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Just to confuse things a little further with some engineering terms... The stiffness of a beam is directly proportional to it's Moment of Inertia, or I value.

For a rectangular beam:
b = base width
h = height

and then I = (1/12) x b x h^3, or one twelfth times the base times the cube of the height.

So any change in base width is directly proportional to the increase in stiffness. If you take the b x 2, the stiffness is doubled. Or if you take the b x 3, the stiffness is tripled.

But any change in height is not directly proportional, it's cubed. So if you take the h x 2, the stiffness is multiplied x 8. Or if you take the h x 3, the stiffness is multiplied by 27!

Hope that helps, for some it may help to see the actual formula.

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Jonathan Kendall, Siloam Springs AR

11+ years of instrument making, and I have yet to measure the deflection of  a top... with anything more accurate than my hands. Flex, and bounce it back and forth a few times, and it will tell you pretty well everything you need to know. The forst dozen or so will all be flukes, but keep notes while building, and then go bac to them once the instrument is completed, and compare the real results with what you thought you felt...

Back on subject, perhaps a simpler way to view Jon's point is that we can use multiplication to find the added stiffness we need.

Let's use an everyday example and everyday language:

For example, how much mass was saved and stiffness was lost by trimming a 5/8" tall brace from 5/16" to 1/4" in width? And then, how much should you add to the height to get that stiffness back again, and what did that cost in mass? Well, we took 20% off the width, and lost 20% of its stiffness. If we wish to keep the same stiffness(say, we knew it was just "right" already), we need to add 5% to the height, in this case, 1/32", and only gained 5% of the mass. (If we'd taken 25% of the width out, we'd add 6.25% to the height, etc, etc, etc....)  But that's not all of it, that 20% you trimmed off the width is 5/8" x 1/16" x the length, while the 5% you added is 1/4" x 1/32" x the length. The mass savings is relatively huge, yes? Cool!

Now, look at a guitar top as a brace. And do the math again. Don;'t think of a .115" thick top as being .010" thinner than a .125" top. Instead, think of the difference as a percentage(which is how you should consider EVERYTHING you do). So, the .115" top is 8% thinner than the .125" top.

 8% of its -height-.

Think of the top as a wide, and low, brace. Do the math, and see what that 8% saved in mass, VS what you lost in stiffness.

Jim, check my math when you get a chance. I'm on my first cup of coffee(late night in the shop), and it's been a long time since I had to do this stuff with actual numbers <g>

[QUOTE=letseatpaste] Just to confuse things a little further with some engineering terms... The stiffness of a beam is directly proportional to it's Moment of Inertia, or I value.

For a rectangular beam:
b = base width
h = height

and then I = (1/12) x b x h^3, or one twelfth times the base times the cube of the height.

So any change in base width is directly proportional to the increase in stiffness. If you take the b x 2, the stiffness is doubled. Or if you take the b x 3, the stiffness is tripled.

But any change in height is not directly proportional, it's cubed. So if you take the h x 2, the stiffness is multiplied x 8. Or if you take the h x 3, the stiffness is multiplied by 27!

Hope that helps, for some it may help to see the actual formula.[/QUOTE]


And how does that forumula change as you remove material out of the sides of the brace?

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Brock Poling
Columbus, Ohio
http://www.polingguitars.com

Brock, math works the same, coming or going. In other words, if doubling the width doubles the stiffness, halving it halves the stiffness, also.

Think of it in percentages(like I tried to convey above) instead of fractions.

[QUOTE=grumpy] 11+ years of instrument making, and I have yet to measure the deflection of  a top... with anything more accurate than my hands. Flex, and bounce it back and forth a few times, and it will tell you pretty well everything you need to know......... [/QUOTE]
It probably won't surprise you to learn that the hand can be very sensitive in sensing stiffness. You have in fact been accurately measuring stiffness with your hand. Well, not exactly measuring stiffness, but, sensing it.
Are you discounting the value of measuring it and keeping track or this value for future reference? It seems to me that you are.

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"An adventure is only an inconvenience rightly considered. An inconvenience is an adventure wrongly considered." G. K. Chesterton.

Right, the formula stays the same, like Mario said. You're just changing your variables. It works the same whether you're increasing or decreasing dimensions.

