Column Moments in Multi-storey Construction (Structural Analysis)

This has always bothered me too, particularly in concrete. In a multi-story building with unbalanced -- and perhaps alternating -- moments coming in at the floors, you pretty much need a 3d model to capture it all adequately.

For the most part, I see columns designed using moments derived from the sub-frame analyses that you mentioned. That relies on the validity of the assumptions that are made regarding the location of column inflection points. In the case of floor to floor repetition and no unbalanced load casing, as shown in your diagram, a model with pinned supports at the column mid-heights makes sense.

The rabbit hole goes even deeper for steel relative to concrete. In steel, you'll have column splices about 4' above the floors every second story or so. Depending on how those column splices are designed, they may behave as pins for part of their load history.

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.

I just don't want to be underestimating the moments in my RC columns. Generally moments don't get bigger as you go down?

Perhaps I need to work backwards to see how much moment can actually be taken by the column (with given reo) and use that as a cap.

Trenno said:

Generally moments don't get bigger as you go down?

Click to expand...

I'd say that's true with two minor exceptions:

1) As your lower floor columns pick up more axial load, they'll be less likely to be cracked. That may increase their stiffness and cause them to attract a bit more load than at upper floors.

2) If your code prescribes a minimum eccentricity for concrete columns, that will grow as you move down your building.

I've tried the moment cap methodology. Two things to consider:

1) You're P-M diagram should be calculated based on over strength in my opinion.

2) You're axial load should fall below the balanced point on the P-M diagram.

If these two conditions aren't met, there's danger that your compression block will blow out before your reo yields. These things tend to add up to inefficient column sizes.



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.

In high rise buildings, the effect of moment on the columns is generally less important on the lower levels. For that reason, it is common to see more reinforcement in upper columns than the ones below.

That's what I've seen in numerous 3D frame models with alternating live loads (for gravity combinations).

Usually the top level corner columns get killed.

Check out Eng-Tips Forum's Policies here:
faq731-376

Yeah I can see that, can someone suggest some possible rules of thumb though in regards to my original question?

Do you need a full 3D model to accurately find the elastic moments?

Why don't you simply compare a 3D model with an equivalent frame calculation and see what the difference is!

And what do you call accurate? Elastic moments are not "accurate". They are what the codes accepts as a reasonable design compromise.

To be accurate you would need to take into account
construction sequence
creep and shrinkage
cracking
temperature
load history
material properties variation
both during the construction of the project and long term.

Design codes allow you to use idealized sub-frame analysis based on the columns being fixed at the floor above and below (except at the opined footings!) for gravity loadings.

For any other loading you need to do full 3D with nominal reductions in member stiffness to allow for cracking/ stiffness loss. So these are not elastic moments, they are allowing for reduction in stiffness. So you may as well do that for the gravity loadings for the columns for column design as well, at least for combination with the sway effects. Probably should then use different values for gravity loading only as the same stiffness reductions may/do not apply.

Thanks rapt, by accurate I meant a good approximation using linear elastic analysis as prescribed by the code. Let's start with the simple stuff before I address all of the other factors associated with RC/PT.

At this stage I'm focusing more on gravity induced column moments, not lateral.

Ok - new example - comparing a full idealized frame model (lets say a nice one way slab and beam frame) with one of it's sub frames.

Observations:

Column moments are generally larger in the full frame model.

The ratio of the smaller to larger column moment will always be 2 in the sub frame, yet in the full frame it is generally less than that. I can see this affecting the determination of a short column.

Floor structure moments are generally similar in both cases.

This:

Trenno said:

The ratio of the smaller to larger column moment will always be 2 in the sub frame, yet in the full frame it is generally less than that. I can see this affecting the determination of a short column.

Click to expand...

Is what leads some to this:

KootK said:

For the most part, I see columns designed using moments derived from the sub-frame analyses that you mentioned. That relies on the validity of the assumptions that are made regarding the location of column inflection points. In the case of floor to floor repetition and no unbalanced load casing, as shown in your diagram, a model with pinned supports at the column mid-heights makes sense.

Click to expand...

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.

I did not think I mentioned RC/PT factors.

Pin the column at the base of your sub-frame example (as you have in the full frame) and see if that has an effect. It should increase the column moment under the floor!

Also, is the frame braced or unbraced? Because your sub-frame is braced and it is very asymmetrical! PS I find it hard to believe the moments at the top of the ground floor columns! I would not expect the first floor column moments to be larger!

For comparison to the column below the roof, the sub-frame would have to be rerun with no columns above.

Yes if you want more accurate moments for slenderness design, a full analysis needs to be done. But the sub-frame results will be conservative in this case. How often in a multi-storey frame are columns not stocky, even using these conservative moments? If using the more conservative values from the sub-frame does result in a non stocky column and you are having trouble making the column work, go to a 2nd order full frame analysis!

Thanks for the help/response, rapt.

Pinning the base of the did increase both the largest span's max midspan moment and the columns above moment.



I agree with everything you have said above. I made up the frame to be very asymmetrical to accentuate the unbalanced moments.

As I said earlier I'm just trying to get a better understanding of how unbalanced moments in columns accumulate down through a multi-storey building - and thus not blindly be unconservative due to ignorance.

I think generally I will stick with the sub frame analysis (fixing each remote end of the column unless it's going into a footing).

Whenever I see the clauses in the codes that permit subframe analysis, they mention slabs and beams but not explicitly columns. I've always wondered if it really is the intent of codes to allow designers to use subframe results for column design.

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.