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Eurocode - Basis of structural design Appunti scolastici Premium

EN 1990 establishes Principles and requirements for the safety, serviceability and durability of structures, describes the basis for their design and verification and gives guidelines for related aspects of structural reliability. EN 1990 is intended to be used in conjunction with EN 1991 to EN 1999 for the structural design of buildings and civil engineering works, including geotechnical... Vedi di più

Esame di Tecnica delle costruzioni docente Prof. F. D'assisi Ricciardelli

Anteprima

ESTRATTO DOCUMENTO

EN 1990:2002 (E)

4.1.3 Other representative values of variable actions

(1)P Other representative values of a variable action shall be as follows :

Q , used for the verification of

(a) the combination value, represented as a product 0 k

ultimate limit states and irreversible serviceability limit states (see section 6 and An-

nex C) ; Q

(b) the frequent value, represented as a product , used for the verification of ulti-

1 k

mate limit states involving accidental actions and for verifications of reversible

serviceability limit states ;

NOTE 1 For buildings, for example, the frequent value is chosen so that the time it is exceeded is 0,01 of

the reference period ; for road traffic loads on bridges, the frequent value is assessed on the basis of a

return period of one week.

BSI Q

NOTE 2 The infrequent value, represented as a product , is used for the verification of certain

1,infq k

© serviceability limit states specifically for concrete bridge decks, or concrete parts of bridge decks. The

Copy, infrequent value, defined only for road traffic loads (see EN 1991-2) thermal actions (see EN 1991-1-5)

and wind actions (see EN 1991-1-4), is based on a return period of one year.

Q

(c) the quasi-permanent value, represented as a product , used for the verification

Uncontrolled 2 k

of ultimate limit states involving accidental actions and for the verification of reversible

serviceability limit states. Quasi-permanent values are also used for the calculation of

long-term effects.

NOTE For loads on building floors, the quasi-permanent value is usually chosen so that the proportion of

the time it is exceeded is 0,50 of the reference period. The quasi-permanent value can alternatively be

determined as the value averaged over a chosen period of time. In the case of wind actions or road traffic

12/07/2004, loads, the quasi-permanent value is generally taken as zero.

4.1.4 Representation of fatigue actions

(1) The models for fatigue actions should be those that have been established in the

relevant parts of EN 1991 from evaluation of structural responses to fluctuations of loads

PORTSMOUTH, performed for common structures (e.g. for simple span and multi-span bridges, tall slender

structures for wind).

(2) For structures outside the field of application of models established in the relevant

Parts of EN 1991, fatigue actions should be defined from the evaluation of measurements

or equivalent studies of the expected action spectra.

OF NOTE For the consideration of material specific effects (for example, the consideration of mean stress

copy:UNIVERSITY influence or non-linear effects), see EN 1992 to EN 1999.

4.1.5 Representation of dynamic actions

(1) The characteristic and fatigue load models in EN 1991 include the effects of accel-

erations caused by the actions either implicitly in the characteristic loads or explicitly by

applying dynamic enhancement factors to characteristic static loads.

Licensed NOTE Limits of use of these models are described in the various Parts of EN 1991.

32 EN 1990:2002 (E)

(2) When dynamic actions cause significant acceleration of the structure, dynamic

analysis of the system should be used. See 5.1.3 (6).

4.1.6 Geotechnical actions

(1)P Geotechnical actions shall be assessed in accordance with EN 1997-1.

4.1.7 Environmental influences

(1)P The environmental influences that could affect the durability of the structure shall

be considered in the choice of structural materials, their specification, the structural con-

cept and detailed design.

BSI NOTE The EN 1992 to EN 1999 give the relevant measures.

(2) The effects of environmental influences should be taken into account, and where

© possible, be described quantitatively.

Copy, 4.2 Material and product properties

Uncontrolled (1) Properties of materials (including soil and rock) or products should be represented

by characteristic values (see 1.5.4.1).

(2) When a limit state verification is sensitive to the variability of a material property,

upper and lower characteristic values of the material property should be taken into ac-

count.

12/07/2004, (3) Unless otherwise stated in EN 1991 to EN 1999 :

– where a low value of material or product property is unfavourable, the characteristic

value should be defined as the 5% fractile value;

PORTSMOUTH, – where a high value of material or product property is unfavourable, the characteristic

value should be defined as the 95% fractile value.

(4)P Material property values shall be determined from standardised tests performed

under specified conditions. A conversion factor shall be applied where it is necessary to

convert the test results into values which can be assumed to represent the behaviour of

OF the material or product in the structure or the ground.

copy:UNIVERSITY annex D and EN 1992 to EN 1999

NOTE See

(5) Where insufficient statistical data are available to establish the characteristic values

of a material or product property, nominal values may be taken as the characteristic val-

ues, or design values of the property may be established directly. Where upper or lower

design values of a material or product property are established directly (e.g. friction

factors, damping ratios), they should be selected so that more adverse values would af-

fect the probability of occurrence of the limit state under consideration to an extent

Licensed 33

EN 1990:2002 (E)

similar to other design values.

(6) Where an upper estimate of strength is required (e.g. for capacity design measures

and for the tensile strength of concrete for the calculation of the effects of indirect ac-

tions) a characteristic upper value of the strength should be taken into account.

(7) The reductions of the material strength or product resistance to be considered re-

sulting from the effects of repeated actions are given in EN 1992 to EN 1999 and can

lead to a reduction of the resistance over time due to fatigue.

(8) The structural stiffness parameters (e.g. moduli of elasticity, creep coefficients) and

thermal expansion coefficients should be represented by a mean value. Different values

should be used to take into account the duration of the load.

BSI NOTE In some cases, a lower or higher value than the mean for the modulus of elasticity may have to be

taken into account (e.g. in case of instability).

© (9) Values of material or product properties are given in EN 1992 to EN 1999 and in the

Copy, relevant harmonised European technical specifications or other documents. If values are

taken from product standards without guidance on interpretation being given in

EN 1992 to EN 1999, the most adverse values should be used.

Uncontrolled (10)P Where a partial factor for materials or products is needed, a conservative value

shall be used, unless suitable statistical information exists to assess the reliability of the

value chosen.

NOTE Suitable account may be taken where appropriate of the unfamiliarity of the application or materi-

als/products used.

12/07/2004, 4.3 Geometrical data

(1)P Geometrical data shall be represented by their characteristic values, or (e.g. the case

of imperfections) directly by their design values.

PORTSMOUTH, (2) The dimensions specified in the design may be taken as characteristic values.

(3) Where their statistical distribution is sufficiently known, values of geometrical

quantities that correspond to a prescribed fractile of the statistical distribution may be

used.

OF (4) Imperfections that should be taken into account in the design of structural members

copy:UNIVERSITY are given in EN 1992 to EN 1999.

(5)P Tolerances for connected parts that are made from different materials shall be mu-

tually compatible.

Licensed 34 EN 1990:2002 (E)

Section 5 Structural analysis and design assisted by testing

5.1 Structural analysis

5.1.1 Structural modelling

(1)P Calculations shall be carried out using appropriate structural models involving

relevant variables.

(2) The structural models selected should be those appropriate for predicting structural

behaviour with an acceptable level of accuracy. The structural models should also be

appropriate to the limit states considered.

BSI (3)P Structural models shall be based on established engineering theory and practice. If

necessary, they shall be verified experimentally.

©

Copy, 5.1.2 Static actions

(1)P The modelling for static actions shall be based on an appropriate choice of the

Uncontrolled force-deformation relationships of the members and their connections and between

members and the ground.

(2)P Boundary conditions applied to the model shall represent those intended in the

structure.

(3)P Effects of displacements and deformations shall be taken into account in the con-

12/07/2004, text of ultimate limit state verifications if they result in a significant increase of the ef-

fect of actions.

NOTE Particular methods for dealing with effects of deformations are given in EN 1991 to EN 1999.

(4)P Indirect actions shall be introduced in the analysis as follows :

PORTSMOUTH, – in linear elastic analysis, directly or as equivalent forces (using appropriate modular

ratios where relevant) ;

– in non-linear analysis, directly as imposed deformations.

5.1.3 Dynamic actions

OF (1)P The structural model to be used for determining the action effects shall be estab-

lished taking account of all relevant structural members, their masses, strengths, stiff-

copy:UNIVERSITY nesses and damping characteristics, and all relevant non structural members with their

properties.

(2)P The boundary conditions applied to the model shall be representative of those in-

tended in the structure.

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EN 1990:2002 (E)

(3) When it is appropriate to consider dynamic actions as quasi-static, the dynamic parts

may be considered either by including them in the static values or by applying equiva-

lent dynamic amplification factors to the static actions.

