Calculating displacement and energy in a structure

[Engineer_s]

Homework Statement

The problem is, calculate the energy and displacement of the structure. What is the displacement (y) in the middle of the beam? See drawing and variables in attached PDF file.

Homework Equations

See PDF file.
Important: To form the moment function M(x), I use delta functions!

The Attempt at a Solution

I did try it, but there are no solutions. Also I use the deltafunction method to write the moment function M(x). This is somewhat difficult. What if I want to calculate the energy due the force on the beam? Do I have to take the full moment equation?

Is my moment equation correct? I do never add moments or forces at the end of the beam because (x-L)=(L-L)=0.

Thanks in advance for helping me!

 

[Engineer_s]

No one that can help me? Thanks