# Bridge Model This tutorial is also available for Matlab in: echodemo TutorialBridgeModel Tutorial for the graphical user interface File -> New -> Tutorial -> Tutorial 6. Bridge Model (see also Import Tutorial)

# Problem definition

In this tutorial the global sensitivity analysis is applied to a practical problem in structural engineering: a mechanical model of a long bridge.

The conceptual model is sketched below.

This model is interesting for several reasons, which makes it suitable for an example application of  the total sensitivity analysis and their upper bounds. The conceptual model contains 123 uncertain parameters.  All the uncertain parameters are considered to be uncorrelated.  The bridge is subjected to a harmonic load with a frequency of 10 Hz, applied  at the mid point of the 3rd bay. The aim of the analysis is to identify the  parameters that affect the variance of the maximum displacement of any points  of the bridge as well as the parameters that have negligible effects.   It is important to note, that in order to avoid unrealistic values of the  input parameters during the simulation, truncated normal distributions are  used.

## Input data

### Random Variables

• Heights h: normal distributed with mean $\mu=0.001 m$  and coefficient of variation 0.05.
• Young's modulus E: normal distributed with mean $\mu = 21.0 GN/m^2$ and coefficient of variation 0.03.
• Length l: normal distributed with mean $\mu=0.36 m$ and and coefficient of variation 0.05.
• Stiffness k: normal distributed with mean $\mu=200 Nm$ m and and coefficient of variation 0.10.
• Rotation stiffness w: normal distributed with mean $\mu=40 Nm/rad$ and and coefficient of variation 0.16.
• Damping c: normal distributed with mean $\mu=0.4 m$ and and coefficient of variation 0.25.

### Parameters

• Density $\rho=7800 kg/m^3$.
• width $w=0.04 m$
• Load frequency: $10 Hz$

# Aim of the Tutorial

The aim of the tutorial is to show how to perform different uncertainty quantification and global sensitivity analysis by means of COSSAN-X.

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