ACI column buckling

[SemiPE]

Dear all, Please help me understand why the Mns (Moment due to slenderness of a non-sway column) is dependent on end moments of columns. Small delta ns is multiplied by larger end moments.

I believe that this should be a function of the eulers buckling load. However, as the equation ACI have it, having no end moments results into zero Mns.

Lets say I have a axially loaded column with zero moment at both ends (due to bracing), with a very high slenderness ratio, then it would be logical that there would be moment at midspan due to the buckling of the column. but under this situation the ACI equation will yield zero moment which is false.

 

[KootK]

This can be a confusing issue when switching between steel and concrete design. Much steel column design is still done using the bifurcation model (Euler). Concrete column design is done using the instability / moment magnification model which many find to be more rational. But then, what is your buckling load when there is no moment? Here's my understanding:

1) Firstly, most codes specify a minimum load eccentricity, either directly or indirectly. That eccentricity results in moments which serve as your buckling perturbations.

2) Most CIP columns carry moments as a result of the marvelous continuity inherent in CIP construction. If your analysis shows no moment on a CIP column, it might be worth reconsidering your analysis. Mid-height bracing will result in small moments, but not necessarily zero moments.

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.

 

[yakpol]

If end moments are small then minimum design moment M2 = M2.min = Pu(0.6+0.03h) (ACI 318R-14 eq. 6.6.4.5.4)

More information provided in commentaries R6.6.4.5.4
ACI 318-11 shall have similar provisions.

Hope it helps!