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Rationale for triangulating braces
http://www.luthiersforum.com/forum/viewtopic.php?f=10101&t=28462		 Page 1 of 3
Author:  James Orr [ Mon Aug 02, 2010 1:01 am ]
Post subject:  Rationale for triangulating braces
I enjoyed voicing a new soundboard today and taking various measurements throughout. This is the top for #2, and since I did the typical scalloped bracing on #1, I'm exploring the ill-named "parabolic" profiles this time, instead. The top weighed 237 grams before triangulating the profiles, and 234 after. A change in tap tone was indistinguishable.

My understanding of the rationale for triangulating was that it maintains stiffness while decreasing weight, but in this case, three grams seems inconsequential. Is there more to it than that?
Author:  sonorgeek [ Mon Aug 02, 2010 1:09 am ]
Post subject:  Re: Rationale for triangulating braces
If i understood you correctly, you just said you minus-ed 3 grams and no detectable change in tap tone?? why would you expect a change in sound??

my point is if you cannot hear the sound now, i bet when the sound plate is installed it will make a huge amount of diffirant voice charctaristics..

R.
Author:  James Orr [ Mon Aug 02, 2010 1:28 am ]
Post subject:  Re: Rationale for triangulating braces
I wasn't really expecting a change in the tap tone after only removing 3 grams of material, but I was expecting the top to weigh more than 3 grams less. It's just hard to imagine 3 grams being significant, but that's partially why I started the thread.
Author:  Dave Fifield [ Mon Aug 02, 2010 1:39 am ]
Post subject:  Re: Rationale for triangulating braces
The next top I brace, I will weigh before and after doing my parabolic bracing thing and let you know the results - I take off a lot of material....way more than 3 grams IMO.....we shall see!

I definately try for as parabolic a curve as I can get across the length and width of all the braces and tonebars. I know I don't come anywhere close to a true parabola across the width, but it's more parabolic than it is triangular. Length-wise I get closer, but still not a true parablola, for sure. Can anyone come up with a better name for it? Eat Drink

Cheers,
Dave F.
Author:  Alexandru Marian [ Mon Aug 02, 2010 3:06 am ]
Post subject:  Re: Rationale for triangulating braces
My ears are not that great at picking up the difference in taptone made by the shaping progression, however, with Chladni, it is a different story. As I work the bracers, the resonance points drop Hz by Hz, and it is perfectly traceable.
Author:  sonorgeek [ Mon Aug 02, 2010 4:03 am ]
Post subject:  Re: Rationale for triangulating braces
i would venture to say on some level even a fraction of gram would make a change in sound. or at least thats what i think.

R.
Author:  Alexandru Marian [ Mon Aug 02, 2010 4:24 am ]
Post subject:  Re: Rationale for triangulating braces
It absolutely does - if we actually hear it is a different story. I do hear a definite difference between the taptone with rough squarish braces and with shaped braces, but I can't hear the difference at every shaving. It is like watching your kids grow, you don't really notice it :D
Author:  Laurent Brondel [ Mon Aug 02, 2010 5:38 am ]
Post subject:  Re: Rationale for triangulating braces
Bracing is a ridiculous fraction of the top's weight. James is onto something: there probably will be no difference in tone between triangulated braces and braces left square. In theory, they will have equal strength. Triangulated looks better, and yes, saves a tiny bit of weight, but do we know how it affects tone? It is the added strength bracing adds to the the plate that counts. I suspect it can be a bit different for nylon strings as string energy is minimal compared to steels, and the top is usually thinner and much lighter.

What matters is where wood is removed as it affects how the plate will vibrate with string tension. And that is mostly in the amount of height and taper of the braces.
Author:  jfmckenna [ Mon Aug 02, 2010 7:43 am ]
Post subject:  Re: Rationale for triangulating braces
3g's is not a whole lot of weight but it doesn't take much to change the stiffness of the bracing.
Author:  Barry Daniels [ Mon Aug 02, 2010 9:33 am ]
Post subject:  Re: Rationale for triangulating braces
In theory they will not have equal strength. When you remove material the strength goes down, always. If you removed height the strength goes down according to the cube rule. When you remove width the strength goes down in a linear fashion.
Author:  Laurent Brondel [ Mon Aug 02, 2010 10:04 am ]
Post subject:  Re: Rationale for triangulating braces
Barry, by triangulating you're not removing width per se, you're… triangulating. I stand by my statement.
Author:  Stuart Gort [ Mon Aug 02, 2010 11:01 am ]
Post subject:  Re: Rationale for triangulating braces
It's probably bold of me to say anything but I've dealt with vibration and bending loads for a few decades in another field. Barry's statement is spot on as a rule of thumb when applied to bending loads regarding the height and width of beam structures. Read it again and memorize it....for it is a fundamental engineering concept that one applies many ways when building instruments.

