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Atrium Column Unbraced Length Question

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structuresguy

Structural
Apr 10, 2003
505
I am designing a 70 foot tall glass atrium, which is basically the shape of a football in plan view, with straight vertical walls and flat roof. The "football" passes through an office building, with 5 stories on one side, and 2 stories on the other. The framing sizes are all preliminary right now, but I am having some problems with the columns. I am modeling it in Staad in full 3D. See attached file for plan view at one end of the atrium.

My columns are HSS12x12x1/2, spaced about 10 feet apart. The columns will be rigidly connected to the foundation and to HSS roof trusses, forming a portal frame, in effect, across the width of the atrium.

I have horizontal "ribs" every 14 feet, which are HSS20x12x3/8. The ribs are fully welded to the columns, to make a continuous rib. Due to the shape, the ribs form a peaked arch in plan view, with the base of the arches tying into the floor slabs at the first two levels on both sides, and on one side only for the full height of the atrium.

So my question is, what do you think the unbraced length of the columns is for the strong axis (out of plane of the wall) direction? Full height of the atrium (70 feet)? Or do you think the rigid "ribs" will contribute to bracing the columns against strong axis buckling? Weak axis is obviously braced by the ribs every 14 feet.

I know that the ribs will contribute to some extent, and that full height is probably too conservative, but I am not sure how to justify a rational approach to reducing the unbraced length.

If you imagine the arch that the ribs form, that is a very stable structure that could withstand an out of plane buckling load from the columns. So can I figure on using 2% of axial compression to calculate a horizontal OOP point load at each column-rib intersection, and then check the model with those additional loads? If the arch can handle that additional lateral load, I think I am good to consider the ribs as bracing the columns out of plane, due to the stiffness of the arch. What do you think?

I told the architect that HSS12x12 would work (based on some prelim hand calcs), and it does in most cases using 70 foot unbraced length. But where I have columns tied to vertical x-bracing at the ends of the atrium, the axial forces due to overturning are exceeding my column capacity (based on 70ft). So if I can justify a reduced unbraced length, then I can make the 12x12 columns work.

Thanks very much.


 
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Well, I don't have the properties of HSS 20 x 12 x 3/8, so I will approximate it to 1312 in^4 (ignoring the corner radii).

If the rib carries all of the wind load, the uniform load on each rib will be 30*14 = 420 plf, giving a moment of 189,000'# and a maximum fiber stress of 17,300 psi.

Deflection = 5*420*(60*12)^4/(384*29e6*12*1312) = 3.2".

Best regards,

BA
 
HSS 20x12x3/8

Weight = 78.52
A = 23.1
Ix = 1280
Sx = 128
rx = 7.45
Iy = 583
Sy = 97.2
ry= 5.03
J = 1270
 
kslee,

Thanks. So the fiber stress becomes 17,700 psi and the deflection becomes 3.3".

That assumes the ribs act as a beam. If they act as an arch, they will be stiffer. In reality, the columns and ribs will act as a two way system, sharing the load as dictated by strain compatibility.


BA
 
BA:

You are correct in 2 way actions. The ribs resemble a series of springs, the stiffness is depending upon the fixity of end connections.
 
If the atrium structure is not supported by buildings on each side, i.e. it stands alone, then the "football" shape is about 130' long and 56' wide. Each arch has a "rise", h of 28' and a span, L of 130'. Thrust is approximately wL^2/8h.

If wind pressure on each wall is 20psf, w = 14*20 = 280plf, so thrust = 21.1k per arch. This could easily be resisted by cross bracing in the end bays.

For a two hinged arch with h/L = 0.215, buckling will occur at a uniform load of approximately 39.5EI/L^3 or 39.5*29e6*1280/(130*12)^3 = 386#/" or about 4600plf, far in excess of the applied wind load.

The columns, in my opinion, are braced by the arches at 14' centers.




BA
 
I would be worried if the horizontal braces taking up too much thrust, which could be very difficult to manage the end reactions. Ideally, I would prefer to make the columns stiffer to pick up the majority of load, if not entirely.
 
kslee,

Columns would need to be extremely stiff to resist lateral forces by frame action alone. If you simply transfer the wind from ground to roof via the columns, you need a stiff element at each end to take the diaphragm force from the roof down to the ground.

The plan of this structure is a natural for using horizontal arches at each floor. Double sets of cross bracing at each end of curved Grid lines AA and BB provide a reliable method of handling the forces and they are perfectly aligned with the arch thrusts.

As a side benefit, the columns are so well braced at each arch that they could be reduced in size.

The piles will need to be well anchored in the ground to develop the large wind forces but it is a small price to pay for the economy available in the superstructure. (End of rant).


BA
 
BA:

I prefer the 2 way model, with the braces as springs, you mentioned previousely. It will help to maintain current column size (it is already in the range if no extrodinary roof load is anticipated), and distribute the wind load more smoothly.

If the atrium is in between two building units, I may agree arch is a good sell. But I sense some difficulty for this case.

Also, we need to watch out for local distorsion, since it will be cladded with glass finishing. Admittedly, I haven't give a thought on that yet.
 
As interesting as the design concept is, I have been wondering about the erection sequence. It will not be easy to plumb the structure after everything is all welded together.

How does everyone visualize the best way to handle the erection sequence?


BA
 
On top of cranes and temporary shoring, I guess it will involve a lot of scaffold, and/or temporary work platforms. Precision holds the key as glass is involved. Also, will there be concerns over stresses induced by temperature differential? Interesting. I couldn't wait to see the construction, and the final product.
 
