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Well, I've been thinking about testing some bracing shapes for awhile and finally got around to it this weekend. I wanted to test four different profiles. My wife has the digital camera out of town right now, so here is a pic from David Schramm's website:



The four I tested were the square shape, triangular shape, the T-brace, and a standard rounded over brace not pictured here. I cut and shaped 11 braces from the same piece of spruce stock. I used a simple deflection test of every brace to gather my data and measured results in 1/10th mm increments. I was really expecting the T-brace to be the strongest based on info from John Gilbert on the Schramm website. Once I had all the data, I used the SAS statistical analysis program and ran a one-way ANOVA to look for differences between the groups. I know this data is probably a bunch of gobbly-goop to most, but I'm including the data for those interested because I know there are more than a few here familiar with the stats listed.



So what are the results in plain English--read on:
The T-brace and triangular brace were both statistically significant as far as being different from the others. The Triangular brace showed significantly more deflection than the other three. The T-brace showed significantly more deflection than the other two (round/square). There was no significant difference between the rounded and square brace. What does significant mean? In this case, according to the p-value listed in the ANOVA, these results would only occur by chance in less than 1 in 10,000 tries. I computed the actual p-value and to be more precise, these results would occur by chance in 1 and 1 (with 22 zeros after it) times. While testing, I should note that I broke 3 of the triangular shaped braces during deflection, so I had to test 14 to actually get a sample size of 11. This test confirms the fact that the rounded over braces many of us use seem to be the best for strength. While the rounded brace was not significantly different from the square, it was significantly lighter, lending credence to that as being the best profile to use out of the braces I tested. I plan on trying to duplicate this test using cedar bracewood, as well as another group of spruce with a much larger sample size (from many different pieces of brace stock). This was just a quick, down and dirty test to see if there would be significant differences, and there were.   

Cheers!

John

Good on ya! Great idea...please keep us informed as you continue this experiment. I'd love to see you compare different species besides sitka and cedar, like maybe Red Spruce and Redwood as well. That would be interesting...

_________________
"I want to know what kind of pickups Vince Gill uses in his Tele, because if I had those, as good of a player as I am, I'm sure I could make it sound like that.
Only badly."

Good work John, thanks for passing that on. I for one am looking forward to seeing what your results are when you duplicate.

Cheers

Kim

Your results are interesting.    You said your expectations were that the T shape would be stronger that it tested. Maybe it depends on the height of the base (top of the T). It could be that an I-beam shape would be stronger. The I-beam shape could even be drilled out for a lower weight. Thanks for the information.

Philip

_________________
aka konacat

If you think my playing is bad you should hear me sing!
Practice breeds confidence and confidence breeds competence. Unfortunately, I'm stuck in practice.

Weigh the braces, too; otherwise, this is all moot.

What we need is a strength to weight ratio, not just strength. If strenth was all that counted, we'd all be using 2x4's under the tops...

I would add to what Mario said and say the glue surface width should also be constant.

Yup, what Keith added, also. The glue surface ties it solidly to the substrate(the top), creating one where there were two, therfor, the glue surface area is vitally important.

In case some are wondering why I asked for weights...

A triangular shape is exactly half as heavy as the same width and height of a rectangular member. But, the strength will not be half, it will be much more than half, therefor, it has a much higher strength to weight ratio. The I beam should be even higher, yet.

This testing is being well done and controlled, but strength to weight ratios of various shaped members is readily availble in any engineering book.

John, good on you. However, I agree whith these guys in that you need to adjust for mass.

Two ways to do this, either change your response variable to the ratio of deflection to mass (defl/mass) or include the mass of each brace as a covariate in your analysis.   This way the sums of squares attributable to variation in mass will be removed from experimental error and the F-test for brace shape will be correct.

Instead of F-tests and P-values, consider reporting means of the response for each brace type with its 95% confidence interval; where those intervals overlap amon brace types, you can conclude no difference is the response (at alpha = 0.05). If the intervals don't overlap each other, you can conclude they differ at the same alpha.

Yeah, I teach a stats class.

