Concrete Column Effective Length 9

[Gus14]

In situations similar to the attached sketch, where one of the stories is higher than the other stories. Looking at the elevator columns. As a concept, I am wondering whether adding concrete beams connecting all of the columns in the middle of the floor height, would be sufficient in reducing their effective length.

My concern is that the middle beams will not be attached to a diaphragm, so I don't think it would be sufficient in preventing buckling. What do you think ?

 

[BAretired]

The beam shown on your sketch does not prevent both columns deflecting in the same direction. If there were more than two columns, a similar detail would help to the extent that some columns may not be fully loaded, so they would improve the buckling load of any particular column, but as a general rule, beams at mid-height do not reduce effective length. In fact, a beam at 1/4 or 3/4 height would be more effective, but still not a good practice.

 

[Gus14]

Thank you BAretired for replying,

If there were more than two columns, a similar detail would help to the extent that some columns may not be fully loaded, so they would improve the buckling load of any particular column.

Yeah the four columns are all connected with concrete beams, I agree that it's not a good detail.

Still, it is interesting to know to what extent they will help each other.

 

[3DDave]

To reduce the effective length they need to stiffen against rotation, but at mid-height there is no rotation. Stopping translation is also an improvement, but under similar loads, similar columns will have similar translation at the mid point. All the mid beam would do is ensure the two columns failed in the same direction, but would do little to stop the failure.

Diagonals from the end(s) of one column to the middle of the neighbor would stop the translation of the neighbor midpoint and reduce the effective length.

 

[JAE]

There's some complexity to this kind of situation.
Some years ago I attended a seminar in Nashville held by AISC with Joseph Yura, the U Texas prof.

He showed that, say, with two columns linked together at mid-height, the overall max. buckling load of the two columns (load applied equally on both columns) was not changed by the mid-height beam linking them together. The effective length was the full length of the columns and was not based on the presence of the linkage beam.

But....you could move some or all of that load over to just one column of the pair and they would still provide that maximum buckling load capacity - the two columns would buckle at that same total load, despite most or all the load being applied to the singular column.

Of course the maximum strength (material strength) of each single column was unaffected by the link beam.

With your four columns linked it is probably the same thing. With steel you can easily separate the max. buckling load on a column from its material strength limiting load. Harder to do with concrete columns.

 

[Gus14]

Thank you 3DDave and JAE for replying. So this configuration is helpful to increase the capacity of the heavily loaded column but at the expense of the lighter ones. In concrete we calculate the buckling load for a column based on it's height, reinforcement and section to determine the magnification factor( the infamous 1.4 ratio ).

So theoretically speaking, we calculate the buckling load for the two columns, the column with applied loads exceeding the buckling load will not buckle unless the lighter column is unable to sustain the difference between the applied load and the buckling load of the heavy column in addition to it's own loads.

But still in concrete we don't go near the buckling load so any improvement should be made use of to remain inside the magnification factor limit.

 

[Tomfh]

Effective height is slab to slab. They will all buckle together in the same direction.

Braces from slab to beam are required if you wish to halve the effective length.

 

[Gus14]

Thank you Tom for replying, I would not consider the height halved, but I do agree with JAE that it will help if one column was loaded more than the other. Still, it won't be enough to decrease the heavily loaded column dimension significantly maybe by ( 5 to 10 percent ). I think it's better to think of this effect as additional safety, rather than a way to reduce the column size.

 

[Tomfh]

Yes I agree you’ll get a bonus given you have the stiffness of four columns maintaining stability, not just one.

 

[KootK]

I think it's better to think of this effect as additional safety, rather than a way to reduce the column size.

I disagree. I would be happy to avail myself of the bracing effect of the unload columns to reduce the column size if I could convince my self of the truthiness of that.

Still, it won't be enough to decrease the heavily loaded column dimension significantly maybe by ( 5 to 10 percent ).

I find that suspect. To me, it implies that the column capacity is limited by cross sectional capacity sans moment magnification. And that would imply that the similarly sized columns at the shorter stories also do not work.

A ballpark way of considering the bracing effect of an unloaded column on a loaded one is to simply add the I-values of the mobilized columns together and use that I-value in the design of the loaded column wherever it appears. In your case, I would have expected this to yield a fairly substantial improvement.

 

[TLHS]

Yura does have some good info in relative and lean-on bracing. Get his papers if you want to look at it. Sharing buckling capacity was indeed one of the conclusions that comes from it. I'd need to have a think regarding how that works with different heights, though. If they are attached such that one beam cannot buckle without the other beam moving as well, then in a situation where one of them is at a buckling condition and the other isn't, there will be capacity gained by the buckling column as it is restrained by the unbuckled neighbour.

One of his documents is here, but there are other presentations that go more into the concepts:

https://www.aisc.org/globalassets/aisc/research-library/bracing-for-stability.pdf

If this is concrete and there's some moment fixity in those beams, you'll have more than just lean-on bracing. That moment fixity will help with buckling. There are ways to figure that out by hand, but realistically it's likely easiest to use an initial deflection or force, cracked section properties and do a p-delta check if you want to take advantage of that.

 

[Tomfh]

If this is concrete and there's some moment fixity in those beams, you'll have more than just lean-on bracing. That moment fixity will help with buckling.

Not when it's at mid height. The primary buckled shape does not induce curvature in the link beams, so they don't resist the buckle. You need them offset to get that veirendeel effect.

 

[Gus14]

Thank you Kootk and TLHS for replying. I am currently not working on a similar situation, I was just wondering about the concept. I plan on taking the time to study this situation with different loading cases on each column and experiment with it.

 

[EZBuilding]

My initial gut reaction to this question was that the beam would provide some moment fixity to the column and improve the slenderness behavior of the frame. Considering the lateral displacement of the buckled shape as an equivalent lateral load, the columns and beam are able to form a frame to resist that equivalent lateral load - which leads me to believe it would be able to resist that lateral displacement. The argument of the columns being able to only "share" the load versus having an improved buckling behavior makes sense to me for a pin-connected beam.

I'll dig into the research papers a bit more - it seems like they are AISC based so I wonder if the studies conducted considered fixity of the beam. I'll add a few more thoughts below to see if anyone can help shape my view.

If the the building was a moment frame building - the global effect of slenderness would be improved by the added mid height beam. Does anyone disagree? Seems like the distinction then would only be in the considerations of the little P-Delta effects.