Atrium Column Unbraced Length Question
Atrium Column Unbraced Length Question
(OP)
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.
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.






RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question
For bending, I afraid you have to use the 70' unbraced length in direction of your concern.
RE: Atrium Column Unbraced Length Question
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?
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
I am not sure they are braced perpendicular to the gridwork, however.
DaveAtkins
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
My hunch is (and I have not done calcs to prove it) that your effective column length is 14'.
Best regards,
BA
RE: Atrium Column Unbraced Length Question
I am willing to bet this entire discussion is moot, because deflection should control on a 70' high column which resists wind load.
DaveAtkins
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
kslee1000:
0.23"???? How about more like 4.12"? Good luck creating that fixed-fixed condition!
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
Thanks for checking. I agree, true fixidy is very difficult to achieve. Well, it is do-able though (takes time & money).
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
Weight = 78.52
A = 23.1
Ix = 1280
Sx = 128
rx = 7.45
Iy = 583
Sy = 97.2
ry= 5.03
J = 1270
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
You are correct in 2 way actions. The ribs resemble a series of springs, the stiffness is depending upon the fixity of end connections.
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question
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
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
How does everyone visualize the best way to handle the erection sequence?
BA
RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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).
RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question
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?
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
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.
RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question
BA
RE: Atrium Column Unbraced Length Question
RE: Atrium Column Unbraced Length Question