Purpose of bridge pins?

[Trevor Gore]

David, Thanks for taking the trouble to do all this analysis and for the additional effort in putting it up on the forum.

The real rotation of a bridge on a responsive guitar is ~2 degrees, obviously without failure, so the strain needs to be distributed over sufficient length of body (including braces) to allow this to happen. Given the variability in wood's material properties and the fact that, on the whole, guitars hold together, I would suggest you set a maximum allowable stress of no more than 50% of failure stress (i.e. ~15MPa for the spruces).

In the real world, the steels have the benefit of their elastic/plastic behaviour which gets them through a lot of stress concentration problems. I've no idea how this happens in the real world of wood.

[David Malicky]

Trevor, you're very welcome -- glad to do it and even better if it's helpful. Those are good suggestions on the allowable stresses and bridge rotation. I would imagine wood undergoes a similar microyielding that metals do in sharp corners, although the vastly different orthotropic yield properties would make that a lot more complex.

All, sorry for the slow update. I ran a bunch of variations of the top length fore/aft of the bridge to try to find lengths that didn't have a strong effect on the stresses. The bad news is there doesn't seem to be such a geometry. And as the lengths get longer, the bridge rotation becomes unreasonable, as expected. Also reducing the string tension to give more reasonable top stresses leads to an inconsistency in the real loads applied at the ballend, etc. I couldn't think of a clean way to simulate the real offloaded torque, and then I realized I could do a left-right symmetric (like a Larrivee or double-X) 3D model and it would save a lot of elements.

So that's the good news -- I've now got a symmetric 3D model of top and braces with decent detail, bonded to a 1/4" (6.35mm) thick side/lining and 0.15" (3.8mm) thick unbraced back. Body is a GA, 15.6" x 20" (396mm x 508mm), flat top and back, constant height sides.

The top and braces are all orthotropic QS spruce, aligned to the individual brace directions. The sides and back are isotropic (E=500ksi, 3450 MPa, for a middling to soft choice to compensate for the thickness). The thicker side and back help keep the number of elements down, as thin parts demand many elements to keep the element quality (aspect ratio) in the good range.

All braces except UTB are 1/4" (6.35mm) wide. All have rectangular cross sections. X bracing is forward shifted, 98 deg, 0.56" (14.2mm) high at the X, scalloped down to 0.30" (7.6mm) high. A thin cap reinforces the broken X leg. There is a small overlap to bridge wings, which are 0.12" thick (3.05mm). LFBs are straight across, scalloped down to 1/4" tall. Bridge plate extends 0.1" (2.54mm) beyond bridge fore and aft.

Symmetry constraints are on all centerline surfaces. The model is fixed at the heel attachment and loaded with individual Lights. I averaged E and E' for 24.2 lb, A and B at 25.9 lb, and D and G at 29.5 lb.

The mesh is about 100k elements, but I'll probalby need another 50k of refinements to get smooth plots on the bridge footprint stresses. Current mesh and solve time is surprisingly good, about 11 minutes.

Below are some pics, the first of z-displacement (the model being 3D, z is now perpendicular to the top) and the second von Mises stresses (with usual caveats, but it's still the easiest single plot to show stresses). Bridge rotation is 1.3 deg -- is that typical of these brace dimensions? Max top stress is about 2200 psi (15 MPa). I'll post more pics this weekend; work's busy now.

I've lots more work to do on the bridge mesh, and more validation is needed, but please offer any suggestions, concerns, or questions on the baseline model -- the first step is to get that vetted to reasonable satisfaction.

I can also start a new thread if wanted, as this is now a long way from bridge pins, and will be looking at many other questions.

Z Displacement (-0.25 - 1.2mm) Only the heel area is fixed, thus the tail picks up a bit.

von Mises stress (0 - 13.4 MPa). Lots to ponder on this one!