EN 1992-1-1 DK NA

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EN 1992-1-1 DK NA, 2007-11-15, 2nd edition

EN 1992-1-1 DK NA:2007 National Annex to Eurocode 2: Design of concrete structures -

Part 1-1: General rules and rules for buildings _______________________________________________________________________

Foreword In connection with the incorporation of Eurocodes into Danish building legislation to replace the Danish structural codes of practice, this National Annex was prepared in 2006-2007 to implement Eurocode 2 in Denmark.

Scope This National Annex lays down the conditions for the implementation of the Eurocode.

Contents This National Annex specifies the national choices prescribed in Denmark. The national choices may be in the form of nationally applicable values, an option between methods given in the Eurocode, or the addition of supplementary guidance. This National Annex addresses:

• Clauses where national choices have been made; • All clauses where national choices have been possible; • Bibliography: Overview of all National Annexes prepared.

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Clauses where national choices have been made 2.4.2.2(2) The following value should be used: 21,, =unfavPγ

2.4.2.4(1) The following partial factors for ultimate limit states should be used for persistent and transient design situations. Table 2.1a NA – Partial factors for materials for ultimate limit states for persistent and transient design situations Structures, in situ Compressive strength and modulus of elasticity of reinforced concrete 345,1 γγ =c

Compressive strength and modulus of elasticity of unreinforced concrete 360,1 γγ =c

Tensile strength of concrete 370,1 γγ =c

Strength of reinforcement 320,1 γγ =s

Prefabricated elements, design Compressive strength and modulus of elasticity of reinforced concrete 340,1 γγ =c

Compressive strength and modulus of elasticity of unreinforced concrete 355,1 γγ =c

Tensile strength of concrete 360,1 γγ =c

Strength of reinforcement 320,1 γγ =s

Prefabricated elements, performance testing Performance testing with ductile failure 32,1 γγ =M

Performance testing with brittle failure 34,1 γγ =M

NOTE - Failure of elements subject to transverse load is assumed to exhibit ductile failure if at least one of the following conditions is fulfilled:

• Yielding of the reinforcement at failure is documented by measurement. • Prior to failure, a uniformly distributed crack pattern occurs corresponding to the load applied. • Prior to failure, deflection exceeds 3/200 of the span.

Other failure modes are regarded as brittle failures. Failure of elements subject to axial forces should always be regarded as brittle failures. The partial factors are determined in accordance with the National Annex to EN 1990 DK, Annex F, where γM = γ1 γ2 γ3 γ4. γ1 takes into account the type of failure γ2 takes into account the uncertainty related to the design model γ3 takes into account the extent of inspection γ4 takes into account the variation of the strength parameter or resistance.

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When determining γ1 the types of failure given in Table 2.1.b NA should be assumed. Table 2.1.b NA – Assumed types of failure for the determination of γ1 Structures, in situ, and precast elements, design Compressive strength and modulus of elasticity of reinforced concrete

Warning of failure without spare resistance

Compressive strength and modulus of elasticity of unreinforced concrete

No warning of failure

Tensile strength of concrete No warning of failure Strength of reinforcement Warning of failure without spare resistance Prefabricated elements, performance testing Performance testing with ductile failure Warning of failure without spare resistance Performance testing with brittle failure No warning of failure Table 2.1.c NA specifies the values of γ3 depending on inspection level. Table 2.c NA - Sub-partial factor γ3 depending on the inspection level Inspection level

Tightened Normal Relaxed

γ3 0,95 1,0 1,10 The following partial factor for ultimate limit states is applied in Denmark for accidental design situations γM = 1,0. For verification of fatigue for persistent design situations the partial factors given in Table 2.1a NA multiplied by 1,1 should be used for the values γC,fat and γS,fat. For the correspondence between partial factors and consequences classes, reference is made to the National Annex to EN 1990. The relaxed inspection level should not be applied for structures in high consequences class. The inspection depending on inspection levels is specified in prEN 13670, where Execution Class 1 corresponds to the relaxed inspection level, Execution Class 2 corresponds to the normal inspection level, and Execution Class 3 corresponds to the tightened inspection level. 2.4.2.5(2) The following value should be used: kf = 1,0 3.1.2(4) The value of kt should be determined on the basis of documented relation relation between the strength of concrete at the time of assessing the strength and the strength after 28 days.