NOTE For some equivalent dynamic amplification factors, the natural frequencies are determined.

(4) In the case of ground-structure interaction, the contribution of the soil may be mod-

elled by appropriate equivalent springs and dash-pots.

(5) Where relevant (e.g. for wind induced vibrations or seismic actions) the actions may

be defined by a modal analysis based on linear material and geometric behaviour. For

structures that have regular geometry, stiffness and mass distribution, provided that only

the fundamental mode is relevant, an explicit modal analysis may be substituted by an

analysis with equivalent static actions.

BSI (6) The dynamic actions may be also expressed, as appropriate, in terms of time histo-

ries or in the frequency domain, and the structural response determined by appropriate

© methods.

Copy, (7) Where dynamic actions cause vibrations of a magnitude or frequencies that could

exceed serviceability requirements, a serviceability limit state verification should be

Uncontrolled carried out.

NOTE Guidance for assessing these limits is given in Annex A and EN 1992 to EN 1999.

5.1.4 Fire design

12/07/2004, (1)P The structural fire design analysis shall be based on design fire scenarios (see EN

1991-1-2), and shall consider models for the temperature evolution within the structure

as well as models for the mechanical behaviour of the structure at elevated temperature.

(2) The required performance of the structure exposed to fire should be verified by ei-

ther global analysis, analysis of sub-assemblies or member analysis, as well as the use of

PORTSMOUTH, tabular data or test results.

(3) The behaviour of the structure exposed to fire should be assessed by taking into ac-

count either :

– nominal fire exposure, or

– modelled fire exposure,

as well as the accompanying actions.

OF

copy:UNIVERSITY NOTE See also EN 1991-1-2.

(4) The structural behaviour at elevated temperatures should be assessed in accordance

with EN 1992 to EN 1996 and EN 1999, which give thermal and structural models for

analysis.

Licensed 36 EN 1990:2002 (E)

(5) Where relevant to the specific material and the method of assessment :

– thermal models may be based on the assumption of a uniform or a non-uniform tem-

perature within cross-sections and along members ;

– structural models may be confined to an analysis of individual members or may ac-

count for the interaction between members in fire exposure.

(6) The models of mechanical behaviour of structural members at elevated temperatures

should be non-linear.

NOTE See also EN 1991 to EN 1999.

5.2 Design assisted by testing

BSI (1) Design may be based on a combination of tests and calculations.

© NOTE Testing may be carried out, for example, in the following circumstances :

– if adequate calculation models are not available ;

Copy, – if a large number of similar components are to be used ;

– to confirm by control checks assumptions made in the design.

See Annex D.

Uncontrolled (2)P Design assisted by test results shall achieve the level of reliability required for the

relevant design situation. The statistical uncertainty due to a limited number of test re-

sults shall be taken into account.

(3) Partial factors (including those for model uncertainties) comparable to those used in

EN 1991 to EN 1999 should be used.

12/07/2004,

PORTSMOUTH,

OF

copy:UNIVERSITY

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EN 1990:2002 (E)

Section 6 Verification by the partial factor method

6.1 General

(1)P When using the partial factor method, it shall be verified that, in all relevant design

situations, no relevant limit state is exceeded when design values for actions or effects of

actions and resistances are used in the design models.

(2) For the selected design situations and the relevant limit states the individual actions for

the critical load cases should be combined as detailed in this section. However actions that

cannot occur simultaneously, for example due to physical reasons, should not be

considered together in combination.

BSI (3) Design values should be obtained by using :

- the characteristic, or

© - other representative values,

Copy, in combination with partial and other factors as defined in this section and EN 1991 to

EN 1999.

Uncontrolled (4) It can be appropriate to determine design values directly where conservative values

should be chosen.

(5)P Design values directly determined on statistical bases shall correspond to at least

the same degree of reliability for the various limit states as implied by the partial factors

given in this standard.

12/07/2004, 6.2 Limitations

(1) The use of the Application Rules given in EN 1990 is limited to ultimate and

serviceability limit state verifications of structures subject to static loading, including cases

where the dynamic effects are assessed using equivalent quasi-static loads and dynamic

amplification factors, including wind or traffic loads. For non-linear analysis and fatigue

PORTSMOUTH, the specific rules given in various Parts of EN 1991 to EN 1999 should be applied.

6.3 Design values

6.3.1 Design values of actions

OF F F

(1) The design value of an action can be expressed in general terms as :

d

copy:UNIVERSITY (6.1a)

F F

d f rep

with :

F F (6.1b)

rep k

where :

Licensed 38 EN 1990:2002 (E)

F is the characteristic value of the action.

k

F is the relevant representative value of the action.

rep

is a partial factor for the action which takes account of the possibility of unfa-

f vourable deviations of the action values from the representative values.

is either 1,00 or , or .

0 1 2 A

(2) For seismic actions the design value should be determined taking account of the

Ed

structural behaviour and other relevant criteria detailed in EN 1998.

6.3.2 Design values of the effects of actions ) can be

(1) For a specific load case the design values of the effects of actions (E

d

BSI expressed in general terms as :

(6.2)

E E F a i

; 1

d Sd f i rep i d

, ,

©

Copy, where : is the design values of the geometrical data (see 6.3.4) ;

a

Uncontrolled d

is a partial factor taking account of uncertainties :

Sd in modelling the effects of actions ;

in some cases, in modelling the actions.

NOTE In a more general case the effects of actions depend on material properties.

12/07/2004, (2) In most cases, the following simplification can be made :

(6.2a)

E E F a i

; 1

d F i rep i d

, ,

with :

PORTSMOUTH,

(6.2b)

F i Sd f i

, ,

e.g.

NOTE When relevant, where geotechnical actions are involved, partial factors can be applied to

F,i

can be globally applied to the effect of the

the effects of individual actions or only one particular factor F

combination of actions with appropriate partial factors.

OF (3)P Where a distinction has to be made between favourable and unfavourable effects of

copy:UNIVERSITY permanent actions, two different partial factors shall be used ( and ).

G,inf G,sup

(4) For non-linear analysis (i.e. when the relationship between actions and their effects is

not linear), the following simplified rules may be considered in the case of a single

predominant action :

a) When the action effect increases more than the action, the partial factor should be

F

applied to the representative value of the action.

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EN 1990:2002 (E)

b) When the action effect increases less than the action, the partial factor should be

F

applied to the action effect of the representative value of the action.

NOTE Except for rope, cable and membrane structures, most structures or structural elements are in

category a).

(5) In those cases where more refined methods are detailed in the relevant EN 1991 to

EN 1999 (e.g. for prestressed structures), they should be used in preference to 6.3.2(4).

6.3.3 Design values of material or product properties

X

(1) The design value of a material or product property can be expressed in general

d

terms as :

X

BSI k

X (6.3)

d m

©

Copy, where :

X is the characteristic value of the material or product property (see 4.2(3)) ;

k

Uncontrolled is the mean value of the conversion factor taking into account

– volume and scale effects,

– effects of moisture and temperature, and

– any other relevant parameters ;

is the partial factor for the material or product property to take account of :

12/07/2004, m – the possibility of an unfavourable deviation of a material or product property

from its characteristic value ; .

– the random part of the conversion factor

(2) Alternatively, in appropriate cases, the conversion factor may be :

– implicitly taken into account within the characteristic value itself, or

PORTSMOUTH,

– by using instead of (see expression (6.6b)).

M m

NOTE The design value can be established by such means as :

– empirical relationships with measured physical properties, or

– with chemical composition, or

– from previous experience, or

– from values given in European Standards or other appropriate documents.

OF

copy:UNIVERSITY 6.3.4 Design values of geometrical data

(1) Design values of geometrical data such as dimensions of members that are used to

assess action effects and/or resistances may be represented by nominal values :

a a

= (6.4)

d nom

Licensed 40 EN 1990:2002 (E)

(2)P Where the effects of deviations in geometrical data (e.g. inaccuracy in the load

application or location of supports) are significant for the reliability of the structure (e.g.

by second order effects) the design values of geometrical data shall be defined by :

a a a (6.5)

d nom

where :

a takes account of :

– the possibility of unfavourable deviations from the characteristic or nominal

values ;

– the cumulative effect of a simultaneous occurrence of several geometrical de-

viations.

BSI

a 0

a a

NOTE 1 can also represent geometrical imperfections where = 0 (i.e., ).

d nom

© NOTE 2 Where relevant, EN 1991 to EN 1999 provide further provisions.

Copy, (3) Effects of other deviations should be covered by partial factors

– on the action side ( ), and/or

F

– resistance side ( ).