Wow! You guys have really dove in the deep end on this discussion. Thanks. I appreciate to here all the varying opinions and thoughts.

So far, deflection (both local and global) is not showing itself to be a big problem. The atrium is so well braced (for global deflection) by the floor diaphragms and shear walls of the office tower, that max lateral deflection is only about 1", according to my Staad model. I am still in the process of veriofying the model, but the results are promissing. The deflected shape and bending moments are as I would expect them to be, for the most part.

I do get some weird distortion of the atrium wall on one side, where it either bulges out or in, depending on wind direction. It looks weird to view when scaled way up. The columns in question are bowing out about 1" at worst case. Since the building is non-symmetric in number of stories, one side gets less restraint than the other, resulting in the non-symmetric deflections.

So far, I am pretty happy with the preliminary results I am getting from my full model. All of my initial member sizes are working well. Right now, I have used an unbraced length of half the building height, instead of 70 feet. I figure that it is a pretty decent compromise. I know the ribs are doing quite a bit of work, but think that using 14 feet unbraced length is maybe too little. Either way, my columns are working, so reducing the unbraced length more wouldn't really help any more. THe architect wants 12x12 columns, so I can't really reduce the size anyway.



 
One add'l cautious:

I would be worried, if you compare the compressive stress from the computer program with the allowable stress derived from half of the column length, because the benefits of the lateral braces is already built into your model (similar to two way slab analysis). The resulting stress is close to the actual you would get under such scheme - braced in two directions (one stiffer than the other).
 
The benefits in terms of load sharing is built in to the model. But the model does not know what the unbraced length is for bending or axial compression. By default, Staad uses the members length, which is 14 feet in my case for the columns. For bending, this is fine. As it is for in-plane buckling due to axial compression. For out of plane buckling due to axial compression, I have redefined the unbraced length for the column to some arbitrary amount. Currently, I have set it to half the column height. This does not affect the calculated stress. It only affects the stress check against teh code, as it uses the length I assign to calculate the allowable stress, based on the "new" KL/r.
 
One thing I don't think I mentioned is that the worst case column loading is in the lower portion of the columns which are part of the braced frame. At the lowest segment (bottom 14'), the axial force is the highest. It then drops a bit with each segment going up. So only the lower 2 or 3 segments were actually failing a stress check, during a lateral wind load combination.

For gravity loads only, and all the "leaning" columns, the stress levels are quite low, not more than about 50% at worst case, even with full height unbraced length.

So does the fact that the loading is worse only at the bottom, and not a uniform axial force over the entire height, make a difference in how you guys feel about the unbraced length?
 
I agree with kslee1000, if the horizontal beams were doing nothing but restraining the columns then you could use them as effective restraints.

But as they are taking some of the wind load then personally you can only really use them to reduce your bending moment.

The only real accurate way is to do a critical buckling analysis, your program may do it. You will then get an effective buckling length under the load case considered.
 
structuresguy:

Let's forget above code check for a moment.

You have constructed a grid as compared to a bunch of columns connected on top and bottom only, isn't the latter will produce higher stress than the former, which presents the near factual stress?

Now, you compare this lesser conservative stress with the artifically increased (by reducing L) allowable stress, wouldn't that be a concern?

Don't mean picky, just want you to think about.
 
BAretired: Erection and sequence of construction is something that I am already thinking about. As we (myslef and the architect) want a nice clean appearance, I am planning on fully welded connection, tube to tube. Obviously, this does not leave a lot of room for large construction tolerances. But I think any kind of gusset plate solution just won't be visaully pleasing enough for the architect or the owner. The building is a world wide headquarters building for the owner, so appearance is very important.

Once we get out of schematic designs, I plan to meet with several of the local steel fabricators to discuss erection of the atrium framing. There is a GC (or maybe CM, not sure yet) on board now, but no subs have been selected yet.

One thought I have to help with erection is to shop fabricate sub assemblies. The spacing from column to column is about 10 feet. They could shop fab an assembly of two columns, with all the ribs. Then ship out these assemblies. Then in the field, they would only have to erect every other rib. Even the braced bays could be fully shop assembled, and shipped out to the site. Of course, they might need to field splice two assemblies for height, since I don't think they could ship a full assembly (total height would be about 82 feet long).

Alternatively, they could shop assemble tree columns, with half of each rib already attached to the column. This would work well, due to the slight angle that each rib is oriented at, relative to square. Then in the field, only a straight butt splice would be needed, which could be built-up a bit using backer plates to bridge the gap.
 
kslee100: definitely, I am trying to think about all the options here, which is why I posted here, to get other peoples opinions. I would agree with you that typical columns, connected only top and bottom, would result in highest stress levels. and in a traditional building, I would not even be questioning the unbraced length. But because I have the shape that I do, I would like to take advantage of the inherently increased stiffness I have, compared to traditional building. I don't want to be underconservative, but I don't want to be over conservative either.

csd72: I have been thinking about doing a buckling analysis, and the more I think about it, the more likely I will do one. I would prefer not to spend the time, but I am curious to see the results. But I won't have time probably until we get out of schematic design, as I have lots of other work to do on the rest of the building.
 
That is the only way you will really find the effective length.
 
It is an extremely interesting project and you seem to have the design well in hand. All the best in the execution of it.


BA
 
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