national annex to eurocode 2: design of concrete...

of 35 Introduction DS/EN 1992-1-1 DK NA:2013

DS/EN 1992-1-1 DK NA:2013

National Annex to

Eurocode 2: Design of concrete structures –

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

Foreword

This national annex (NA) is a revision of DS/EN 1992-1-1 DK NA:2011 and replaces the latter on

2013-05-15. For a transition period until 2013-09-01, this National Annex as well as the previous

National Annex will be applicable. Technical changes have been made in clauses 2.4.2.4(1) (γ0 add-

ed), 3.1.4(2), 3.2.2(3)P, 5.2(1)P, 6.2.5(1), 8.3(2) (first paragraph), 9.10.2.2(2), C.1(1), C.3(1)P, and

finally Annex 3 has been deleted (see 5.2(1)P).

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

1992-1-1 for construction works in conformity with the Danish Building Act or the building legisla-

tion. Other parties can put this NA into effect by referring thereto.

National provisions are nationally applicable values and options between methods as specified in

the Eurocode as well as complementary information.

This NA includes:

an overview of possible national choices and complementary information;

national choices;

complementary (non-contradictory) information.

Headings and numbering refer to the clauses of EN 1992-1-1 where choices have been made and/or

complementary information is given.

of 35 Overview of national choices and complementary infor-

mation

DS/EN 1992-1-1 DK NA:2013

Overview of possible national choices and complementary information

The list below identifies the clauses where national choices are possible and the applicable/not ap-

plicable informative annexes. Furthermore, clauses giving complementary information are identi-

fied. Complementary information is given at the end of this document.