Leaving a brace square will have the effect of concentrating the dynamic load (vibration) at the end of the brace. So....as a top vibrates and resonates (two different things) whatever movement occurs at the edge is more concentrated at the edge. Thinking through this one should conclude that triangulating a brace will have the effect of causing the bending of the top, caused by vibration and resonance, to be SPREAD OUT IN A NON LINEAR FASHION along the section of the brace that is triangulated. Without any experience I guess that triangulating braces goes a long ways to eliminate unwanted odd resonant vibrations that could occur with a focused point load. At the very least I imagine that the brace geometry has a fair effect on tone and constitutes a significant aspect of the art of building.

One thing I can say for certain is that a brace that is squared, and therefore concentrates and amplifies a dynamic load at a focused point on the edge of the body, will fatigue that point faster than triangulated braces, if all other structural geometry is the same. So if the main point of building a box is to have it vibrate and resonate across a full bandwidth, it would seem that a homogenous resonate quality must be obtained as a primary goal with lightness as a secondary goal - for volume. If squaring the braces also requires additional material at the edges in order to deal with the additional stress that will be focused there, then it follows that triangulating braces removes stress point loads, which spreads out the stress, and helps both to reduce resonate nodes and allows for a lighter structure.

Experienced builders weigh in. Experience trumps theory...in my experience. :)
Author:  Kent Chasson [ Mon Aug 02, 2010 11:40 am ]
Post subject:  Re: Rationale for triangulating braces
This is an argument that can be solved in 15 minutes in the shop. Make a rectangular brace, load it, measure deflection. Make it triangular, load it, measure deflection.

If stiffness is what you are measuring, you will find a triangular brace is certainly less stiff than a rectangular brace of the same height and width (at the base).

That's with a simple span. In my way of thinking, an X brace also has some torsional load and I'm guessing a triangular brace is even less stiff compared to rectangular under that more complex loading but that's just a guess.

The question I'm more concerned with is, for my target stiffness, what profile has the best strength/weight ratio. From the testing I've done, triangular or inverted "T" is best depending on the height of the brace. Taller braces seem to perform a bit better with an inverted "T" shape. Shorter do a bit better when triangular. Both are easily better than rectangular.

James, if you are only losing 3 grams, you probably aren't taking off enough material. But Laurent is correct that the plate is where the bulk of the weight is and if weight is your main concern, a thinner plate and taller braces is the way to go.
Author:  Jim Watts [ Mon Aug 02, 2010 1:02 pm ]
Post subject:  Re: Rationale for triangulating braces
A triangular shaped brace can be the same stiffness as a rectangular one. it will have to be taller though. See Todd's post. It should weigh a touch less however.
You can make slower changes and remove more weight by shaving the sides of the brace vs. take it off the height, this is the height cubed vs linear thing in play.
Author:  Andy Birko [ Mon Aug 02, 2010 1:06 pm ]
Post subject:  Re: Rationale for triangulating braces
Kent Chasson wrote:
This is an argument that can be solved in 15 minutes in the shop.


This argument has already been solved in engineering texts. On page 147, 148 and 149 of "Left Brain Luthiery", David Hurd explains the differences in strength & weight characteristics between rectangular and triangular braces.

To summarize, for a given rectangular brace of a given material, one must make a triangular brace that is 1.44 times taller to achieve the same stiffness. The resulting brace will weigh ~ 28% less than the rectangular brace. You can calculate this yourself by calculating the second moment of the various cross sections (which he does in the book).

