DS/EN 1990 DK NA:2013 Version 2 National Annex to Eurocode: Basis of structural design _______________________________________________________________________
Foreword This National Annex (NA) is a consolidation and revision of DS/EN 1990 DK NA 2010 and DS/EN 1990 DK NA Addendum 1:2010 and supersedes these documents as of 2013-05-15. For a transition period until 2013-09-01, this National Annex as well as the previous National Annex will be applicable. This NA does not deal with bridges and therefore EN 1990/A1:2005 and EN 1990/A1/AC:2010 have not been taken into consideration. In addition to the consolidation and editorial changes, the contents of Table A.1.1 DK NA regarding natural actions, clause A.1.3 and Annex F (2) have been considerably modified. This version 2 is issued due to an error in the translation of NOTE 2 to Table A1.2(B+C) DK NA in the first version. Previous versions, addenda and an overview of all National Annexes can be found at www.Eurocodes.dk This national Annex (NA) lays down the conditions for the implementation in Denmark of EN 1990 for construction works in conformity with the Danish Building Act or the building legislation. Other parties can put this NA into effect by referring thereto. The national choices may be in the form of nationally applicable values, an option between methods given in the Eurocode, or the addition of complementary information. This NA includes: • • •
an overview of possible national choices and complementary information; national choices; complementary (non-contradictory) information which may assist the user of the Eurocode.
The numbering refers to the clauses containing choices and/or complementary information. To the extent possible, the heading/subject is identical to the heading of the clause, but as references are at a more detailed level than the headings, the heading/subject has in several cases been made more explicit.
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Overview of possible national choices and clauses containing complementary information The list below identifies the clauses where national choices are possible and the applicable/not applicable informative annexes. Furthermore, clauses giving complementary information are identified. Complementary information is given at the end of this document. Clause
Field of application (design working life) Combinations of actions, General Modifications of combinations of actions for geographical reasons Values of ψ factors
Design values of actions in persistent and transient design situations: Choice of approach regarding geotechnical actions Design values of actions in accidental and seismic design situations Serviceability criteria
A1.2.2 / Table A1.1 A1.3.1(1)/ Table A1.2(A)-(C) A1.3.1(5)
A1.3.2 (Table A1.3) A1.4.2(2) A1.4.3 A1.4.4 Annex B
National choice Design values of actions in persistent and National transient design situations choice
Deformations and horizontal displacements Vibrations
Management of structural reliability for construction works Basis for partial factor design and reliability analysis Design assisted by testing
Partial factors for resistance
National choice National choice Complementary information National choice Complementary information Complementary information Complementary information Complementary rules Complementary rules
NOTE Unchanged: Recommendations in the Eurocode are followed.
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National choices A1.2.2/Table A1.1 DK NA Recommended values of ψ factors for buildings Values given in Table A.1.1 DK NA. Table A1.1 DK NA ψ factors for buildings Action Imposed loads in buildings, see EN 1991-1-1 Category A: domestic, residential areas Category B: office areas Category C: congregation areas Category D: shopping areas Category E: storage areas Category F: traffic area, gross vehicle weight: < 30 kN Category G: traffic area, 30 kN < gross vehicle weight < 160 kN Category H: roofs Snow loads For combinations with leading imposed loads of category E or leading thermal actions For combinations with leading wind actions otherwise Wind actions For combinations with leading imposed loads of category E otherwise Thermal actions
0,5 0,6 0,6 0,6 0,8 0,6
0,3 0,4 0,6 0,6 0,8 0,6
0,2 0,2 0,5 0,5 0,7 0,5
0,6 0,3 0,6
0,2 0,2 0,5
0 0 0
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A1.3.1(1) / Table A1.2(A)-(C) DK NA Design values of actions in persistent and transient design situations Combinations of actions and partial factors for EQU, UPL, STR and GEO are listed in Tables A1.2(A) DK NA and A1.2(B+C) DK NA. Table A1.2(A) DK NA Design values of actions for persistent and transient design situations (EQU and UPL) (Set A) Limit state Combination of actions Reference formula
Weight, general (**)
Variable action (*)
EQU / UPL
Weight of soil and (ground) water, geotechnical structures (***)
(*) Variable actions are those considered in Table A.1.1 DK NA. (**) Comprises all types of permanent self weight, see clause 2.1 in EN 1991-1-1. (***) Comprises the weight of soil and (ground) water affecting the geotechnical structure as geotechnical action, see 184.108.40.206 in EN 1997-1. NOTE 1 Combination of actions 2 is applied only for geotechnical structures where the water pressure is maximised in the case of overflow arrangements, see DS/EN1997-1 DK NA. NOTE 2 KFI depends on the consequences class defined in Annex B, Table B3, as follows: – consequences class CC3: KFI = 1,1 – consequences class CC2: KFI = 1,0 – consequences class CC1: KFI = 1,0. Consequences class CC1 is not applied for geotechnical structures. NOTE 3 Anchors or similar devices added in order to achieve static equilibrium is to be designed to accommodate the design force that is needed to ensure static equilibrium.