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3.2.2(3)P The upper limit of the yield strength fyk shall be taken as 650 MPa. 3.2.7(2)

The following value should be used: s

ydud E

f=ε

4.4.1.2(5) The following apply:

One structural class should be applied, and the exposure classes should be assigned to environmental classes. Four environmental classes are applied: passive, moderate, aggressive and extra aggressive, denoted P, M, A and E. These four environmental classes cover the climatic and environmental conditions normally prevailing in Denmark. The exposure classes defined in DS/EN 206-1 are reproduced in DS/EN 1992-1-1, Table 4.1. The exposure classes are assigned to four environmental classes as stated in DS 2426 and reproduced below. Table 2426-1 – Normative assignment of exposure classes to environmental classes:

Environmental class Passive Moderate Aggressive Extra aggressive Covers the following exposure classes according to DS/EN 206-1

X0 XC1

XC2 XC3 XC4 XF1 XA1

XD1 XS1 XS2 XF2 XF3 XA2

XD2 XD3 XS3 XF4 XA3

Examples of environmental classes to which individual structural members should normally be assigned:

• Generally the passive environmental class should include the following structural elements:

o structures in indoor dry environments; o buried foundations belonging to low and normal reliability classes.

• Generally the moderate environmental class should include the following structural members :

o foundation piles o foundations partly above terrain; o buried foundations in high reliability class; o external walls and facades; o external columns; o external beams with structurally protected surfaces; o balcony parapets; o installation ducts; o service corridors;

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o lift shafts. • Generally the aggressive environmental class should include the following structural

elements: o external slabs; o external beams without structurally protected surfaces; o retaining walls; o light shafts; o external staircases; o external basement walls partly above terrain; o ducts, piles and pits in moderately aggressive ground water; o structural members in moderately aggressive ground water.

• The extra aggressive environmental class should be considered for the following structural members:

o access balconies, balcony slabs and balcony corbels; o parking floors; o swimming pools; o bridge piers; o edge beams on bridges; o marine structures, e.g. splash zones; o ducts, piles and pits in highly aggressive ground water; o structural members in highly aggressive ground water.

For tightened and normal inspection levels the concrete cover should be at least as specified in Table 4.4 NA for unstressed reinforcement in conformity with DS/EN 10080 and as specified in Table 4.5 NA for prestressing steel. In the case of relaxed inspection level the prescribed concrete cover should be increased by 5 mm.

Table 4.4NA – Values of minimum cover, cmin,dur , requirements with regard to durability for unstressed reinforcing steel in accordance with EN 10080

Environmental class Minimum concrete cover

mm

Extra aggressive 40 mm

Aggressive 30 mm

Moderate 20 mm

Passive 10 mm

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Table 4.5NA – Values of the minimum concrete cover, cmin,dur , requirements with regard to durability for prestressing steel

4.4.1.3(1)P The deviation addition ∆cdev shall normally not be less than 5 mm for normal and tightened inspection levels and 10 mm forrelaxed inspection level. 4.4.1.3(3) The situation is covered by the provisions in (1)P. 5.1.3(1)P In addition to the simplification stated, the following approach may be adopted. The analysis of continuous beams based on the theory of plasticity may be carried out by verifying that each span is capable of resisting the load effects corresponding to the maximum load on the entire span and the minimum load on the entire span, taking for both cases the total values of the chosen restraint moments. Restraint moments should be chosen between the values found by the theory of elasticity and one third thereof. For continuous beams with approximately equal spans and uniformly distributed load, verification of the chosen restraint moments in relation to the values of the theory of elasticity may be omitted if the reinforcement at restraints and intermediate supports is able to take moments numerically not less than 1/3 of and not more than twice the design moments in adjacent spans. 5.2(5) The following should be used: Instead of using (5.1) and θ0, a minimum value for the horizontal action on a building should be applied. It is the mass load specified in the National Annex to EN 1990.