Uncontrolled M

NOTE Tolerances are defined in the relevant standards on execution referred to in EN 1990 to EN 1999.

6.3.5 Design resistance R

(1) The design resistance can be expressed in the following form :

d

12/07/2004,

X

1 1 k i

,

R R X a R a i

; ; 1 (6.6)

d d i d i d

,

Rd Rd m i

,

where :

is a partial factor covering uncertainty in the resistance model, plus geometric

PORTSMOUTH, Rd deviations if these are not modelled explicitly (see 6.3.4(2));

X i.

is the design value of material property

d,i

(2) The following simplification of expression (6.6) may be made :

OF X k i

,

R R a

; i 1 (6.6a)

d i d

copy:UNIVERSITY M i

,

where :

(6.6b)

M i Rd m i

, ,

may be incorporated in , see 6.3.3.(2).

NOTE i M,i

Licensed 41

EN 1990:2002 (E)

(3) Alternatively to expression (6.6a), the design resistance may be obtained directly from

the characteristic value of a material or product resistance, without explicit determination

of design values for individual basic variables, using :

R k

R (6.6c)

d M

NOTE This is applicable to products or members made of a single material (e.g. steel) and is also used in

connection with Annex D “Design assisted by testing”.

(4) Alternatively to expressions (6.6a) and (6.6c), for structures or structural members that

are analysed by non-linear methods, and comprise more than one material acting in

association, or where ground properties are involved in the design resistance, the following

expression for design resistance can be used :

BSI

1 m ,

1

R R X X a

; ; (6.6d)

d k i k i i d

1 ,

1 , ( 1

)

© M m i

,

1 ,

Copy, partial factors to the

NOTE In some cases, the design resistance can be expressed by applying directly M

individual resistances due to material properties.

Uncontrolled 6.4 Ultimate limit states

6.4.1 General

(1)P The following ultimate limit states shall be verified as relevant :

12/07/2004, a) EQU : Loss of static equilibrium of the structure or any part of it considered as a

rigid body, where :

– minor variations in the value or the spatial distribution of actions from a single

source are significant, and

– the strengths of construction materials or ground are generally not governing ;

PORTSMOUTH, b) STR : Internal failure or excessive deformation of the structure or structural mem-

bers, including footings, piles, basement walls, etc., where the strength of construc-

tion materials of the structure governs ;

c) GEO : Failure or excessive deformation of the ground where the strengths of soil or

rock are significant in providing resistance ;

OF d) FAT : Fatigue failure of the structure or structural members.

copy:UNIVERSITY NOTE For fatigue design, the combinations of actions are given in EN 1992 to EN 1999.

(2)P The design values of actions shall be in accordance with Annex A.

Licensed 42 EN 1990:2002 (E)

6.4.2 Verifications of static equilibrium and resistance

(1)P When considering a limit state of static equilibrium of the structure (EQU), it shall be

verified that :

E E (6.7)

d ,dst d ,stb

where :

E is the design value of the effect of destabilising actions ;

d ,dst

E is the design value of the effect of stabilising actions.

d ,stb

BSI (2) Where appropriate the expression for a limit state of static equilibrium may be

supplemented by additional terms, including, for example, a coefficient of friction between

© rigid bodies.

Copy, (3)P When considering a limit state of rupture or excessive deformation of a section,

member or connection (STR and/or GEO), it shall be verified that :

Uncontrolled

E R (6.8)

d d

where :

E is the design value of the effect of actions such as internal force, moment or a vector

d representing several internal forces or moments ;

12/07/2004, R is the design value of the corresponding resistance.

d

NOTE.1 Details for the methods STR and GEO are given in Annex A.

NOTE 2 Expression (6.8) does not cover all verification formats concerning buckling, i.e. failure that

happens where second order effects cannot be limited by the structural response, or by an acceptable

PORTSMOUTH, structural response. See EN 1992 to EN 1999.

6.4.3 Combination of actions (fatigue verifications excluded)

6.4.3.1 General

OF (1)P For each critical load case, the design values of the effects of actions (E ) shall be

d

determined by combining the values of actions that are considered to occur

copy:UNIVERSITY simultaneously.

(2) Each combination of actions should include :

– a leading variable action, or

– an accidental action.

(3) The combinations of actions should be in accordance with 6.4.3.2 to 6.4.3.4.

Licensed 43

EN 1990:2002 (E)

(4)P Where the results of a verification are very sensitive to variations of the magnitude of

a permanent action from place to place in the structure, the unfavourable and the

favourable parts of this action shall be considered as individual actions.

NOTE This applies in particular to the verification of static equilibrium and analogous limit states, see

6.4.2(2).

(5) Where several effects of one action (e.g. bending moment and normal force due to self-

weight) are not fully correlated, the partial factor applied to any favourable component

may be reduced.

NOTE For further guidance on this topic see the clauses on vectorial effects in EN 1992 to EN 1999.

(6) Imposed deformations should be taken into account where relevant.

BSI NOTE For further guidance, see 5.1.2.4(P) and EN 1992 to EN 1999.

© 6.4.3.2 Combinations of actions for persistent or transient design situations (funda-

Copy, mental combinations)

(1) The general format of effects of actions should be :

Uncontrolled

E E G P Q Q j i

; ; ; 1 ; 1 (6.9a)

d Sd g j k j p q k q i i k i

, , ,

1 ,

1 , 0 , ,

(2) The combination of effects of actions to be considered should be based on

– the design value of the leading variable action, and

– the design combination values of accompanying variable actions :

12/07/2004, NOTE See also 6.4.3.2(4).

E E G P Q Q j i

; ; ; 1 ; 1 (6.9b)

d G j k j P Q k Q i i k i

, , ,

1 ,

1 , 0 , ,

(3) The combination of actions in brackets { }, in (6.9b) may either be expressed as :

PORTSMOUTH,

G P Q Q

"+" "+" "+" (6.10)

, k, j P Q,1 k,1 Q, i 0, i k, i

G j

j 1 i >

1

or, alternatively for STR and GEO limit states, the less favourable of the two following

expressions:

OF

(6.10a)

G P Q Q

" " " " " "

G j k j P Q k Q i i k i

, , ,

1 0 ,

1 ,

1 , 0 , ,

j i

1 1

copy:UNIVERSITY

(6.10b)

G P Q Q

" " " " " "

j G j k j P Q k Q i i k i

, , ,

1 ,

1 , 0 , ,

j i

1 1

Where :

"+ " implies "to be combined with"

implies "the combined effect of"

G

is a reduction factor for unfavourable permanent actions

Licensed 44 EN 1990:2002 (E)

NOTE Further information for this choice is given in Annex A.

(4) If the relationship between actions and their effects is not linear, expressions (6.9a) or

(6.9b) should be applied directly, depending upon the relative increase of the effects of

actions compared to the increase in the magnitude of actions (see also 6.3.2.(4)).

6.4.3.3 Combinations of actions for accidental design situations

(1) The general format of effects of actions should be :

E E G P A Q Q j i

; ; ; ( or ) ; 1 ; 1 (6.11a)

d k j d k i k i

, 1,1 2,1 ,

1 2 , ,

(2) The combination of actions in brackets { } can be expressed as :

BSI

(6.11b)

G P A Q Q

" " "+" "+" ( or ) "+"

1,1 2,1 2, i

k, j d k,1 k, i

© j 1 i 1

Copy,

Q Q

(3) The choice between or should be related to the relevant accidental

1,1 k,1 2,1 k,1

design situation (impact, fire or survival after an accidental event or situation).

Uncontrolled NOTE Guidance is given in the relevant Parts of EN 1991 to EN 1999.

(4) Combinations of actions for accidental design situations should either

A

– involve an explicit accidental action (fire or impact), or

– refer to a situation after an accidental event (A = 0).

12/07/2004, A

For fire situations, apart from the temperature effect on the material properties, should

d

represent the design value of the indirect thermal action due to fire.

6.4.3.4 Combinations of actions for seismic design situations

(1) The general format of effects of actions should be :

PORTSMOUTH,

E E G P A Q j i

; ; ; 1 ; 1 (6.12a)

d k j Ed i k i

, 2 , ,

(2) The combination of actions in brackets { } can be expressed as :

G P A Q

" " "+" "+" (6.12b)

2, i

OF , Ed k, i

k j

j 1 i 1

copy:UNIVERSITY 6.4.4 Partial factors for actions and combinations of actions

(1) The values of the and factors for actions should be obtained from EN 1991 and

from Annex A.

Licensed 45

EN 1990:2002 (E)

6.4.5 Partial factors for materials and products

(1) The partial factors for properties of materials and products should be obtained from

EN 1992 to EN 1999.

