Designing a One-Storey Column Supporting a Flat Slab (reaction eccentricity)?

[drile007]

Hi to all,

I am currently working on the design of a single-storey reinforced column supporting a reinforced flat slab. The slab is subjected to vertical loads only, with no horizontal forces (e.g., from wind or earthquake). The structure includes both exterior walls and interior columns, with inconsistent bay spacing.

I have modeled the slab using FEM, where the columns are treated as pinned supports. This means the columns carry only vertical reaction forces without attracting moments. However, I understand that in reality, some eccentricity must be considered when designing the columns, even if they are modeled as pinned.

The issue arises because the slab will undergo rotation under the pinned column support, and the column will tend to follow that rotation. This suggests that there will be some moment in the column due to the vertical reaction force acting through the eccentricity caused by the slab's rotation.

How should I approach this design problem? Are there best practices or specific methods to handle this situation effectively?

I would appreciate any comments or advice.

Thank you!

 

[HTURKAK]

I have modeled the slab using FEM, where the columns are treated as pinned supports. This means the columns carry only vertical reaction forces without attracting moments. However, I understand that in reality, some eccentricity must be considered when designing the columns, even if they are modeled as pinned.

I understand that you have modelled the flat slab as FEM plate bending element and the columns only with pin support or line element. Is this true ? Although the pin support modelling could be assumed reasonable at interior columns of the symmetric slab however, corner columns and perimeter columns will attract substantial moment and moreover , at point support locations , the theoretical stress will approach to infinity for elastic conditions.

 

[drile007]

Thank you @HTURKAK, but how do you handle this situation?

 

[jayrod12]

Have you tried changing your model to allow fixity from the column to the slab? Generally speaking that's my approach, model both pinned and fixed and design for the worst case for each item. In this case that would likely take the shape of the slab design being based on pinned column assumptions and the column design being based on fixed assumptions. The actual performance is likely somewhere halfway in between.

 

[JAE]

I would imagine that the top of your column is rigidly connected to the slab so a pinned connection there makes no sense.

At the bottom of your column, it is also probably doweled into the footing or a footing pedestal/plinth such that there is a semi-rigid connection there (subject to the stiffness of rotation in the foundation).

You say there's zero seismic?? How can that be? There's always some seismic in buildings and always at least some measure of deformation compatibility in that, as the building drifts a bit with either wind or seismic, you will have some induced moments in your column from that.

 

[HTURKAK]

Thank you @HTURKAK, but how do you handle this situation?

The modelling ( for the gravity loads ) could be one of the following options;
- Model the flat slab with FEM plate bending elements and the column with line element . The column line element is connected rigidly . Then use the interpolated effects ( design BM ) at a distance a/4 ( a is the size of the column ),
- The same modelling at above mentioned case but use the moment for unit length Mxx /m , ( i preffered this method in past )
- Model some portion of the column as rigid inclusion with a master node at column center .

The following excerpt from Analytical modelling of structural systems (by Iain A MacLeod )

 

[lexpatrie]

Personally I would think that the rotations involved in the slab would be relatively small and thus negligible for the gravity columns, they'd probably see more eccentricity from the drift of the roof diaphragm.

Well I went looking for that Wooten's third law paper from 1971 MSC and didn't find it. (well, Scribd seems to have it if you're patient enough). https://www.scribd.com/document/499214701/AISC-1971-v02. (This was a bit of a cause celebre circa 2001 where I was working, but I could have sworn it had a modern reprint in MSC.

Now, maybe this is the internet, but Wooten here is Jim Wooten, and somehow I found another Wooten's third law, and it's a Robert Wooten. https://www.celottawa.ca/wooten-s-third-law-and-the-ai-among-us

Apparently Jim Wooten created the Wooten corrolary to the other Robert Wooten's third law, ah the more you know.

Alright, weird search result but this is actually the thing and it's from AISC's web site, even. Modern Steel Construction, 1971, second quarter (it was quarterly for a number of years, as I recall)

 

[drile007]

Thanks, guys, for the convo! If I sum up what y’all are saying, there’s really no point in designing the column as pinned support. Gotta say, I’m totally with @jayrod12 on designing the slab with pinned column supports—it makes sense for balancing moments in the slab.

Stay solid, y’all!

 

[JAE]

Don't forget per code you should look at alternating live loads on adjacent, skipped and diagonal bays - this will indeed induce live load moments into your columns.