Environmental class Pre-tensioned tendon

not bundled

mm

Post-tensioned tendon

in ducts

mm

Extra aggressive 40 mm 50 mm

Aggressive 30 mm 40 mm

Moderate 20 mm 35 mm

Passive 10 mm 30 mm

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5.8.3.1(1) The following value should be used:

Ed

cdc

N

fA20lim =λ (5.13NA)

5.8.5(1) The following simplified method should be used: Method (a) 5.8.6(3) The following value should be used: ccE γγ = , cf. Table 2.1NA

5.10.1(6) The following method should be used: Method A 5.10.8(2) The following value should be used: 0, =ULSpσ∆

5.10.8(3) The following value should be used: 0,1inf,sup, == PP ∆∆ γγ

5.10.9(1)P The following value shall be used: 0,1infsup == rr

6.2.2(6) The value of ν should be found on the basis of the additional information in 5.6.1(3)P 6.2.3(2) The following applies: Where class B and class C steels are used according to Annex C of DS/EN1992-1-1 the following applies: The inclination θ of the concrete compressive stress should be chosen such that

5,2cot2

tan ≤≤ θα (6.7aNA)

Where curtailed reinforcement is chosen

0,2cot2

tan ≤≤ θα (6.7bNA)

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Normally, the upper limits for θcot ensure that no unacceptable shear cracks occur at the serviceability limit state for beams and slabs without prestress. The limits for the concrete strut inclination may be exceeded if the circumstances permit. For example θcot may be increased for fully prestressed structures where shear cracks do not normally cause problems.

Class A steel according to Annex C of EN 1992-1-1 may be used to resist shear forces, provided that adequate translation capacity ensures that shear failure can develop as predicted by the shear design. This should normally be expected if cotθ is taken as the value giving the optimum reinforcement which for shear corresponds to 1cot =θ 6.2.3(3) The following value should be used: νν =1 according to the additional information in 5.6.1(3)P The recommended value of αcw should be used 6.2.4(4) The recommended value should be applied if class B and/or class C steels according to Annex C of EN 1992-1-1 are used. Class A steel according to Annex C of EN 1992-1-1 should be used if adequate translation capacity is ensured. This should normally be expected if cotθ is taken as the value giving the optimum reinforcement which for shear corresponds to 1cot =θ 6.4.5(4) The following value should be used: k = 2,0 6.5.2(2) The following value should be used: νν ='6,0 according to the additional information in 5.6.1(3)P 6.5.4(4) The following values should be used: k2 = k3 = 1,0 and νν =' according to the additional information in 5.6.1(3)P. The recommended value of k1 should be used. 6.5.4(6) The following value should be used: k4 = 1,0, which is on the safe side. The value depends on transverse compression. 7.3.1(5) The following applies: The recommended values for relevant environmental classes are given in Table 7.1N.

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T

Environmental class Unstressed reinforcement Tendons Extra aggressive 0,2 mm 0,1 mm Aggressive 0,3 mm 0,2 mm Moderate 0,4 mm 0,3 mm 9.2.1.1(1) The recommended value of As,min should be used supplemented by: Deep beam webs should be provided with evenly distributed reinforcement along the sides of the beam web and parallel to the beam axis. The ratio of reinforcement should be at least equal to that for shear reinforcement, cf. 9.2.2(5). 9.2.2(5) The following value should be used: ykckw,min ff /)063,0(=ρ (9.5NA)

9.8.3(2) q1 should be determined in consideration of the compaction equipment. 9.10.2.2(2) The value of q1 should be at least 15 kN/m for normal consequences class and 30 kN/m for high consequences class. The tensile force Ftie,per should at least be taken as a characteristic value of 40 kN for normal consequences class and 80 kN for high consequences class. 9.10.2.3(3) The tensile force Ftie,int should be taken as equal to a characteristic value of 15 kN/m for normal consequences class and 30 kN/m for high consequences class. 9.10.2.3(4) q3 should be taken as a characteristic value of 15 kN/m for normal consequences class and 30 kN/m for high consequences class. q4 should be taken as a characteristic value of 40 kN for normal consequences class and 80 kN for high consequences class. 9.10.2.4(2) ftie,fac should be taken as a characteristic value of 15 kN/m for normal consequences class and 30 kN/m for high consequences class. Ftie,col should be taken as a characteristic value of 80 kN for normal consequences class and 160 kN for high consequences class.

