Round vs square carbon fiber rods

[renniw]

Hi all,

I'm looking for opinions on carbon fiber rods here.

Stewmac is selling square (and rectangle) shape carbon rods.

LMII is selling the square one and a few round ones.

When looking a prices, the round ones are almots 1/3 the price of the square.

Is there a big difference in stiffness to justify paying 3 time the price to get a square one?

Also, I'm living in Quebec, Canada and eveything I get shipped from the US, I'm getting ripped off by customs.

I know a local hobby store that has round rods at a reasonnable price, so your experience may be helpful here...

Thanks

[Phil Mailloux]

If you can get carbon fibre rods locally for cheaper, buy them there. It's all the same thing.
I bought some in the past from a kite store and they were great. Came out to about $12 for 2 meter lenght of it if I remember correctly. So a lot cheaper. Check out the flex of it first when you buy it. the tubular stuff works wonders.

[Nelson Guitars]

I don't know about tube vs rectangle from a strength to weight standpoint but I like the rectangle stuff from Dragon Plate. Good people to work with.

http://www.dragonplate.com/ecart/categories.asp?cID=44

Greg N

[erikbojerik]

If you look at the equations for deflection of a a rectangular beam, you'll see that the resistance to bending (a measure of stiffness) increases as the square of the width, but as the cube of the height.

The take-home message is that, for a given cross sectional area of carbon fiber, the most efficient geometry for stiffening a neck is a narrow tall beam...and the least efficient is a wide flat beam.

Cylindrical rods are in between.

This applies only to solid beams....I'd have to ponder more about hollow beams.

[pilotjones]

Originally Posted by erikbojerik

If you look at the equations for deflection of a a rectangular beam, you'll see that the resistance to bending (a measure of stiffness) increases as the square of the width, but as the cube of the height.

Correction: even more extreme difference than you stated: first power (linear direct proportion) to the width, cubed height.

        3
     b h
I = -----
      12    for a rectangular beam, about its midline

Also,

         4
     pi d
I = -----
      64    for a cylinder, about its midline

So, comparing two rods of the same dimension--that is, say, a 1/4" square to a 1/4" round--and neglecting the remainder of the beam (the neck)--the square rod will be 170% as stiff as the round rod. Or put another way, the dimension of the round rod must be 114% that of the square in order to have the same stiffness.

And, of course agreed that the tall narrow rod has far more effect than the wide, flat orientation.

[renniw]

Thanks guys for the detailed response.

I just gotta see what exact size I can have and we're done to order again from the states...

[erikbojerik]

Originally Posted by pilotjones

Correction: even more extreme difference than you stated: first power (linear direct proportion) to the width, cubed height.

Thanks for the correction PJ!

<Note to self: recalibrate thumbs for rules of thumb....>

[pilotjones]

Originally Posted by erikbojerik

This applies only to solid beams....I'd have to ponder more about hollow beams.

Hollow tube:

     pi            4           4
I = ---- [ d(outer)  - d(outer)  ]
     64    
for a hollow cylinder, about its midline

[erikbojerik]

Originally Posted by pilotjones

Hollow tube:

     pi            4           4
I = ---- [ d(outer)  - d(inner)  ]
     64    
for a hollow cylinder, about its midline

...the second term should be "inner", right?

Interesting...makes sense that a tube is always weaker than a cylinder of the same diameter, BUT....since mass decreases as L*(d/2)^2 the stiffness/mass ratio actually increases as you increase the inner bore diameter.

PJ, what is the quantity (and units) of "I"? Do you have an equation for this that includes Youngs modulus?

I'm interested to see at what size a hollow CF tube attains the same Youngs Modulus as an equivalent volume of (say) maple....or mahogany...

[Mikey R]

Are all carbon fibre rods the same grade? Would rods bought from a kite shop be the same as rods bought from a luthiers merchant?

Originally Posted by pilotjones

        3
     b h
I = -----
      12    for a rectangular beam, about its midline

Also,

         4
     pi d
I = -----
      64    for a cylinder, about its midline

Cheers for the info! So, the rectangular rods from Stewmac would have the equivalent stiffness to the following round rods:

5mm x 6.35mm rectangular => 6.83mm round section
3.18mm x 9.5mm rectangular => 8.25mm round section

(dont trust my calculations, its before midday)

So, I would guess that two 8mm round rods would be an ok substitute to the Stewmac ones?

[MPU]

[I'm interested to see at what size a hollow CF tube attains the same Youngs Modulus as an equivalent volume of (say) maple....or mahogany...[/quote]

Don't know about Young but isn't this easily tested? Take rimilar sized rods of carbon, maple and mahogany, clamp one end of the rods to a table and put similar weights on the other ends. Compare the amount of bend.

Marko

[pilotjones]

Originally Posted by erikbojerik

...the second term should be "inner", right?

Yes. And i should have been asleep when I posted.

Interesting...makes sense that a tube is always weaker than a cylinder of the same diameter, BUT....since mass decreases as L*(d/2)^2 the stiffness/mass ratio actually increases as you increase the inner bore diameter.

Exactly. That's a main reason thin sections are used, most effect with least material.


But... It's all more complicated once anything becomes part of a composite structure, such as a bass neck. Then, there's the parallel axis theorem to contend with.

