# Cantilever Beam This tutorial is also available for Matlab in: echodemo TutorialCantileverBeam Tutorial for the graphical user interface File -> New -> Tutorial -> Tutorial 1. Cantilever Beam (see also Import Tutorials)

# Problem definition

A cantilever beam of length L and rectangular cross section of width b and height h is loaded at the end by a concentrated point load P.

The displacement w at the tip of the beam should be determined for the case where the point load P, the Young's modulus E, the density $\rho$ of the material and the height h are uncertain. Uncertainties of the width b and of the length L are assumed to be negligible.

In this simple case, the displacement w at the tip can be expressed in closed form, where g denotes the gravity constant: $w = \frac{\rho g b h L^4}{8EI}+\frac{PL^3}{3EI}; \qquad I = \frac{bh^3}{12}$

In the used stochastic approach, all uncertainties are modelled mathematically by random variables. These random variables are characterised by its probability density function (PDF) or alternatively by the culmultive probability function (CDF).

COSSAN-X provides most standard distributions. In case non-standard distributions are used, user-defined distribution must be specified. In this tutorial, only standard distribution should be used.

## Input data

Length L = 1.80 m.

Width b = 0.12 m.

Load P: log-normal distributed with mean $\mu=$ 5.0 kN and standard deviation $\sigma=0.4$ kN.

Height h: Normal distributed with mean $\mu=0.24$ m and standard deviation $\sigma=0.01$ m.

Density $\rho$: Log-normal distributed with mean $\mu=600$ $kg/m^3$ and standard deviation of $140$ $kg/m^3$.

Young's modulus E: Log-normal distributed with mean $\mu = 10.0$ $GN/m^2$ and standard deviation of $\sigma = 1.6$ $GN/m^2$.

# Aim of the Tutorial

The aim of the tutorial is to show how to perform different analysis type by means of the graphical user interface of COSSAN-X.

Please refer to the following pages to see how to perform a specific analysis type for problem defined above.