If you cut your base width in half, you get half the stiffness. But if you half your height, you get 1/8 (or 1/2 cubed) the stiffness.

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Jonathan Kendall, Siloam Springs AR

[QUOTE=grumpy] Brock, math works the same, coming or going. In other words, if doubling the width doubles the stiffness, halving it halves the stiffness, also.Think of it in percentages(like I tried to convey above) instead of fractions.[/QUOTE]

Yes, your description was very clear. In fact I picked up a couple ideas from the way you described it.

I guess my comment/question was asking about his qualifier that the math was for a rectangular brace. I wondered if there was more too it for a non standard shape. (removing material out of the sides, etc.)

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Brock Poling
Columbus, Ohio
http://www.polingguitars.com

The math gets a lot more complicated when you get away from a rectangular shape, but the general principal that changes in height will affect stiffness more than a similar change in width... or that a taller brace has a higher strength-to-weight ratio than a wider brace of the same cross-sectional area.

At work, I just use Autocad to work out the I-value on non-rectangular stuff, since most of the shapes I work on are extruded aluminum window frames. Part of my job is making sure the window frame won't deflect enough on a windy day to break the glass or pull apart the sealant around the edges.

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Jonathan Kendall, Siloam Springs AR

[QUOTE=Brock Poling]
And how does that formula change as you remove material out of the sides of the brace?
[/QUOTE] The formula is rather simple, but it applies to rectangular sections. It does not deal with the fact that the brace is glue to a top. Last time I checked, no one here uses rectangular braces.
Braces are often rounded at the top and somewhat triangular. Material that is away from the soundboard adds the most stiffness. Material right next to the soundboard adds the least stiffness.
Be smart about how you shape your braces.
The ideal shape would be skinny in the middle and wide at the top and bottom. Wide at the bottom for good bonding and wide at the top so that more material is farther away from the soundboard, imparting the most stiffness for the least amount of weight.

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"An adventure is only an inconvenience rightly considered. An inconvenience is an adventure wrongly considered." G. K. Chesterton.

This is really just the beginning of the path in terms of a soundboard stiffness analysis. The real challenge is in analyzing the stiffness of the whole assembly, as it exists in the guitar. The stiffness of irregularly shaped objects that are constrained all along their edge is not a trivial thing to analyze. Computer simulations can make this a LOT easier...but even those should be taken with a grain of salt baselined with some actual testing.

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http://www.PeakeGuitars.com

Are you discounting the value of measuring it and keeping track or
this value for future reference? It seems to me that you are.

Almost. I am offering another view, another method of measuring. I flexed and bounced tops and kept notes for years. Instead of numbers, I wrote and described, to myself, what I felt. Try writing a description of something you felt, today. Anything. Grab a brace, and describe how it feels, sounds, looks, everything, in writing. You'll be surprised at how much you learned from having to write it down, because it forces you to "pull out" what your mind was storing while you handled the piece. It's an education in itself. Reading and recording the number(s) given out by a jig tells you very little, in comparison.

Yes, things get complicated quickly when triangulation enters the equation, so I left that out, and based everything on rectangular members, for clarity. Still, all the principles apply.

we need an emoticon that's all ears.

I'm enjoying all the great comments. You can bet I'm going to be flexing more tops and braces in the future.

I did enjoy the thread about what the cube rule is and does, thanks!

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http://www.dickeyguitars.com

Ya'll get a thumbs up from me. Cube rules!!

[QUOTE=SteveS]The ideal shape would be skinny in the middle and wide at the top and bottom. Wide at the bottom for good bonding and wide at the top so that more material is farther away from the soundboard, imparting the most stiffness for the least amount of weight.[/QUOTE]

This is spot on; what Steve is describing is an I-beam, which in theory has all the stiffness of a rectangular member of equal height and width but only a fraction of the mass.

[QUOTE=lex_luthier] [QUOTE=SteveS]The ideal shape would be skinny in the middle and wide at the top and bottom. Wide at the bottom for good bonding and wide at the top so that more material is farther away from the soundboard, imparting the most stiffness for the least amount of weight.[/QUOTE]

This is spot on; what Steve is describing is an I-beam, which in theory has all the stiffness of a rectangular member of equal height and width but only a fraction of the mass. [/QUOTE]

Nope. An I-beam would have a higher stiffness/weight ratio than a rectanglur shape with the same dimension, but would not be as stiff overall.