Clause Subject National choice

Complementary infor-

mation 1.2.2 Other reference standards Complementary information

2.3.1.4(2) Prestress Complementary information

2.3.3(3) Deformations of concrete Unchanged

2.4.2.1(1) Partial factor for shrinkage action Unchanged

2.4.2.2(1) Partial factors for prestress Unchanged

2.4.2.2(2) Partial factors for prestress National choice

2.4.2.2(3) Partial factors for prestress Unchanged

2.4.2.3(1) Partial factor for fatigue loads Unchanged

2.4.2.4(1) Partial factors for materials National choice

2.4.2.4(2) Partial factors for materials Unchanged

2.4.2.5 (2) Partial factors for materials for

foundations

National choice

3.1.1(1)P General Complementary information

3.1.2(2)P Strength Unchanged

3.1.2(4) Strength National choice

3.1.3(2) Elastic deformation National choice

3.1.4(2) Creep and shrinkage Complementary information

3.1.6(1)P Design compressive and tensile

strengths

Unchanged


strengths

Unchanged

3.2.1(1)P General Complementary information

3.2.2(3)P Properties Unchanged Complementary information

3.2.7(2) Design assumptions National choice

3.3.1 General Complementary information

3.3.4(5) Ductility characteristics Unchanged

3.3.6(7) Design assumptions Unchanged

4.2 Environmental conditions National choice

4.4.1.2(3) Minimum cover, cmin National choice

4.4.1.2(5) Minimum cover, cmin National choice

4.4.1.2(6) Minimum cover, cmin Unchanged




4.4.1.3(1)P Allowance in design for tolerance National choice

4.4.1.3(3) Allowance in design for tolerance National choice

4.4.1.3(4) Allowance in design for tolerance Unchanged


mation

DS/EN 1992-1-1 DK NA:2013



mation 5.1.3(1)P Load cases and combinations National choice

5.2(1) Geometric imperfections Complementary information

5.2(5) Geometric imperfections Unchanged

5.5(4) Linear analysis with limited redistri-

bution

Unchanged

5.6.1(3)P (Plastic analysis) General Complementary information

5.6.3(4) Rotation capacity Unchanged

5.8.3.1(1) Slenderness Criterion for isolated

members

Unchanged

5.8.3.3(1) Global second order effects in build-

ings

Unchanged

5.8.3.3(2) Global second order effects in build-

ings

Unchanged

5.8.5(1) Methods of analysis National choice

5.8.6(3) General method National choice

5.10.1(6) General National choice

5.10.2.1(1)P Maximum stressing force Unchanged

5.10.2.1(2) Maximum stressing force Unchanged

5.10.2.2(4) Limitation of concrete stress Unchanged

5.10.2.2(5) Limitation of concrete stress Unchanged

5.10.3(2) Prestress force Unchanged

5.10.8(2) Effects of prestressing at ultimate

limit state

National choice

5.10.8(3) Effects of prestressing at ultimate

limit state

National choice

5.10.9(1)P Effects of prestressing at serviceabil-

ity limit state and limit state of fa-

tigue

National choice

6.2.1(2) General verification procedure Complementary information

6.2.2(1) Members not requiring design shear

reinforcement

National choice


reinforcement

National choice Complementary information

6.2.3(2) Members requiring design shear

reinforcement

National choice


reinforcement

National choice

6.2.4(4) Shear between web and flanges of

T-sections

National choice

6.2.4(6) Shear between web and flanges of

T-sections

Unchanged

6.2.5(1) Shear at the interface between con-

cretes cast at different times

Complementary information

6.3.2(6) Design procedure Complementary information

6.4.3(6) Punching shear calculation

Unchanged


mation

DS/EN 1992-1-1 DK NA:2013



mation 6.4.4(1) Punching shear resistance of slabs

and column bases without shear

reinforcement

Unchanged

6.4.5(3) Punching shear resistance of slabs

and column bases with shear rein-

forcement

Unchanged

6.4.5(4) Punching shear resistance of slabs

and column bases with shear rein-

forcement

National choice

6.5.2(2) Struts National choice

6.5.4(4) Nodes National choice

6.5.4(6) Nodes National choice

6.8.4(1) Verification procedure for reinforc-

ing and prestressing steel

Unchanged

6.8.4(5) Verification procedure for reinforc-

ing and prestressing steel

Unchanged

6.8.6(1) Other verifications Unchanged

6.8.6(3) Other verifications Unchanged

6.8.7(1) Verification of concrete under com-

pression or shear

Unchanged

7.2(2) Stress limitation Unchanged



7.3.1(5) General considerations National choice

7.3.2(1)P Minimum reinforcement areas Complementary information

7.3.2(3) Minimum reinforcement areas Complementary information

7.3.2(4) Minimum reinforcement areas Unchanged

7.3.4(1) Calculation of crack widths Complementary information

7.3.4(3) Calculation of crack widths National choice

7.3.4(4) Calculation of crack widths Complementary information

