Verifying the stiffness of a pipe, Al vs. Steel

[HSWSac]

First off, I'm not a Structural Engineer, but I'm an electrical engineer and we install equipment on poles. We recently changed our pole design from Steel to Aluminum and found a drastic difference in stiffness. After researching the numbers, I believe I've found the info I'm looking for. If I can get verification that I did this correctly, that'd be a HUGE help.

Original pipe: 12' long, Sch 40 3" Nominal

Youngs Modulus of Elasticity (E):
- 29.5 million PSI for Steel
- 10 million PSI for Aluminum

This immediately tells me the Aluminum pole of the same dimension is going to be 3 times less stiff. (Right?)

I found the Moment of Inertia (I) values for various size pipe. By calculating I*E, I found that I'd need a 4" Nominal Pipe at Sch 80 to get the same I*E as a 3" Sch 40 Steel pipe. 4" Sch 40 would be a lot better than the 3", but still short of the stiffness of the steel.

I also found a deflection formula on Wikipedia for Cantilever Deflection, which I think is applicable.

Cantilever Deflection = (Force * Length^3) / (3 * E * I)

This seemed to be helpful for comparing the different results.

Attached is a screen cap of a table I created in excel. If I'm on the right track, that would be a huge help. Basically, we need to verify what we need to do in Aluminum to match the performance of the steel.

 

[HSWSac]

Here's the table as a JPG.. .might be easier to view.

 

[rb1957]

you were going great untill you mentioned "cantilever" ... is this a pole (vertical) or a cantilever (horizontal) ?

a pole's critical load is governed by EI, see euler column, so making the two columns (steel and Al) have the same EI is one thing to check. EI also governs displacement, so that's matched too.

i would also check the stress in the pole, Al has a lower allowable than Steel (at least in my business, but you may have lower strength Steel (annealled ?). Look up your allowable stresses ... a column stress is going to be governed by Area (is weight a factor ??), bending stress (lateral load on your pole) is governed by R/I ...

good luck

 

[bdSE]

I have taken a look at your spread sheet, you are on the right track, but here are a few comments about your calculations.

Nominal Diameter, correct.
Schedule, correct.
O.D. & I.D. & Wall thickness - correct.
Weight... not correct for steel, and not too important.
Inside area... doesn't matter structurally.
Moment of Inertia, very important, and wrong.

The values you produced match the answer from using correct formula, but they differ from values found in the Steel Construction manual. Use these values for I instead.

3 Sch.40 = 2.85
3 Sch.80 = 3.70
3.5 Sch.40 = 4.52
3.5 Sch.80 = 5.94
4 Sch. 40 = 6.82
4 Sch. 80 = 9.12

At this time I do not know the reason for the difference between the values. Use the same values for both steel and aluminum pipe unless you hear differently from someone more familiar with aluminum, but it seems that they have exactly the same dimensions.

It is correct to assume a cantilever deflection equation if the base is fixed (no rotation or translation in any direction) and the loads considered are lateral (such as wind loads or seismic). With a pole design, the gravity loads are relatively light and the controlling factor is likely the lateral loads. So your deflection equation is correct, but you need to modify the I values which will increase your total deflection at the free end.

Question: Will you need to cut any holes in the side wall for any reason, or is it simply welded to a base?

The next thing to look at will be this connection at the base. Is everything strong enough here to handle the forces? Base plate? Weld? Etc.

I am unaware of how you connect your pole to a foundation, if you use a base plate and embedded anchor bolts, please be aware that there are potential galvanic reactions when you have bare steel and aluminum in contact with one another. The resulting corrosion will compromise the connection and could fail given time and conditions. So, you may need to use aluminum anchor bolts as well, but someone with more experience in this area may need to offer their advice. However, you may not connect to your foundation in that fashion and this may be an unnecessary rabbit trail.

 

[HSWSac]

Thanks. That's helpful.

I thought the cantilever equation would be useful, as to illustrate the stiffness in a practical example. I'm not sure, though, that the equation I found takes into account the weight of the cantilever itself, but I figured for a vertical pole, it may not matter (except for the momentum the pole has when swaying).

Our poles are simple: Metal welded base plate, 12' main pole with 2' on top for an antenna. The pole has a box with a battery mounted about 3' up, a solar panel about 10' up and an antenna up top.

I didn't go to the trouble to calculate torsional or wind loads, since I knew that the steel pole met our needs. So, the exercise is to try to identify an equivalent EI in aluminum as to steel.

I wasn't able to find a text that instructed me to compare EI, I just somewhat figured it. So, thanks much for helping me to verify that!!!

 

[HSWSac]

DanRonB,

The weights in the table were from an Al pipe chart. That was just copy and pasting a chart, so since I didn't need it for the IE calculation, I didn't bother adding the steel values.