6.5 Serviceability limit states

6.5.1 Verifications

(1)P It shall be verified that :

C

E (6.13)

d d

BSI where :

© C is the limiting design value of the relevant serviceability criterion.

d

Copy, E is the design value of the effects of actions specified in the serviceability

d criterion, determined on the basis of the relevant combination.

Uncontrolled 6.5.2 Serviceability criteria

(1) The deformations to be taken into account in relation to serviceability requirements

should be as detailed in the relevant Annex A according to the type of construction

works, or agreed with the client or the National authority.

12/07/2004, NOTE For other specific serviceability criteria such as crack width, stress or strain limitation, slip

resistance, see EN 1991 to EN 1999.

6.5.3 Combination of actions

(1) The combinations of actions to be taken into account in the relevant design

PORTSMOUTH, situations should be appropriate for the serviceability requirements and performance

criteria being verified.

(2) The combinations of actions for serviceability limit states are defined symbolically

by the following expressions (see also 6.5.4) :

OF NOTE It is assumed, in these expressions, that all partial factors are equal to 1. See Annex A and

EN 1991 to EN 1999.

copy:UNIVERSITY a) Characteristic combination :

E E G P Q Q j i

; ; ; 1 ; 1 (6.14a)

d k j k i k i

, ,

1 0

, ,

in which the combination of actions in brackets { } (called the characteristic

combination), can be expressed as :

Licensed 46 EN 1990:2002 (E)

G P Q Q (6.14b)

"+" "+" "+"

k j

, k,1 0, i k, i

j i

1 1

NOTE The characteristic combination is normally used for irreversible limit states.

b) Frequent combination :

E E G P Q Q j i (6.15a)

; ; ; 1 ; 1

d k j k i k i

, 1

,

1 ,

1 2 , ,

in which the combination of actions in brackets { }, (called the frequent combination),

can be expressed as :

G P Q Q (6.15b)

"+" "+" "+"

k j

, 1,1 k,1 2, i k, i

j i

1 1

BSI NOTE The frequent combination is normally used for reversible limit states.

©

Copy, c) Quasi-permanent combination :

E E G P Q j i

; ; 1 ; 1 (6.16a)

Uncontrolled d k j i k i

, 2 , ,

in which the combination of actions in brackets { }, (called the quasi-permanent

combination), can be expressed as :

G P Q (6.16b)

"+" "+"

k j

, 2, i k, i

j i

1 1

12/07/2004, where the notation is as given in 1.6 and 6.4.3(1).

NOTE The quasi-permanent combination is normally used for long-term effects and the appearance of the

structure.

PORTSMOUTH, P P

(3) For the representative value of the prestressing action (i.e. or ), reference

k m

should be made to the relevant design Eurocode for the type of prestress under

consideration.

(4)P Effects of actions due to imposed deformations shall be considered where relevant.

OF NOTE In some cases expressions (6.14) to (6.16) require modification. Detailed rules are given in the

relevant Parts of EN 1991 to EN 1999.

copy:UNIVERSITY 6.5.4 Partial factors for materials

(1) For serviceability limit states the partial factors for the properties of materials

M

should be taken as 1,0 except if differently specified in EN 1992 to EN 1999.

Licensed 47

EN 1990:2002 (E) Annex A1

(normative)

Application for Buildings

A1.1 Field of application

1) This annex A1 gives rules and methods for establishing combinations of actions for

(

buildings. It also gives the recommended design values of permanent, variable and acci-

dental actions and factors to be used in the design of buildings.

NOTE Guidance may be given in the National annex with regard to the use of Table 2.1 (design working

life).

BSI A1.2 Combinations of actions

© A1.2.1 General

Copy, (1) Effects of actions that cannot exist simultaneously due to physical or functional

reasons should not be considered together in combinations of actions.

Uncontrolled NOTE 1 Depending on its uses and the form and the location of a building, the combinations of actions

may be based on not more than two variable actions.

NOTE 2 Where modifications of A1.2.1(2) and A1.2.1(3) are necessary for geographical reasons, these

can be defined in the National annex.

12/07/2004, (2) The combinations of actions given in expressions 6.9a to 6.12b should be used when

verifying ultimate limit states.

(3) The combinations of actions given in expressions 6.14a to 6.16b should be used

when verifying serviceability limit states.

PORTSMOUTH, (4) Combinations of actions that include prestressing forces should be dealt with as

detailed in EN 1992 to EN 1999.

A1.2.2 Values of factors

(1) Values of factors should be specified.

OF

NOTE Recommended values of factors for the more common actions may be obtained from Table

copy:UNIVERSITY A1.1.

Licensed 48 EN 1990:2002 (E)

Table A1.1 - Recommended values of factors for buildings

Action 0 1 2

Imposed loads in buildings, category (see

EN 1991-1-1) 0,3

0,5

0,7

Category A : domestic, residential areas 0,3

0,5

0,7

Category B : office areas 0,6

0,7

0,7

Category C : congregation areas 0,6

0,7

0,7

Category D : shopping areas 0,8

0,9

1,0

Category E : storage areas

Category F : traffic area, 0,6

0,7

0,7

vehicle weight 30kN

Category G : traffic area, 0,3

0,5

0,7

30kN < vehicle weight 160kN 0

0

0

Category H : roofs

Snow loads on buildings (see EN 1991-1-3)*

BSI Finland, Iceland, Norway, Sweden 0,70 0,50 0,20

Remainder of CEN Member States, for sites 0,70 0,50 0,20

© located at altitude H > 1000 m a.s.l.

Remainder of CEN Member States, for sites 0,50 0,20 0

Copy,

located at altitude H 1000 m a.s.l.

Wind loads on buildings (see EN 1991-1-4) 0,6 0,2 0

Temperature (non-fire) in buildings (see EN 0,6 0,5 0

Uncontrolled 1991-1-5)

NOTE The values may be set by the National annex.

* For countries not mentioned below, see relevant local conditions.

A1.3 Ultimate limit states

A1.3.1 Design values of actions in persistent and transient design situations

12/07/2004, (1) The design values of actions for ultimate limit states in the persistent and transient

design situations (expressions 6.9a to 6.10b) should be in accordance with Tables

A1.2(A) to (C). e.g.

NOTE The values in Tables A1.2 ((A) to (C)) can be altered for different reliability levels in the

National annex (see Section 2 and Annex B).

PORTSMOUTH, (2) In applying Tables A1.2(A) to A1.2(C) in cases when the limit state is very sensitive

to variations in the magnitude of permanent actions, the upper and lower characteristic

values of actions should be taken according to 4.1.2(2)P.

(3) Static equilibrium (EQU, see 6.4.1) for building structures should be verified using

OF the design values of actions in Table A1.2(A).

copy:UNIVERSITY (4) Design of structural members (STR, see 6.4.1) not involving geotechnical actions

should be verified using the design values of actions from Table A1.2(B).

(5) Design of structural members (footings, piles, basement walls, etc.) (STR) involving

geotechnical actions and the resistance of the ground (GEO, see 6.4.1) should be veri-

fied using one of the following three approaches supplemented, for geotechnical actions

and resistances, by EN 1997 :

Licensed 49

EN 1990:2002 (E)

– Approach 1: Applying in separate calculations design values from Table A1.2(C) and

Table A1.2(B) to the geotechnical actions as well as the other actions on/from the

structure. In common cases, the sizing of foundations is governed by Table A1.2(C)

and the structural resistance is governed by Table A1.2(B) ;

NOTE In some cases, application of these tables is more complex, see EN 1997.

– Approach 2 : Applying design values from Table A1.2(B) to the geotechnical actions

as well as the other actions on/from the structure ;

– Approach 3 : Applying design values from Table A1.2(C) to the geotechnical actions

and, simultaneously, applying partial factors from Table A1.2(B) to the other actions

on/from the structure,

NOTE The use of approaches 1, 2 or 3 is chosen in the National annex.

BSI (6) Overall stability for building structures (e.g. the stability of a slope supporting a

© building) should be verified in accordance with EN 1997.

Copy, (7) Hydraulic and buoyancy failure (e.g. in the bottom of an excavation for a building

structure) should be verified in accordance with EN 1997.