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Table A1.2(B+C) DK NA Design values of actions for persistent and transient design situations (STR/GEO) (sets B and C) Limit state
Combination of actions Reference formula
Partial factors for actions Unfavourable
1,0 (γM = γR = 1,0)
Variable action (*)
Weight, general (**)
Weight of soil and (ground) water, geotechnical structures (***)
Coefficient applied to partial factors for strength parameters and resistance Structural materials, cf. EN 1992 - 1996 and 1999 Soil parameters and resistance, cf. EN 1997-1
(*) Variable actions are those considered in Table A.1.1 DK NA. (**) Comprises all types of permanent self weight, see clause 2.1 in EN 1991-1-1. (***) Comprises the weight of soil and (ground) water affecting the geotechnical structure as geotechnical action, see 220.127.116.11 in EN 1997-1. NOTE 1 Equations 6.10a and 6.10b are applied for STR as well as GEO. Equation 6.10a relates only to permanent actions. NOTE 2 For structures not subject to geotechnical actions, verification can be achieved solely by applying combinations of actions 1 and 2. For structures subject to geotechnical actions, verification is to be achieved by applying combinations of actions 1 and 2, combinations of actions 3 and 4 and combination of actions 5. For structures solely subject to geotechnical actions, verification may be achieved by applying combinations of actions 3 and 4 and combination of actions 5.
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For KFI = 1,0, combinations of actions 1 and 2 are identical to combinations of actions 3 and 4. For KFI ≠ 1,0, the factor KFI may be applied to the load effects (internal forces and moments) instead of to the action, provided that the load effects are linearly proportional to the associated action. Geotechnical actions are actions transmitted to the structure by the ground, fill, standing water or ground water. In addition to the weight, the action from the ground and fill is determined by the strength and deformation properties of the ground and fill, e.g. expressed as the angle of friction. Examples of geotechnical actions include earth and water pressures on a wall structure. NOTE 3 – Coefficient γ0 for the partial factor for strength parameters and resistances is obtained as follows. For combinations of actions 3 and 4 used for geotechnical structures, cf. EN 1997-1, the KFI factor applies to all relevant partial factors for the strength parameters and resistance of the ground and for the material strengths and resistances, respectively. For combination of actions 5 which is used for verification of STR for structural materials forming part of geotechnical structures, the usual partial factors are applied for structural materials multiplied by 1,2 KFI. For strength parameters and resistances of the ground, a partial factor of γM = γR =1,0, cf. EN 1997-1, is applied. NOTE 4 KFI depends on the consequences class defined in Annex B, Table B3, as follows: – consequences class CC3: KFI = 1,1 – consequences class CC2: KFI = 1,0 – consequences class CC1: KFI = 0,9 Consequences class CC1 is not applied for geotechnical structures. See also EN 1991 to EN 1999 for γ values for imposed deformations. NOTE 5 - The characteristic values of all permanent actions from one source are multiplied by γGj,sup if the total resulting action effect is unfavourable and by γGj,inf if the total resulting action effect is favourable. As an 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.
Design values for fatigue actions (1) Design values for fatigue actions should be determined by applying a partial factor equal to 1,3 for loads where the uncertainty of the individual spans are described by a coefficient of variation of the magnitude of 30%. For loads where the coefficient of variation is less than 10%, a partial factor equal to 1,0 is applied. For other values of the coefficient of variation, the partial factor should be determined by linear interpolation. The coefficient of variation may be stated in connection with the action specification.
