# Eurocode 1 – probability factor cprob

## What is the probability factor for ?

The wind pressures are calculated relative to the average characteristic wind speed over 10 min with an annual probability of exceeding p = 0.02 (ie once every 50 years).

When the design working life of a building is les or more than 50 years, you have to use the probability factor c_{prob} to calculate the basic wind velocity v_{b} with a return period equivalent to the design working life of your building.

- v
_{b0}is the fundamental value of the basic wind velocity given by the maps in the national annexes. - c
_{dir}is the directionnal factor.

## How to calculate the probability factor ?

\[\displaystyle c_{prob} = \left( \frac{ 1 – K \cdot \ln(-\ln(1-p)) } { 1 – K \cdot \ln(-\ln(0.98)) } \right) ^{n}\]- p is the annual probability of exceedence :

- dwl is the design working life, in years. It can be found by country in the tables below.
- K is the shape parameter depending on the coefficient of variation of the extreme-value distribution.
- n is the exponent.

## What is the design working life of a building ?

### Belgium

Design working life category | Indicative design working life (years) | Examples | |
---|---|---|---|

1 | from 2 to 10 | Temporary structures ^{1} | |

2 | from 10 to 25 | Replaceable structural parts | |

3 | from 15 to 30 | Agricultural and similar structures | |

4 | 4a | from 20 to 100 | Chimneys, towers, masts, silos and tanks |

4b | 50 | Hoists (including overhead cranes), pipelines | |

4c | 100 | Buildings: dwellings, collective equipment, offices | |

5 | 100 | Monumental building structures, bridges, and other civil engineering structures |

Parameters used in the calculation of c_{prob} : K=0,2 and n=0,5.

### France

Design working life category | Indicative design working life (years) | Examples |
---|---|---|

1 | 10 | Temporary structures ^{1} |

2 | 25 | Replaceable structural parts, e.g. gantry girders, bearings |

3 | 25 | Agricultural and similar structures |

4 | 50 | Building structures and other common structures |

5 | 100 | Monumental building structures, bridges, and other civil engineering structures |

Parameters used in the calculation of c_{prob} :

- 0.02 < p : K=0.15 and n=0.5
- p < 0.02 : K=0.20 and n=0.5

### Italy

Design working life category | Indicative design working life (years) | Examples |
---|---|---|

1 | ⩽ 10 | Temporary structures – Structures in construction phase ^{1} |

2 | ⩾ 50 | Building structures and other common structures (bridges, infrastructure works and dams small in size or of normal importance) |

3 | ⩾ 100 | Monumental building structures, and other civil engineering structures (bridges, infrastructure works and dams large or of strategic importance) |

Parameters used in the calculation of c_{prob} :

- 0.02 < p : K=0.20 and n=0.5
- p < 0.02 : K=0.138 and n=1.0