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| Carbon fiber - question for engineers/math wizzes http://www.luthiersforum.com/forum/viewtopic.php?f=10101&t=37644 |
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| Author: | John A [ Wed Sep 05, 2012 1:32 pm ] |
| Post subject: | Carbon fiber - question for engineers/math wizzes |
Hi everyone - I am ordering carbon strips to put in both my mando necks and classical necks. I am considering two sizes - .20 x .25 or .125 x .325 I am trying to calculate which rod is more resistant to bending ? The thinner rod (.125) is deeper at .325 depth - would that be stronger than the thicker rod (.20) at a smaller depth of .25 ? quote found on web - "You can think of your CF strip as a beam with a rectangular cross section. The resistance of this beam to bending is in proportion to the breadth of the cross section multiplied by its depth cubed. i.e. b x d x d x d." calculate for my thinner strip - (1.25 x 3.25 x 3.25 x 3.25)/10 = 42.91 calculate for my thicker strip - (2.0 x 2.5 x 2.5 x 2.5)/10 = 31.25 *I multiplied the dimensions by 10 and then divided it out by 10 Does this mean that the thinner strip is more resistant to bending, thus better for my necks ? |
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| Author: | Dave Stewart [ Wed Sep 05, 2012 2:15 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
What Todd said. The beam strength of a 1/8" x 3/8" is about twice that of a 3/16" x 1/4" for near same weight. |
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| Author: | John A [ Wed Sep 05, 2012 2:36 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
great thanks - the thinner strips are cheaper and easier to router if using a 1/8" straight bit or a 1/4" straight and doubling the rods - |
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| Author: | Spyder [ Wed Sep 05, 2012 3:45 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
It's been a while, but if I remember right, the formula for beam stress is: Stress = MC/I M = bending moment C = distance to neutral axis from top or bottom of beam I = section modulus I = (base X height^3)/12 So, with the section modulus being in the denominator of the equation for stress, the height of the beam has a much larger effect, a cubic effect compared to width. Provided, of course, that my memory is still good! 
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| Author: | hugh.evans [ Thu Sep 06, 2012 11:36 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
The general statement in this thread that resistance to flexure is proportional to the cube of the thickness is correct. However, keep in mind that your necks are three dimensional. Chances are good that both options will be more than sufficient. So far you've only been analyzing the problem from one axis. The overall picture is difficult enough to calculate that I would rather work it with finite element analysis (stress model) than by hand. If you make good wood and construction decisions either set of strips should be fine. Excuse the pun, but I wouldn't fret too much. |
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| Author: | David Malicky [ Fri Sep 07, 2012 1:28 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Just to be clear, strength and stiffness are different and have a little different formula. For example, fine china is very stiff but not strong; rubber is pretty strong but not stiff. Usually neck inserts are for stiffness, and the b * h^3 formula is good for that. Stress (the inverse of strength) does go by Mc/I, but the "c" is h/2, so you lose an h overall... b * h^2. The rods are pretty similar in strength. If you're after long term creep resistance, both stiffness and strength are relevant. As Hugh alluded, all this assumes that the rod acts alone, apart from the contribution the neck and fretboard woods provide. With the rod placed just under the fretboard, it's pretty close to the neutral axis of the system, so just looking at b*h^3 should be a good measure. If the rod were placed much deeper (near the bottom of the C), then its cross-sectional area (b*h) would probably be most relevant. |
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| Author: | SteveSmith [ Fri Sep 07, 2012 8:03 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
John A wrote: great thanks - the thinner strips are cheaper and easier to router if using a 1/8" straight bit or a 1/4" straight and doubling the rods - I install using a table saw with a 7 1/4" Diablo blade. Same as trussrod. |
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| Author: | John A [ Fri Sep 07, 2012 11:03 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
SteveSmith wrote: John A wrote: great thanks - the thinner strips are cheaper and easier to router if using a 1/8" straight bit or a 1/4" straight and doubling the rods - I install using a table saw with a 7 1/4" Diablo blade. Same as trussrod. Good idea - I have been avoiding the table saw and I have had it packed up for over a year now - I can find a way to cut myself with plain hand tools, so I really don't trust myself with a table saw. Shop is too small and messy to use it safely. That being said - I have been eyeing it lately and thinking my binding stock process could be so much more better, easier, and accurate to size with the TS> |
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| Author: | Dave Stewart [ Fri Sep 07, 2012 12:27 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
FWIW, I route the trussrod slot with a 1/8" bit on the router table, doing passes each side of centerline & opening to a good fit. Then without altering the setup (except depth) I just put a spacer against the fence & route the CF slot each side, knowing with my spacer there'll be a 1/8" wall between the CF & trussrod. |
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| Author: | John A [ Fri Sep 07, 2012 2:25 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