A1.3.1(5) Design values of actions in persistent and transient design situations Choice of design approach for geotechnical actions Design Approach 3 is applied, see DS/EN 1997-1 DK NA.
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A1.3.2 Design values of actions in accidental and seismic design situations Combinations of actions are listed in Table A1.3 DK NA. Table A1.3 DK NA Design values of actions for use in accidental and seismic combinations of actions Design situation
Permanent actions Unfavour- Favouraable ble
Leading accidental or seismic action
Fire Gkj,sup Gkj,inf Ad (Formula 6.11a/b) Other accidental Gkj,sup Gkj,inf Ad (Formula 6.11a/b) Seismic Gkj,sup Gkj,inf Ad (Formula 6.12a/b) *) Variable actions are those considered in Table A.1.1 DK NA.
Accompanying variable actions* Main (if any)
ψ2,i Qk,i ψ2,i Qk,i
NOTE 1 – Seismic actions are used to evaluate the structure for the seismic design situation. Seismic actions do not include imperfections of the structure as imperfections are considered according to rules specified in the individual Eurocodes for materials.
Seismic actions include actions taken into account in order to safeguard the structure's strength and stability from small ground motions. Seismic actions are the smallest horizontal actions assumed to affect a structure. All vertical actions are assumed to be capable of contributing to the calculation of seismic actions. Seismic actions are taken as fixed actions. Seismic actions are assumed to occur simultaneously with the associated vertical actions only. Seismic actions act at the centres of gravity of the associated vertical actions and are assumed to be capable of acting in any horizontal direction, but such that this direction is the same for all seismic actions occurring at the same time. The design value of the seismic action, Ad, is determined on the basis of the vertical action as follows: A = 1,5% ∑ Gk , j "+ " ∑ψ 2,i Q j ,i d
Structures are not to be designed for seismic and wind actions acting simultaneously.
A1.4.2(2) Serviceability criteria Empirical values for vertical vibrations are given in clause A1.4.4 of this NA. A1.4.3 Deformations and horizontal displacements For serviceability limit states that relate to the functionality and appearance of the structure, reference is made to EN 1992-1999.
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A1.4.4 Vibrations - Vertical Requirements regarding natural frequencies may be based on the empirical values in Table A1.4 DK NA. If a more detailed analysis is carried out, the functioning of the structure will normally be satisfactory if the variation of the structure's accelerations originating from the stated action does not exceed the acceleration limit in the table. The risk of unsatisfactory functioning increases with increasing span and the risk is particularly great for lightweight or poorly damped structures. For these structures, the natural frequency requirement in the table does not always result in satisfactory functioning. Table A1.4 DK NA Empirical values for acceptable natural frequencies and acceleration limits Structure
Normally satisfactory functioning
Grandstands, fitness centres, sports halls and public premises
Rhythmic load caused by movement of people Load from walking Load from walking
ne > 10
Often unsatisfacto- Acceleration limit ry functioning in % of the gravity acceleration 10 % ne < 6 Hz
ne > 8
ne < 5
ne > 8
ne < 5
NOTE - Natural frequencies and accelerations are calculated during normal use, where the fluctuating action is typically considerably less than the action corresponding to the quasi-permanent combination specified in clause 6.5.3 of EN 1990.
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Complementary (non-contradictory) information Annex B - Management of structural reliability for construction works Annex B may be used with the following modifications: - Table B1 (Consequences classes) - Table B2 (Minimum values for reliability index) - Clause B4 (Design supervision differentiation) - Clause B5 is not applied - Clause B6 is not applied. Table B1 DK NA Definition of consequences classes Consequences class CC3 High consequences class
CC2 Medium consequences class CC1 Low consequences class
Consequences of posExamples sible damage High risk of loss of – Buildings with several storeys where the height to the human life, or considfloor of the uppermost storey is more than 12 m erable economic, social above the ground, if they are often used for accomor environmental conmodating people, e.g. residential or office buildings – Buildings with large spans, if they are often used by sequences many people, e.g. for concerts, sporting events, theatrical performances, or exhibitions – Grandstands – Large road bridges and tunnels – Large masts and towers – Large silos near a built-up area – Dams and similar structures where a failure would result in considerable damage. Medium risk of loss of Buildings or structures not belonging to CC3 or CC1. human life. Considerable economic, social or environmental consequences. Low risk of loss of – 1 and 2 storey buildings with moderate spans, which human life, and small people enter only occasionally, e.g. storage buildings, or negligible economsheds and small agricultural buildings ic, social or environ– Small masts and towers, including general street masts mental consequences – Small silos – Secondary structural members, e.g. partitions, window and door lintels and cladding
(1) The consequences for adjacent structures and surroundings can be decisive when determining the consequences class. (2) Structural members that are not part of the main structure can often be referred to a lower consequences class than the main structure.
