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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.

\[\displaystyle v_{b} = c_{prob} \cdot c_{dir} \cdot v_{b,0}\]

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 :
\[\displaystyle P_{n} = \frac{1}{dwl}\]
  • 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 categoryIndicative design working life (years)Examples
1from 2 to 10Temporary structures 1
2from 10 to 25Replaceable structural parts
3from 15 to 30Agricultural and similar structures
44afrom 20 to 100Chimneys, towers, masts, silos and tanks
4b50Hoists (including overhead cranes), pipelines
4c100Buildings: dwellings, collective equipment, offices
5100Monumental 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 categoryIndicative design working life (years)Examples
110Temporary structures 1
225Replaceable structural parts, e.g. gantry girders, bearings
325Agricultural and similar structures
450Building structures and other common structures
5100Monumental 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 categoryIndicative design working life (years)Examples
1⩽ 10Temporary structures – Structures in construction phase 1
2⩾ 50Building structures and other common structures (bridges, infrastructure works and dams small in size or of normal importance)
3⩾ 100Monumental 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