I'm going to try to attach an image of the newly constructed pole to this post. Yes, pole is welded to a plate and has some ports welded into it. The fabricator did an excellent job on the welds. But, yes, we do have the aluminum plate attached to the steel j-bolts in the foundation.

 

[bdSE]

The EI will give you a good stiffness comparison, but realize that your loads will likely be higher than 25 lbs. for high wind events (50 year wind) with the solar panel on the pole.

Wind speeds and forces depend on your location, terrain, elevation, etc. ... but you could simply use 100 lbs. as a starting estimate. (may be higher or lower)

But, deflection in a pole like this is the least of your concerns (although interesting), you need to know if it will fail at the base or not.

You will need to consider both the pole base, weld connection, and the base plate designs.

Intuition says, no problem, but the math is fun to do anyway.

Moment at the base due to 100 lbs. at 12' off the ground is 1200 lb-ft. Convert to lb-inches and get 14,400 lb-in. Convert to kip-in and get 14.4 k-in. 1 kip = 1,000 lbs.

The yield stress of schedule 40 steel pipe is 35 kips per square inch (35 ksi). To give ourselves a safety factor for allowable bending stress we divide this value by 1.67 (this is the Allowable Stress Design approach, ASD).

So our original bending capacity was 21 ksi.

The 3" Sch. 40 pipe has a section modulus of 1.63 (again, steel table values differ from equations.)

Section modulus x bending capacity = allowable moment.
1.63 in^3 x 21 ksi = 34.16 k-in.
34.1 k-in > 14.4 k-in... Pipe base is OK.

It looks as though the original pipe could have easily handled a force of 100 lbs and gives us a level of comfort that the original design was sufficient.

The bending stresses for aluminum will be different and the accepted safety factor could be different as well, not familiar with this material.

Aluminum Alloy 6061-T6 has a Yield Strength of 40 ksi... greater than our 35 ksi on the steel. That's a good start, so even though it is not as stiff, it is still a strong and light material.

I would say, based on a quick inspection, that the aluminum pole of the same size (3" Sch. 40) may be strong enough to survive the wind loads... but the deflections will be greater than steel and that may not be acceptable for your equipment.

 

[HSWSac]

So, that's interesting. Though the 6061 would be less rigid, it'd have a higher yield strength.

You're assumption about our poles is correct, the pole seems plenty strong enough, but the swaying isn't great for the long term on the equipment. Though the equipment can handle it just fine, I fear that prolonged movement will effect long term robustness and tightness of bolted connections and wiring connections inside the box.

We have some plans to brace the installed poles, and will hopefully use these calculations to determine a course of action for our next set of poles. If we want to keep using Al, looks like we're going to have to go to at least Sch 80 4", or a tapered pole.

The other option is to just go back to steel, but the Al poles are pretty darn cool (and light!!!).

 

[rb1957]

tapered poles would be expensive, unless they're readily available.

poles waving in the breeze like corn stalks tend to make the passer-bys worried !

Al corrodes more than Steel and weldability sucks (tho' sucks less for 6061).

 

[rb1957]

also i thought your I calc was right, = pi/64*(D^4-d^4), don't know why damronb derated them by about 5% ?

 

[bdSE]

A simple bracing technique for this pole would be three guy lines in tension. It would be less material than compression knee braces. But, in the end, it would likely cost less to simply go with a stiffer pole to reduce the labor and material of installing additional foundations and cables for the tension system.

Another stiffening option, but not as practical to employ, you can fill the pole cavity with concrete slurry. It would increase both the I and E values, but not easy to accomplish if your pole arrives in the field pre-assembled with the cap I saw in the photo.

Just brain storming with you.

 

[HSWSac]

This is all very helpful. The main advantage to the Al pole was the corrosion and the weight. We didn't have problems with the steel poles, other than they were heavy and it's hard to get things galvanized in CA.

In comparison, I figure a 4" Sch 40 Al pole will weight about 75 lbs, where our 3" steel pole is about 115. The weight savings isn't THAT great.

We can look into the galvanizing issue, or perhaps powder coating is good enough. I'm not sure if it's worth suggesting starting with galvanized plain pipe and painting the joints, as I know it's not healthy to weld galvanized materials...

 

[HSWSac]

DamRonB,

We're against guys, if not just for the looks of it. Build a nice pole for the customer, then have to guy it... grrr...

I have a plan to brace the poles with threaded rod anchored and tensioned to the edge of the foundation. It's not a lot of angle, I know, but I have a feeling it will significantly reduce the wobble.

The backup plan is to have a welder come out and weld a section of c-channel up the back of the pole to stiffen it up.

Anything more than these two options wouldn't be practical. If the braces don't work and we have to guy it, so be it.

 

[bdSE]

Here's how I defend my numbers...