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NOTE The main structure is that part of a load-bearing structure the failure of which will have considerable consequences for the reliability and functionality of the entire structure. Examples of structural members that are often considered not to be part of the main structure include roofs, independent decks, stairways and balconies.
Table B2 DK NA Minimum values for reliability index ß (ultimate limit states) for a 1 year reference period Reliability class RC3 corresponding to CC3 RC2 corresponding to CC2 RC1 corresponding to CC1
Minimum values of β 4.7 4.3 3.8
NOTE It is assumed for the determination of the reliability index for RC2 that permanent actions have a normal distribution and variable actions have a Gumbel distribution. All strength parameters and model uncertainties should be assumed to have a log-normal distribution. Information on the choice of coefficients of variation are given in DS/INF 172 Background investigations in relation to the drafting of National Annexes to EN 1990 and EN 1991 - Reliability verification formats, combination of actions, partial coefficients, fatigue, snowload, windload, etc.(Available in Danish only). The reliability index ß is defined in Annex C.
B4 Design supervision differentiation (1) Design supervision includes checking of the project material relating to the load-bearing structures, viz. project basis, statistical calculations, drawings/models and execution specifications. The design brief is the specifications on which the design is based, including the static system and mode of operation, robustness, fire, material data, action data, etc. NOTE Design supervision is to contribute to ensuring: – that the assumptions of the design brief are correct and are used as a basis for the structural design; – that the assumptions made in the static calculations have been correctly incorporated into any other project material; – that drawings and execution specifications are adequate for the execution of the load-bearing structures.
(2) Design supervision, except self-checking, is to be documented in accordance with guidelines drawn up in advance. The method, scope, any points of focus and the results of the design supervision is to be stated in the documentation. (3) For all project material, the people responsible for preparation and design supervision, respectively, are to be identified. (4) For structures in consequences class CC3 where the consequences of failure are particularly serious, special requirements apply to design supervision. (5) Examples of structures covered by (4) include: – buildings with more than 15 storeys above ground level, if they are used for accommodating persons, e.g. for residential, office or educational buildings; – hospitals with more than 5 storeys above ground level; – industrial buildings where failure would have a particularly major impact on society;
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buildings with large spans, provided they are used by many people, e.g. for concerts, theatrical performances, exhibitions, sporting events, or entertainments; grandstands.
(6) The following types of supervision are applied in connection with design: self-checking, independent checking and third party checking. The types of supervision are defined in Table B4a DK NA. Table B4a DK NA Definition of types of supervision Type of supervision Self-checking Independent checking
Definition Checking performed by the person who has prepared the design Checking by different persons than those involved in the design of the structure Checking by an organisation that is neither directly nor indirectly linked financially to the organisation(s) involved in the design of the structure
Third party checking
(7) The minimum requirements for the type of supervision depend on the consequences class to which the structure is assigned. The minimum requirements are specified in Table B4b DK NA. Table B4b Minimum requirements for types of supervision for project material Consequences class CC1 CC2 CC3 CC3 if covered by (4)
Self-checking X X X X
Independent checking X *) X X
Third party checking
*) The requirement for independent checking in CC2 applies to the design brief only. For any other project material, checking may be carried out by persons who have not been involved in the design of the relevant section of the structure.
B6 Partial factors for resistance Comment: This clause is not applied. Reference is made to Annex F (7) for complementary rules concerning the determination of partial factors for resistance, according to the level of checking. Annex C Basis for partial factor design and reliability analysis The Annex may be used with a changed Table C2 DK NA (target reliability indices).
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Table C2 - Target reliability index β for class RC2 structural members 1 Limit state
Target reliability index 1 year 4,3
Ultimate Fatigue 2,9 Serviceability (irreversible) 1 See Annex B. 2 Depends on the degree of inspectability, reparability and damage tolerance.