so Dave - I do not use truss rods - but I have a question - if you have a truss rod - that is adjustable to bend the neck or create relief in a certain direction - isn't the 2 CF rod you are putting in fighting the truss rod ? why have truss rods and CF ? |
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| Author: | hugh.evans [ Fri Sep 07, 2012 3:42 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
The truss rod can still work, although depending on its position relative to the CF it will likely take more effort to change the neck's curvature. I-beams are a nice example of the effect of depth on thickness. In this case, from a structural standpoint, the CF strips are not far off from functioning like a couple of I-beams and will increase stiffness to some extent. Thanks for the book recommendation, Todd. I'm always on the lookout for non-technical reference texts. While studying Mechanical Engineering I went through all the usual courses: enough math to get a minor in the subject, statics, dynamics, strength of materials, failure methods, vibration, etc. and often feel most people working with guitars would benefit from understanding the underlying physics... But not everyone appreciates mathematical explanations. In conversations I've generally fared better explaining that making a part twice as thick will also make it 8 times stiffer. I've successfully described creep by talking about carrying a gallon of milk home from the market in a plastic bag. Needless to say, I will be checking the book out soon and have high hopes based on your description. While working in the adhesives industry I nearly went crazy on several occasions attempting to explain why yield strength is generally a less useful value than proportional limit and design safety factor. |
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| Author: | Dave Stewart [ Fri Sep 07, 2012 7:19 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
John, Hugh basically said it..... the CF stiffens the neck quite a bit and the trussrod is there for final adjustment. A lot of builders use both I believe (I got the slotting tip from Tom Ribbecke's methods). |
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| Author: | James Ringelspaugh [ Fri Sep 07, 2012 9:30 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
So, not to throw a wrinkle into this because I'm sure both CF choices will work just fine, but not knowing my statics I am quite curious: though the depth of the CF dictates stiffness to a higher degree than width (with stiffness being proportional to the cube of the thickness), that is just for the CF block itself... when the beam is actually CF on one end and wood on the other as in a guitar neck, does that change the outcome considerably? With the beam being (fretboard-->CF block-->neck wood) does that change the numbers even more? |
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| Author: | Trevor Gore [ Fri Sep 07, 2012 10:07 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
When I last did the calcs, using two of the ~3mm x ~10mm CF rods from one of the usual suppliers, embedded immediately beneath the fret board, increased the neck stiffness by ~9%, iirc. The same increase in stiffness can be achieved by increasing the neck depth by 1mm (using typical neck wood properties and dimensions) and missing out the CF. If your objective is to guard against neck relief and some action changes due to humidity changes, your best bet is to choose woods for the fretboard and neck that have similar coefficients of dimensional change with humidity variation, i.e. woods of similar longitudinal humidity stability (not a number that's easy to find, BTW!). However, some of the usual choices e.g. ebony/cedro or ebony/mahog are amongst the worst combinations, because both cedro and mahog are quite stable with humidity change and ebony is quite unstable, as indicated by the fret-poke that is often seen on ebony boards in dry conditions (this is not longitudinal variation, but it illustrates the point). The rosewoods are generally more stable with humidity variation than the ebonies. Things still move with humidity change, of course, and the residual can be taken care of by using an adjustable truss rod. |
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| Author: | Don Williams [ Sat Sep 08, 2012 6:07 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Dave Stewart wrote: FWIW, I route the trussrod slot with a 1/8" bit on the router table, doing passes each side of centerline & opening to a good fit. Then without altering the setup (except depth) I just put a spacer against the fence & route the CF slot each side, knowing with my spacer there'll be a 1/8" wall between the CF & trussrod. I just use the CNC...  More to my needs, since I'm somewhat of a neanderthal both mathematically and intellectually - where are you guys sourcing CF these days? I've always sourced from LMI, but was about to switch to Jim Watts' Los Alamos Composites when he announced that they were going to quit the business awhile back. Would love to find an alternative that is has good products and is economically more desirable... Thanks. |
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| Author: | Darryl Young [ Sun Sep 09, 2012 5:52 pm ] |
| Post subject: | Carbon fiber - question for engineers/math wizzes |
As Todd mentioned, the neck creeping over time from constant string pressure is something we would like to prevent. Is the creep due to wood fibers stretching on the back of the neck or is it due to wood fibers compressing on the fretboard/front side of the neck? When bending wood, the fibers compress on the inside of the bend but I'm not sure about creep. |
