# The cantilever beam model¶

We are interested in the the vertical deviation of a diving board created by a child diver. We consider a child whose weight generates a force approximately equal to 300N (i.e. almost 30 kg). Because of the uncertainties in the weight of the person, we consider that the force is a random variable. The length of the diving board is between 2.5 m and 2.6 m. The Young modulus is uncertain and between 65 and 75 GPa, which corresponds to the fiberglass material, a material often used for diving boards. Uncertainties in the production of the material are taken into account in the Young modulus and the section modulus of the board.

We consider a cantilever beam defined by its Young’s modulus , its length and its section modulus . One end of the cantilever beam is built in a wall and we apply a concentrated bending load at the other end of the beam, resulting in a deviation .

The beam geometry

Inputs

• : Young modulus (Pa), Beta(, , a = , )

• : Length of beam (m), Uniform(min=2.5, max= 2.6)

• : Moment of inertia (), Beta(, , , ).

In the previous table and are the mean and the standard deviation of .

We assume that the random variables E, F, L and I are dependent and associated with a gaussian copula which correlation matrix is :

In other words, we consider that the variables L and I are negatively correlated : when the length L increases, the moment of intertia I decreases.

Output

The vertical displacement at free end of the cantilever beam is:

A typical event of interest is when the beam deviation is too large which is a failure :

>>> from openturns.usecases import cantilever_beam