## shpae functions FEM

1. The problem statement, all variables and given/known data

The displacement functions:

Derive the displacement functions 2-10 up to 2-13.

2. Relevant equations
Third cubic polynomial and elementary beam theory

3. The attempt at a solution
I don't understand how the displacement functions can be derived can somebody give me a hint?

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 Hmmm, the title should read displacement functions. The thing is I know that $\xi$ should run between 0 and 1 (because $\xi = x/L)$. But why is the displacement: $$y(0) = \theta_1 \cdot L$$ shouldn't there be a correction for the second angle? Moreover why is the displacement at the end zero e.g. why is y(1) =0? By the way the picture ends like this: ands starts like this: