# A simple stressed beam¶

We consider a simple beam stressed by a traction load F at both sides.

Beam geometry

The geometry is supposed to be deterministic; the diameter D is equal to:

By definition, the yield stress is the load divided by the surface. Since the surface is , the stress is:

Failure occurs when the beam plastifies, i.e. when the axial stress gets larger than the yield stress:

where is the strength.

Therefore, the limit state function is:

for any .

The value of the parameter is such that:

We consider the following distribution functions.

Variable

Distribution

R

LogNormal( , ) [Pa]

F

Normal( , ) [N]

where and are the mean and the variance of .

The failure probability is:

The exact is

>>> from openturns.usecases import stressed_beam as stressed_beam