Statics of hangman beam / guitar neck under load

[shabbily]

Hello all, I am trying to understand what the relationship is between the length or height h of a guitar neck and how far in the x direction it is displaced (δ) given the same tension in the strings and width of the neck, and assuming the neck is anchored and rigid at the guitar's body. Is it analogous to the attached hangman diagram? My gut says the two seem analogous to an end load cantilever beam but I don't know if it is that simple. Hopefully this makes sense... I am not a physics person and may be using some of these terms incorrectly.

 

[Valerie Park]

Yes, the relationship between the length or height h of a guitar neck and its displacement (δ) is analogous to the hangman diagram. It is also analogous to an end load cantilever beam. The tension in the strings and the width of the neck are factors that will affect the amount of displacement (δ). In the case of an end load cantilever beam, the displacement (δ) is proportional to the load (F) divided by the stiffness (k) of the beam, where F is the force applied at the end of the beam and k is the stiffness of the beam itself. So, if you increase the tension in the strings, the displacement (δ) of the guitar neck will increase. Similarly, if you increase the width of the neck, the stiffness (k) of the beam will increase, resulting in less displacement (δ).