50 years 3,3 1,5 to 3,3 2 1,5
Annex D Design assisted by testing The Annex may be used with the exception of D7.3 and D8.3; see comment. Comment: Annex D may be used to check characteristic values and to establish characteristic values and design values. Clauses D7.3 and D8.3 may not be used as they assume a reliability level corresponding to β = 3,8 and application of the design approach in Annex C. Instead reference is made to Annex F in which the determination of material partial factors and design values is described.
Annex E Robustness Complementary rules for the verification of robustness This Annex may be used for the examination of robustness, see 2.1.4(P) - 2.1.5(P). (1) A structure is robust: – when the parts of the structure that are decisive for safety are only slightly sensitive to unintended effects and defects; or – when there is no extensive failure of the structure if a limited part of the structure fails. (2) Examples of unintended effects and defects include: – unforeseen action effects; – unintended discrepancies between the structure's actual behaviour and the design models used; – unintended discrepancies between the implemented project and the project material; – unforeseen geometrical imperfections; – unforeseen settlements; – unforeseen degeneration. Increased robustness may in certain cases also help to reduce the effects of any gross errors, although verification of robustness neither can nor must be regarded as designing against gross error. (3) Robustness is discussed in more detail in DS/INF 146 Robustness - Background and principles (available in Danish only).
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(4) The robustness of a structure should be proportional to the consequences of a failure of the structure. Documentation of robustness is only required for structures in consequences class CC3. However, for structures in consequences class CC2 an assessment of the robustness is to be made. The amount of detail of the assessment is to be increased in the case of large spans, large concentrated loads, few supports and special (rare or new) types of structures. (5) A robust structure is achieved by an appropriate choice of materials, general static principle and construction and by appropriate design of key members. A key member is a restricted part of the structure that, in spite of its limited extent, is of central importance to the robustness of the structure such that failure of this member would result in the failure of the whole structure or significant parts of the structure. (6) Where documentation of robustness is required, an expert engineering report is to be drawn up verifying that at least one of the robustness criteria specified in (1) is met. This is achieved –
by verifying that the essential parts of the structure, i.e. key members, have low sensitivity to unintended effects and defects, cf. (2); – by verifying that no extensive failure of the structure occurs if a limited part of the structure fails (loss of a member), see (7)-(8); – by verifying adequate safety of key members, such that the whole structure to which they belong attains at least the same level of system safety as an equivalent structure for which the robustness is documented by verification of adequate safety in the event of the “loss of a member”. In addition to the verification itself, the expert engineering report is to contain a critical evaluation of the construction, including identification of key members and action scenarios. Verification that the first criterion has been fulfilled is only possible in special cases, and therefore verification is usually performed by verifying one of the two latter criteria. (7) Where robustness is verified by ”loss of a member”, the acceptable extent of collapse for buildings of up to 15 storeys be taken as: collapse of no more than two floors, extending in this case to two vertically adjacent floors. At each of the two floors, the extent of collapse is not to affect more than 15% of the floor space, and no more than 240 m2 per floor and no more than a total area of 360 m2. Adequate resistance is verified in an accidental design situation by using the formula (6.11 a/b), see Table A1.3 DK NA. (8) Robustness verified in the event of “loss of a member” may, for residential and grandstand structures, be regarded as met if it is verified that the damaged structure will continue to constitute a stable system even if one or more structural members are lost. It is assumed that failure may comprise the equivalent of the maximum permissible extent of collapse, cf. (7), including: – either a floor or roof structure and an arbitrary pillar; – or a floor or roof structure and an arbitrary piece of wall 3 m in length or width.
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The ability of a structure to retain its coherence after a failure of the specified extent is primarily conditional upon the damaged structure continuing to constitute a stable system, which means that the structure or large parts of it are not transformed into a mechanism. If this condition is met, a rough calculation will be sufficient. (9) Where robustness is verified by introducing additional reliability of key members, this can usually be achieved by applying a material partial factor γM, which has been increased by the factor 1,2 compared to the value specified in 6.3.5. With respect to modelling this is equivalent to a system with key members in series having the same system reliability as a system of parallel members. As a general rule, every effort should be made in the design to document the robustness of a structure as far as possible without the use of increased safety factors on the key members. Where increased safety factors are applied to the key members, it should however be ensured that the resistance of the structure to unintended effects and defects is actually increased. NOTE For example, the robustness of hinged pillars in a residential building will not generally be sufficiently secured by applying a factor of 1,2, unless at the same time a structural connection is arranged through each building floor in the form of a continuous tensile and shear connector in the pillar.
