7.

 

[Althalus]

So, my point is that the 2.1 amplification factor has little to do with notional loads and much more to do with P-Delta approximations.

Thanks, Josh.

That is so much clearer now. Why on earth did AISC use the same term for two different things? That just confused me.

I guess, in overall concept they both address something similar (geometry induced load). I think it would have been easier if they came up with a different term.