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11.3.5(1)P The following value shall be used: 0,1=lccα

11.3.5(2)P The following value shall be used: 0,1=lctα

11.6.1 (1): The following value should be used: vl,min = 0,03 k2/3 fck

1/2 11.6.2(1) The following value should be used:

νρν

+=2200

6,04,01 flck in MPa (11.6.6NA)

where ν conforms to the additional information provided in 5.6.1(3)P 12.3.1(1) αcc,pl and αct,pl should be taken as 1,0. E.1(2) Exposure classes are in 4.4.1.2(5) assigned to environmental classes. For reinforced concrete, the following minimum value of the prescribed fck is required depending on the environmental class:

Environmental class minimum value of prescribed fck MPa Extra aggressive 40 Aggressive 35 Moderate 25 Passive 12

Annex 1 Design of columns cast in situ In housing construction, reinforced columns cast together with beams or slabs may be assumed to be centrally loaded, eccentric action being accounted for by increasing the axial force in the column. The approximate calculation may be used provided:

• that λ < 90, the free column length being taken equal to the clear length of the column;

• that the column is not subject to significant moments, and that it forms part of a structure which is restrained against sidesway, and which has commonly used dimensions;

• that the total design action from the floor directly over the column in question is multiplied by

a) a factor of 2 when the column is subjected to actions from two adjacent sides only by beams or slabs;

b) a factor of 1,25 when the column is subjected to actions from continuous beams or continuous slabs. For a beam or slab to be taken as continuous, it should have approximately the same stiffness on either side of the column. Otherwise, calculation shall be performed as under a or c, respectively;

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c) a factor of 1,5 for all other columns.

Annex 2 Verification of robustness For structures in low consequences class and for housing structures in normal consequences classes with a maximum of two storeys and collapse of not more than 360 m2, the requirement for robustness will be fulfilled by a design for the normal actions etc. in accordance with the Eurocodes. For housing structures in normal consequences class in general where the main structure of the building consists of connected walls and floors, the requirements for robustness will normally be fulfilled by the requirements for ties described in 9.10 of EN 1992-1-1 and the National Annex to EN 1992-1-1. For housing structures in a high consequences class where the main structure of the building consists of connected walls and floors that following collapse as stated in this National Annex to EN 1990 will continue to constitute a stable static system, the requirements for robustness may normally be assumed to be fulfilled by the requirements for ties described in 9.10 of EN 1992-1-1 and this National Annex to EN 1992-1-1. For other structures, robustness should be verified according to the National Annex to EN 1990 in addition to the verification of the requirements for ties.

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Overview of possible national choices The list below identifies the clauses where national choices are possible and the applicable/not applicable informative annexes. Furthermore, this National Annex refers to additional (non-conflicting) information that may be of assistance to the user of the Eurocode. Clauses Comment 2.3.3 (3) Unchanged 2.4.2.1 (1) Unchanged 2.4.2.2 (1) Unchanged 2.4.2.2 (2) Amended 2.4.2.2 (3) Unchanged 2.4.2.3 (1) Unchanged 2.4.2.4 (1) Amended 2.4.2.4 (2) Unchanged 2.4.2.5 (2) Amended 3.1.2 (2)P Unchanged 3.1.2 (4) Amended 3.1.6 (1)P Unchanged 3.1.6 (2)P Unchanged 3.2.2(3)P Amended 3.2.7 (2) Amended 3.3.4 (5) Unchanged 3.3.6 (7) Unchanged 4.4.1.2 (3) Unchanged 4.4.1.2 (5) Amended 4.4.1.2 (6) Unchanged 4.4.1.2 (7) Unchanged 4.4.1.2 (8) Unchanged 4.4.1.2 (13) Unchanged 4.4.1.3(1)P Amended 4.4.1.3 (3) Amended 4.4.1.3 (4) Unchanged 5.1.3(1)P Amended 5.2 (5) Amended 5.5 (4) Unchanged 5.6.3 (4) Unchanged 5.8.3.1 (1) Amended 5.8.3.3 (1) Unchanged 5.8.3.3 (2) Unchanged 5.8.5 (1) Amended – a method has been chosen

