Fatigue failure of the structure or structural members.

Serviceability limit states correspond to conditions beyond which specified service requirements for a structure or structural member are no longer met. Exceeding these limits causes limited damage but means that the structures do not meet design requirements: functional requirements (not only of the structure, but also of machines and services), comfort of users, appearance (where the term "appearance" is concerned with high deformation, extensive cracking, etc.), damage to finishes and to non-structural members. Usually the serviceability requirements are agreed for each individual project.

EN1990 indicates three different types of combinations for serviceability limit states verifications: characteristic combination (called "rare combination" in the previous versions of Eurocodes), frequent combination and quasi-permanent combination.

The choice of combinations to be taken into account is related to the distinction between reversible and irreversible limit states: frequent and quasi-permanent combinations apply to the first case, characteristic combinations to the second case.

The definition of relevant limit states for a certain construction requires above all the analysis of the different situations to which it can be exposed.

The situations chosen for design shall cover all situations that can reasonably occur during the execution and working life of the structure. In common cases, design situations are classified as:

•persistent design situations, referring to conditions of normal use; •transient situations, referring to temporary conditions of the structure, e.g. during construction or repair;

•accidental situations, involving exceptional conditions of the structure or its exposure, including fire, explosion, impact, etc.; •seismic situations, where the structure is subjected to a seismic event.

2.3 Basic variables

2.3.1 Actions and environmental influences

Each design situation is characterized by the presence of several types of actions on the structure. "Action" means, as EN1990 states, either a set of forces (loads) applied to the structure (direct actions), or a set of imposed deformations or accelerations caused for example, by temperature changes, moisture variation, uneven settlement or earthquakes (indirect action). Actions are classified as:

- permanent actions (G), the duration of which is continuous and equal to the design working life of the structure, or for which the variation in magnitude with time is negligible (e.g. self-weight). Those actions, like prestressing or concrete shrinkage, for which the variation is always in the same direction (monotonic) until the action attains a certain limit value, are also permanent actions;

- variable actions (Q), divided in variable actions with discrete and regular occurrence in time (e.g. imposed load of people and low-duration imposed load in general on building floors); and variable actions characterized by variable and non-monotonic intensity or direction (e.g. snow, wind, temperature, waves);

- accidental actions (A), which are not easily foreseeable and of low duration (e.g. explosions, impacts, fire).

Each permanent action with low variability has a single characteristic value Gk. This is the case of actions due to self-weight: they are generally represented through a nominal value calculated on the basis of the design drawings (structural and non-structural member dimensions) and of the average specific gravity of materials (Gk = Gm).

If a permanent action has relevant uncertainties (coefficient of variation bigger than 10%, where the coefficient of variation is the ratio between standard deviation and average) and if sufficient statistical information is available, two characteristic values (upper, Gk,sup, and lower, Gk,inf) should be used. Gk,sup is the 95% fractile and Gk,inf is the 5% fractile of the statistical distribution for G, which may be assumed to be Gaussian.

There is a 5% probability that these two values will be exceeded, the probability that the real value of action is more than Gk,sup or less than Gk,inf is less than 5% (fig. 2.2).

Gkmf Gl^Gm Gk.u,p

Figure 2.2. Characteristic value of a permanent action: Gk = Gm if the coefficient of variation is negligible; a lower and an upper characteristic value Gk,n and Gk,sup are defined if the coefficient of variation is high

Gkmf Gl^Gm Gk.u,p

Figure 2.2. Characteristic value of a permanent action: Gk = Gm if the coefficient of variation is negligible; a lower and an upper characteristic value Gk,n and Gk,sup are defined if the coefficient of variation is high

Each variable action has four representative values. The main representative value of a variable action is its characteristic value Qk; the other representative values are, in decreasing order:

- the combination value, represented as a product y0 Qk,

- the frequent value, represented as a product yi Qk,

- the quasi-permanent value, represented as a product y2 Qk.

For simplicity, each of these last three values is defined as a fraction of the characteristic value, obtained by applying a reducing factor to Qk. In reality, the frequent value and the quasi-permanent value are inherent properties of the variable action, and the yi and y2 factors are simply the ratios between these values and the characteristic value. On the other hand, the yo factor, called the combination factor, determines the level of intensity of a variable action when this action is taken into account, in design, simultaneously with another variable action, called "leading variable action", which is taken into account by its characteristic value.

The y0 factor takes therefore into account the low probability of simultaneous occurrence of the most unfavourable values of independent variable actions. It is used both for ULS verifications and for irreversible SLS verifications.

The frequent (yi Qk) and the quasi-permanent (y2 Qk) values are used for ULS verifications including accidental actions and for reversible serviceability limit states. Values of y factors for buildings are defined in the National Annex. Table 2.10 shows the values recommended by EN1990.

The characteristic value of a variable action has a defined probability, beforehand accepted, of being exceeded on the unfavourable side within a fixed reference period. This period is normally coincident with the design working life of the structure.

For the majority of climatic variable actions, as well as for service loads on building floors, the characteristic value is based upon the probability of 0,02 of its time-varying part being exceeded within a reference period of one year. In other words, this is equivalent to a mean return period of 50 years.

Table 2.10. Recommended values of yfactors for buildings [Table (A1.1)-EN1990]

Imposed loads in buildings, category (see EN 1991-1-1)

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