I am trying to model the curvature of a musical instrument neck under string tension, for example, an electric guitar neck.

What I specifically need is the deflection of the neck as a function of distance from the fixed end, an equation for the curve.

I've been able to find the equation for a horizontal beam, one end fixed, and one and free. This resembles the instrument

neck in it's rest position. But in all the examples I have found, the load is always vertical, and perpendicular to the beam

(horizontal beam, vertical load).

The string pull on an instrument is almost parallel to the neck, though. In this case the load would be nearly horizontal.

The configurations for columns and the load directions resemble the instrument neck much more closely. But I can't find

anything related to deflection (or at least deflection as a function of distance). All of it deals with critical load for buckling.

Also the load in the case of an instrument neck would be different than what is normally considered in column theory as

it relates to buckling; the load from the strings would only cause a portion of the deflection that leads to buckling. The load

would never actually reach that point.

For the case of a horizontal beam, one end fixed, and one end free, would the same equation apply to a load vector that

was not vertical, aside from the deflection as a function of load being different? If not, do equations exist for non vertical

loads?

Or for the case of a column with the bottom end fixed and the top end free, and an eccentric load, are there equations for

deflection?