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5.8.6 (3) Amended 5.10.1 (6) Amended – a method has been chosen 5.10.2.1 (1)P Unchanged 5.10.2.1 (2) Unchanged 5.10.2.2 (4) Unchanged 5.10.2.2 (5) Unchanged 5.10.3 (2) Unchanged 5.10.8 (2) Amended 5.10.8 (3) Amended 5.10.9(1)P Amended 6.2.2 (1) Unchanged 6.2.2 (6) Amended 6.2.3 (2) Amended 6.2.3 (3) Amended 6.2.4 (4) Amended 6.2.4 (6) Unchanged 6.4.3 (6) Unchanged 6.4.4 (1) Unchanged 6.4.5 (3) Unchanged 6.4.5 (4) Amended 6.5.2 (2) Amended 6.5.4 (4) Amended 6.5.4 (6) Amended 6.8.4 (1) Unchanged 6.8.4 (5) Unchanged 6.8.6 (1) Unchanged 6.8.6 (2) Unchanged 6.8.7 (1) Unchanged 7.2 (2) Unchanged 7.2 (3) Unchanged 7.2 (5) Unchanged 7.3.1 (5) Amended 7.3.2 (4) Unchanged 7.3.4 (3) Unchanged 7.4.2 (2) Unchanged 8.2 (2) Unchanged 8.3 (2) Unchanged 8.6 (2) Unchanged 8.8 (1) Unchanged 9.2.1.1 (1) Amended 9.2.1.1 (3) Unchanged 9.2.1.2 (1) Unchanged 9.2.1.4 (1) Unchanged 9.2.2 (4) Unchanged 9.2.2 (5) Amended 9.2.2 (6) Unchanged

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9.2.2 (7) Unchanged 9.2.2 (8) Unchanged 9.3.1.1(3) Unchanged 9.5.2 (1) Unchanged 9.5.2 (2) Unchanged 9.5.2 (3) Unchanged 9.5.3 (3) Unchanged 9.6.2 (1) Unchanged 9.6.3 (1) Unchanged 9.7 (1) Unchanged 9.8.1 (3) Unchanged 9.8.2.1 (1) Unchanged 9.8.3 (1) Unchanged 9.8.3 (2) Amended 9.8.4 (1) Unchanged 9.8.5 (3) Unchanged 9.10.2.2 (2) Amended 9.10.2.3 (3) Amended 9.10.2.3 (4) Amended 9.10.2.4 (2) Amended 11.3.5(1)P Amended 11.3.5(2)P Amended 11.3.7 (1) Unchanged 11.6.1 (1) Unchanged 11.6.1 (2) Unchanged 11.6.2 (1) Amended 11.6.4.1 (1) Unchanged 12.3.1 (1) Amended 12.6.3 (2) Unchanged A.2.1 (1) Unchanged A.2.1 (2) Unchanged A.2.2 (1) Unchanged A.2.2 (2) Unchanged A.2.3 (1) Unchanged C.1 (1) Unchanged C.1 (3) Unchanged E.1(2) Amended J.1 (3) Unchanged J.2.2 (2) Unchanged J.3 (2) Unchanged J.3 (3) Unchanged Annex A Annex A is not applicable Annex G Annex G is not applicable Annex H Annex H is not applicable Annex I Annex I is not applicable Annex J Annex J is not applicable

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Additional information:

Annex 1: Design of some columns cast in situ Annex 2: Verification of robustness

Additional (non-conflicting) information 3.1.3(2) For Danish concretes according to DS 2426 an initial modulus of elasticity of

1351000

+=

ck

ckcok f

fE should be assumed, where ckf and cokE are given in MPa. The secant value

Ecm should be taken as cokcm EE ⋅= 7,0 for linear elastic analyses of short-term loading. For linear

elastic analyses of long-term loading an effective modulus of elasticity effcE , should be used, which

may indicatively be taken as cmeffc EE4

1, = . A more exact value may be found using (7.20).

5.6.1(3)P General provisions The determination of internal forces and moments may be based on the theory of plasticity using the generally acknowledged approximations.