An I-beam is also not the ideal shape, though it's an efficient one for construction where you need to fit it within a constrained space and you need to attach things to it at right angles.

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Jonathan Kendall, Siloam Springs AR

[QUOTE=jtkirby]

Therein lies my pet peeve as an engineer - why can't we standardize a deflection test so that Andy's numbers (or anyone else's) actually mean something to someone else?
[/QUOTE]

I haven't started collecting deflection data yet, so I have a selfish suggestion:
If Andy (or somebody else) were to post details of his measuring setup, we could start to use the same method for measurement. Whether we chose to publish our results could be our own decision, but at least there'd be the option of meaningful data exchange when we wanted it.

Anybody?

Cheers
John

[QUOTE=letseatpaste]

Nope. An I-beam would have a higher stiffness/weight ratio than a rectangular shape with the same dimension, but would not be as stiff overall.

An I-beam is also not the ideal shape, though it's an efficient one for construction where you need to fit it within a constrained space and you need to attach things to it at right angles.[/QUOTE]

You are right about the higher stiffness to weight ratio. If you carry the thought out a bit you can see that for the same weight, the stiffness is dramatically increased. Make the brace a little taller, thin out the middle.....

Of course you have to fit the model into practical terms. I wasn't suggesting that anyone switch to an I-beam, I'm sorry if anyone thought that. I was trying to help people understand that when they carve braces that making the top of the brace narrow isn't the best thing to do, you'd be better off making the middle narrow like an I-beam and leaving more thickness at the top. I don't know anyone who does that, but I have thought about doing it. You would have great strength to weight ratio.
'The other part of the equation is how much stiffness do you want. I know I want it fairly loose so that I can get good monopole response. So while I could make it very stiff, I choose not to. I choose to make the stiffness I need as light as possible so that I get good attack.

YMMV

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"An adventure is only an inconvenience rightly considered. An inconvenience is an adventure wrongly considered." G. K. Chesterton.

[QUOTE=SteveS]
I was trying to help people understand that when they carve braces that making the top of the brace narrow isn't the best thing to do, you'd be better off making the middle narrow like an I-beam and leaving more thickness at the top. I don't know anyone who does that, but I have thought about doing it. You would have great strength to weight ratio.
[/QUOTE]
Rather than making the top of the brace thicker, wouldn't you be further ahead (on the stiffness/weight scale) by just making your brace a bit taller if necessary, and keeping it thin at the top?
I thought the 'plates' at the top and bottom of I-beams had to do with resisting twisting-type failures, as well as providing a place for attachments.
Obviously, I'm no engineer, and there are lots around here, so the corrections should come flooding in!

Cheers
John

[QUOTE=JohnAbercrombie] [QUOTE=jtkirby]

Therein lies my pet peeve as an engineer - why can't we standardize a deflection test so that Andy's numbers (or anyone else's) actually mean something to someone else?
[/QUOTE]

I haven't started collecting deflection data yet, so I have a selfish suggestion:
If Andy (or somebody else) were to post details of his measuring setup, we could start to use the same method for measurement. Whether we chose to publish our results could be our own decision, but at least there'd be the option of meaningful data exchange when we wanted it.

Anybody?

Cheers
John
[/QUOTE]

Brian Burns provides a description of a setup at his web site. That would work - it's just a matter of a group larger than 1 saying "this is the setup used". And at the least his is described and available.

JK

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Jim Kirby
kirby@udel.edu

[QUOTE=grumpy] Sigh.... In the above example, a 1/4" wide by 1/2" tall brace will be 8 times stiffer(twice cubed, or 2x2x2) than a 1/4'' by 1/4" brace, but a 1/2" wide  by 1/4" tall is only twice as stiff as the 1/4 x 1/4.[/QUOTE]

In the direction of the tall dimension....couldn't resist

[QUOTE=JohnAbercrombie] [QUOTE=SteveS]
I was trying to help people understand that when they carve braces that making the top of the brace narrow isn't the best thing to do, you'd be better off making the middle narrow like an I-beam and leaving more thickness at the top. I don't know anyone who does that, but I have thought about doing it. You would have great strength to weight ratio.
[/QUOTE]
Rather than making the top of the brace thicker, wouldn't you be further ahead (on the stiffness/weight scale) by just making your brace a bit taller if necessary, and keeping it thin at the top?
I thought the 'plates' at the top and bottom of I-beams had to do with resisting twisting-type failures, as well as providing a place for attachments.
Obviously, I'm no engineer, and there are lots around here, so the corrections should come flooding in!

