Calculating displacement and energy in a structure

AI Thread Summary
The discussion focuses on calculating the energy and displacement of a beam structure, specifically seeking the displacement at the midpoint. The user is attempting to form the moment function M(x) using delta functions but is struggling with the complexity of the calculations. They question whether the full moment equation is necessary for calculating energy due to the applied force. Additionally, there is uncertainty about the correctness of their moment equation, particularly regarding the treatment of moments and forces at the beam's end. The user is seeking assistance to clarify these concepts and resolve their calculations.
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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!
 

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