ACI moment magnification factor for nonsway frames 1

[mpdst11]

The moment magnification factor for nonsway frames equals

Cm/[1-Pu/(0.75Pc)]

which is equation 10-9 in ACI 318-02.

As the column gets longer, the critical load Pc gets smaller, and the factor approaches infinity as 0.75Pc approaches Pu.

My question is, what happens if Pu > 0.75Pc?

This results in a negative value for the moment magnification factor. Is 0.75Pc the maximum limit for Pu?

The code does not address this, so I am wondering if anyone has any experience with this situation. Thanks.

 

[Lion06]

I don't think ACI gives explicit guidance, but if you think about, Pu can't be greater than 0.75Pc. If Pu=0.74Pc then the moment magnifier becomes almost infinite. That's because as you approach the critical buckling load the lateral displacement just keeps growing and growing which significantly increases second order effects. The factor of safety on this is obviously the 0.75 (for Pc) and the load factors (for Pu).

 

[mpdst11]

Thanks StructuralEIT.

I agree, just looking for some reassurance. A colleague told me that since the moment magnification factor couldn't be less than one, a negative factor should be taken as one. Obviously that's not right, but I just wanted some clarification.

So I guess in this case 0.75Pc is the real critical load. Thanks.

 

[JoshPlumSE]

Yes, any axial force greater than 0.75 Pc would represent an elastic buckling failure of the column.

Honestly, this would be true for a sway frame as well. It's just that ACI requires you to run a 2nd order analysis (P-Delta) which to some extent will end up predicting that failure.

The 2008 ACI code has a bit more guidance on using "analysis" to predict 2nd order effect rather than relying on the Cm / (1-Pu/0.75Pc) equation. Unfortunately, I don't have this with me right now. So, I cannot comment in detail....other than to tell you to take a look.

Josh