AISC Flexural Buckling Equation

[North2South]

Can someone help explain section E3 of AISC 360-10. It seems counterintuitive to me. The critical compression stress is a function of the elastic buckling stress which is a function of the unbraced length. As the unbraced length decreases, the elastic buckling increases which in turn decreases the critical stress. It seems like the critical stress should decrease if unbraced length decreases.

 

[JoshPlumSE]

Equation E3-4: Fe = (pi^2)E / (L/r)^2
This represents the elastic buckling stress, right? Pure Euler buckling theory.

Substitute this into Equation 3-3 (Fcr = 0.877Fe) and you've got the code specified elastic buckling strength. It doesn't 100% follow buckling theory because of that 0.877 reduction. But, you understand that concept.

Equation E3-2, on the other hand, is supposed to represent the critical buckling strength when the column is controlled by INELASTIC buckling. In order to calculate this, we need to know the euler buckling stress and the yield strength.... Because this Fy/Fe ratio tells us where we fall on the inelastic buckling curve. Essentially, how much inelasticity are we going to see in the column when it buckles.

If you plot out these equations in excel for various L/r ratios, you will see that this doesn't actually decrease the capacity for L/r values that are lower than the the limiting value (4.71(sqrt (E/Fy)). Instead, it increases those values. But, it increases at a much slower rate than would be expected if this were based on L/r alone.

 

[JoshPlumSE]

I thought it might help if I added in this file of the buckling curves (from an older version of the code).

 

[North2South]

Thanks for the response. The graph definitely helps.