# 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:

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

## API documentation¶

class AxialStressedBeam

Data class for the axial stressed beam example.

Examples

>>> from openturns.usecases import stressed_beam
>>> # Load the axial stressed beam
>>> sm = stressed_beam.AxialStressedBeam()

Attributes:
dimThe dimension of the problem

dim=2.

DConstant

Diameter D = 0.02 (m)

modelSymbolicFunction

The limit state function.

muRConstant

muR=3.0e6, yield strength mean

sigmaRConstant

sigmaR = 3.0e5, yield strength variance

distribution_RLogNormalMuSigma distribution of the yield strength

ot.LogNormalMuSigma(muR, sigmaR, 0.0).getDistribution()

muFConstant

sigmaFConstant

sigmaR = 50.0, traction load variance

distribution_FNormal distribution of the traction load

ot.Normal(muF, sigmaF)

distributionJointDistribution

The joint distribution of the inpput parameters.

## Examples based on this use case¶

Estimate a probability with Monte Carlo

Estimate a probability with Monte Carlo

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Axial stressed beam : comparing different methods to estimate a probability

Axial stressed beam : comparing different methods to estimate a probability

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling