Direct analysis of braced frame columns 1

[Nate2017]

Hello everyone,

I have recently studied direct analysis method introduced in AISC 2005. After reading lots of materials, I still have questions on my mind regarding situations where compression members have effective length factor k < 1. For example, the columns in a fully braced frame, compression chords of laterally braced planar truss.

It makes sense to me to base the design on the unity effective length factor k for members have a larger than 1 effective length factor. However, if the member has an effective length factor less than 1, with all of the reduction to the stiffness and adding notional loading/geometric imperfections, would direct analysis give more conservative design results in those situations? Assuming a rigorous 2nd order p-delta analysis was employed, the design forces derived from the Direct Analysis would be larger than that of effective length method. From my understanding, the member axial strength calculations are the same for both Direct Analysis and effective length method except different k been used. So for those situations where the k < 1, would that yield a larger design force lesser available strength for the compression member?

 

[KootK]

I believe that you're correct on all counts Peter. In the situations that you've described, the direct analysis method (DAM) would likely be more conservative than the effective length method (ELM). DAM is really only intended for use with systems that have sway buckling modes or something analogous to them (moment frames etc). The current expectation is that, where K would normally be 1.0 or less, designers will continue to use the effective length method.

If, for some reason, I chose to use DAM for a braced frame or compression chords, I wouldn't hesitate to modify the method and use K<1 where appropriate. It's pretty rare that I take advantage of K<1 situations though. I only use it when I'm desperate to make a go of something or I'm really trying to push the envelope for architectural reasons.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Nate2017]

Thanks KootK. I thought I missed something in the equation. At least you confirmed my speculation about the DAM.

As I recall, the AISC 2010 states that the overall structural stability calculations can be dropped in some of the member strength check provisions if DAM was employed.

But the provision at chapter E (compression member design) does not mention anything regarding modifying the available strength equation if DAM was used in the first place. To my understanding, the factor of 0.877 of the elastic buckling strength is intended to account for the effect of geometry imperfection and initial out of plumbness. Since DAM already takes into account those effects at the stage of member force calculation, no further reduction shall be taken at the available strength calculations.

Furthermore, perfect elastic buckling never occur in reality to my knowledge. In another word, compression members will not suddenly go into buckling state from a perfect straight position. Instead compression members will always experience increasing lateral deformation as the axial load gradually approaches critical load, Pcr. At some point, the deformation becomes large enough to trigger the flexural failure of the member.

So one of my thought is that if a rigorous 2nd order P-delta analysis or even a more robust nonlinear analysis which formulates large deformation theory correctly combines with the DAM treatment of analysis (notional load, initial imperfection, stiffness reduction, and etc.), the buckling failure would be correctly recognized by checking the interaction equation of member axial and bending. Assuming the stability concern (Fe term) is completed dropped in the available axial strength calculation.

Peter

 

[WillisV]

Correct. ELM less conservative than DAM for K=1 systems.

 

[mathcadboy]

If you are shifting to using DAM, its better to forget the K method. I heard from someone before that the AISC is trying to remove the K method since its mostly just applicable in typical looking frames.