Bob Steidl38801.5652199074

I did do as you both mentioned above. The glue surface width was the exact same on every piece, and I did weigh all the braces. The braces weighed the following in grams, averaged:

T-brace - 7.5
trianglular - 5.3
rounded - 7.2
square - 9.0

Mario -- you gotta take everything a step at a time. You can't just plug everything in a single equation to get the answer--you could, but you'd give up a bunch of variance and increase your odds of type I and II errors (showing sig. results when there aren't any, or not showing sig. results when there are some). This was just the first step I posted for those interested. There's plenty more to be done.   

Bob - That's a good idea about reporting confidence intervals. I didn't think of that. There's all kinds of good things you can do with the data.

John Elshaw38801.5793981481

Good work so far! I would have to agree with Mario and Keith on this one as well. The strength to weight ratio is going to be the most important factor. Once that is found, the next test would be what is the smallest size that brace can be in a particular brace pattern to maintain structural integrity of the given instrument. Of course this has been the goal of all builders, but there are so many factors in this equation that finding an absolute scientific answer to one particular brace style/wood/size/pattern would take years and years. Not to mention money. One thing I would find interesting is if you planed down some thin braces and laminated them. Could 3 to 5 layers of laminated spruce produce a stronger brace?

Your triangular isn't a true triangular shape; if it was it would be exactly half the weight of the rectangle....

Gotta be anal if you wanna trust the results <g>

You can, and should, gather all this info at the same time. Each brace should be weighed, then measured for deflection, at the same time. Then it's math, and the answer.

I'm sure it's a fun way to spend a Saturday afternoon....Mario38801.6076388889

[QUOTE=Bob Steidl] John, good on you. However, I agree whith these guys in that you need to adjust for mass.
Two ways to do this, either change your response variable to the ratio of deflection to mass (defl/mass) or include the mass of each brace as a covariate in your analysis.   This way the sums of squares attributable to variation in mass will be removed from experimental error and the F-test for brace shape will be correct.
Instead of F-tests and P-values, consider reporting means of the response for each brace type with its 95% confidence interval; where those intervals overlap amon brace types, you can conclude no difference is the response (at alpha = 0.05). If the intervals don't overlap each other, you can conclude they differ at the same alpha.
Yeah, I teach a stats class.
[/QUOTE]


Huh?
Bob, there you go speaking Greek on me again....

_________________
"I want to know what kind of pickups Vince Gill uses in his Tele, because if I had those, as good of a player as I am, I'm sure I could make it sound like that.
Only badly."

Perhaps a better way to test the shapes would be to use the same piece of wood in each test, reshaping iteach time. With the shapes your using it looks like that might be possible.

_________________
Tickle your guitar daily, and it'll tickle you back.

[QUOTE=Mario] Your triangular isn't a true triangular shape; if it was it would be exactly half the weight of the rectangle....

Gotta be anal if you wanna trust the results <g>

[/QUOTE]

The triangular shape is the 2nd one from the right in the pic. It's the one with the flat top, not a true triangle. Also, I am very accurate with my measurements and did take them all at the same time. I just didn't run all the stats analysis yet. Programming the code in SAS isn't nearly as fun as making sawdust!   

I am personally a big fan of t-bracing. The primary reason being that I
can select absolutely perfect and extremely strong pieces for the center
section. It is certainly more work to have to laminate the three pieces
together to make the braces but I think from an intuitive standpoint -
that you can eliminate a lot more mass with little loss in strength. Sure a
rectangular brace will be the strongest but I have found the "T" profile to
be plenty strong and it is very light.

One of the positives to T-bracing is that you can be very selective with
how you make the braces. I look for flawlessly quartersawn and very stiff
pieces - if you don't pay significant attention to the material - I think you
won't be using this type of bracing to its fullest potential.

For my guitars, I am trying to build a very light but strong bracing system
- in this regard, I think the "T-bracing" is a very viable option.

It's great to see real testing results - sometimes tradition can drive designs, even when the reasons for the traditional solutions don't exist anymore. Testing can uncover that kind of situation, and lead to improved designs.


A word about stiffness vs strength:

By measuring deflection, John is measuring the stiffness of these beams, not the strength. Stiffness is defined as load divided by deflection, so it would be easy to calculate the stiffnesses of these beams using his test data.

