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 cprob to calculate the basic wind velocity vb with a return period equivalent to the design working life of your building.
\[\displaystyle v_{b} = c_{prob} \cdot c_{dir} \cdot v_{b,0}\]- vb0 is the fundamental value of the basic wind velocity given by the maps in the national annexes.
- cdir 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 cprob : 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 cprob :
- 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 cprob :
- 0.02 < p : K=0.20 and n=0.5
- p < 0.02 : K=0.138 and n=1.0
Germany
| Design working life category | Indicative design working life (years) | Examples |
|---|---|---|
| 1 | 10 | Temporary structures 1 |
| 2 | 10 à 25 | Replaceable structural elements, e.g. running girders, supports |
| 3 | 15 à 30 | Agricultural and similar structures |
| 4 | 50 | Building structures and other common structures |
| 5 | 100 | Monumental structures for buildings, bridges and civil engineering works |
Parameters used in the calculation of cprob : K=0,1 et n=1.