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| Author: | Trevor Gore [ Sun Sep 09, 2012 6:33 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Darryl Young wrote: Is the creep due to wood fibers stretching on the back of the neck or is it due to wood fibers compressing on the fretboard/front side of the neck? Many woods (especially the softwoods) fail in compression due to cell/fibre buckling before the more apparent catastrophic failure in tension. Not sure if that is true for all woods. However, a neck assembly usually has a wood that is very strong in compression for the fretboard compared to the strength in tension of the neck wood, so it would be reasonable to expect most of the creep to be occurring in tension (i.e. the neutral axis is somewhere just below the neck/fretboard glueline). This, of course, is where most people put the CF, close to the neutral axis, and it is therefore probably doing less than you think in resisting long term creep. |
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| Author: | Darryl Young [ Sun Sep 09, 2012 10:04 pm ] |
| Post subject: | Carbon fiber - question for engineers/math wizzes |
Agreed, I don't see a lot of benefit if installed near the neutral axis (where it's easiest to install). |
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| Author: | Jim Watts [ Sun Sep 09, 2012 10:38 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Todd Stock wrote: The best reasons to use CF neck reinforcement that I can see are for insurance against long term permanent deformation of the neck in service and allowing some less stiff woods to be used for necks without as much concern for stability. +1, some claim it helps eliminate dead spots of the fingerboard too. |
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| Author: | grumpy [ Mon Sep 10, 2012 7:40 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
However, a neck assembly usually has a wood that is very strong in compression for the fretboard compared to the strength in tension of the neck wood, so it would be reasonable to expect most of the creep to be occurring in tension (i.e. the neutral axis is somewhere just below the neck/fretboard glueline). This, of course, is where most people put the CF, close to the neutral axis, and it is therefore probably doing less than you think in resisting long term creep. I agree that the neutral axis is near the glue line between fretboard and neck, and may actually be at or or above it, in some cases(for example, if the builder chooses to use a thicker fretboard and a thinner neck, or a very shallow neck profile combined with a thick fretboard), therefor the CF placed immediately below the fretboard is the --ideal--placement for it. CF is strongest, most stable when in tension, and as noted, the area below the glue line(neutral axis) is in tension. Of course, the further away we can place the CF(or steel, for that matter) reinforcement from said neutral axis, the more we gain, so the tallest CF(or steel) member we can place within the neck, the better, even if it is thinner(as per the original poster's question). The above is also backed-up by the many builders, and repairmen, who have used CF or steel to stiffen necks by placing the reinforcement right below the glue line. Oh, and let's no forget that any reinforcement we add will be for not if we don't install it in a tight-fitting channel and use an adhesive that will prevent long-term creep. |
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| Author: | Darryl Young [ Mon Sep 10, 2012 9:49 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Good point about the adhesive. |
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| Author: | PeterF [ Mon Sep 10, 2012 10:06 am ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Why don't you use hollow carbon fibre rods instead of solid ones? That would give you the same stiffness with far less weight like an I beam. |
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| Author: | SteveSmith [ Mon Sep 10, 2012 1:35 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
PeterF wrote: Why don't you use hollow carbon fibre rods instead of solid ones? That would give you the same stiffness with far less weight like an I beam. The hollow ones are tubular. The strength we're looking for is in the vertical dimension so, for example, I use a 1/8" x 3/8" rectangular rod. A tubular rod large enough to get the strength in the dimension I want would be too wide. |
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| Author: | Barry Daniels [ Mon Sep 10, 2012 2:10 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Hollow rods are not as stiff as a solid rod of the same diameter, but they are stiffer per unit of weight which is not a significant factor in this application. |
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| Author: | Ron Belanger [ Mon Sep 10, 2012 3:16 pm ] |
| Post subject: | Re: Carbon fiber - question for engineers/math wizzes |
Don Williams wrote: Dave Stewart wrote: FWIW, I route the trussrod slot with a 1/8" bit on the router table, doing passes each side of centerline & opening to a good fit. Then without altering the setup (except depth) I just put a spacer against the fence & route the CF slot each side, knowing with my spacer there'll be a 1/8" wall between the CF & trussrod. I just use the CNC... More to my needs, since I'm somewhat of a neanderthal both mathematically and intellectually - where are you guys sourcing CF these days? I've always sourced from LMI, but was about to switch to Jim Watts' Los Alamos Composites when he announced that they were going to quit the business awhile back. Would love to find an alternative that is has good products and is economically more desirable... Thanks. Hi Don, I've used Dragon Plate http://www.dragonplate.com/ecart/categories.asp?cID=20 and Aerospace Composites http://www.acpsales.com/.125-x-.325-Rec ... r-Rod.html I've had good service from both. ![[:Y:]](./images/smilies/smiley20.gif "Thumbs Up") Regards Ron |
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