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Column Base Fixity

Column Base Fixity

Column Base Fixity

(OP)
I have heard different opinions on this matter and wanted to see what some other people thought.

Problem:
Assume a portal frame. The rotational stiffness of the partial moment connection at the beam level is known but the rotational stiffness of the column base connection is unknown. As a starting point, we split the moment in the column 50-50 between the bottom of the column and the beam level. The moment in the bottom of the column is less than the vertical force in the column multiplied half of the width of the column section. For instance, let's say the moment at the base of the column, M = 2k-ft, the gravity force in the column is 24k and the column is a 4" tube. The resisting moment would be (24k)(2")= 4k-ft which is greater than the overturning moment of 2k-ft.

Conclusion:
Since the resisting moment in the column is greater than the overturning moment, the base is "fixed under it's own weight" even though the anchor bolt pattern would not qualify it as a "moment connection".

In order to model the structure to find drift and P-Delta effects, would you fix the base since the vertical force eliminates any net overturning moment at the base? Or would you pin the base or use partial fixity since the anchor bolt pattern is not a good moment connection?

Thank you!

RE: Column Base Fixity

Quote:

Conclusion:
Since the resisting moment in the column is greater than the overturning moment, the base is "fixed under it's own weight" even though the anchor bolt pattern would not qualify it as a "moment connection".

I think you are confusing stress with stiffness here.

The P/A of the column axial load does indeed "overwhelm" the moment tensile stress on the one side of the column such that there is always compression the column base area all around.

However, this has nothing to do with whether your column has a "fixed" type of rigidity at the base. There is still a level of flexibility in both the column itself, the base plate, the footing and soils below, etc.

The attempt to split the moment between beam and column base 50-50 assumes that the relative rigidities of the beam, beam-column connection, column, and footing base are all such that the moments behave as such. I'm not sure that is true either.

The general approach is to assume that the column base, its footing and the underlying soils are such that you pin the base and drive all the moment resistance to the beam-column connection (conservative).
Then if it makes sense, provide some partial rotational rigidity at the base to conservatively design the footing.

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RE: Column Base Fixity

(OP)
JAE, thank you for your response.
Here is my specific situation: I'm dealing with lightly loaded miscellaneous and non-building structures which have less than ideal moment connection. I'm trying to calculate an acceptable drift and to do so I need to rely on some level of rotational fixity at the base.

First, I understand and agree that I won't have a 50-50 split unless I have the same relative stiffness in the base as in the beam level. I was just trying to make an example so that I had some actual number to discuss.

Second, I'm thinking that since the overturning moment is overwhelmed by axial load, it would force the column into double curvature bending which would indicate some level of rotational fixity at the base. I'm anchoring into a continuous slab on grade so, the stiffness of the base far exceeds the stiffness of the first beam level. I am also not even relying on the width of the base plate for overturning resistance because my resisting moment is taken from the wall of the tube column to the center of the tube. So it's not like I will have rotation from the base plate deforming. I'm not sure what component of the base connection would even rotate.

RE: Column Base Fixity

I think your axial load perhaps negates the base plate bending aspect of the column-base overall stiffness.

As the axial load decreases and the base moment increases there would come a point where the base rotational stiffness would abruptly change At some load limit the heel of the column would reach a net tension and the plate bending stiffness suddenly would become part of the system. Once the heel picks up then there would be an instant change (reduction) in the base stiffness.

But initially the stiffness (or flexibility) of the overall base would depend upon:
1. The column stiffness itself
2. The footing stiffness (slab in your case), and
3. The underlying soil stiffness

These three create rotational stiffnesses that are all independent of the load applied to them...i.e. their stiffnesses do not change with changing load.
(soil stiffness might reduce abruptly also to some extent if there was footing heel net uplift. But this wouldn't apply to your high axial condition)

But to assume fixity at the base in my view is wrong.

For most "typical" slabs-on-grade, the stiffness isn't much...not sure why you suggest that the slab far exceeds a steel beam-column stiffness.
Soils often are even more flexible than we think so rotation about the base will happen.

So the base is quite flexible and will rotate despite the axial load.

The true answer is somewhere in between full fixity and full pinned conditions.
I think by assuming fixity at the base you are being unconservative in the design of the upper beam-columns.

But as I stated above - you could assume a base pin - design the upper beam-column connection - then use some partial (or full) fixity on the bottom to check your footing (slab???) for the resulting higher moment at the base.

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