 Increasing tube stiffness with strapping tape

TLDR; It’s theoretically possible to increase tube stiffness by using fiberglass packing tape.

Intro

A common trick from R/C planes is to stiffen wings with strapping/filament tape. I got curious if this method would make a difference for the steel tubes used in a Lowrider.

The tape application would leave space for the bearings, so it would have no effect on the rolling surface. The calculations suggest that standard tape would be enough to increase stiffness by a bit. With an optimized tape the result might even be significant enough to warrant the effort. Theory

Absolute deflection of a fixed beam is \frac{P*x^2*(3L-4x)}{48EI}. In our case we have a beam composed of two different materials so we need to take that into account.

Nicely, this part of solid mechanics is linear, so in this case overall composite deflection of two materials is \frac{P*x^2*(3L-4x)}{48(E_1I_1+E_2I_2)}. In other words, if we want to look at relative changes in deflection, we can compare E_1I_1 to E_1I_1+E_2I_2. Thus, the percent increase in stiffness is simply:

\psi = \frac{E_2I_2}{E_1I_1}

Worked example

Let’s apply a few strips of 1" wide strapping tape to a 1" steel tube and see what happens.

Strapping tape mechanical properties

For the sake of the example, let’s use https://www.weasyadhesives.com/product/heavy-duty-strapping-filament-tape-232h/, which is with 0.17mm in thickness and has a breaking strength of 1450N/25mm wide.

Area moment of inertia

We can calculate I_2 by using area moment equations. I’ll leave those off here, but because tape application is relatively uniform and symmetric let’s just calculate the area moment as the percentage of a tube:

I_{tape} = \frac{\pi}{4} (r_{o.d.}^4-r_{i.d.}^4) \frac{3 w_{tape}}{\pi r_{i.d.}}

where the r_{i.d.} is the o.d. of the steel tube, the r_{o.d.} is the i.d. + the tape’s thickness, and w_{tape} is the tape’s width.

I_{tape} = \pi/4((0.5*.0254+.00017)^4-(0.5*.0254)^4) * (3*1)/(\pi*1) = 1.07*10^{-9}\bf{m^4}

Modulus of Elasticity

We can calculate I_{tape} from the above, but we need to know the tape’s Modulus of Elasticity (MoE). This isn’t given, but we can get a reasonable guess by assuming that the tape uses standard E-glass. We get there by trying to calculate what percentage of the tape is fiberglass (while assuming the rest is backing and adhesive).

1. The area of 25mm of tape is 0.17*25 = 4.25mm^2.
2. The breaking strength of this piece of tape is 1450N.
3. This gives 1450N/4.25mm^@ = 341N/mm^2 = 341MPa.
4. The ultimate yield strength for E-glass is 2GPa. (https://www.azom.com/properties.aspx?ArticleID=764)
5. We calculate the percent strength .341/2 = 17%

(17% is a surprisingly reasonable percent fill. Standard vacuum-infused layups get around 40%. The highest you’ll see is in pulltruded rods, the best of which come close to 70%.)

Therefore our MoE is 17% of pure glass (~75GPa), which gives us:

E_{tape} = 13\bf{GPa}

Steel tube mechanical properties

Assume a standard 1" x 0.049" steel tube, and published mechanical properties.

E_{steel} = 200\bf{GPa}
I_{steel} = \frac{\pi}{4} (r_{o.d.}^4-r_{i.d.}^4) = \frac{\pi}{4}(1^4-(1-0.049*2)^4)\frac{.0254^4}{2^4} = 6.91*10^{-9}\bf{m^4}

Conclusion

\psi = \frac{E_{tape}I_{tape}}{E_{steel}I_{steel}} = \frac{13\rm{e}9 * 1.07\rm{e}-9}{200\rm{e}9 * 6.91\rm{e}-9} = 1\%

Caveats

1%, just with a few pennies in tape?!! Well, there are a couple things to keep in mind:

I didn’t account at all for the loss of shear strength due to the adhesive. This will probably be substantial, but certainly not overwhelming.

Construction

I don’t think it would be easy to get 3 strips of 1" wide tape onto a 1" tube. Sure, it’s possible, but it’s gonna be hard. Better would be a 1/2" or 3/4" tape.

Tube wall

I choose a pretty thin wall. A 0.065" wall would be naturally 25% stiffer.

Afterward

I’ve not tested this. This is pure theory with some educated guesses, so the reality is going to be somewhat different, probably with less impact than predicted. Still, the theory is sound and I would be shocked to see a dramatic departure from the results.

I also don’t know how long the tape would last. It could be days, weeks, months, or years. YMMV.

More and thicker tape would increase the benefits. If there were some kind of carbon fiber strapping tape (does that exist?) then there would be an almost automatic 6x jump in the additional stiffness. Pultruded rods, adhered with double-stick tape, might have a tremendous bang for the buck.

BTW, if you’d like to buy the above tape, it’s so similar to mcmaster’s product, https://www.mcmaster.com/7686A13/, that it’s a good guess they’re the same part number and manufacturer.

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My covid headache is officially killer.now This would certainly be entertaining to try out. The theoretical outcome does suggest it is worth the effort.

That is indeed surprising. I’m seeing different values for the modulus of elasticity from here

This indicates glass as 2 to 4x less than steel, not 5x greater, so the overall contribution might be about 10 to 20x less…

I haven’t gone through the rest in detail but it looks otherwise sound.