7.4.2(2) Cases where calculations may be

omitted

Unchanged

8.2(2) Spacing of bars Unchanged

8.3(2) Permissible mandrel diameters for

bent bars

Unchanged Complementary information

8.4.1(2) General Complementary information

8.4.2(2) Anchorage capacity Complementary information

8.4.3(2) Basic anchorage length Complementary information

8.4.4 Design anchorage length Complementary information

8.6(2) Anchorage by welded bars National choice

8.7.3 Lap length Complementary information

8.8(1) Additional rules for large diameter

bars

Unchanged

8.9 Bundled bars Complementary information

9.2.1.1(1) Minimum and maximum reinforce-

ment areas

National choice


mation

DS/EN 1992-1-1 DK NA:2013



mation 9.2.1.1(3) Minimum and maximum reinforce-

ment areas

Unchanged

9.2.1.2(1) Other detailing arrangements

Unchanged

9.2.1.4(1) Anchorage of bottom reinforcement

at an end support

Unchanged

9.2.2(4) Shear reinforcement Unchanged

9.2.2(5) Shear reinforcement National choice




9.3.1.1(3) General Unchanged

9.5.2(1) Longitudinal reinforcement Unchanged



9.5.3(3) Transverse reinforcement Unchanged

9.6.2(1) Vertical reinforcement Unchanged

9.6.3(1) Horizontal reinforcement Unchanged

9.7(1) Deep beams Unchanged

9.8.1(3) Pile caps Unchanged

9.8.2.1(1) General Unchanged

9.8.3(1) Tie beams Unchanged

9.8.3(2) Tie beams National choice

9.8.4(1) Column footing on rock Unchanged

9.8.5(3) Bored piles Unchanged

9.10.2.2(2) Peripheral ties National choice

9.10.2.3(3) Internal ties National choice

9.10.2.3(4) Internal ties National choice

9.10.2.4(2) Horizontal ties to columns and/or

walls

National choice

9.10.3(3) Continuity and anchorage of ties Complementary information


strengths

National choice


strengths

National choice

11.3.7(1) Confined concrete Unchanged


reinforcement

National choice


reinforcement

Unchanged


reinforcement

National choice

11.6.4.1(1) Punching shear resistance of slabs or

column bases without shear rein-

forcement

Unchanged


mation

DS/EN 1992-1-1 DK NA:2013



mation 12.3.1(1) Concrete: additional design assump-

tions

National choice

12.6.3(2) Shear

Unchanged

Annex A Modification of partial factors for

materials

Not applicable

C.1(1) General National choice Complementary information

C.1(3) General Unchanged

C.3(1)P Bendability Complementary information

E.1(2) General National choice

F.1(4) General Complementary information

Annex G Soil structure interaction Not applicable

Annex H Global second order effects in struc-

tures

Not applicable

Annex I Analysis of flat slabs and shear walls Not applicable

Annex J Examples of regions with disconti-

nuity in geometry or action

Not applicable

Annex 1 Design of certain columns cast in

situ

Complementary information

Annex 2 Verification of robustness Complementary information

NOTE Unchanged: Recommendations in the Eurocode are followed.

of 35 National choices DS/EN 1992-1-1 DK NA:2013

National choices

2.4.2.2(2) Partial factors for prestress

The following value is to be applied: γP,unfav = 1,2.

2.4.2.4(1) Partial factors for materials

The partial factors given in Table 2.1N NA are used for ultimate limit states for persistent and tran-

sient design situations.

Table 2.1Na NA - Partial factors for materials for ultimate limit states for persistent and tran-

sient design situations

Structures, general

Compressive strength and modulus of elasticity of reinforced concrete γc = 1,45 γ0 γ3

Compressive strength and modulus of elasticity of plain concrete 3)

γc = 1,60 γ0 γ3

Tensile strength of concrete 4)

γc = 1,70 γ0 γ3

Strength of non-prestressed reinforcement γs = 1,20 γ0 γ3

Strength of prestressing tendons γs = 1,20 γ0 γ3

Precast concrete elements, calculation 1)

Compressive strength and modulus of elasticity of reinforced concrete γc = 1,40 γ0 γ3

Compressive strength and modulus of elasticity of plain concrete 3)

γc = 1,55 γ0 γ3

Tensile strength of concrete 4)

γc = 1,60 γ0 γ3

Strength of non-prestressed reinforcement γs = 1,20 γ0 γ3

Strength of prestressing tendons γs = 1,20 γ0 γ3

Precast concrete elements, testing 1)

Testing leading to ductile failure 2)

γM = 1,20 γ0 γ3

Testing leading to brittle failure γM = 1,40 γ0 γ3

1) The partial factor for precast concrete elements may be used if the elements are covered by a harmonised product

standard or subject to third party surveillance according to EN 13369, Annex E.

2) Precast elements subject to transverse load are assumed to exhibit ductile failure if at least one of the following con-

ditions 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 precast concrete elements subject to axial forces is always

to be assumed to be brittle failure.

