Flexural rigidity & Co

You can ask questions here about Trevor and Gerard's exciting new book on Luthiery.

Moderators: kiwigeo, Jeremy D

Post Reply
JurgenV
Myrtle
Posts: 74
Joined: Mon Dec 10, 2018 6:58 am
Location: Bavaria, Germany

Flexural rigidity & Co

Post by JurgenV » Tue Jun 25, 2019 5:34 am

Hi.
I´ve got a question concerning flexural rigidity for falcate steel strings and classical. But first quite a long text to show that I most probably managed to get my spreadsheets working
After a quite long break due to my job I continued work through the Book to start with the excel sheets for target thickness of the soundboard and the flexural rigidity of the soundboard including braces. First the calculation of the predicted final thickness:
Example 2 from Table 4.5-3 reproduced
steel string thickness.png
So far so good, now to the brace section:
Example 1 from Table 4.4-2 (brace stress…) to test my excel sheet with known values:
EI example 1.jpg
Works as well.

Ok now I can start with my questions:
1. When entering the values for a falcate steel string taken from the plans I have an effective soundboard width of 345mm in 50mm distance to the bridge (btw. I assume I start measuring in front of the bridge and not at the position of the saddle), the cross section in this case shows 4 braces with 7mm height and a base of 5mm. This gives me an EI of 47.8Nm^2 if I take for the soundboard and the braces the Engelmann spruce from the example above. Which means I would be exactly where I should be for a falcate steel string but without carbon fibres. Somewhere in the forum Trevor wrote one should never go below 7mm for the falcate braces of a steel string. But if I add the carbon fibre EI will increase again. So how should I reach the goal of around 50Nm^2? Or where did I go wrong?
steeltring test.JPG
2. To build a classical with falcate bracing I change the vibrational stiffness parameter in Equ. 4.5-7 to 60 which gives me a target thickness of 2.15mm. Let´s say I keep the dimensions of the steel string and put the numbers into my spreadsheet for EI. The result is 40Nm^2 for unchanged braces. To get to 15 I need to change the braces somehow. I decided to change the height and used the built in optimizer of excel . This give me a height of 4.1mm (again without carbon fibre). Is it possible to calculate this way?
classical test.JPG
3. Concerning the typical modulus of rupture used in table 4.4-2: these are values determined by experiment? How to measure that?

Sorry for the quite long text but any comments to my questions are appreciated

Jürgen

User avatar
Trevor Gore
Blackwood
Posts: 1605
Joined: Mon Jun 20, 2011 8:11 pm

Re: Flexural rigidity & Co

Post by Trevor Gore » Mon Jul 01, 2019 9:32 am

JurgenV wrote:
Tue Jun 25, 2019 5:34 am
1. When entering the values for a falcate steel string taken from the plans I have an effective soundboard width of 345mm in 50mm distance to the bridge (btw. I assume I start measuring in front of the bridge and not at the position of the saddle), the cross section in this case shows 4 braces with 7mm height and a base of 5mm. This gives me an EI of 47.8Nm^2 if I take for the soundboard and the braces the Engelmann spruce from the example above. Which means I would be exactly where I should be for a falcate steel string but without carbon fibres. Somewhere in the forum Trevor wrote one should never go below 7mm for the falcate braces of a steel string. But if I add the carbon fibre EI will increase again. So how should I reach the goal of around 50Nm^2? Or where did I go wrong?
I don't recall saying don't go below 7mm (I may have, but there are few absolutes in guitar building!). If you check out Table 4.4-1 you'll see that adding CF to a 7 x 5mm brace gives you about 25% increase in flexural rigidity (EI) of that brace. If you punch the numbers into a spreadsheet for the whole braced top assembly (using the full parallel axis theorem), that's not going to give you a 25% increase in flexural rigidity for the whole assembly; it will be quite a bit less than that. I haven't done the calc, but if your answer comes out 5-10% stiffer overall, you'll be in the ball park. To make a 25% reduction in just the brace stiffness with CF, you will only need about a 0.5mm reduction in brace height. The primary purpose of the CF is to guard against cold creep rather than add stiffness for less mass.
JurgenV wrote:
Tue Jun 25, 2019 5:34 am
2. To build a classical with falcate bracing I change the vibrational stiffness parameter in Equ. 4.5-7 to 60 which gives me a target thickness of 2.15mm. Let´s say I keep the dimensions of the steel string and put the numbers into my spreadsheet for EI. The result is 40Nm^2 for unchanged braces. To get to 15 I need to change the braces somehow. I decided to change the height and used the built in optimizer of excel . This give me a height of 4.1mm (again without carbon fibre). Is it possible to calculate this way?
Yes, it is. However, you're usually looking for a higher T(1,1)2 on a classical than on a steel string, so you have mass effects to consider. The "50mm in front of the bridge" rule is a simplification to help you get in the ball park. It clearly excludes the effects of bridge mass and stiffness which is a significant variable on classical guitars. You can see from Fig 4.4-9 that there is a very wide spread (a factor of 5) in EI over a range of historical guitars.
JurgenV wrote:
Tue Jun 25, 2019 5:34 am
3. Concerning the typical modulus of rupture used in table 4.4-2: these are values determined by experiment? How to measure that?
Yes, determined by testing. The typical test procedure is described here: https://www.wood-database.com/wood-arti ... f-rupture/. Like most other wood properties it is quite variable and that is why for design purposes it is typically discounted by ~50%, as in Table 4.4-2, to give an "allowable stress", (i.e. a safety factor).