Application of the theory of plasticity presupposes that the structure has adequate yield capacity, i.e. yielding in the reinforcement will develop to a sufficient extent before other forms of failure, such as instability, ends the progressing, ductile failure When applying the theory of plasticity, verification of sufficient yield capacity may be omitted if the following conditions are fulfilled:

• The distribution of internal forces and moments does not deviate strongly from that corresponding to the theory of elasticity. An accurate calculation of the distribution of internal forces and moments corresponding to the theory of elasticity is not required. It will normally be adequate to apply a qualified estimate or simple approximation methods. For lower value solutions the following principle should be used: Where the reinforcement area associated with a plastic design at any point of the structure is denoted AsP and the reinforcement area associated with the elastic solution at the same point of the structure is denoted AsE, the above may be assumed to be fulfilled if 1/3 AsE ≤ AsP ≤ 3 AsE in all points of the structure. The elastic solution may be assumed to correspond to the plastic solution where the overall design reinforcement for the structure is a minimum.

• The structure is provided with normal reinforcement, i.e. requirements for minimum reinforcement are fulfilled and the reinforcement yields at failure.

• Only steels of Class B and Class C according to Annex C of DS/EN 1992-1-1 are used.

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• A stress-strain curve for the reinforcement is used where it is assumed that stress will not increase after the point corresponding to the yield stress. Where a stress-strain curve is used assuming that stress increases may occur after the point corresponding to the yield stress, equilibrium as well as compatibility conditions should be fulfilled.

• The ultimate failure is not caused by instability. Satisfactory performance of the structure in the ultimate limit state may require an arrangement of the reinforcement that takes account of the actual distribution of internal forces and moments. Where e.g. a plastic solution is applied disregarding torsional moments in the design, the reinforcement shall be arranged so that it allows for the actual torsional moments, e.g. by using closed stirrups as shear reinforcement, and by closing free edges of slabs by U-stirrups.

Plastic redistribution of the requisite reinforcement, e.g. by applying cotθ, cf. 6.2.3(2), 6.2.4(4), 6.3.2(2) and Annex F(4) of EN 1992-1-1, requires the use of steels of Class B or Class B according to Annex C of EN 1992-1-1. Class A steel should be used only in cases where an optimum value of cotθ is applied, cf. Annex F, equation (F2)-(F7). For pure shear the optimum value is cotθ=1. Satisfactory performance of the structure at the serviceability limit may require that the obtained distribution of stress resultants does not deviate significantly from that determined by the theory of elasticity assuming cracked sections. Where the action and thus the internal forces and moments depend on the deformation capacity of the structure, e.g. in structures subject to earth pressure, the structural deformation capacity should be assessed. Special consideration should be given to the influence of the deformation capacity on the magnitude of e.g. shear forces and reactions at bearings. For structures where the action at the serviceability limit state is greater than at the ultimate limit state, e.g. in certain structures subject to earth pressure, the serviceability limit state should always be assessed. Design methods, in-plane stress conditions For plane stress conditions, the lower-bound methods of the theory of plasticity, the stringer method, the strut-and-tie method and separation into homogeneous stress fields may be applied. Stringer method

• The stringer method simplifies an in-plane stress condition by assuming that all axial

stresses are resisted by stringers, while the rectangular shear fields resist the shear stresses between the stringers. The lengths of the shear fields are defined as the distance between the centroids of the stringers. The intersections between the stringers are called nodes. The width of the stringers should not exceed 20% of the width of the adjacent shear field with the smallest length perpendicular to the longitudinal direction of the stringer.

• To resist tension in the stringers, the necessary reinforcement should be provided. The variation of the force of the tension stringers - should not be greater than corresponding to the stringer force increasing from zero to the design yield force over a length corresponding to the anchorage length. The compressive stress of the

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stringers should not exceedcdfν , where the efficiency factor should be taken as ν =

νm, assuming a section provided with normal reinforcement. The force in the compression reinforcement should not be assumed to exceed the design load-bearing capacity of the concrete. If the reinforcement is assumed to resist forces exceeding half the design force resisted in the concrete, lap splices should not be used.