3) The partial factor for the compressive strength and modulus of elasticity of plain concrete, γc, applies to structures

not provided with minimum reinforcement conforming to the rules in this Eurocode. The rules for minimum reinforce-

ment can be modified if it is documented by experiments that the type of failure will not differ from the type of failure

for the structure which complies with the rules for minimum reinforcement given in the Eurocode.


4) The partial factor for the tensile strength of concrete γc is applied in cases where failure of the concrete is depending

upon tensile failure and/or where the structure is not provided with minimum reinforcement. For beams and slabs with-

out shear reinforcement and for punching, shear failure can be considered to be compressive failure. For unreinforced

structures, at construction joints not provided with minimum reinforcement, and at anchorages/laps, failure is assumed

to be tensile failure.

The partial factors are determined in accordance with the National Annex to EN 1990, Annex F,

where γM = γ0 γ1 γ2 γ3 γ4, where:

γ0 applies to members forming part of geotechnical structures, cf. EN 1990, Table A.1.2(B+C),

and Annex F

γ1 takes into account the type of failure

γ2 takes into account the uncertainty related to the design model

γ3 takes into account the scope of checking

γ4 takes into account the variation of the strength parameter or resistance.

When determining γ1, the types of failure given in Table 2.1.Nb NA are applied.

Table 2.1 Nb NA – Assumed types of failure for the determination of γ1

Structures, general, and precast concrete elements, calculation

Compressive strength and modulus of elasticity of reinforced concrete Warning of fail-

ure without residual 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 fail-

ure without residual resistance

Precast concrete elements, testing

Testing leading to ductile failure Warning of failure without residual

resistance

Testing leading to brittle failure No warning of failure

Table 2.1Nc NA specifies values of γ3 depending on the scope of checking.

Table 2.1Nc NA - 3 depending on scope of checking

Inspection lev-

el

Extended Normal Reduced

γ3 0,95 1,0 1,10

The following partial factor is applied for ultimate limit states for accidental design situations γM =

1,0.


For the verification of fatigue for persistent design situations, the partial factors given in Table

2.1Na NA multiplied by 1,1 are used for the values C,fat and S,fat.

The reduced inspection level is not to be applied for structures assigned to the high consequences

class.

The provisions, including the scope of checking related to the individual levels of checking are

specified in EN 1990 DK NA, EN 13670 and DS 2427.

2.4.2.5(2) Partial factors for materials for foundations

The following value is to be applied: kf = 1,0.

3.1.2(4) Strength

The value of kt is determined based on documentation of the concrete strength regarded in relation

to the concrete strength at 28 days.

3.2.7(2) Design assumptions

Assumption b, corresponding to a horizontal top branch, is applied.

For εuk, the value εuk = Agt is used in accordance with the definition given in EN 10080.

4.2 Environmental conditions

The exposure classes defined in EN 206-1 are reproduced in EN 1992-1-1, Table 4.1.

Elements are assigned to the exposure classes specified in Table 4.1. An element may be subject to

several of the exposures contained in Table 4.1, and the environmental conditions to which the

structural member is exposed can be described by a combination of exposure classes.

The exposure classes are related to environmental classes as specified in DS 2426 and reproduced

in Table 4.1 NA. Four environmental classes are used: passive, moderate, aggressive and extra ag-

gressive, designated P, M, A and E, respectively.

The strictest environmental class is applied, corresponding to the ranking P, M, A and E.

For individual elements, exposed surfaces may be assigned to different exposure classes depending

on the environmental actions.

Table 4.1 NA - Normative assignment of exposure classes to environmental classes:

Environmental class Passive Moderate Aggressive Extra aggressive

Covers the following exposure

classes according to EN 206-1

X0

XC1

XC2

XC3

XC4

XF1

XA1

XD1

XS1

XS2

XF2

XF3

XA2

XD2

XD3

XS3

XF4

XA3


NOTE – Conservative examples of environmental classes to which individual elements should normally be

assigned are as follows:

Generally, the passive environmental class should include the following elements:

o structures in indoor dry environments;

o buried foundations belonging to low and normal consequences classes.