He doesn't speculate on how this may affect tone though.
Author:  WaddyThomson [ Mon Aug 02, 2010 1:40 pm ]
Post subject:  Re: Rationale for triangulating braces
Sheds some light on why Hauser left his fan braces rectangular in the center, under the bridge.
Author:  Howard Klepper [ Mon Aug 02, 2010 1:44 pm ]
Post subject:  Re: Rationale for triangulating braces
Zlurgh wrote:

Leaving a brace square will have the effect of concentrating the dynamic load (vibration) at the end of the brace. So....as a top vibrates and resonates (two different things) whatever movement occurs at the edge is more concentrated at the edge. Thinking through this one should conclude that triangulating a brace will have the effect of causing the bending of the top, caused by vibration and resonance, to be SPREAD OUT IN A NON LINEAR FASHION along the section of the brace that is triangulated. )


I sure can't understand any of this. Why would a square beam concentrate its load at the end, and a triangular one instead spread its load, and why would it do so in a non linear fashion?
Author:  Andy Birko [ Mon Aug 02, 2010 1:49 pm ]
Post subject:  Re: Rationale for triangulating braces
One thing I forgot to add to my summary - the 1.44x and .72x between rectangular and triangular assumes the same "footprint". I.e. if the rectangular brace is 1/4" wide, the triangular brace would be 1.44x higher at 1/4" wide.

As to tonal speculation, I will add this. From a stiffness perspective, the two are the same. Not close, but the same. With less mass for the same stiffness, the frequency of "things" should go up. By things, I mean probably the bigger modes on the top. I don't care to speculate what happens to the smaller modes.

Honestly, I don't understand Stuart's speculation.
Author:  Laurent Brondel [ Mon Aug 02, 2010 2:05 pm ]
Post subject:  Re: Rationale for triangulating braces
I do not have the engineering knowledge to agree or disagree with Stuart or David Hurd's points, and remain sceptical. However, what I know is that for a guitar, triangulating has an absolutely minimal, if any, effect on strength. I should add that I am from the school of using a thicker top than most, and short bracing. That may explain it. Builders from the opposite school (thin tops and tall braces) may have to pay more attention. I do triangulate my braces I should add, although less and less. A lot of makers didn't (don't?) bother to shape the braces and leave them square and rough. Like a lot of pre-war Gibsons.
Author:  Alan Carruth [ Mon Aug 02, 2010 2:10 pm ]
Post subject:  Re: Rationale for triangulating braces
I'm a little confused as to the sense in which you 'triangulated' the braces. Are you talking about a brace that's rectangular in section, but tall in the center and tapered toward the ends, or is it that you took your 'parabolic' tapered braces down from a rectangular section to a triangular one? We're seeing folks discussing both in this thread, and they're _much_ different.

FWIW, snce you only removed three grams with your trimming, I'm assuming you went from a rectangular section to a more or less triangular one. If you tapered the braces in the other sense I think you'd have removed a bit more mass.

If I got that right I'm not surprised you didn't hear much change in the tap tones. As has been pointed out, most people don't hear well enough to detect the couple of Hz alteration in pitch you might reasonably see. You _might_ hear a change in the 'quality' of the sound; say more sustain or a 'clearer' tone, but, again, you might well not.

This is not the same as saying such a change won't effect the tone of the completed guitar. As Dante said in the 'Divine Comedy': "The closer a thing is to perfection, the more it feels of pleasure or of pain"(Chiardi translation). Good guitars, even steel strings, can be quite sensitive to small changes in local brace stiffness. Classicals can be balanced on the head of a pin. I've cleared up a 'wolf' note on a steel string with some minor re-shaping of a tone bar in the right place, and fixed a very uneven sounding classical with eight very small shavings, about 2" long, from the ends of the outer fans.

In the case of the classical, which was one of mine, the problem seems to have been associated with a oddly-shaped 'free' top resonant mode. It was the only thing about that guitar that was 'different', and when I applied the fix that cleared up the odd mode shape on a free plate, the assembled gutiar sounded fine. So there's one example of how the free plate mode shapes could tell you things about the assembled guitar.

In the end, it's as much, or more, about _where_ you remove the material as it is about how much you take off. As Laurent points out, the braces are only a fraction of the total top weight, and they seem mostly to act as 'fine tuners' of the sound. But, of course, the difference between a 'poor' guitar and a 'good' one is precisely in those details. It's probably also true of the difference between 'good' ones and 'great' ones, but we know a lot less about that, darn it.
Author:  Kent Chasson [ Mon Aug 02, 2010 2:28 pm ]
Post subject:  Re: Rationale for triangulating braces
Laurent Brondel wrote:
...However, what I know is that for a guitar, triangulating has an absolutely minimal, if any, effect on strength.....