E.g. see "general shapes" here:

http://en.wikipedia.org/wiki/Beam_%28structure%29

PJ, what is the quantity (and units) of "I"? [

distance^4, as you an figure from both the cylinder and square beam equations.

http://en.wikipedia.org/wiki/Second_moment_of_area

Do you have an equation for this that includes Youngs modulus?

The equation for beam stiffness uses the second moment of area (I), with the young's modulus (E).

I'm interested to see at what size a hollow CF tube attains the same Youngs Modulus as an equivalent volume of (say) maple....or mahogany...[/quote]In addition to not figuring for a real neck, we're also not figuring for the fact that both CF bars and trees are non-iso materials: different properties depending on the direction through the material, which is neglected in all the preceding equations.

Without trying to sound snotty about it, there's a reason why this subject matter takes an entire semester course in structural analysis in engineering school, not just a few forum posts.

[pilotjones]

Originally Posted by Mikey R

Are all carbon fibre rods the same grade? Would rods bought from a kite shop be the same as rods bought from a luthiers merchant?



Cheers for the info! So, the rectangular rods from Stewmac would have the equivalent stiffness to the following round rods:

5mm x 6.35mm rectangular => 6.83mm round section
3.18mm x 9.5mm rectangular => 8.25mm round section

(dont trust my calculations, its before midday)

Sorry, I don't have time to check the calcs, got to get off to work. Hopefully you used the proper assignments for b and h.

So, I would guess that two 8mm round rods would be an ok substitute to the Stewmac ones?

Here again we are entering "just enough knowledge to get into trouble" territory. One should consider the entire (neck) beam.

[pilotjones]

Originally Posted by MPU

[I'm interested to see at what size a hollow CF tube attains the same Youngs Modulus as an equivalent volume of (say) maple....or mahogany...

Don't know about Young but isn't this easily tested? Take rimilar sized rods of carbon, maple and mahogany, clamp one end of the rods to a table and put similar weights on the other ends. Compare the amount of bend.

Marko

Yes, deflection of equally sized beams with equal loading would be proportional to... IIRC.. the square of the stiffness, which is proportional to the young's modulus.

[Mikey R]

Originally Posted by pilotjones

...there's a reason why this subject matter takes an entire semester course in structural analysis in engineering school, not just a few forum posts.

Originally Posted by pilotjones

Here again we are entering "just enough knowledge to get into trouble" territory. One should consider the entire (neck) beam.

Understood that I dont understand I'll do some more reading and then time for a little more thinking... Again, thanks for the time sharing this information, you've given a good starting point!

[erikbojerik]

Originally Posted by pilotjones

http://en.wikipedia.org/wiki/Second_moment_of_areaThe equation for beam stiffness uses the second moment of area (I), with the young's modulus (E).

Got it, thanks! Also HERE.

And yes...please...let's stay linear for now....

This part of the discussion goes back to a debate I had on another forum, in which it was argued that CF tubes worked just as well as solid CF bars in terms of increasing the bending stiffness of the neck. Clearly that was wrong...it seemed intuititive to me, but now I can see why from the equations for second moment of area.

But it also got me wondering whether routing out a channel of neck wood and replacing it with a CF tube resulted in a net gain or net loss of bending stiffness compared with the material that was removed to make the channel....this comes down to stiffness/weight ratios and requires the equation for bending stiffness.

For a 1/4" x 1/4" beam, the second moment of area is fixed, so the bending stiffness comes down to the difference in Modulus of Elasticity (MoE, or Youngs Modulus). The MoE of hard maple is ~14 GPa, the MoE of pure carbon fiber (standard modulus) is about 250 GPa, falling to ~150 GPa when cast with epoxy in bar form. So for a given size CF bar, solid CF bar has ~10x higher bending stiffness compared with an equivalent volume of maple, while being 2x heavier (density of 1500 kg/m3 for CF solid, 750 kg/m3 for maple).

For a common 1/4" O.D. CF tube available at kite-building sites (0.162" I.D.), the second moment of area is about half that of a 1/4" square rod...so a CF tube still has 5x higher bending stiffness compared with the rectangular strip of maple you remove to make room for it....and the CF tube (being 45% lighter than the square CF bar) is barely heavier than the maple. (the epoxy holding in the round tube might add something in both stiffness and weight).

Conclusion #0: We all know that CF bar increases the stiffness of the neck. Duh.

Conclusion #1: The stiffness/weight ratio of CF bar and CF tube is similar (provided they fit in the same channel). YMMV for different geometries...i.e. bar and tube get closer in stiffness/weight ratio as the diameter decreases because the tube's wall thickness gets proportionally larger.

Conclusion #2: For a 1/4" square channel size, a CF tube that fits that channel has about the same weight as the amount of maple you remove, but 5x higher stiffness. Again YMMV for different geometries.

Unless I've missed something....which is entirely possible...

[pilotjones]

Sounds good, Eric.

BTW an interesting (at least to tech-geek-types) way of looking at the hollow tube equation: it is the stiffness of a solid rod (the OD), minus the stiffness of an "anti-rod" (the ID) which has been virtually bored out from the center.

[erikbojerik]

Thanks again PJ for pointing me to the relevant Wiki pages.

The 2nd moment equations for composite beams are going to come in handy, I want to play with various geometries of spruce-CF laminates for acoustic guitar braces.

[renniw]

I'll print this thread to read it later, my french brains are a little confused.

Thanks to everyone for sharing the knowledge...