Atrium Column Unbraced Length Question

[structuresguy]

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.

 

[structuresguy]

Here is an elevation of one end of the atrium, so you can see the bracing layout.

 

[structuresguy]

And here is a section cut through the atrium.

 

[kslee1000]

I could be wrong. But HSS itself and all wall elements are compact, is there a problem with buckling?

For bending, I afraid you have to use the 70' unbraced length in direction of your concern.

 

[jike]

I agree, I would use 70 foot unbraced length.

However, you may have bigger problems, but maybe you have already addressed it.....

Won't you have deflection problems with your columns spanning that far trying to resist wind load or are you creating a rigid gridwork spanning 2 directions?

 

[kslee1000]

For propped beam, the deflection may not be overly severe.
Concrete fill may help to some degree for both compression & deflection. However, the foundation design could possess the biggest challenge, especially if it is located in moderate earthquake zone or above, as well as the wind effect. Have fun, and good luck.

 

[BAretired]

The horizontal ribs on Gridline AA are spanning about 60' from end to end. The orientation of the rib is difficult to ascertain from your section. If the horizontal dimension is 20" the rib is a lot stiffer than any column. Even if the horizontal dimension is only 12", it is still stiffer, so provided the ends of the rib are restrained against translation, the rib offers significant restraint to the columns.

Perhaps you could treat each column as an axially loaded member with elastic restraints at 14' centers. You would need to be able to estimate an equivalent spring stiffness at each node.

I think it could be analyzed for axial loads. But if the ribs are 20" high x 12" wide, the framework may be too limber for wind forces.

Best regards,

BA

 

[DaveAtkins]

These columns are certainly braced at each level in the plane of the gridwork, by the braced frames.

I am not sure they are braced perpendicular to the gridwork, however.

DaveAtkins

 

[DaveAtkins]

OK--I apologize for restating the obvious. Everything I just said was in the original post.

This is one of those cases where I would err on the side of conservatism. I would assume the columns are unbraced full height. I understand how you are trying to justify this, by treating the entire gridwork like some sort of arch (in plan) that resists buckling, but how would the reactions at the end of the arch be resisted? By the braced frames?

If you can get comfortable with the forces induced, and with the load paths, go for it.

Another way of making the 12 X 12 column work--are you assuming K < 1 for your buckling check? You said the columns are fixed top and bottom. Or are these columns stabilizing themselves in the strong direction (you mentioned they are part of portal frames)? If so, K > 1.

DaveAtkins

 

[structuresguy]

Thanks for your input. I agree with most of what you recommend. I started off being conservative and using full height unbraced. But with members failing due to the reduced axial capacity with KL/r of about 180, I am looking to see if I can justify any reduced unbraced length.

Sorry, forgot to mention that the horizontals are laid flat, so that the 20" dimension is out of plane of the wall. And for deflection, I am treating it as a 2-way rigid structure, using the stiffness of both the columns and the ribs, to control local deflection. I don't have the final numbers yet on the actual deflection, so I may need to increase column sizes anyway. To control overall drift, I have the X-bracing in the vertical planes at the ends of the atrium. I also have a rigid horizontal truss at the roof level, to enhance my diaphragm over the atrium, that ties back to shear walls in the adjacent office tower.

Fortunately I do not have any seismic loads to worry about (Florida), but I do have 120 mph wind loads.

 

[jike]

structuresguy:

If you are using a 2 way rigid structure to resist wind loads, I would suggest using the same size members (both vertical and horizontal) to simplify connections.

 

[kslee1000]

I had second thought about this system.

Let's turn the wall 90 degree, now it is a floor. Each column is a beam supported on both end with the ribs acting as braces at 14' on centers, is this floor braced against flexural instability? I think the answer is "yes".

At conclusion, I would check compression using 70' length. For bending, use Lb = 14' (this turns out will not help in your favor, since Fb is limited to 0.6 Fy or less for shapes other that I & channel. Check me on this). Then check the interaction.

 

[BAretired]

With the HSS 20x12 on the flat, there is no question in my mind that you will get significant restraint for the columns in both directons. If, in addition the curved rib is capable of spanning as a horizontal arch, it will be even stiffer. This means that the end regions of the arch must be capable of taking thrusts.

My hunch is (and I have not done calcs to prove it) that your effective column length is 14'.

Best regards,

BA

 

[DaveAtkins]

I am not sure I would use 14' for unbraced length for axial loads (bending, yes, but then tubes don't buckle due to bending). I would assume K = 0.65 (fixed top and bottom), resulting in KL = 45.5'.

I am willing to bet this entire discussion is moot, because deflection should control on a 70' high column which resists wind load.

DaveAtkins

 

[BAretired]

Dave,

Don't you think the wind would be carried by the HSS 20 x 12 ribs? Even if they act like a beam instead of an arch, they would be stiffer than the columns.

Best regards,

BA

 

[kslee1000]

I guess the system would work as suggested.

Assume full fixity on both ends, with 30 psf uniform load, the max. deflection turns out to be 0.23", if I didn't make mistake in the cal.

For compression, using Dave's K number (.65), the allowable compressive stress is in the range of 10.71 ksi.

For bending due to 30 psf wind pressure, the resulting bending stress is merely 1.82 ksi.

The scheme looks promising.

 

[jike]

structuresguy: Are you planning to have the horizontals be continuous? Are they in the same plane as the columns or outboard? If continuous, are they spanning to some support at either end or are they just tying the columns together?

kslee1000:

0.23"???? How about more like 4.12"? Good luck creating that fixed-fixed condition!

 

[kslee1000]

jike:

Yes, there was a mistake in my cal for deflection. Check me on this.

10' column spacing:
W = 30psf x 10' = 300 plf (forgot this step previously)
L = 70'
E = 29000000 psi
I = 485 in^4

D = WL^4/384 EI = 300*(70^4)*1728/(384*29000000*485) = 2.3"
D = L/365

 

[jike]

kslee:

Now we are on the same page. I assumed 14 foot spacing and 12x12x3/8. I guess I didn't read it carefully enough! 2.3" is correct for fixed ends.

 

[kslee1000]

jike:

Thanks for checking. I agree, true fixidy is very difficult to achieve. Well, it is do-able though (takes time & money).