If by strength, you mean stiffness, that's just not true. Making a rectangular brace triangular in cross-section has a fairly large effect on the stiffness of the brace. Try what I suggested if you don't believe it.
Author:  truckjohn [ Mon Aug 02, 2010 2:38 pm ]
Post subject:  Re: Rationale for triangulating braces
The 1st thing that comes to mind is that either your braces or your top (or both) is still much too thick....

If you carved and carved and carved -- and nothing happened when you Bonk it... you may not really be at the threshold for when things start to "Loosen up a bit".... Still too stiff....

Try taking some material off the "Top" of the triangle a little bit at a time... then see what happens.... You may find you end up with a flat or rounded top triangle shape rather than a pointy one...

Any chance you can post a pic or some dimensions for where you are at?

Thanks

John
Author:  Andy Birko [ Mon Aug 02, 2010 2:42 pm ]
Post subject:  Re: Rationale for triangulating braces
Laurent Brondel wrote:
I do not have the engineering knowledge to agree or disagree with Stuart or David Hurd's points,


Well, I happen to have an engineering degree and can add that David Hurd's points aren't really his, he just did the engineering analysis using standard engineering techniques.

The moment of inertia for standard geometric shapes is very well documented and it's easy to solve for whatever parameter you're interested in between two different shapes. It's a fact that for a given width and height, a rectangular brace will be stiffer but heavier than a triangular one. To get the same stiffness, you must increase the height of the triangular brace by 44% but it will end up 28% lighter.

The effects on tone still evade my grasp but like I said, pitches of things should go up a bit and I would think that output would go up as well. Sustain possibly down a bit. Whether they're detectable and by whom is another thing.
Author:  Stuart Gort [ Mon Aug 02, 2010 3:24 pm ]
Post subject:  Re: Rationale for triangulating braces
:oops: Sometimes a guy just wants to erase a post.

I was thinking in terms of tapering the braces vs. not tapering when I made my comments....not in terms of the extruded shape. Howard's question made me realize we were taliking about two different things.

Sorry...Laurent....you seem WAY smarter now :) and I more foolish...but I'll be dead in thirty years so...

Andy's got it. A triangular brace can be made lighter to produce the same bending strength...which would theoretically make it louder I guess....not by much.
Author:  David Malicky [ Mon Aug 02, 2010 4:08 pm ]
Post subject:  Re: Rationale for triangulating braces
A suggestion for posting -- including terms like "cross-section" or "longitudinal profile" would clarify what we mean when saying "triangular", "tapered", "parabolic", etc.

Here's my attempt to explain the engineering concepts: The string torque puts the X-braces in a state of bending. Bending causes the upper and lower surfaces of the brace to "work" the hardest, while the middle is mostly along for the ride. So, the cross-sectional shape that is the stiffest and strongest--at the least weight--will have a lot of material where it's needed most, and the least material where it's needed least. The I-beam and hollow rectangular tube do this very well, which is why so many structures are built out of them. These shapes are inconvenient for guitar braces (though some builders like Kevin Ryan follow the principles with lightening holes), so we're left with cross-sections like triangles, parabolas, rectangles, etc. Among these, the triangular cross-section is the worst, because it asks a very small amount of material (the tip) to carry the highest stress. The tall rectangle is the best of these, because it has the most material where it's most needed.

Here's an illustration that may help: suppose a single wood fiber at the tip of the triangular cross-section were unusually weak and broke, or was damaged somehow. That brace would then be effectively shortened in height at that location. And by the cube rule, we know that brace would also be disproportionately less stiff (and strong). Conversely, if a single wood fiber at the top of a rectangular cross-section broke, that cross-section would be insignificantly less stiff (and strong) because there are a bunch of other wood fibers right next to it at the same height.

It's true that a triangular cross-section can be made stiffer than a rectangular c-s by increasing its height. But if a rectangular c-s had that taller height, and then was trimmed in width until its weight was the same as the triangular c-s, that tall rectangular c-s would have more strength and stiffness than any of them.
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