• The reinforcement area and the magnitude of the concrete compressive stress in the

shear fields should be calculated using the equations in Annex F. The concrete compressive stress is checked by applying the efficiency factor given below It is a prerequisite for the applicability of the method that the shear reinforcement is effectively anchored in the stringers. Where shear reinforcement is omitted, the stringers and the nodes related to the shear fields considered should be designed according to the rules applying to the strut-and-tie model.

Efficiency factor

For the analysis of failure of reinforced concrete an effective design concrete compressive strength

cdfν should be used, where ν is the efficiency factor.

Unless otherwise specified, the values for the efficiency factor given in this clause apply, provided that the reinforcement at least corresponds to the minimum reinforcement.

Where the requirement for minimum reinforcement is not fulfilled, ν should be determined by:

ckf

2=ν (fck in MPa) (5.100NA)

The value determined using (5.100NA) always constitutes a lower limit for the value of ν.

In the following it is assumed that actions are referred to an orthogonal coordinate system that coincides with the directions of reinforcement.

Pure actions

Pure compressive axial stress

The efficiency factor for pure pressure is denoted νn and should be determined by:

=bending to due ncompressioby produed is stressaxial the where

force axial anby produced is stressaxial the where

mn ν

υ0,1

The efficiency factor νm should be determined by

300500097,0 ckyk

m

ff−−=ν , however, not less than 0,6 (fck and fyk in MPa) (5.101NA)

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For bending and normally reinforced cross-sections, however, the following expression should be used:

50098,0 ck

m

f−=ν , however, not less than 0,6 (fck in MPa) (5.102NA)

For combined axial force and bending a weighted mean value of νn between the values for pure axial force and pure bending should be used.

Pure shear

The efficiency factor for pure shear is denoted νv and should be determined by

2007,0 ck

v

f−=ν , however not less than 0,45 (fck in MPa) (5.103NA)

The value of νv also applies to beams in cases where inclined reinforcement is used as shear reinforcement. νv applies where shear is produced by a shear force. Where shear is due to a torsional force, the efficiency factor is denoted νt and should be determined by

)200

7,0(7,0 ckt

f−=ν (fck in MPa) (5.104NA)

For pure shear caused by both an external shear force and an external torsional force, a weighted mean value of ν v og ν t should be used. For thin-walled sections with torsion where the individual subwalls constituting the section are reinforced with closed stirrups along the perimeter and uniformly distributed longitudinal reinforcement at both sides, ν t should be taken as ν v. This also applies to reinforced slabs provided with shear reinforcement along edges subject to torsion.

ν = νt ν = νv

Figure 5.100 - Efficiency factor for pure torsion

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Combined effects for in-plane stress conditions

Where concrete struts in compression contribute to resist shear forces, e.g. in the truss model, the efficiency factor should as a maximum be taken as ν = νv.

σcd ≤ νvfcd

reinforcement

reinforcement

Figure 5.101- Efficiency factor for concrete struts contributing to shear resistance

For nodes, e.g. for the strut-and-tie model and bearings, the efficiency factor should generally be taken as ν = 0,8. For nodes where no reinforcement is provided through the node and the stress in the node is caused by an external pressure, the efficiency factor may, however, be taken as ν = 1,0.

Where a compressive axial stress is subject to a perpendicular tensile axial stress due to a tensile axial force or a bending moment, the efficiency factor is denoted νnr and should be determined by

yd

Ednnr fρ

σνν 2,0−= (σEd and fyd in MPa) (5.105NA)

where σEd is the external design tensile axial stress and рfyd is the design tensile strength perpendicular to the direction of compression.

σEdσEd

σcd ≤ νnrfcd

σcd

Figure 5.102 - Efficiency factor for compression combined with transverse tension For combined shear and axial stresses a conservative efficiency factor corresponding to pure shear should be used. As an alternative, the concrete compressive stress is obtained by fulfilling the following conditions:

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cdxEdx f−≥σ (5.106NA)

cdyEdy f−≥σ (5.107NA)

))((2

EdycdyEdxcdxEdxy ff σστ ++≤ (5.108NA)

cdvEdxy f½≤τ (5.109NA)

where

σEdx, σEdy and τEdxy are the external actions, assumed to be positive as tension.

fcdv is the effective design compressive strength for pure shear, i.e. either fcdv = νvfcd, fcdv = νtfcd or a weighted value of νvfcd and νtfcd, depending on the external action.

fcdx and fcdy are the design compressive strengths of the considered point in the x direction and the y direction, respectively, taking the contribution of the concrete in equations (5.106NA) and (5.107NA) as not greater than νnrfcd, while the contribution in equation (5.108NA) should be taken as not greater than νnfcd.