Generally, the moderate environmental class should include the following elements:

o foundation piles;

o foundations partly above terrain;

o buried foundations in high consequences classes;

o external walls and facades;

o external columns;

o external beams with structurally protected surfaces at the top side;

o balcony parapets;

o installation ducts;

o service corridors;

o lift shafts.

Generally, the aggressive environmental class should include the following elements:

o external slabs;

o external beams without structurally protected surfaces at the top side;

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 members in moderately aggressive ground water.

The extra aggressive environmental class should be considered for the following elements

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 members in highly aggressive ground water.

Deviation from the examples is allowed if the exposure classes in Table 4.1 and their relation to the envi-

ronmental classes in Table 4.1 NA justify assignment to a lower environmental class. A concrete boundary

can be exposed both through the actual surface and through other surfaces of the element.

4.4.1.2(3) Minimum cover, cmin

For circular ducts for post-tensioned structures, the upper limit of cmin,b is 65 mm.

4.4.1.2(5) Minimum cover, cmin

Structural classes are not applied.

For extended and normal inspection levels, the concrete cover is at least as specified in Table 4.4N

NA for non-prestressed reinforcement in conformity with EN 10080 and as specified in Table 4.5N

NA for prestressing steels.


In the case of reduced inspection levels, the prescribed concrete cover it to be increased by 5 mm.

The values given can be assumed to correspond to a design working life of 50 years.

Table 4.4N NA – Requirements for minimum cover, cmin,dur, with respect to the durability of

non-prestressing steel in accordance with EN 10080

Table 4.5N NA – Requirements for minimum cover, cmin,dur, with respect to the durability of

prestressing steel in accordance with EN 10080

4.4.1.3(1)P Allowance in design for deviation

The allowance in design for deviation cdev should normally not be less than 5 mm for normal and

extended inspection levels and 10 mm for reduced inspection levels.

4.4.1.3(3) Allowance in design for deviation

The situation is covered by the provisions in 4.4.1.3(1)P.

5.1.3(1)P Load cases and combinations NOTE - The analysis of continuous beams based on the theory of plasticity may be carried out by verifying that each

bay is capable of resisting the load effects corresponding to the maximum load on the entire bay and the minimum load

on the entire bay, taking for both cases the total values of the restraining moments chosen.

Environmental class Minimum cover

mm

Extra aggressive 40 mm

Aggressive 30 mm

Moderate 20 mm

Passive 10 mm

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


Restraining moments are chosen between the values found by the theory of elasticity and one third thereof. For

continuous beams and slabs of approximately equal spans and uniformly distributed loads, verification of the position of

the restraining moments in relation to the theory of elasticity may be omitted if at restraints and intermediate supports

reinforcement is applied for restraining moments which are taken numerically as not less than 1/3 and not more than

twice the maximum design moments in adjacent spans.

5.2(1)P Geometric imperfections

See the complementary information.

5.6.1(3)P (Plastic analysis) General

See the complementary information.

5.8.5(1) Methods of analysis

The following simplified method is to be applied: (a) Method based on nominal stiffness.

5.8.6(3) General method

The following value is to be applied: γcE = γc, cf. Table 2.1Na NA .

5.10.1(6) General

The following method is to be applied: Method A.

5.10.8(2) Effects of prestressing at ultimate limit state

The following value is to be applied: .0, ULSp

5.10.8(3) Effects of prestressing at ultimate limit state

The following value is to be applied: .0,1inf,sup, PP

5.10.9(1)P Effects of prestressing at serviceability limit state and limit state of fatigue

The following value is to be applied: .0,1infsup rr

6.2.2(1) Members not requiring design shear reinforcement

vmin is determined by:

(

)

⁄

⁄


The value of ν is found on the basis of the complementary information in 5.6.1(3)P.

