CHARACTERISTIC VALUES .1 General

The characteristic value of an action is its principal representative value and the basis for defining the accompanying values. When there is data enough to fix its value on statistical bases, it is chosen so as to correspond to a prescribed probability of not being exceeded on the unfavourable side during the "reference period" taking into account the design working life of the structure and the duration of the design situation. If not, a nominal value or a value fixed in the project documentation is chosen, provided that consistency is achieved with methods given in EN 1991.

4.2 Permanent actions

The characteristic value of a permanent action shall be assessed as follows:

– if the variability of G during the working life can be considered as small, one single value Gk equal to the mean value may be used;

– if the variability of G cannot be considered as small, two values shall be used: an upper value Gk,sup and a lower value Gk,inf. Where Gk,inf is adopted generally as the 5% fractile and Gk,sup the 95% fractile of the statistical distribution for G, which may be assumed to be Gaussian.

With these assumptions Gk,inf and Gk,sup can be obtained from:

Gk,inf = μG -1,64 σ_G = μG ( 1- 1,64 VG) (1a)

Gk,sup = μG +1,64 σ_G = μG ( 1+ 1,64 VG) (1b)

where μG is the mean value, σ_G is the standard deviation and VG the coefficient of variation of the distribution of G. See Figure 3.

The self-weight of the structure may be represented by a single characteristic value and be calculated on the basis of the nominal dimensions and mean unit masses, see EN 1991-1.1.

Figure 3. Characteristic values of permanent actions.

In the case that reference periods different from the whole working life were considered, assuming that the time length of the reference periods is exponentially distributed, the number of changes in the working life is Poisson’s distributed. In this case the distributions of the

FGmin (x) = 1-exp [-λT FG(x)] (2a)

FGmax (x)= exp [-λT (1-FG(x))] (2b)

where λT represents the expected number of reference periods, (changes of use/owner) in the working life (values between 5 to 10 are usually considered) and FG(x) the distribution function of the permanent action. It is usually assumed that this distribution function do not change with the time in the different reference periods.

From these expressions, the characteristic values lower and upper, corresponding to values with a 5 and 95 % of not being reached or being over passed, respectively, in function of the fractiles of the distribution of FG(x), are given in the following table, depending in the mean number of changes:

λT 5 7 10

Gk,inf 0.010 0.007 0.005

Gk,sup 0.990 0.993 0.995

Assuming a Normal distribution for FG (x), the characteristic values are obtained as:

Fk,inf = μG - kσ_G = μG ( 1- k VG) (3a)

Fk,sup = μG + kσ_G = μG ( 1+ k VG) (3b)

where μG andσ_G are the mean value and coefficient of variation of FG and k is obtained from the standardized Normal distribution values. Examples in function of the mean number of changes in the working life are given in the following table :

λT 5 7 10

k 2,32 2,44 2,57

4.3 Variable actions

For variable actions, the characteristic value (Qk) shall correspond to either:

– an upper value with an intended probability of not being exceeded or a lower value with an intended probability of being achieved, during some specific reference period;

– a nominal value, which may be specified in cases where a statistical distribution is not known.

For characteristic value of climatic actions (wind, snow, etc,) a year reference period is generally chosen with a probability of excedence taken as 0,02 during the working life. This is equivalent to a mean return period of 50 years for the time-varying part.

However, in other cases, different values for the reference period may be more appropriate, e.g.: for imposed loads on buildings a reference period corresponding to the mean time between changes of ownership or a general refurbishment might be more appropriate. In these cases the probability of excedence will have to be different in order to obtain a similar return

4.4 Accidental actions

There is a lack of statistical data referred to accidental actions and the design value should be specified on the basis of nominal values for individual projects. Generally, the design value for accidental actions Ad, for a structure with medium consequences of failure can be fixed as such a level that the probability of excedence can be assessed in the order of magnitude of 10^–4 per year.

There are specific parts of the Eurocodes to deal with the seismic actions (Eurocode 8) and fire (the Part 1-2 of Eurocode 1 and Part 1-2 of the material related Eurocodes (EN1992-1-2 to EN19991-2, except EN1997 and EN 1998)

4.5 Examples Example 1:

Consider, for instance, a beam of normal weight concrete: from EN 1991-1-1 the mean value of the density can be taken as γ = 24 kN/m³. In normal situations the characteristic value of the permanent load due to the self-weight of the beam is obtained multiplying this value by the nominal dimensions of the cross section. That is:

gk = 24 a b kN/m,

where a and b are the dimensions of the cross section in metres.

Consider, now, that, for any circumstance, the structure is very sensitive to this self-weight and, then, is necessary to take account of the inferior and superior characteristic values. In [7]

a coefficient of variation of 0,04 is given for the density of concrete. Introducing this value in the formulas (1a) and (1b), with the nominal dimensions of the cross section

gk,inf = μG ( 1- 1,64 VG) = 24 a b (1-1,64 0,04) = 22,4 a b kN/m gk,sup = μG ( 1+ 1,64 VG) = 24 a b (1+1,64 0,04) = 25,6 a b kN/m Example 2:

Considering now that the material of the beam is glulam of the type GL 36h. The mean density for this material given in EN 1991-1-1 is 4,4 kN/m³ and in [7] a coefficient of variation of 0.1. This coefficient is in the limit indicated in EN 1990 for the consideration of a unique (mean) characteristic value or two values. To one or two in this case will depend in the ratio between the self-weight load and other loads. Substituting the mean and coefficient of variation values in (1a) and (2a) we obtain:

gk,inf = μG ( 1- 1,64 VG) =4.,4 a b (1-1,64 0,1) = 3,7 a b kN/m gk,sup = μG ( 1+ 1,64 VG) = 4,4 a b (1+1,64 0,1) = 5,1 a b kN/m

where a and b are the dimensions of the cross section in metres. We can see that now the characteristic values are a 16% inferior or superior to the mean values, while in the case of concrete were only a 7%.

Example 3:

Finally, consider a building where it is foresee that changes or use or owner can modify the permanent load of some non-structural elements or equipments. It is assumed that this part of the permanent loads has a mean value of 0,8 kN/m² with a coefficient of variation of 0,15. If a mean number of changes of 7 is adopted, i.e.: changes with a rate of approximately 7 years in the 50 years working life of the structure, from the equation (3b) the following characteristic value is obtained:

Fk,sup = μG ( 1+ k VG) = 0,8 ( 1 + 2,44 0,15) = 1,09 kN/m² That is a 37% bigger than the mean value.

5 REPRESENTATIVE VALUES