Calculating displacement and energy in a structure

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SUMMARY

The discussion focuses on calculating the displacement and energy of a beam structure using delta functions to form the moment function M(x). The user expresses difficulty in determining the correct moment equation and whether to include the full moment equation for energy calculations. Key points include the importance of accurately applying delta functions and understanding the implications of moment calculations at the beam's endpoints.

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  • Understanding of structural mechanics principles
  • Familiarity with delta functions in mathematical modeling
  • Knowledge of moment equations in beam theory
  • Ability to interpret structural diagrams and variables
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  • Study the application of delta functions in structural analysis
  • Learn about calculating energy in beam structures using moment equations
  • Research methods for determining displacement in beams under various loads
  • Explore advanced topics in beam theory, such as boundary conditions and their effects on moment calculations
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Students and professionals in civil engineering, structural engineering, and applied mathematics who are involved in analyzing beam structures and their mechanical properties.

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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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