Cheers
John
[/QUOTE]

Right, tall skinny braces are still the king in this particular realm.

We've isolated one specific part of a system and looked at one specific aspect of that part. In reality the engineering of a guitar top is crazy-complicated (that's the technical term for it)... Twisting forces, rotational, compression, etc... And it's all built with an organic material that may exhibit different properties on each end of the same stick. It's helpful to isolate single parts, but it certainly doesn't tell the whole story.

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Jonathan Kendall, Siloam Springs AR

John there are ton of ways to do deflection testing.
I do it with 2 wooden rods placed a fixed distance apart and use a 5# weight that I stole from my wife... Luckily she doesn't read my posts!!!!   I don't know the distance off hand, I would have to go measure it. I use a dial indicator attached to an adjustable arm.
I zero the indicator, add the weight and see the change.
Thin the wood, measure again. I also keep track of weight so that I can keep track of density etc. I give me another means of comparison of different woods.
When you use deflection, the wood had to be the same width if you are going to compare longitudinal deflections.

I only had 1 pict on my computer so I will post it.

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Andy Z.
http://www.lazydogguitars.com

This discussion often leads to theorizing about what the single most weight efficient brace shape is.  I beams, drilling holes in the web, etc.

Seems to me that you quickly reach of point of a lot of extra work for very diminished returns.

A brace with a cross section somewhere between a truncated triangle and and inverted T has a great stiffness/weight ratio and good resistance to torsional loading.  It's easy to make and easy to adjust/shave/voice before or after assembly, and it doesn't create any stress risers that might be a place for a split to start.

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http://www.chassonguitars.com

[QUOTE=JohnAbercrombie] Rather than making the top of the brace thicker, wouldn't you be further ahead (on the stiffness/weight scale) by just making your brace a bit taller if necessary, and keeping it thin at the top?
[/QUOTE] Yes. We do like to have a nice wide base to make that glue joint reliable, so we start with something pretty wide. You are absolutely right that taller is better than wider.


[QUOTE=JohnAbercrombie] I thought the 'plates' at the top and bottom of I-beams had to do with resisting twisting-type failures, as well as providing a place for attachments.
[/QUOTE] No. They do resist twisting for the same reason that they wave a high strength to weight ratio - it is all about putting the most material away from the center line. A tube is the most efficient structure for strength and stiffness because it has no material at the center line. It is very hard to attach things to tubes.
I doubt a tube would make a good guitar brace.

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"An adventure is only an inconvenience rightly considered. An inconvenience is an adventure wrongly considered." G. K. Chesterton.

Interesting topic! When I actually get around to some more serious building I will test for and keep records of the deflection. I don’t have the craftsman touch so I will need to have some firm details so that I can repeat successes and avoid failures.

David Hurd (left-brain lutherie) has some good information on his site if you look around. He also shows a simple too for testing deflection. David has told me that the best thing I can do is to measure and document all my work so that I can repeat quality work.

One thing that David Hurd has said that I will always remember is:
It's a reasonable question to ask "Why measure wood properties when so many builders don't and still make good instruments?" For me the answer is two-fold: first, I feel that these builders actually do make such measurements, but choose to do so using their own senses rather than measuring devices such as micrometers and balances and such. They've developed their own internal databases to refer to and function well within that environment. No one makes a great instrument time and again without some sort of reference knowledge. Second, some of us are more comfortable putting actual numbers down so that we can refer to them later when we see how an instrument turns out well. Such numbers are also useful when we want to compare our measurements with work done by others.

I love how this leaves room for hands on builder and for the testing builder.
Ukuleles by Kawika

Here is a link to David Hurd’s site and a link to his homemade deflection tester.
Deflection tester

Philip

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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.