Slenderness Ratio for Architectural Structure

[VSS Engineering]

My team is designing Faux Trees that will be on display inside a building at a resort in Florida. The trees themselves have a self-weight of about 2,500 lb fully assembled and stand 32' tall. The customer is wanting to use HSS 4.5 x 0.337 Pipe. The pipe easily passes design checks from anticipated loading; however, it is failing slenderness requirements.

Does anyone have any code information that may allow us to negate the slenderness requirement for something that is purely architectural and subject to very little loading?

Thanks!

 

[SWComposites]

How much offset of the 2500 lb weight if assumed to conservatively be at the top of the pole will cause the pole to buckle and collapse?
Have you checked buckling with no offset?

 

[dik]

Where is the load applied to the tree? or, is the HSS for stability only?

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[BAretired]

A 32' high cantilevered pipe with I = 9.61 in^4 and r = 1.48 inch has a maximum slenderness ratio of 32*12*2.1/1.48 = 545, which is a long way over the maximum allowable of 200. That makes a pretty wobbly structure if load is applied at the top, but perhaps the c.g. of load is more like 16' above the floor, so a more realistic slenderness ratio might be 272, still well above maximum permitted.

Another consideration is internal wind pressure; for walls, 5 psf is sometimes used. If the same criteria is used for the trees, deflection would likely be a factor for such a slender column. And deflection would cause an eccentricity which would negatively affect the Euler buckling value.

The customer's suggestion sounds a bit risky without some form of lateral bracing to stabilize the columns.

 

[JStephen]

I think there is a design standard for flagpoles. Is it any more lenient with respect to L/r?
How about utility poles?
If a pole gets too long, you run into problems handling it in the horizontal position, but I doubt you're there yet.

 

[hokie66]

Deflection is a serviceability criteria. We don't worry about deflection for diving boards or sailboat masts.

Buckling is certainly a strength issue, but that would depend on applied loading and deflection.

How is the 'tree' connected at the base? Any chance of kids, or others, climbing the trees?

 

[JStephen]

From this link:

https://www.aisc.org/steel-solution...qs/4.1.-aisc-specification-requirements/#9529

"4.1.2. IT IS INDICATED IN THE AISC SPECIFICATION SECTION D1 THAT THE SLENDERNESS RATIO OF A TENSION MEMBER SHOULD PREFERABLY NOT EXCEED 300. WHY? IS THIS REQUIREMENT STRENGTH RELATED?
"From the AISC Specification Commentary Section D1, Users Note, this recommended limit is "based on professional judgment and practical considerations of economics, ease of handling, and care required to minimize inadvertent damage during fabrication, transport and erection." It is further indicated that this requirement is not strength related.
:Essentially, this rule also ensures that a non-pretensioned structural brace will be stiff enough that significant lateral deflection of the structure will not be required to activate the strength of the brace. As such, this requirement does not pertain to rod bracing, cable bracing and other light bracing systems that are fabricated and installed with draw to activate the brace."

More discussion here:

https://www.eng-tips.com/viewthread.cfm?qid=93502

Interesting article here, not sure if it would give any reasonable information in this case:

https://en.wikipedia.org/wiki/Self-buckling

 

[JLNJ]

You might have several inches of sway (or "lean") due to eccentric gravity loads. Factor in the flexibility of your base plate and anchorage and that number increases significantly.

Seems a little iffy. Maybe fill the pipe with concrete to stiffen it up? Good fixity at the base will be a must.

 

[KootK]

I believe the slenderness ratio limits to be at the ultimate discretion of the engineer. That said, were I to exceed those limits in compression, as I assume you intend to, I would back that up with a rigorous 2nd order analysis considering many of the potential source of incidental load mentioned by the other folks here.

When I think "tree" I think of a structure that has a lot of its load applied at a considerable eccentricity to the trunk. Even with an HSS trunk member, weird stuff like torsional buckling or compound torsional / flexural buckling might not be out of the realm of possibility. Your unbraced length for flexural and torsional buckling is 64' @ K=2. That feels like a lot for a 4.5" pipe even if the axial load is very small. A compression that slender will tend to be quite sensitive to various sources of eccentricity.

 

[XR250]

Ironically, a real tree with a similar sized trunk would probably withstand a hurricane.

 

[KootK]

Ironically, a real tree with a similar sized trunk would probably withstand a hurricane.

I'm not so sure. Even a 32' date palm, which is basically just an over grown weed with little mass in the branches, comes in around 15" diameter at the base.

 

[canwesteng]

Filling the pipe with concrete, or using thicker walls, or any other method of stiffening that doesn't increase I in greater proportion to A actually increases the slenderness ratio and makes the OPs problem worse. Agreed with kootk, that the ratio can be ignored, as long as you've done proper 2nd order analysis (both from global p-delta effects and moment amplification from member curvature). For what it's worth, steel columns are often erected with kl/r>200 before all the weak axis bracing is in place, and this is something of a similar problem (kid climbing tree, iron worker hanging off column).

 

[XR250]

I'm not so sure. Even a 32' date palm, which is basically just an over grown weed with little mass in the branches, comes in around 15" diameter at the base.

Plenty of 4", 32 ft. pine trees around here. Don't weigh 2,500 lbs though.

 

[KootK]

Plenty of 4", 32 ft. pine trees around here.

I've little reason to doubt it as my dendrology is nothing to write home about.

Similar to JLNJ's comment, I suspect that much of what makes nature's free standing cantilevers work is the, typically, kick ass base connection stiffness.

I also speculate that some of these very slender trees wind up leaning over to lower moment demand at the expense of tension demand. That old adage about it being better to be able to bend than to stand rigid.

 

[bhiggins]

Analyze the structure using direct analysis method (DAM). Apply notional loads to a the structure with reduced stiffness, perform p-delta analysis. Check lateral drift and column stability.

 

[XR250]

I also speculate that some of these very slender trees wind up leaning over to lower moment demand at the expense of tension demand. That old adage about it being better to be able to bend than to stand rigid.

They most definitely do!

 

[VSS Engineering]

Thanks for the input. We are designing for the 5 psf interior lateral load, the trees themselves have relatively little area to catch any lateral loads so we have not had any issue with axial or bending stresses in the column. We are able to achieve a completely fixed base for these columns as they have rather large base plates w/ stiffeners.

The "limbs" of the tree are attached at 3 different heights, the highest of which being approx. 25' above grade. My inclination is to size the pipe to meet KL/r at 25' since that is the highest point of axial load application.

 

[KootK]

My inclination is to size the pipe to meet KL/r at 25' since that is the highest point of axial load application.

I doubt that anyone would bemoan that approach.