Deriving displacement functions 2-10 to 2-13 for shape functions in FEM

[dirk_mec1]

Homework Statement

http://img545.imageshack.us/img545/8149/13862239.png

The displacement functions:http://img256.imageshack.us/img256/2743/13939694.png

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

Homework Equations

Third cubic polynomial and elementary beam theory

The Attempt at a Solution

I don't understand how the displacement functions can be derived can somebody give me a hint?

 

[dirk_mec1]

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: $$y(0) = <br /> \theta_1 \cdot L$$ 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:

http://img252.imageshack.us/img252/4352/31333995.png

ands starts like this:

http://img341.imageshack.us/img341/4606/99014438.png