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NOTE The y values may be set by the National annex. * For countries not mentioned below, see relevant local conditions.

The characteristic value of seismic action for ULS verification is fixed by Eurocode 8 (EN1998), based on a return period of 475 years, corresponding to a probability of 10% of being exceeded in 50 years. It is possible to modify the return period by means of an importance factor yi.

The frequent value and the quasi-permanent value of floor loads on building are determined so that the average periods of time within which they are exceeded are respectively 10% (ratios of the sum of intercepts of time BC, DE, FG, HI and the reference period of 50 years represented by segment AJ in Fig. 2.3) and 50% (ratio of listed segments and segment AJ). Figure 2.3 resumes the representative values of variable actions.

For accidental actions, a single nominal value is determined because, due to the nature of these actions, sufficient information for the appropriate application of statistical methods is not available.

In order to take into account the uncertainties on the choice of characteristic values for actions and some uncertainties concerning the action modelling, design does not use characteristic values, but amplified values, called "design values", which are obtained by multiplying characteristic values by a partial factor.

Symbols representing the design values are indicated with index d. Table 2.11 shows the steps to pass from the representative values of actions to the design values of their effects on construction.

Table 2.11. Procedure to determine the design values of effects on structures _starting from the representative values of actions_

Expression

Comment

F;

Actions on the structure are identified

Fk,i 0 (V Fk,i) where ( = ¥g,¥i,¥2 )

Representative values are assigned to actions: characteristic values or other (combination, frequent, quasi-permanent) values.

( = ¥g,¥I,¥2 )

Design values of actions are determined by multiplying the representative values Fki or y Fki (where y = yo,yi,y 2 ) by a partial factor yfi. yfi is a partial factor generally covering the uncertainties related to the choice of characteristic values for actions and, sometimes, part of the uncertainties related to action modelling. In case of permanent actions, when it is necessary to split the action into a favourable and an unfavourable part, two different partial factors, indicated as yc,sup and Tcjnf , are used.

Ed = E (y f,if Fk,i;ad )

Actions that can occur simultaneously are considered; combinations of actions are calculated and the effects of these combinations on the structure are assessed (e.g. action effect in a cross section).

ad represents either the design value of the set of geometrical data (in general, values indicated on the design drawings) or data that take into account the possibility of geometrical imperfection liable to cause second order effects.

Ed = YsdE (f,iV Fk,i;ad )

The design value of effects is obtained by multiplying the values produced by the design actions, by a partial factor ysd mainly covering the uncertainties of the structural model.

Ed = E ( YfjV Fk,i; ad )

In normal cases, the previous expression is simplified in this one, where: yFi =f(ySd,yfi) so that the model coefficient ySd does not explicitly appear.

The product: FdJ = yF, • FKi or (yF^; y = Yo,Vi,V2)is often directly assumed as the design value of the action Fk,i.

2.3.1.2 Thermal effects

2.3.1.3 Differential settlements/movements

2.3.1.4 Prestress

Several material properties are involved in structural design. The main one is strength, i.e. the ability to resist forces without breaking or failing.

Strength of materials is represented through a characteristic value, indicated as fk. This is the value that has a given probability of not being attained or exceeded during a hypothetical unlimited test series. Eurocode EN1990 defines the characteristic value of a property of a material as the 5% fractile of its statistical distribution where a minimum value of the property is the nominal failure limit (general case), and as the 95% fractile where a maximum value is the limiting value. For the structural stiffness parameters (moduli of elasticity, creep coefficient, thermal expansion coefficient, etc.), the characteristic value is taken as a mean value because, depending on the case, these parameters can be favourable or unfavourable.

Product properties are also represented by a single characteristic value or a set of characteristic values, according to their constituent materials.

Table 2.12 shows the steps to pass from the characteristic values of individual material strengths or product resistances to the design values of structural resistance.

Table 2.13 gives the values of partial safety factors to be assumed for concrete and steel for ULS, in case of persistent, transient and accidental load combinations.

Table 2.12. Procedure to determine ^ the design values of resistances starting from the characteristic values of strength

Expression

Comment

Xi

Material strengths and product resistances involved in the verifications are identified.

Xk,i

Characteristic values of material strengths and product resistances are introduced.

X - Xk,i Xd,i - — Ym,i

The design value of a material property is determined on the basis of its characteristic value, through the two following operations:

a) divide by a partial factor ym, to take into account unfavourable uncertainties on the characteristic of this property, as well as any local defaults.;

b) multiply, if applicable, by a conversion factor ^ mainly aimed at taking into account scale effects.

f Xki 1

1 Ym,i

Determine the structural resistance on the basis of design values of individual material properties and of geometrical data.

YRd V Ym,i )

Following a procedure similar to the one for calculating the design value of action effects, the design value of structural resistance is determined on the basis of individual material properties and of geometrical data multiplied by a partial factor YRd that covers the model uncertainties of resistance and the geometrical data variations, if these are not explicitly taken into account in the model.

V YM,i

As for the action effects, factor YRd is often integrated in the global safety factor yM,i, by which the characteristic material strength is divided: ym,i = f(YRd, Ym,i).

2.3.2 Material and product properties

2.3.2.1 General

Fig. 2.4 summarise in a schematic way the relation between the single partial factors used in Eurocodes.

Uncertainty in material properties

Uncertainty in representative values

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