# A simple stressed beam¶

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

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:

which leads to the equation:

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

## Load the use case¶

We can load this classical model from the use cases module as follows :

```
>>> from openturns.usecases import stressed_beam as stressed_beam
>>> # Load the use case axial stressed beam
>>> sb = stressed_beam.AxialStressedBeam()
```

## API documentation¶

See `AxialStressedBeam`

.