Radius of Gyration of a Noncomposite steel and concrete section 2

[Who_I_Am]

Hello, when calculating the radius of gyration (for moment magnifiers based on KL/r) for a non-composite steel and concrete circular section would you use the hollow steel section's 'r' value? If so, why? Can you provide me some code or AISC reference for this?

When researching this, Table 4-13 of the AISC 14th edition shows a composite section radius of gyration to be equal to the hollow HSS sections 'r'. Unfortunately there's no non-composite circular section 'r' value given in these tables. Any help is appreciated.

 

[KootK]

Correct me if wrong, but ACI 318 doesn't have the kL/r limit, just the limit on second order effects compared to linear effects? That seems to be similar to how you would want to 'cheat' AASHTO.

Yes, that's how see the 318 situation as well.

Moment magnification is mentioned as the reason for the question being raised and I came from the Australian perspective where the kL/r=120 limit in our code (compared with AASHTO's 100) is just a limit on the moment magnifier method. We can push past if we do a higher-tier analysis. So I suspect the same applies to the AASHTO code, but don't know for sure. That would rule out cheating based on structural behaviour as it's the simplified analysis method that is being limited.

I'm not sure that I agree that it would rule out "cheating" in this instance. If the simplified method is limited because it becomes inaccurate as the axial load approaches the Euler load, then this too should be something that could be addressed by way of comparison to the actual axial load rather than the squash load.

 

[KootK]

I'm not familiar with the US code references, but moment magnification/amplification becomes less accurate as the second order effects increase.

I'm also curious to know what informs your opinion on that. My understanding of our conventional moment amplification setup is that it is based on a truncation of an infinite series. As P/Pcr approaches unity, the truncated terms of that series become less "neglectable". So there's that. Do you know of more?

 

[Settingsun]

Nawy mentions it, but I was actually mis-remembering the second image. The problem isn't caused by the magnifier per se, but the inaccurate moment-curvature relationship that goes hand in hand with it. Good to be forced to brush up occasionally.

In terms of cheating, it depends on what the rules are. If structural adequacy is the only constraint, a purely geometric limit has no validity (unless the column is so tall the self-weight exceeds strength, I suppose).

If it's compliance with a rigid code limit on geometry, no cheating.

If you have something like the Australian code, you might judge that a column would pass the rigorous analysis without actually doing it, based on utilisation calculated from the moment magnifier despite using it beyond its code limit. But, in the bridge world in my area, such a slender column would be subject to independent review, and the reviewer might call your bluff.

 

[le99]

The true property of a "non-composite" concrete-filled pipe column can only be established by testing. It is conservative yet reasonably accurate to use the "r" value for the steel pipe only when the column is subjected to bending.

 

[BridgeSmith]

We can push past if we do a higher-tier analysis. So I suspect the same applies to the AASHTO code, but don't know for sure.

That's correct. A higher-tier analysis, considering P-delta effects is required by AASHTO if the range of applicability for moment magnification is exceeded. The lower limit for AASHTO could be for efficiency. When columns get to be that slender, there are usually boundary conditions (limits on displacements due to the connection to the bridge superstructure) that limit the moment.

There's also that the length to fixity is typically dependent on soil properties, which are highly variable, so defining the unbraced length cannot be done with any great degree of accuracy.

Rod Smith, P.E., The artist formerly known as HotRod10