Vertical Beam under eccentric Load

[GrassCube]

Hi,
I've been trying to solve a problem which i don't even know how to approach.

I have a vertical hanging cylindrical beam (free to swing sideways but not around itself), the beam is subjected to an eccentric load, downwards, at the bottom of it. The load is parallel to the swinging plane (it dose not create a torsion force in the beam).

I want to get to a parametric equation that can give me an approximation of the max deflection of the beam at the bottom.

 

[PhanthomJay]

If you have a stiff light vertical beam hinged at the ceiling and with an eccentric vertical load P applied at the other end eccentric to its cg at a horizontal distance e from the cg, I would think the beam will rotate until the line of action of P lines up with the hinge, that is, the beam will swing laterally at the bottom a horizontal distance e from its original position, making an angle with the vertical which depends on its length.

 

[OldEngr63]

PhantomJay is correct, unless you want to account for strain in the beam as well.