Uncontrolled

12/07/2004,

PORTSMOUTH,

OF

copy:UNIVERSITY

Licensed 50 EN 1990:2002 (E)

Table A1.2(A) - Design values of actions (EQU) (Set A)

Persistent Permanent actions Leading Accompanying variable

and variable actions

transient action (*)

design

situations Unfavourable Favourable Main Others

(if any)

(Eq. 6.10) G G Q

Q

Gj,sup kj,sup Gj,inf kj,inf Q,1 k,1 Q,i 0,i k,i

(*) Variable actions are those considered in Table A1.1

BSI

NOTE 1 The values may be set by the National annex. The recommended set of values for are :

= 1,10

Gj,sup

© = 0,90

Gj,inf

Copy, = 1,50 where unfavourable (0 where favourable)

Q,1

= 1,50 where unfavourable (0 where favourable)

Q,i

Uncontrolled NOTE 2 In cases where the verification of static equilibrium also involves the resistance of structural

members, as an alternative to two separate verifications based on Tables A1.2(A) and A1.2(B), a

combined verification, based on Table A1.2(A), may be adopted, if allowed by the National annex, with

the following set of recommended values. The recommended values may be altered by the National

annex.

= 1,35

Gj,sup

= 1,15

Gj,inf

12/07/2004, = 1,50 where unfavourable (0 where favourable)

Q,1

= 1,50 where unfavourable (0 where favourable)

Q,i = 1,00 both to the favourable part and to the unfavourable part of permanent

provided that applying Gj,inf

actions does not give a more unfavourable effect.

PORTSMOUTH,

OF

copy:UNIVERSITY

Licensed 51

Licensed copy:UNIVERSITY OF PORTSMOUTH, 12/07/2004, Uncontrolled Copy, © BSI

EN 1990:2002 (E) Table A1.2(B) - Design values of actions (STR/GEO) (Set B) Accompanying

Permanent actions Leading

Accompanying Persistent

Permanent actions Leading

Persistent variable actions (*)

variable

variable actions (*) and

variable

and action (*)

transient

action

transient design

design situations

situations Unfavourable Favourable Main Others Unfavourable Favourable Action Main Others

(if any)

(Eq. 6.10) (Eq. 6.10a)

Q Q Q Q

G G G G

Q,1 k,1 Q,i 0,i k,i Q,1 0,1 k,1 Q,i 0,i k,i

Gj,sup kj,sup Gj,inf kj,inf Gj,sup kj,sup Gj,inf kj,inf

(Eq. 6.10b) Q Q

G G Q,1 k,1 Q,i 0,i k,i

Gj,sup kj,sup Gj,inf kj,inf

(*) Variable actions are those considered in Table A1.1

NOTE 1 The choice between 6.10, or 6.10a and 6.10b will be in the National annex. In case of 6.10a and 6.10b, the National annex may in addition modify 6.10a to include

permanent actions only.

NOTE 2 The and values may be set by the National annex. The following values for and are recommended when using expressions 6.10, or 6.10a and 6.10b.

= 1,35

Gj,sup

= 1,00

Gj,inf

= 1,50 where unfavourable (0 where favourable)

Q,1

= 1,50 where unfavourable (0 where favourable)

Q,i

= 0,85 1,35 1,15).

= 0,85 (so that Gj,sup

See also EN 1991 to EN 1999 for values to be used for imposed deformations.

NOTE 3 The characteristic values of all permanent actions from one source are multiplied by if the total resulting action effect is unfavourable and if the total resulting

G,sup G,inf

action effect is favourable. For example, all actions originating from the self weight of the structure may be considered as coming from one source ; this also applies if different

materials are involved.

NOTE 4 For particular verifications, the values for and may be subdivided into and and the model uncertainty factor . A value of in the range 1,05 to 1,15 can be used

G Q g q Sd Sd

in most common cases and can be modified in the National annex.

52 EN 1990:2002 (E)

Table A1.2(C) - Design values of actions (STR/GEO) (Set C)

Persistent Permanent actions Leading Accompanying variable

and variable actions (*)

transient action (*)

design

situation Unfavourable Favourable Main (if any) Others

(Eq. 6.10) G G Q Q

Gj,sup kj,sup Gj,inf kj,inf Q,1 k,1 Q,i 0,i k,i

(*) Variable actions are those considered in Table A1.1

NOTE The values may be set by the National annex. The recommended set of values for are :

BSI = 1,00

Gj,sup

= 1,00

© Gj,inf

= 1,30 where unfavourable (0 where favourable)

Copy, Q,1

= 1,30 where unfavourable (0 where favourable)

Q,i

Uncontrolled A1.3.2 Design values of actions in the accidental and seismic design situations

(1) The partial factors for actions for the ultimate limit states in the accidental and seis-

mic design situations (expressions 6.11a to 6.12b) should be 1,0. values are given in

Table A1.1.

12/07/2004, .

NOTE For the seismic design situation see also EN 1998

Table A1.3 - Design values of actions for use in accidental and seismic

combinations of actions

PORTSMOUTH, Design Permanent actions Leading Accompanying

situation accidental variable actions (**)

or seismic

action

Unfavourable Favourable Main (if any) Others

Accidental (*) G G A or Q

kj,sup kj,inf d 11 2,i k,i

OF

(Eq. 6.11a/b) Q

21 k1

copy:UNIVERSITY

Seismic G G A or A Q

kj,sup kj,inf I Ek Ed 2,i k,i

(Eq. 6.12a/b)

(*) In the case of accidental design situations, the main variable action may be taken with its frequent or, as in

seismic combinations of actions, its quasi-permanent values. The choice will be in the National annex,

depending on the accidental action under consideration. See also EN 1991-1-2.

(**) Variable actions are those considered in Table A1.1.

Licensed 53

EN 1990:2002 (E)

A1.4 Serviceability limit states

A1.4.1 Partial factors for actions

(1) For serviceability limit states the partial factors for actions should be taken as 1,0

except if differently specified in EN 1991 to EN 1999.

Table A1.4 - Design values of actions for use in the combination of actions

Combination Permanent actions G Variable actions Q

d d

Unfavourable Favourable Leading Others

Characteristic G G Q Q

kj,sup kj,inf k,1 0,i k,i

BSI Frequent

G G Q Q

kj,sup kj,inf

© 1,1 k,1 2,i k,i

Copy, Quasi-permanent

G G Q Q

kj,sup kj,inf 2,1 k,1 2,i k,i

Uncontrolled A1.4.2 Serviceability criteria

(1) Serviceability limit states in buildings should take into account criteria related, for

example, to floor stiffness, differential floor levels, storey sway or/and building sway

and roof stiffness. Stiffness criteria may be expressed in terms of limits for vertical de-

flections and for vibrations. Sway criteria may be expressed in terms of limits for hori-

zontal displacements.

12/07/2004, (2) The serviceability criteria should be specified for each project and agreed with the

client.

NOTE The serviceability criteria may be defined in the National annex.

PORTSMOUTH, (3)P The serviceability criteria for deformations and vibrations shall be defined :

– depending on the intended use ;

– in relation to the serviceability requirements in accordance with 3.4 ;

– independently of the materials used for supporting structural member.

A1.4.3 Deformations and horizontal displacements

OF

copy:UNIVERSITY (1) Vertical and horizontal deformations should be calculated in accordance with

EN 1992 to EN 1999, by using the appropriate combinations of actions according to

expressions (6.14a) to (6.16b) taking into account the serviceability requirements given

in 3.4(1). Special attention should be given to the distinction between reversible and

irreversible limit states.

(2) Vertical deflections are represented schematically in Figure. A1.1.

Licensed 54 EN 1990:2002 (E)

Figure A1.1 - Definitions of vertical deflections

Key :

w Precamber in the unloaded structural member

c

w Initial part of the deflection under permanent loads of the relevant combination of

1 actions according to expressions (6.14a) to (6.16b)

BSI w Long-term part of the deflection under permanent loads

2

w Additional part of the deflection due to the variable actions of the relevant combi-

3 nation of actions according to expressions (6.14a) to (6.16b)

© Total deflection as sum of w , w , w

w

Copy, tot 1 2 3

w Remaining total deflection taking into account the precamber

max

Uncontrolled (3) If the functioning or damage of the structure or to finishes, or to non-structural

members (e.g. partition walls, claddings) is being considered, the verification for de-

flection should take account of those effects of permanent and variable actions that oc-

cur after the execution of the member or finish concerned.

NOTE Guidance on which expression (6.14a) to (6.16b) to use is given in 6.5.3 and EN 1992 to

EN 1999.

12/07/2004, (4) If the appearance of the structure is being considered, the quasi-permanent combina-

tion (expression 6.16b) should be used.

(5) If the comfort of the user, or the functioning of machinery are being considered, the

verification should take account of the effects of the relevant variable actions.

PORTSMOUTH, (6) Long term deformations due to shrinkage, relaxation or creep should be considered

where relevant, and calculated by using the effects of the permanent actions and quasi-

permanent values of the variable actions.

(7) Horizontal displacements are represented schematically in Figure A1.2.