(10) The structural Eurocodes may provide guidelines for adequately ensuring robustness.
Annex F (informative) Partial factors for resistance Complementary rules for establishing partial factors for resistance (1) The design resistance value, Rd, should be determined either by formula (6.6a) if it is determined on the basis of design strength parameters and a calculation model, or by formula (6.6c) if it is determined on the basis of measured characteristic resistances. (2) The partial factors for strength parameters and resistance should be determined using the following expressions: ,
where γ M = γ mγ R
γm =γ4 γ R = γ 1γ 2 γ 3 (6.6c)
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The sub-partial factors take account of the following: failure mode, see Table F.2 γ1 uncertainty related to the calculation model, see Table F.3 γ2 γ3 scope of checking, see Table F.4
uncertainty of measured strength parameter or resistance, see Table F.1.
The factor γ0 is applied to the partial factor γM for strength parameters and resistances (and γR for resistance according to EN 1997-1), depending on the combination of actions, see Table A1.2(B+C) DK NA. (3) Division of the partial factors into sub-partial factors does not imply a probability theoretical consideration of the conditions associated with the individual sub-partial factor only. (4) The sub-partial factor γ4 depends on the coefficient of variation for the measured strength parameter or resistance. The coefficient of variation is to include the uncertainty associated with the transfer from laboratory conditions to conditions in an actual structure. γ4 is given in Table F1 DK NA. Table F.1 DK NA Sub-partial factor γ4 for measured strength parameter or resistance Coefficient of variation for measured strength parameter or resistance
(5) The sub-partial factor, γ1, depends on the type of failure of the structure. γ1 is given in Table F2 DK NA. No warning of failure refers to failure that occurs without prior warning (e.g. in the form of increased crack formation or deformation) and significant reduction of resistance immediately after a failure (e.g. in the event of stability failure or brittle fracture). Warning of failure without residual resistance refers to failure where a warning is given of exhausted resistance (e.g. in the form of increased crack formation or deformation) and the resistance is retained for some time after the warning. Warning of failure with residual resistance refers to failure where the resistance increases (e.g. as a result of strain hardening) after a formal failure has occurred (e.g. in the event of the permissible strain being exceeded). If the residual resistance is utilised in the calculation models, the failure type is to be taken as “Warning of failure without residual resistance”.
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Table F2 DK NA Sub-partial factor γ 1 depending on type of failure
Type of failure
Warning of failure with residual resistance 0,90
Warning of failure without residual resistance 1,00
No warning 1,10
(6) The sub-partial factor γ2 depends on the coefficient of variation for the calculation model. The coefficient of variation is established by comparing resistances determined by testing the structural members and by applying the calculation model, with the use of measured/given strength parameters and geometric dimensions. As an exception, the coefficient of variation may be determined as an estimate. γ2 is given in Table F3 DK NA. Table F.3 DK NA Sub-partial factor γ2 for uncertainty of the calculation model Coefficient of variation of the calculation model
(7) Sub-partial factor γ 3 depends on the level of checking in connection with the production of components and execution at the construction site. Requirements for levels of checking may be given in EN 1992 to EN 1999 and in the Danish national annexes thereto. γ 3 is given in Table F4 DK NA. The extended level of checking is used on the condition that third party checking is conducted. Table F4 DK NA Sub-partial factor γ3 dependent on the scope of checking in connection with the production of components and execution at the construction site. Level of checking
(8) In (2), γ4 covers the variation of the strength parameter. By checking the strength parameter it will be possible to evaluate both the characteristic value and the coefficient of variation, which may differ from what was assumed when the partial factor was set, see EN 1992 to EN 1998. (9) When examining accidental design situations or seismic design situations, the partial factor γM = 1,0 is used unless otherwise stated in EN 1992, EN 1993, EN 1994, EN 1995, EN 1996, EN 1997, EN 1998 or EN 1999.
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