Calculating load handling for graphite/spruce laminated struts

[Chris Sisson]

I'm in the design phase on a custom project for a customer.  It will be an electric version of his acoustic harp guitar.  For the purpose of defining structure for design I'm looking at this as 3 zithers combined with a guitar neck.  The current instrument is shown in the attached picture.  The primary goal is to for the finished instrument to be significantly lighter than the approximate 20 pounds the current one weighs.  My question for the forum is:

Do any of you have knowledge of how to calculate the load bearing properties and limits of struts that would be used to support the string load of each of the three theoretical zithers here?  I'm looking at these individually right now as box zithers of varying sizes with strings over the top surface.  The primary supports run parallel to the strings and made using laminated spruce and graphite sheet (like the LMII Part # GR40 .040 sheet).  I've been told that structural engineers use something like "finite element analysis" which may be incorporated into AutoCad but I can't really take the time to learn that package, or have the money to buy it.  I'm looking or something like a formula that would incorporate the physical properties of a strut and yield some measure of deflection under load.  

Has anyone seen articles that might dress the issue in say the GAL red book or monthlies?

Thanks for your time and interest

[Frank Ford]

First, I hope that the "approximate 20 pounds" is an exaggeration. Even considering two dozen heavy tuners, I'd expect less than half that.

A zither works on a slightly different plan, with the strings bearing on bridges that sit directly on the blocks at both ends, where the flattop guitar has the strings anchored to the top at the bridge.  So, rather than considering them as zithers, I'd think of the three harp sections as more similar to a normal guitar setup.  

I'd also expect that there isn't any convenient way to calculate the stresses involved based on standard engineering because of the crazy shapes and angles involved with a harp guitar.  With all the info available online and in texts, there might be some guidance available from current harp-guitar makers.  Of course, there's the "fossil" record - namely photos and diagrams of designs from 100 years ago.

[Chris Sisson]

Thanks for your reply.  Unfortunately the 20 pound figure is a little low.  The original instrument (Pictured) was built by a very accomplished luthier but had problems handling the load of the bass string set.  The builder added some heavy reinforcement to that area but now the thing is too heavy for the player and gives him back problems.  To allow the guy to continue his career as he gets older I need to make him something that will be as light as possible hence I'm looking to get some engineering done before I build something that would need extensive rework to be adequate.   I'm really hoping to get some calculations, probably from the engineering field. I thought I'd throw the situation out there to see if anyone had ideas.  

Getting the lbs. of string load should be easy, it should be the sum of products of the length, mass, and pitch for each harp or zither section.  Assuming that each set uses two struts as longitudinal supports the goal is to find the lightest configuration that will have some arbitrary deflection value (I'm guessing a few millimeters)

Again, I appreciate your thoughts.

Chris Sisson

Restoration Guitar

Cincinnati Ohio

http://www.restorationguitar.com

[Doc Rathwell]

Chris,

   If you don't own the book, try following the link and reading from Page 12 onwards. It may help with what you're trying to calculate: https://books.google.ca/books?id=l5uInDconwAC&pg=PA10&lpg=P...

Best wishes,

Doc :-)

Left-brain Lutherie  By: David C. Hurd - it's an interesting read...

[Chris Sisson]

Thanks!  I've heard of that one, expensive though.  Have you heard of this one?  

Engineering the Guitar: Theory and Practice 2009th Edition

by Richard Mark French (Author)

 

[Doc Rathwell]

I have that one too Chris. Same same :-)

Seems like a fun project..a thinker..good luck :-)

Doc

[Russell Vance]

Hi Chris,

Poltruded graphite fibre bar stock or Titanium bar stock (KTM Japan), which is conformal  would seem to be a super light overkill option here. Both of these options stick to wood or you can slot/embedd them.

Logic here is why go for a marginal or best guess calculation when the mega strength option weighs much the same?  Im not a fan of room temperature cured graphite fiber matt/skinny sheet as a useful strength adding option. A .070 poltruded bar or a titanium bar in the mix seems to me to represent a high strength to weight ratio when the option is thick lumps of hardwood. The electric guitar fraternity use this stuff on a regular basis and it seems to fit your brief.

Regards,

Rusty.

Rusty. 

[Chris Sisson]

Good Ideas, the titanium is quite expensive but carbon fiber rods inserted into each strut AKA truss rods might be a good option.

Thanks

[Russell Vance]

 Longitudinal poltruded graphite fibre bar stock and titanium bar stock is a lot stronger than the equivalent rod section when oriented correctly - usually noted when neck reinforcement is required in one plane.  Or, this case as a longitudinal (anti-bending) stiffner.  Rod is an omnidirectional stiffner and "wastes" it's dimensions (and weight) when compared to a vertically oriented "bar". 

Poltruded graphite is made from directionally oriented longitudinal fibres as opposed to chopped or woven conventional graphite bar stock layers - it's stronger in the brace laminate application.

Titanium is only expensive if you are going to make a submarine or SR-71 out of the stuff.  The design problems that you have, and the solutions that you wish to avoid (heavy weight of traditional bracing sections) are not going to be cheap to solve and the future of an expensive instrument build are dependent upon you getting this strong and light.   Embedded light weight reinforcement attached.

Rusty.

[Andrew]

Hey Rus. Whats your adhesive of choice to bond this stuff to wood?

[Russell Vance]

Hi Andrew,

West Systems Epoxy which comes with the option of a standard or slow hardener for working time/ambient temperature considerations.  Its thin stuff and capillaries/wicks like superglue to get a really good wetting action which makes it great for laminates, cracks and crevices etc but it does like to flow with gravity in the un-thickened state and is a bit messy.

I abrade the graphite surface to give it a good keying action in accordance with the WSystems advice and have no reservations with this stuff.

Rusty.