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I’m seeing different values for the modulus of elasticity from here. This indicates glass as 2 to 4x less than steel, not 5x greater, so the overall contribution might be about 10 to 20x less…

That’s strange! I know I had seen 2-3[units] in several spots which is why I settled on 2.5, but now that you’ve pointed it out to me I can also find several that say the 200GPa. I need to dig into this some more. Perhaps I unwittingly mixed units metric and SAE units. Mars meet Climate Orbiter…

Certainly, if the mechanical properties are input incorrectly then the results are flawed. Good job catching this! Until I can find sources to the contrary, I have updated the post to include the number you found for steel. Thanks for reviewing and providing critical feedback.

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While I don’t understand any of the calculations involved here, wouldn’t the strength of the glue on the tape be the limiting factor … not the strength of the fiberglass strands? Or maybe the clamping force of the end blocks would be enough to mitigate the glue and put all the stress on the fiberglass in the tape.

That is what I thought too, but then I recalled a video by Tech Ingredients on YouTube about strapping tape adhesive and how its shear strength (or something to that regard) is higher than it needs to be. I.e., the fiberglass strands should break before the adhesive shears.

Of course, I’m sure there are limitations to this based on the material being adhered to.

These are good questions. The adhesive has mechanical properties far below that of fiberglass, but it has the advantage of being a very thin layer and having a very wide bond line. In my first-order analysis, I don’t take the glue into account because I believe it is a minor player.

Adhesives have become so good that they are frequently considered to be stronger and stiffer than mechanical fasteners. For instance, 3M’s VHB is used in highway trailer construction.

Tape adhesive would oxidize and fail.
Tape material would fail due to UV exposure over time.
Low density expanding foam inside the tubes would increase rigidity, be protected from UV and most of the gaseous damage. Plus it has an added benefit of noise absorption.
(Yes my mind has been kicking this idea around)

Hmm that’s very interesting about the shear strength of the glue being greater than the fiberglass strands.

I think this is a good opportunity to also formalize the notion of “fill the tubes with X”

Let r_{id} and r_{od} be the inside and outside diameter of the tube. Let’s assume 1 inch tube with 0.065 wall, which in meters would be r_{od}=0.0127 and r_{id}=0.01105

Then I_{steel}=(r_{od}^4-r_{id}^4)*\pi/4=8.72 \times 10^{-9}

And let’s say E_{steel}=200GPa

Then let’s say there is some filling, with I_{fill} and E_{fill}.

The moment is fixed by the tube geometry, at I_{fill}=r_{id}^4\pi/4 which for our 0.065 inch wall thickness is 0.01105^4\pi/4=1.17\times10^{-8}

So the moment of inertia is about 1.78 times higher for the filling than for the hollow tube.

The relative increase in stiffness is therefore
\psi=\frac{E_{fill}I_{fill}}{E_{steel}I_{steel}} = \frac{E_{fill}}{E_{steel}}\cdot 1.78

The modulus of the filling can be somewhat lower than the tube and still have some contribution, but there are not that many materials that are in the range of stiffness that will help. The tricky part is that materials that seem to be stiff like concrete and glass are often not really high modulus, they are just brittle and thereby give an impression that they don’t bend.

If concrete has a modulus of about 17GPa, then the improvement from filling would be
\psi=17\cdot 1.78/200=15\%

A solid aluminum (E=69 GPa) casting of the interior of the tube woud be
\psi=69\cdot 1.78/200=61\%

Solid cast acrylic (E=3.2 GPa) as an example would be
\psi=3.2\cdot 1.78/200=2.8\%

Carbon fiber composite (assume E=150) would be
\psi=150\cdot 1.78/200=134\% (more than twice the stiffness of the hollow tube)

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I think this is a good opportunity to also formalize the notion of “fill the tubes with X”

That’s good thinking, and a good way of expressing things so people can ask a simple question, look up a simple mechanical property, and get their answer.

I think the relatively poor results show why in a situation where strength is massively unimportant relative to stiffness, the practical solution is to augment diameter. This is what’s motivating me to look for things I can stick on the OD.

(That and it’s a heck of a lot easier to prep the tube’s surface on the outside than it is on the inside.)

I ran the numbers for Graphlite, a pulltruded CF rod which is one of the best in the industry. Their solid rectangular rod is 4.32mm wide and 1.53 tall. It has listed MoE of 142MPa.

Three graphlite rod’s moment of inertia is 1.91e-9, and assuming 1"x0.049" tube this gives

\psi = \frac{1.91e^{-9}*142e^6}{6.91e^{-9}*200e^6} = 19\%

So that’s in the ballpark of any ID solution, and uses a lot less material.

On the downside, I’m assuming the rod is held on with thin VHB, which while it is an awesomely good adhesive tape, its thickness and low shear modulus will certainly somewhat reduce the rod’s stiffening effect.

And of course, bumping up the diameter to 1" EMT is both cheaper and more effective, yielding a 45% stiffness gain for only 3% more weight vs. a 1"x0.065" tube. I think the conclusion is that stiffening of any form-- OD or ID-- will only make sense if there is no alternative.

See Modular Lowrider build (can use any steel tubing from 18mm (1/2" EMT) to 32mm (1.25")) for the alternative. P.S., it’s still really cool to me to think that a length of packing tape can have a measurable difference on a steel tube!

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