The equation than rb1957 and HSWSac used is absolutely correct for a physics book problem. The reduced values of I and S that are listed in the Steel Construction Manual (AISC)are due to acceptable manufacturing tolerances of standard pipe. AKA - real world. I don't know any manufacturers personally, but someone with low morals might try to hit the low side of the tolerances to boost their profit margin. Not sure how often this happens, but it is possible while still being within regulation.

The values come from Table 1-14 in the 13th edition.

Table 1-28 gives the tolerances for ASTM A53 steel pipe as follows.
Diameter: For pipe 2 in. and over in nominal diameter, the outside diameter shall not vary more than +/- 1 percent from the standard specified.
Thickness: The minimum wall thickness at any point shall not be more than 12.5 percent under the nominal wall thickness specified.

So, with these two minimums in mind you would actually result with an even lower number than is listed in the table. I suppose the table values are simply a conservative estimate of what can be expected within reasonable manufacturing tolerances.

 

[Grahammachin]

With regards to the yield strength of the aluminium noted as 40ksi, this should be reduced where a elements are welded together.

As when welded together the region surrounding the weld is softened resulting in a lower yield strength. This region is referred to as the Heat Affect Zone (HAZ).

I work in the UK and as such this comes out of BS8118, but for a 6061 alloy the reduction factor for HAZ is 0.5, which would result in a yield strength in the HAZ of 20ksi which is significantly below that noted for the steel pipe. As such the connection between the pipe and the baseplate would need to be checked for all forces on the column to ensure that there is sufficient strength in the connection to resist them.

 

[swearingen]

Based on wall thickness tolerances for ASTM A500 and A53 (+/-10% and -12.5%, respectively), AISC recommends that designers use 93% of wall thickness for calculations (B3.12 in the AISC 13th Commentary).

As damronb surmised, the manufacturing technology has increased to the point where the manufacturers can snuggle up to the lower bound and still not be out of spec. Your steel pipe from the mill will consistently average less wall thickness than that listed. Note that this holds for HSS as well (aka tube steel).

This may or may not be true for aluminum pipe...


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

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[bdSE]

Here's an additional idea that I borrowed from the auto racing industry. Rather than concrete, you can fill the hollow core with a liquid that expands and hardens such as poly urethane foam. This has been used to stiffen racing frames for years without adding much weight. You could fill your pole with the foam prior to welding the base plate on.

I am not sure how to calculate the deflection improvements without doing a physical comparison test since I don't have any E values for the foam. I'm sure they vary greatly between products and manufacturers.

Here's one site that sells this type of product if it is something you are interested in pursuing.

http://www.shopmaninc.com/foam.html

It is not conventional for the construction industry, but it has proven itself in the auto industry and they test their stuff in pretty hostile and dynamic environments. It should work for your application as well. If you find an E value that you want to use, post it here and we can help identify how much benefit it would be to your project.

 

[drawoh]

With regards to the yield strength of the aluminium noted as 40ksi, this should be reduced where a elements are welded together.

Is your 20ksi figure with or without heat treatment? Without heat treatment, I thought it was something like 8ksi.

Also, 40ksi is the yield stress for Aluminium 6061-T6. All of my handbooks show higher yield stresses for steel. Is the 35ksi for wrought iron, or is it some kind of arbitrary proof stress?

JHG

 

[bdSE]

To drawoh:
Good question on the yield question for steel.
The Manual of Steel Construction from AISC gives a table (2-3) to help determine which ASTM Designation is typically used in the different shapes produced in the industry today. There are different grades and alloys of steel used for W-shapes, HSS, Pipes, Angles, etc.

The same table gives the ASTM Designation also gives the basic material properties of the steel. The preferred material specification for steel Pipe is A53 Grade B. In fact, in the case of pipe, it is the only acceptable steel type. This type has an Fy minimum of 35 ksi and an Fu of 60 ksi.

Your handbooks are likely referencing the more common steel types of A36, A992, or A500. All of these result in higher yield stresses and in most cases a higher ultimate stress as well.

 

[HSWSac]

DamRonB,

Your idea about the foam is an interesting one!!! I would want to try it, simply out of curiosity!!!

I went to one site today and braced one of the aluminum poles in a non-ideal, but aesthetic way which we think should be sufficient. Ideally, guy wires would probably work the best, but these locations aren't ideal to run guys. Instead, I used a threaded coupler to attach two 8' lengths of 1/2 inch all-thread from the tops of the mounting bolts to 8' up on the pole (to uni-strut w/ L-Bracket). I then tightened the connection at the l-bracket to put a load on the pole and tension the all-thread. The pole still wobbles, but a lot less and seems considerably dampened.

It should work just fine for the application. In terms of future poles, I've discussed it with the boss and we both agree we're just going to go back to steel. If we can't easily/affordibly have the constructed poles galvanized, we'll have them powder coated.

Thanks again, for all the help. I'm impressed at the level of involvement of members on this forum. I'm definitely going to stick around!