Strength is a different beast, entirely. Strength is a measure of how much load each beam can support before it fails. We could further define "fails" as being either total fracture, or failing to return to it's original shape when the load is removed.

It seems to me that, to evaluate them for use as guitar bracing, there are three important properties for each shape of brace : stiffness, strength, and weight.

Now, the REALLY tricky part is understanding what value for each of these is best in a guitar. I think everyone would agree that more strength is always better, and most would agree that less weight is generally better, right? But, there is probably a "best" stiffness, that, like Mama Bear, is just right. And, it probably depends on the style of music you want to play and the sound you are looking for.


Back to the tests:

The stiffness of the beams, by themselves, can be reliably predicted using strength of materials, if you assume that all the material (each fiber in each beam) behaves the same way. And, if you assume that the shear effects are small; this is generally true for what engineers call "slender" beams - maybe 10 time (or more) longer than their height. This means that the "sliding" of the fibers relative to one another is not important, and that the major effect is compression and stretching of the material at the top and bottom of the beam as it's loaded.

In that case, if you hold the maximum height and width the same for all of the beam types, the rectangular section will be the stiffest. (pretty obvious, since all the other sections fit within it's outline, and, consist of the rectangle with some material removed). The traditional rounded-top section will be less stiff than the rectangle, and also, less efficient, in terms of stiffness per weight, than the rectangle.

I know that John's testing hasn't shown that - I don't understand why that is. It would help to know the actual dimensions of each shape.


The most efficient shape in terms of stiffness vs weight (for a beam alone) is an I-beam. That's why I-beams are used so often in structures.

Another way to increase stiffness is just to increase beam height. A tall, thin beam will be much stiffer (and, stronger, also) But, there might be other problems. If it's too tall and thin, it may buckle under load, or be too fragile to direct loads on the side of the beam. Also, since it would be stiffer, it would be more vulnerable to impact loads. And, for a guitar brace, the glue surface might become too small. ( It's possible that the current typical brace height is a carry-over from the time when glues were not as good.)



But, what's really important in a guitar (as someone posted) is how the beam/plate combination - whether the plate is the top or back - acts. Understanding the brace by itself is the logical starting place.

When you couple these beams to a plate (top or back of a guitar, for example) it gets a lot more complicated.
The beam and plate act together - you get much more stiffness from the combination than from either part by itself. Now, to get the most stiffness per weight (at least theoretically) you want the beam to be a "T" shape, with the top of the "T" away from the plate. Now, you have something that looks a bit like an I-beam with the plate acting as the bottom of the I-beam. And, the stiffness ( and strength) of the glue joint becomes important.



Enough of my babbling -

Phil

Great post Phil--I take it you are some type of engineer? I will use the info you provided and incorporate it into a structural equation model I'm working on. I'm thinking I'll use the three main factors you listed (stiffness, weight, strength) plus a few other I'm mulling over and try and link it to total top strength/stiffness, etc. I think the bottom line everybody would be interested in is how does each brace affect the finished soundboard. I'll have to do develop a way to test the brace once it's glued to the sound board (or a dummy board for testing). If any of you guys come up with any other critical variables, let me know.   

John

    There are alot of benifits to this study. Math is one subject I allways enjoyed and to see the numbers is nice.
     Strength to weight ratios and if I may ad strength to shape will also be something I will be very intrigued.
      The one input that I would like to see is while unglued braces are one thing but the synergy once glued to the top and the pattern relationship would be something to see if this is also an influence.
Thanks for all your work I appritiate your time and study
john hall

If you're not familiar with Young's Modulus, you will be!

MOE

There is a pretty good literature on working with structural plates. The most relevent to what we do is David Hurd's book. If you're serious about this, that would be a good place to start.

Have fun!

First: what Phil said about the T brace. When you glue it to the top it becomes more of an I beam, and it's what it does on the top that counts.

Second: weight is certainly a big factor here, but there are other considerations as well. Two in particular that interest me are how 'tunable' the brace is, and how much work it is to use it.

If you look at a normal guitar top, the actual plate itself might weigh anywhere from 120-150 grams. The bracing is usually something like 20-30 grams, and that includes the 'structural' stuff, like the shoulder brace, that has little effect on the tone IMO. The bridge will normally be another 20-30 grams: as much as all of the bracing put together.