OF

copy:UNIVERSITY

Licensed 55

EN 1990:2002 (E)

Figure A1.2 - Definition of horizontal displacements

BSI Key :

© u Overall horizontal displacement over the building height H

Copy, u Horizontal displacement over a storey height H

i i

A1.4.4 Vibrations

Uncontrolled (1) To achieve satisfactory vibration behaviour of buildings and their structural

members under serviceability conditions, the following aspects, amongst others,

should be considered :

a) the comfort of the user;

b) the functioning of the structure or its structural members (e.g. cracks in

12/07/2004, partitions, damage to cladding, sensitivity of building contents to vibrations).

Other aspects should be considered for each project and agreed with the client.

(2) For the serviceability limit state of a structure or a structural member not to be

exceeded when subjected to vibrations, the natural frequency of vibrations of the

PORTSMOUTH, structure or structural member should be kept above appropriate values which

depend upon the function of the building and the source of the vibration, and agreed

with the client and/or the relevant authority.

(3) If the natural frequency of vibrations of the structure is lower than the appropriate

value, a more refined analysis of the dynamic response of the structure, including the

OF consideration of damping, should be performed.

copy:UNIVERSITY NOTE For further guidance, see EN 1991-1-1, EN 1991-1-4 and ISO 10137.

(4) Possible sources of vibration that should be considered include walking,

synchronised movements of people, machinery, ground borne vibrations from traffic,

and wind actions. These, and other sources, should be specified for each project and

agreed with the client.

Licensed 56 EN 1990:2002 (E)

Annex B

(informative)

Management of Structural Reliability for Construction Works

B1 Scope and field of application

(1) This annex provides additional guidance to 2.2 (Reliability management) and to ap-

propriate clauses in EN 1991 to EN 1999.

NOTE Reliability differentiation rules have been specified for particular aspects in the design Eurocodes,

e.g. in EN 1992, EN 1993, EN 1996, EN 1997 and EN 1998.

BSI (2) The approach given in this Annex recommends the following procedures for the

management of structural reliability for construction works (with regard to ULSs, ex-

© cluding fatigue) :

Copy, a) In relation to 2.2(5)b, classes are introduced and are based on the assumed

consequences of failure and the exposure of the construction works to hazard. A

Uncontrolled procedure for allowing moderate differentiation in the partial factors for actions and

resistances corresponding to the classes is given in B3.

NOTE Reliability classification can be represented by indexes (see Annex C) which takes account of

accepted or assumed statistical variability in action effects and resistances and model uncertainties.

b) In relation to 2.2(5)c and 2.2(5)d, a procedure for allowing differentiation between

12/07/2004, various types of construction works in the requirements for quality levels of the design and

execution process are given in B4 and B5.

NOTE Those quality management and control measures in design, detailing and execution which are given

in B4 and B5 aim to eliminate failures due to gross errors, and ensure the resistances assumed in the design.

PORTSMOUTH, (3) The procedure has been formulated in such a way so as to produce a framework to al-

low different reliability levels to be used, if desired.

B2 Symbols

In this annex the following symbols apply.

OF K Factor applicable to actions for reliability differentiation

FI

copy:UNIVERSITY Reliability index

Licensed 57

EN 1990:2002 (E)

B3 Reliability differentiation

B3.1 Consequences classes

(1) For the purpose of reliability differentiation, consequences classes (CC) may be

established by considering the consequences of failure or malfunction of the structure

as given in Table B1.

Table B1 - Definition of consequences classes

Consequences Description Examples of buildings and civil

Class engineering works

Grandstands, public buildings where

CC3 consequence for loss of human

High consequences of failure are high (e.g. a

life, or economic, social or concert hall)

environmental consequences very great

BSI Residential and office buildings, public

CC2 consequence for loss of human

Medium buildings where consequences of failure

life, economic, social or environmental

© are medium (e.g. an office building)

consequences considerable Agricultural buildings where people do

CC1 consequence for loss of human life,

Low

Copy, not normally enter (e.g. storage

and economic, social or environmental buildings), greenhouses

consequences small or negligible

Uncontrolled (2) The criterion for classification of consequences is the importance, in terms of

consequences of failure, of the structure or structural member concerned. See B3.3

(3) Depending on the structural form and decisions made during design, particular

members of the structure may be designated in the same, higher or lower consequences

class than for the entire structure.

12/07/2004, NOTE At the present time the requirements for reliability are related to the structural members of the

construction works.

B3.2 Differentiation by values

(1) The reliability classes (RC) may be defined by the reliability index concept.

PORTSMOUTH, (2) Three reliability classes RC1, RC2 and RC3 may be associated with the three

consequences classes CC1, CC2 and CC3.

(3) Table B2 gives recommended minimum values for the reliability index associated with

reliability classes (see also annex C).

OF

copy:UNIVERSITY

Licensed 58 EN 1990:2002 (E)

Table B2 - Recommended minimum values for reliability index (ultimate limit

states)

Reliability Class Minimum values for

1 year reference period 50 years reference period

RC3 5,2 4,3

RC2 4,7 3,8

RC1 4,2 3,3

NOTE A design using EN 1990 with the partial factors given in annex A1 and EN 1991 to EN 1999 is

considered generally to lead to a structure with a value greater than 3,8 for a 50 year reference period.

Reliability classes for members of the structure above RC3 are not further considered in this Annex, since

BSI these structures each require individual consideration.

© B3.3 Differentiation by measures relating to the partial factors

Copy,

(1) One way of achieving reliability differentiation is by distinguishing classes of F

factors to be used in fundamental combinations for persistent design situations. For ex-

Uncontrolled ample, for the same design supervision and execution inspection levels, a multiplication

factor K , see Table B3, may be applied to the partial factors.

FI Table B3 - K factor for actions

FI

K factor for actions Reliability class

FI RC1 RC2 RC3

12/07/2004, K 0,9 1,0 1,1

FI

NOTE In particular, for class RC3, other measures as described in this Annex are normally preferred to

using K factors. K should be applied only to unfavourable actions.

FI FI

(2) Reliability differentiation may also be applied through the partial factors on resistance

PORTSMOUTH, . However, this is not normally used. An exception is in relation to fatigue verification

M

(see EN 1993). See also B6.

(3) Accompanying measures, for example the level of quality control for the design and

. In this Annex, a three

execution of the structure, may be associated to the classes of F

level system for control during design and execution has been adopted. Design supervision

OF levels and inspection levels associated with the reliability classes are suggested.

copy:UNIVERSITY (4) There can be cases (e.g. lighting poles, masts, etc.) where, for reasons of economy, the

structure might be in RC1, but be subjected to higher corresponding design supervision

and inspection levels.

B4 Design supervision differentiation

(1) Design supervision differentiation consists of various organisational quality control

measures which can be used together. For example, the definition of design supervision

Licensed 59

EN 1990:2002 (E)

level (B4(2)) may be used together with other measures such as classification of designers

and checking authorities (B4(3)).

(2) Three possible design supervision levels (DSL) are shown in Table B4. The design

supervision levels may be linked to the reliability class selected or chosen according to the

importance of the structure and in accordance with National requirements or the design

brief, and implemented through appropriate quality management measures. See 2.5.

Table B4 - Design supervision levels (DSL)

Minimum recommended requirements for

Design Supervision Characteristics checking of calculations, drawings and

Levels specifications

Extended supervision Third party checking :

DSL3 Checking performed by an organisation different from

BSI relating to RC3 that which has prepared the design

Checking by different persons than those originally

© DSL2 Normal supervision responsible and in accordance with the procedure of

relating to RC2 the organisation.

Copy, Self-checking:

DSL1 Normal supervision Checking performed by the person who has prepared

Relating to RC1 the design

Uncontrolled (3) Design supervision differentiation may also include a classification of designers

and/or design inspectors (checkers, controlling authorities, etc.), depending on their

competence and experience, their internal organisation, for the relevant type of con-

struction works being designed.

NOTE The type of construction works, the materials used and the structural forms can affect this classifi-

12/07/2004, cation.

(4) Alternatively, design supervision differentiation can consist of a more refined detailed

assessment of the nature and magnitude of actions to be resisted by the structure, or of a

system of design load management to actively or passively control (restrict) these actions.

PORTSMOUTH, B5 Inspection during execution

(1) Three inspection levels (IL) may be introduced as shown in Table B5. The inspection

levels may be linked to the quality management classes selected and implemented through

appropriate quality management measures. See 2.5. Further guidance is available in

relevant execution standards referenced by EN 1992 to EN 1996 and EN 1999.