For slabs with small reinforcement ratios, i.e. (ρfyd/fcd) less than approx. 0,1, the efficiency factor should be taken as ν = νm when calculating the moment actions, viz. the influence of torsion on the efficiency factor should be disregarded. F1(4) For Class A steels, the reinforcement should be determined using (F.2)-(F.7). For Class B or Class C steels, (F.8)-(F.10) should be used.

Page 21 of 21


Bibliography List of all National Annexes

EN 1990 DK NA:2007 National Annex to Eurocode 0 – Basis of structural design EN 1991-1-1 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-1: General actions – Densities, self-

weight, imposed loads for buildings EN 1991-1-2 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on

structures exposed to fire EN 1991-1-3 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-3: General actions – Snow loads EN 1991-1-4 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions EN 1991-1-5 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-5: General actions – Thermal actions EN 1991-1-6 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-6: General actions – Actions during

execution EN 1991-1-7 DK NA:2007 National Annex to Eurocode 1: Actions on structures – Part 1-7: General actions – Accidental actions EN 1992-1-1 DK NA:2007 National Annex to Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for

buildings EN 1992-1-2 DK NA:2007 National Annex to Eurocode 2: Design of concrete structures - Part 1-2: General rules – Structural fire

design EN 1993-1-1 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for

buildings EN 1993-1-2 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-2: General rules – Structural fire

design EN 1993-1-3 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-3: General rules - Supplementary

rules for cold-formed members and sheeting EN 1993-1-4 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-4: General rules - Supplementary

rules for stainless steels EN 1993-1-5 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-5: Plated structural elements EN 1993-1-6 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-6: Strength and stability of shell

structures EN 1993-1-7 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-7: Plated structures subject to out of

plane loading EN 1993-1-8 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-8: Joints EN 1993-1-9 DK NA:2007 National Annex to Eurocode 3: Design of steel structures – Part 1-9: Fatigue EN 1993-1-10 DK NA:2007 National Annex to Eurocode 3: Design of steel structures - Part 1-10: Material toughness and through-

thickness properties EN 1994-1-1 DK NA:2007 National Annex to Eurocode 4: Design of composite steel and concrete structures - Part 1-1: General

rules and rules for buildings EN 1994-1-2 DK NA:2007 National Annex to Eurocode 4: Design of composite steel and concrete structures - Part 1-2: General

rules – Structural fire design EN 1995-1-1 DK NA:2007 National Annex to Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and

rules for buildings EN 1995-1-2 DK NA:2007 National Annex to Eurocode 5: Design of timber structures - Part 1-2: General – Structural fire design EN 1996-1-1 DK NA:2007 National Annex to Eurocode 6: Design of masonry structures - Part 1-1: General rules for reinforced

and unreinforced masonry structures EN 1996-1-2 DK NA:2007 National Annex to Eurocode 6: Design of masonry structures - Part 1-2: General rules – Structural fire

design EN 1996-2 DK NA:2007 National Annex to Eurocode 6: Design of masonry structures - Part 2: Design considerations,

selection of materials and execution of masonry EN 1997-1 DK NA:2007 National Annex to Eurocode 7: Geotechnical design - Part 1: General rules EN 1999-1-1 DK NA:2007 National Annex to Eurocode 9: Design of aluminium structures - Part 1-1: General rules EN 1999-1-2 DK NA:2007 National Annex to Eurocode 9: Design of aluminium structures – Part 1-2: Structural fire design EN 1999-1-3 DK NA:2007 National Annex to Eurocode 9: Design of aluminium structures – Part 1-3: Fatigue

Documents

EN 1992-1-1 DK NA