determination of soundboard flexural rigidity

[benvaneven]

I am reading the sections 4.4 design of braces and 4.5 design plates.
My calculations for plate thickness were successful. Now I am trying to determine the soundboard flexural rigidity.
I don’t see how to calculate the neutral axis of the soundboard cross section in fig. 4.4-19.
I understand what is written on page 4-37.
For calculating the x for the soundboard cross section do I have to take the area of the soundbourd, 2 triangels (triangle braces), 2 triangles (gabled braces) and 2 rectangles (gabled braces)?
Thanks, Ben

[Trevor Gore]

I don’t see how to calculate the neutral axis of the soundboard cross section in fig. 4.4-19.

Take the moments of all the component areas about the base, setting up a large equation similar to the penultimate one on p 4-37.

For calculating the x for the soundboard cross section do I have to take the area of the soundbourd, 2 triangels (triangle braces), 2 triangles (gabled braces) and 2 rectangles (gabled braces)?

Yes.

[benvaneven]

thanks a lot for your answer!

[IanHemphill]

First off, a big thank you to all you forum-folk, this forum is a really great resource for a newbie. I’ve been working on my spreadsheet for calculation of soundboard flexural rigidity and still have some problem getting it to provide me with the results in Table 4.4-2.

I’m ok with spreadsheets, so not asking for any help there - just with my understanding of what exactly I’m trying to get it to do. If my understanding comes into line, I’m confident I can wrestle the sheet into submission! I took Trevor’s course last summer and thought then that I was following along just fine, but of course when I try to actually implement it, no cigar.

From what I’ve been able to glean from the books, the course, the forum posts, and reading on first and second moments of area on the net, I *think* this is what I’m trying to do. If anyone with more experience could just give me a “yep, that’s it” or “nope, you forgot…insert obvious thing I’m missing” Then I can focus my energy on fixing the real problem!

1. First, figure out the equivalent neutral axis of the entire system, with x=0 at the base of the soundboard, and the cross-sections of the braces at the 50mm line, as in Figure 4.4-19.

Trevor’s reply here seems crystal clear, but my numbers still don’t come out. Just to be clear on Trevor’s response about “taking the moments of all the components”. My understanding from the figure is that there are 7 elements that have to be used: the soundboard rectangle, the two finger brace triangles, the two x-brace rectangles, and the two x-brace triangles (gables). Each of these will have a distance of its corresponding centre of area from the x=0 baseline. First moment of area gets used to sum the products of each element area with its centroid distance and then divide that result by the sum of the areas to get the equivalent neutral axis. as per the derivation following figure 4.4-6. (I don’t get the result in the table. close but not the same. Possibly a typo or rounding error in my sheet, but I haven’t been able to find it. still looking).

2. with the new neutral axis in hand, use the parallel axis theorem on each of the seven elements individually to translate it’s contribution to I-system to the new axis.

3. Now that each elements contribution is aligned with the axis of interest, the I’s get added up in a straight summation to find the total I-system. (Or am I wrong here? We are only addressing resistance to rotation around the selected neutral axis, so I don’t think there is a need to do anything more fancy than add them up. Is this true?)

4. Equivalent EI for the entire braced system is just the I-system just calculated times the E of the material used (or if the system has multiple materials, the E of the material used as the reference for the equivalent dimensions calculation.)

Thanks in advance for any feedback on what I’ve mis-interpreted. It’s much appreciated!

[IanHemphill]

Well, as usual it is just nice to get your thoughts together to explain them to someone else! Helps get your head on straight.

I did manage to sort out the typo that was sliding my results off target, and have now got everything playing nicely and my results now validate against Figure 4.4-19 and Table 4.4-2.

When I build Excel workbooks for myself, I tend to "talk to myself" a lot in them about what I'm doing and how to use the sheets - it makes it a lot easier to debug and modify, and it helps me use the sheet after I come back to it some time later and forget everything about how I built it and how to use it!

I really appreciate all the great info I've been gleaning from the forums and hope to be able to contribute more as I get further down this road (just on guitar #2 now, so a ways to go!). I know that there is a LOT to be said for building your own spreadsheets, but not everyone is as comfortable with Excel as they are with a fret-saw, so there might be some value in looking over my shoulder. I've made this workbook for my own use but am happy to share with anyone coming along after this and trying to figure this stuff out. I've tried to be really clear about where everything comes from and expose as many of the intermediate calculations as make sense. those values might be helpful in debugging your own sheets.

I don't see a way to attach executables (probably a very good thing!), so I'll generate a PDF, but if anyone would like the excel file, I'd be happy to oblige.

Now, back to the shop!

[kiwigeo]

Thanks Ian.

Anyone wanting the excel file can email/PM Ian and he'll email same to you.

[GregHolmberg]

Here's my spreadsheet (google docs).

I have used average values for many species listed on wood-database.com.

[IanHemphill]

Wow! a lot of really good data in there, Greg, thanks for that.