OF Table B5 - Inspection levels (IL)

copy:UNIVERSITY Inspection Levels Characteristics Requirements

IL3 Extended inspection Third party inspection

Relating to RC3

IL2 Normal inspection Inspection in accordance with the

Relating to RC2 procedures of the organisation

IL1 Normal inspection Self inspection

Relating to RC1

Licensed 60 EN 1990:2002 (E)

NOTE Inspection levels define the subjects to be covered by inspection of products and execution of

works including the scope of inspection. The rules will thus vary from one structural material to another,

and are to be given in the relevant execution standards.

B6 Partial factors for resistance properties

(1) A partial factor for a material or product property or a member resistance may be

reduced if an inspection class higher than that required according to Table B5 and/or more

severe requirements are used.

NOTE For verifying efficiency by testing see section 5 and Annex D.

NOTE Rules for various materials may be given or referenced in EN 1992 to EN 1999.

NOTE Such a reduction, which allows for example for model uncertainties and dimensional variation, is

BSI not a reliability differentiation measure : it is only a compensating measure in order to keep the reliability

level dependent on the efficiency of the control measures.

©

Copy,

Uncontrolled

12/07/2004,

PORTSMOUTH,

OF

copy:UNIVERSITY

Licensed 61

EN 1990:2002 (E) Annex C

(informative)

Basis for Partial Factor Design and Reliability Analysis

C1 Scope and Field of Applications

1) This annex provides information and theoretical background to the partial factor

(

method described in Section 6 and annex A. This Annex also provides the background

to annex D, and is relevant to the contents of annex B.

(2) This annex also provides information on

BSI – the structural reliability methods ;

© – the application of the reliability-based method to determine by calibration design

Copy, values and/or partial factors in the design expressions ;

– the design verification formats in the Eurocodes.

Uncontrolled C2 Symbols

In this annex the following symbols apply.

Latin upper case letters

12/07/2004, P Failure probability

f

Prob(.

) Probability

P survival probability

s

Latin lower case letters

PORTSMOUTH, a geometrical property

g performance function

Greek upper case letters

OF cumulative distribution function of the standardised Normal distribution

copy:UNIVERSITY Greek lower case letters

FORM (First Order Reliability Method) sensitivity factor for effects of

E actions

FORM (First Order Reliability Method) sensitivity factor for resistance

R

reliability index

model uncertainty

µ mean value of X

X

Licensed 62 EN 1990:2002 (E)

standard deviation of X

X

V coefficient of variation of X

X

C3 Introduction

1) In the partial factor method the basic variables (i.e. actions, resistances and geomet-

(

rical properties) through the use of partial factors and factors are given design values,

and a verification made to ensure that no relevant limit state has been exceeded. See C7.

NOTE Section 6 describes the design values for actions and the effects of actions, and design values of

material and product properties and geometrical data.

(2) In principle numerical values for partial factors and factors can be determined in

either of two ways :

BSI a) On the basis of calibration to a long experience of building tradition.

©

NOTE For most of the partial factors and the factors proposed in the currently available Eurocodes this

Copy, is the leading Principle.

b) On the basis of statistical evaluation of experimental data and field observations.

Uncontrolled (This should be carried out within the framework of a probabilistic reliability the-

ory.)

(3) When using method 2b), either on its own or in combination with method 2a), ulti-

mate limit states partial factors for different materials and actions should be calibrated

such that the reliability levels for representative structures are as close as possible to the

target reliability index. See C6.

12/07/2004, C4 Overview of reliability methods

(1) Figure C1 presents a diagrammatic overview of the various methods available for

calibration of partial factor (limit states) design equations and the relation between

them.

PORTSMOUTH, (2) The probabilistic calibration procedures for partial factors can be subdivided into

two main classes :

– full probabilistic methods (Level III), and

– first order reliability methods (FORM) (Level II).

OF NOTE 1 Full probabilistic methods (Level III) give in principle correct answers to the reliability problem

as stated. Level III methods are seldom used in the calibration of design codes because of the frequent

copy:UNIVERSITY lack of statistical data.

NOTE 2 The level II methods make use of certain well defined approximations and lead to results which

for most structural applications can be considered sufficiently accurate.

(3) In both the Level II and Level III methods the measure of reliability should be identi-

fied with the survival probability P = (1 - P ), where P is the failure probability for the

s f f

considered failure mode and within an appropriate reference period. If the calculated

Licensed 63

EN 1990:2002 (E)

failure probability is larger than a pre-set target value P , then the structure should be

0

considered to be unsafe.

NOTE The ‘probability of failure’ and its corresponding reliability index (see C5) are only notional val-

ues that do not necessarily represent the actual failure rates but are used as operational values for code

calibration purposes and comparison of reliability levels of structures.

(4) The Eurocodes have been primarily based on method a (see Figure C1). Method c or

equivalent methods have been used for further development of the Eurocodes.

NOTE An example of an equivalent method is design assisted by testing (see annex D).

Deterministic methods Probabilistic methods

BSI Historical methods FORM Full probabilistic

Empirical methods (Level II) (Level III)

©

Copy, Calibration Calibration Calibration

Uncontrolled Semi-probabilistic

methods

(Level I)

Method c

12/07/2004, Method a Partial factor Method b

design

Figure C1 - Overview of reliability methods

PORTSMOUTH,

C5 Reliability index

(1) In the Level II procedures, an alternative measure of reliability is conventionally de-

fined by the reliability index which is related to P by :

f

P ( ) (C.1)

f

where is the cumulative distribution function of the standardised Normal distribution.

OF

The relation between and is given in Table C1.

copy:UNIVERSITY

Table C1 - Relation between and P

f

-1 -2 -3 -4 -5 -6 -7

P 10 10 10 10 10 10 10

f

1,28 2,32 3,09 3,72 4,27 4,75 5,20

(2) The probability of failure P can be expressed through a performance function g such

f

that a structure is considered to survive if g > 0 and to fail if g 0 :

Licensed 64 EN 1990:2002 (E)

P = Prob(g 0) (C.2a)

f

If R is the resistance and E the effect of actions, the performance function g is :

g = R – E (C.2b)

with R, E and g random variables.

(3) If g is Normally distributed, is taken as :

g

(C.2c)

g

where :

µ is the mean value of g, and

BSI g

is its standard deviation,

g

© so that :

Copy,

µ (C.2d)

0

g g

Uncontrolled and

P Prob ( g 0 ) Prob ( g µ ) (C.2e)

f g g

For other distributions of g, is only a conventional measure of the reliability

P = (1 - P ).

s f

12/07/2004,

C6 Target values of reliability index

(1) Target values for the reliability index for various design situations, and for refer-

ence periods of 1 year and 50 years, are indicated in Table C2. The values of in Table

C2 correspond to levels of safety for reliability class RC2 (see Annex B) structural

members.

PORTSMOUTH,

NOTE 1 For these evaluations of

Lognormal or Weibull distributions have usually been used for material and structural resistance pa-

rameters and model uncertainties ;

Normal distributions have usually been used for self-weight ;

For simplicity, when considering non-fatigue verifications, Normal distributions have been used for

variable actions. Extreme value distributions would be more appropriate.

OF NOTE 2 When the main uncertainty comes from actions that have statistically independent maxima in

copy:UNIVERSITY

each year, the values of for a different reference period can be calculated using the following expression

:

n

(C.3)

( ) ( )

1

n

where :

is the reliability index for a reference period of n years,

n

is the reliability index for one year.

1

Licensed 65

EN 1990:2002 (E) 1 )

Table C2 - Target reliability index for Class RC2 structural members

Limit state Target reliability index

1 year 50 years

Ultimate 4,7 3,8 2)

Fatigue 1,5 to 3,8

Serviceability (irreversible) 2,9 1,5

1) See Annex B

2) Depends on degree of inspectability, reparability and damage tolerance.

(2) The actual frequency of failure is significantly dependent upon human error, which

are not considered in partial factor design (See Annex B). Thus does not necessarily

BSI provide an indication of the actual frequency of structural failure.

© C7 Approach for calibration of design values

Copy, (1) In the design value method of reliability verification (see Figure C1), design values

need to be defined for all the basic variables. A design is considered to be sufficient if

Uncontrolled the limit states are not reached when the design values are introduced into the analysis

models. In symbolic notation this is expressed as :

E < R (C.4)

d d

where the subscript ‘d’ refers to design values. This is the practical way to ensure that

the reliability index is equal to or larger than the target value.

12/07/2004, E and R can be expressed in partly symbolic form as :

d d

E = E {F , F , ... a , a , ... , , ...} (C.5a)

d d1 d2 d1 d2 d1 d2

R = R {X , X , ... a , a , ... , , ...} (C.5b)

PORTSMOUTH, d d1 d2 d1 d2 d1 d2

where :

E is the action effect ;

R is the resistance ;

F is an action ;

OF X is a material property ;

copy:UNIVERSITY a is a geometrical property ;

is a model uncertainty.