JurgenV
Myrtle
Posts: 74
Joined: Mon Dec 10, 2018 6:58 am
Location: Bavaria, Germany

Re: Flexural rigidity & Co

Post by JurgenV » Tue Jul 02, 2019 4:27 am

Thanks for your comments Trevor. This helps to get further.
Concerning the braces with and without carbon fibre... yeah, I should have checked that first instead of just guesssing. According to my spreadsheet it´s around 0.6mm I would have to remove.
With the MOR would guess one needs a good statistic to get a meaningful result. As I´m not a professional luthier with unlimited supply of material I think I will have to take cut a piece from the wood I want to use for braces and do the test every time again.

Thanks again for the confimation concerning the calculation for the classical. But the next classical has to wait. The plans for this year are to start with something proven or at least known to reduce the number of variables. If this will be successful I will start thinking about new designs and classicals :) So actually this year I want to
a) give your falcate bracing (with live back) a try. Actually I think about using a OOO mould which would result in a body of 505mm length and a width of around 380mm. I´m not sure if I can directly use your proposed bracing scheme or if I have to adjust it as the body is around 2cm longer.
b) see if I can use data from an existing guitar and come as close as possible to it. But for that I still need to finish the test rig for the monopole mobility (hopefully I will find some time this week) and get my old guitar back to do the tap testing.

One more thing about braces and flexural rigidity: when using x-bracing with non scalloped braces (means just tapered braces) is the method for calculating EI still valid? In the Book you are stating that with scalloped bracing it´s not possible to use this method. You are not saying if it´s applicable for non scalloped bracing. I´m asking because the guitar from my second goal for this year was originally build with scalloped x-bracing and I was asking myself if I could use non scalloped braces and your 50mm-before-the-bridge ballpark calculation to have more control about the parameters. Or is it not possible at all to exchange scalloped braces in this way?

Jürgen

User avatar
Trevor Gore
Blackwood
Posts: 1605
Joined: Mon Jun 20, 2011 8:11 pm

Re: Flexural rigidity & Co

Post by Trevor Gore » Tue Jul 02, 2019 8:58 am

JurgenV wrote:
Tue Jul 02, 2019 4:27 am
With the MOR would guess one needs a good statistic to get a meaningful result. As I´m not a professional luthier with unlimited supply of material I think I will have to take cut a piece from the wood I want to use for braces and do the test every time again.
Unless you're using unusual materials for bracing, there is no real need to test MOR every time. If you use spruce (for example) and the techniques in the book with an allowable stress of 50% MOR you should be fine. More important is to check the stiffness (Young's modulus).
JurgenV wrote:
Tue Jul 02, 2019 4:27 am
...when using x-bracing with non scalloped braces (means just tapered braces) is the method for calculating EI still valid?
Yes, it will give reasonable answers provided the tapers are not too radical. The problem with scallops is that their position and depth can vary considerably, so it is very difficult to get a simple analytical technique to approximate the overall flexural rigidity.

Post Reply

Who is online

Users browsing this forum: No registered users and 29 guests