Most of the 'radical' new designs, such as the Smallman lattice and the 'sandwich' tops work by cutting plate weight. They have a thin membrane, or two, often .030" thick or thereabouts, with closely spaced bracing. Indeed, the 'sandwich' top can be looked at as an extended "I" beam. This can cut the overall top weight by 40% or so, and when you're working with as little horsepower as we've got, that's a biggie.

There's problem with these things in the 'tunability' area: you can't. They pretty much either work or they don't. Smallman adds weights to fine tune certain resonances, and, if that doesn't make it, cuts the top off and starts over. Both of these 'radical' designs are also more work to make.

The 'standard' brace sections do allow for a lot of tunability, and they are quite easy to make. In terms of overall top weight they are not so far from optimum: I'd be pretty surprised if you could shave more than 10 grams off a top by using the most effective of these shapes. Also, the "T" section, which is likely to be the most efficient when used properly, is also more work to make and not very 'tunable'. Given the normal variation in wood properties, and the difficulties of predicting exactly what brace sizes will be needed to yeild the best tone, I'm loath to give up the chance to fine tune my bracing.

I'm coming across as a lot more negative than I want to. I'm _really_ happy to see people doing experiments and getting real data, and certainly do not want to discourage that. It's just that brace weight per se is less of a problem , IMO, than the way the bracing works with the top. Shaving a few grams off the braces in a way that ties your hands in the pursuit of better tone is a poor bargain, I think.

One last observation: lutes use tall, narrow braces. They are generally about five times as tall as they are wide, and I take this as being the upper limit of practical glue joint strength. There has to be some reason why guitar designs generally don't go to such extreme proportions. Maybe we beat on them harder?

Lute braces are also frequently cut on the slab. I have done deflection tests on braces cut both ways, quartered and slabbed, and generally the slab cut braces were stiffer. This flew so diametrically in the face of accepted wisdom that i have decided not to trust those results...yet. I plan to do a better job of testing and try that variable again.

They can be stiffer when flat sawn; this is old knowledge, but they'll split many times more easily in they're taper(where the taper to meet the body, in the scallops, etc...) and split further. Not good...

There's a reason for everything...Mario38801.9193287037

[QUOTE=Don Williams] [QUOTE=Bob Steidl] John, good on you. However, I agree whith these guys in that you need to adjust for mass.
Two ways to do this, either change your response variable to the ratio of deflection to mass (defl/mass) or include the mass of each brace as a covariate in your analysis.   This way the sums of squares attributable to variation in mass will be removed from experimental error and the F-test for brace shape will be correct.
Instead of F-tests and P-values, consider reporting means of the response for each brace type with its 95% confidence interval; where those intervals overlap amon brace types, you can conclude no difference is the response (at alpha = 0.05). If the intervals don't overlap each other, you can conclude they differ at the same alpha.
Yeah, I teach a stats class.
[/QUOTE]


Huh?
Bob, there you go speaking Greek on me again....


[/QUOTE]

Don, i think that speaking french is a breeze compared to their alpha, beta, omega and gamma. All i know is when i see tonewood, i get some saliva!

I use coved sided "X" braces...that peanut shape mentioned earlier.   It gives the "I" beam effect.   I measured several shapes cut from the same billet of spruce, and the I beams cut weight about 15% over rectangular stock yet only lost about 5% in stiffness in deflection tests.   I therefore assume about a 10% increase in stiffness to weight.

I top my rectangular back braces and the center seam reinforcement with .020" CF (graphite), and there is an enormous increase in stiffness to weight gain there.   On "Miss Antarctica", the guitar Henry Kaiser took to the cold continent, I was able to stand on the back of the guitar before gluing on the top, and that was without the graphite on the center seam.   For that feature, I bridge the back braces over the continuous center seam reinforcement so the graphite goes continuously from neck block to tail block.   You'd be amazed at how just that one strip holds the doming of the back when you pop it out of the go bar deck.

This assumes, of course, that your goal is to make a very strong and stiff back. I do because I believe it helps the guitars project well.   And they do.

Rick, how is it possible for you to take wood off the rectangular brace stock and it weigh more?