For particular limit states (e.g. fatigue) a more general formulation may be necessary to

express a limit state.

Licensed 66 EN 1990:2002 (E)

(S) failure boundary g = R – E = 0

P design point

BSI

Figure C2 - Design point and reliability index

© according to the first order reliability method (FORM) for Normally distributed

Copy, uncorrelated variables

(2) Design values should be based on the values of the basic variables at the FORM de-

Uncontrolled sign point, which can be defined as the point on the failure surface (g = 0) closest to the

average point in the space of normalised variables (as diagrammatically indicated in

Figure C2). and resistances R should be defined such that

(3) The design values of action effects E

d d

the probability of having a more unfavourable value is as follows :

12/07/2004, )

P(E > E ) = (+ (C.6a)

d E

)

P(R R ) = (- (C.6b)

d R

where :

is the target reliability index (see C6).

PORTSMOUTH, and , with || 1, are the values of the FORM sensitivity factors. The value of

E R

is negative for unfavourable actions and action effects, and positive for resis-

tances.

and may be taken as - 0,7 and 0,8, respectively, provided

E R

0,16 < / < 7,6 (C.7)

E R

OF

copy:UNIVERSITY

where and are the standard deviations of the action effect and resistance, respec-

E R

tively, in expressions (C.6a) and (C.6b). This gives :

(-0,7)

P(E > E ) = (C.8a)

d

(-0,8)

P(R R ) = (C.8b)

d

Licensed 67

EN 1990:2002 (E)

(4) Where condition (C.7) is not satisfied = ± 1,0 should be used for the variable with

the larger standard deviation, and = ± 0,4 for the variable with the smaller standard

deviation.

(5) When the action model contains several basic variables, expression (C.8a) should be

used for the leading variable only. For the accompanying actions the design values may

be defined by :

P (E > E ) = (-0,40,7) = (-0,28) (C.9)

d

NOTE For = 3,8 the values defined by expression (C.9) correspond approximately to the 0,90 fractile.

(6) The expressions provided in Table C3 should be used for deriving the design values

of variables with the given probability distribution.

BSI Table C3 - Design values for various distribution functions

©

Copy, Distribution Design values

µ

Normal

/

Lognormal for V = < 0,2

µ exp( V )

Uncontrolled Gumbel 1

u - ln

{- ln (- )}

a 0

,

577

where u ; a

a 6

NOTE In these expressions and V are, respectively, the mean value, the standard deviation and the

coefficient of variation of a given variable. For variable actions, these should be based on the same refer-

12/07/2004,

ence period as for

(7) One method of obtaining the relevant partial factor is to divide the design value of a

variable action by its representative or characteristic value.

C8 Reliability verification formats in Eurocodes

PORTSMOUTH, (1) In EN 1990 to EN 1999, the design values of the basic variables, X and F , are usu-

d d

ally not introduced directly into the partial factor design equations. They are introduced

in terms of their representative values X and F , which may be :

rep rep

– characteristic values, i.e. values with a prescribed or intended probability of being

OF exceeded, e.g. for actions, material properties and geometrical properties (see

1.5.3.14, 1.5.4.1 and 1.5.5.1, respectively) ;

copy:UNIVERSITY – nominal values, which are treated as characteristic values for material properties (see

1.5.4.3) and as design values for geometrical properties (see 1.5.5.2).

(2) The representative values X and F , should be divided and/or multiplied, respec-

rep rep

tively, by the appropriate partial factors to obtain the design values X and F .

d d

NOTE See also expression (C.10).

Licensed 68 EN 1990:2002 (E)

(3) Design values of actions F, material properties X and geometrical properties a are

given in expressions (6.1), (6.3) and (6.4), respectively.

Where an upper value for design resistance is used (see 6.3.3), the expression (6.3) takes

the form :

= X (C.10)

X

d fM k,sup

where is an appropriate factor greater than 1.

fM

NOTE Expression (C.10) may be used for capacity design.

(4) Design values for model uncertainties may be incorporated into the design expres-

BSI sions through the partial factors and applied on the total model, such that :

Sd Rd

© E E G ; P

; Q ; Q ; a ... (C.11)

d Sd gj kj P q

1 k 1 qi 0 i ki d

Copy,

R R X / ; a ... / (C.12)

d k m d Rd

Uncontrolled

5) The coefficient which takes account of reductions in the design values of variable

(

actions, is applied as , or to simultaneously occurring, accompanying variable

0 1 2

actions.

(6) The following simplifications may be made to expression (C.11) and (C.12), when

required.

12/07/2004, a) On the loading side (for a single action or where linearity of action effects exists) :

E = E { F , a } (C.13)

d F,i rep,i d

b) On the resistance side the general format is given in expressions (6.6), and further

PORTSMOUTH, simplifications may be given in the relevant material Eurocode. The simplifications

should only be made if the level of reliability is not reduced.

NOTE Nonlinear resistance and actions models, and multi-variable action or resistance models, are

commonly encountered in Eurocodes. In such instances, the above relations become more complex.

OF C9 Partial factors in EN 1990

copy:UNIVERSITY (1) The different partial factors available in EN 1990 are defined in 1.6.

(2) The relation between individual partial factors in Eurocodes is schematically shown

Figure C3.

Licensed 69

EN 1990:2002 (E)

Uncertainty in representative values f

of actions F

Model uncertainty in actions and Sd

action effects

Model uncertainty in structural resistance Rd M

Uncertainty in material properties m

BSI Figure C3 - Relation between individual partial factors

©

Copy,

C10 factors

0

(1) Table C4 gives expressions for obtaining the factors (see Section 6) in the case of

0

Uncontrolled two variable actions.

(2) The expressions in Table C4 have been derived by using the following assumptions

and conditions :

– the two actions to be combined are independent of each other ;

12/07/2004, or T ) for each action is constant ; T is the greater basic period ;

– the basic period (T 1 2 1

– the action values within respective basic periods are constant ;

– the intensities of an action within basic periods are uncorrelated ;

PORTSMOUTH, – the two actions belong to ergodic processes.

(3) The distribution functions in Table C4 refer to the maxima within the reference pe-

riod T. These distribution functions are total functions which consider the probability

that an action value is zero during certain periods.

OF

copy:UNIVERSITY

Licensed 70 EN 1990:2002 (E)

Table C4 - Expressions for for the case of two variable actions

o

Distribution = F / F

o accompanying leading

General N

1 1

F ( 0

, 4 ' )

s N

1

1

F ( 0

, 7 )

s

1

with ' ( 0

, 7 ) / N

1

Approximation for very large N 1

1 F exp N ( 0

, 4 ' )

s 1

1

F ( 0

, 7 )

s

1

with ' ( 0

, 7 ) / N

1

Normal (approximation) 1 0

, 28 0

, 7 ln N V

1

BSI 1 0

, 7 V

Gumbel (approximation) 1 0

, 78

V 0

,

58 ln ln 0

, 28 ln N

1

©

1 0

, 78

V 0

,

58 ln ln ( 0

, 7 )

Copy, F (.) is the probability distribution function of the extreme value of the accompanying ac-

s

tion in the reference period T ;

(.) is the standard Normal distribution function ;

Uncontrolled T is the reference period ;

is the greater of the basic periods for actions to be combined ;

T 1

N is the ratio T/T , approximated to the nearest integer ;

1 1

is the reliability index ;

V is the coefficient of variation of the accompanying action for the reference period.

12/07/2004,

PORTSMOUTH,

OF

copy:UNIVERSITY

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DESCRIZIONE APPUNTO

EN 1990 establishes Principles and requirements for the safety, serviceability and durability of structures, describes the basis for their design and verification and gives guidelines for related aspects of structural reliability. EN 1990 is intended to be used in conjunction with EN 1991 to EN 1999 for the structural design of buildings and civil engineering works, including geotechnical aspects, structural fire design, situations involving earthquakes, execution and temporary structures.
Contents:
- principles of limit states design;
- basic variables;
- structural analysis and design assisted by testing;
- verification by the partial factor method;
- application for buildings;
- management of structural reliability for construction works;
- basis for partial factor design and reliability;
- analysis;
- design assisted by testing.


DETTAGLI
Corso di laurea: Corso di laurea in ingegneria civile
SSD:
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher vipviper di informazioni apprese con la frequenza delle lezioni di Tecnica delle costruzioni e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Mediterranea - Unirc o del prof D'assisi Ricciardelli Francesco.

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