# Beam 3-point bending (Inputs Preparation)

This section explains how to prepare the input for the Simply Supported Beam problem. This model will be used later on for simulation and reliability analysis.

## Probabilistic model

The following table summaries the random variables that have been used for simulation analysis:

Description
Distribution
Mean
Standard deviation
Young's modulus (E)
Normal
210,000 (MPa) 10,000 (MPa)
Point force (f)
Lognormal
10 (N) 1.4 (N)
Height of the beam (h)
Uniform
5 (mm) 0.577 (mm)
Width of the beam (w)
Deterministic
8.1 (mm) - Unit convention In this example, the units are MPa for stress and mm for displacements. The choice of the units is not important as long as they are not changed during the study

## Creation of the Random Variables

The three Random variables described in previous section are created. Random variables are the inputs of analysis considering uncertainties (reliability, simulation, etc).

## Creation of a Parameter

The width of the beam is modelled using a Parameter. Parameters are the input of simulations without considering uncertainties (optimization, etc). Parameters can also be used for values that may need to be changed easily within COSSAN-X.

## Creation of a Function

The inertia moment will be expressed using a Function, which depends on the height and width of the beam. In the function definition tab, the name of the objects to used has to be placed between the identifiers <& and &>. Thus the inertia moment of the beam is defined using the following formula:

``` <&b&>.*<&h&>.^3/12
```