Shear stress in braces

[GregHolmberg]

Page 4-45 talks about shear stress in braces, and warns that it can be exceeded in some species, especially balsa.

But it doesn't explain how to calculate the shear stress in a brace or the maximum shear stress in a given material. It defines the shear modulus, but doesn't tell us how to get it or how to use it.

I have calculated the flexural stress of the braced top as a composite beam per section 4.4.7. How do I get from there to shear stress?

Greg

[GregHolmberg]

Trying to answer my own question, could the shear force be the moment (torque) at the saddle divided by the length of the beam?

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F = M/l

So if I had a string tension of 709 N and a saddle height of 14 mm, then the moment M = 709*0.014 = 9.9 N·m.

I could say that the length of the "beam" (i.e. the top) is the distance from tail block to the transverse brace. Let's say 350 mm.

Then the shear force would be 9.9/0.350 = 28.3 N.

Now the shear stress would be the force / area. If my main braces are rectangles 5 mm wide and 10 mm tall, then stress = 28.3 / (0.005 * 0.010) = 566,000 Pa.

OK, but what is the maximum shear stress of a piece of wood?

Maybe I can get the shear modulus, G, from the frequency of the twisting vibration mode, as in Equ. 4.5-4? For example, in Table 4.5-3 an average G for Engelmann Spruce 1.09 GPa.

Then the last piece of information I would need would be the shear strain angle?

I don't know. Obviously, I've exceeded my engineering knowledge.

Greg

[kiwigeo]

Dunno mate.....maybe this will help. The calculator might be useful for double checking calculations.

https://www.omnicalculator.com/physics/shear-stress

Trevor will no doubt respond as he always does with his sagely advice and make it all look embarrassingly simple

[Trevor Gore]

Trevor will no doubt respond as he always does with his sagely advice and make it all look embarrassingly simple

Ha! I just looked up one of my old engineering text books.... it took 119 pages of "background" before it could sensibly discuss shear stress in beams. That's why the detail is not in the books.

Googling up "Shear stress in beams" brings up some reasonable results, but you'll likely already need a good background in engineering to get the most from them. Here are a few links:

https://wp.optics.arizona.edu/optomech/ ... 22_W10.pdf

https://www.bu.edu/moss/mechanics-of-ma ... ar-stress/

https://www.purdue.edu/freeform/me323/w ... k06-2-.pdf

[GregHolmberg]

Trevor, thanks for the links. I'll take a look. I'm definitely out of my depth. I took some of this in freshman engineering 45 years ago, before switching to computer science. Unfortunately, I did not do well in those engineering classes (too much beer, I guess!).

I've been working from this source: MachaniCalc: shear stress in beams

First, I learned that shear force in a beam simply supported at each end with a moment in the center is the same at all positions along the beam, and it is

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V = M/L

where M is the moment (torque) and L is the length of the beam (or distance between the supports).

Second, I learned that V/A is just the average shear, and not the peak shear. A is the cross-section area.

Actual shear at a given point in a cross-section is

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τ = VQ/Ib

where V is the shear force (M/L), Q is the first moment of area, I is the second moment of area, and b is the width of the cross section at the desired distance from the centroid. It has some examples for simple cross-sections, but of course a guitar top is a composite beam of differing materials, so it's more complicated.

However, I already have I (the second moment of area) from the calculation I did for bending stress. And calculating Q (the first moment) doesn't look to difficult. So I have all the pieces.

Then it's a question of finding the point in the cross-section where the stress is maximum.

Unfortunately, I think I've made a mistake somewhere, since I'm getting a value of about 2 MPa. I think Balsa max is about 400 MPa, so my value is way off.

I'm still working on it. If anyone wants to help, here's my spreadsheet. Look at worksheet 'top_braces', cell C69, labeled 'τ_peak'. You can make a copy with File->Make a copy, or download an Excel file with File->Download.

Greg