6.2.3(2) Members requiring design shear reinforcement

Where class B and class C steels are used according to Annex C of EN1992-1-1 the following ap-

plies:

The inclination θ of the concrete compressive stress is chosen such that


5,2cot2

tan

(6.7a NA)

Where curtailed reinforcement is used, the following applies

0,2cot2

tan

(6.7b NA)

Normally, the upper limits for cotθ ensure that no unacceptable shear cracks occur at the servicea-

bility limit state for beams and slabs without prestress. The limits for the strut inclination may be

exceeded if circumstances permit. For example cotθ may be increased for fully prestressed struc-

tures where shear cracks do not normally cause problems.

Class A steel in accordance with Annex C of EN 1992-1-1 may be used to resist shear, provided

that adequate deformation capacity ensures that shear failure can develop as predicted by the shear

design. This can be assumed to be the case if the value applied for cotθ implies that the overall de-

sign reinforcement for the structure is a minimum. For statically determinate beams subjected solely

to shear (V), torsion (T) and bending (M), and where vertical stirrups (α = 90°) are used, the values

1 ≤ cotθ≤ 2 may be applied for cotθ, if T ≤ 0,1V, where T is given in kNm and V in kN.


The value of ν1 is found on the basis of the complementary information in 5.6.1(3)P.

6.2.4(4) Shear between web and flanges

The recommended value is to be applied if class B and 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 may be used if adequate deformation capacity

is ensured. This can be assumed to be the case if the value applied for cotθ implies that the overall

design reinforcement for the flange structure is a minimum.

6.2.5(1) Shear at the interface between concrete cast at different times See also the complementary information.

6.4.5(4) Punching shear resistance of slabs and column bases with shear reinforcement

The following values are to be applied: k = 2,0.

6.5.2(2) Struts

The following value is to be applied: '6,0 according to the complementary information in

5.6.1(3)P.

6.5.4(4) Nodes

The following values are to be applied: k2 = k3 = 1,0 and ' according to the complementary

information in 5.6.1(3)P.


6.5.4(6) Nodes

The following value is to be applied: k4 = 1,0, which is a conservative value. The value depends on

transverse compression.

7.3.1(5) General considerations

The recommended values for relevant environmental classes are given in Table 7.1 NA.

Table 7.1 NA - Recommended maximum values of calculated crack widths wmax (mm)

Environmental class Non-prestressed rein-

forcement

Prestressing ten-

dons

Extra aggressive 0,2 mm 0,1 mm

Aggressive 0,3 mm 0,2 mm

Moderate 0,4 mm 0,3 mm

8.6(2) Anchorage by welded bars

The applied value of Fwd is to be documented by experiments and conform to the safety level pre-

scribed by the standard, and at the same time documentation is to be provided that the properties of

the reinforcement after welding continues to fulfil the requirements specified in this standard for the

properties of reinforcement.

NOTE – See also Annex C.1(1).

9.2.1.1(1) Minimum and maximum reinforcement areas

Deep beam webs are provided with evenly distributed reinforcement along the sides of the beam

web and parallel to the beam axis. The reinforcement ratio should be at least equal to that for stirrup

reinforcement, cf. clause 9.2.2(5).

9.2.2(5) Shear reinforcement

The following value is to be applied:

( √ )

(9.5N NA)

9.8.3(2) Tie beams

The following value is to be applied: q1 is determined in consideration of the compaction equip-

ment.

9.10.2.2(2) Peripheral ties

The following is to be applied: The value of q1 is taken at least as 7,5 kN/m for the normal conse-

quences class and 15 kN/m for the high consequences class.

The tie force, Ftie,per, is at least taken as a characteristic value of 40 kN for the normal consequences

class and 80 kN for the high consequences class. The limitation q2 is not applied in Denmark.

9.10.2.3(3) Internal ties

The following value is to be applied: The tie force, Ftie,int, is taken as equal to a characteristic value

of 15 kN/m for the normal consequences class and 30 kN/m for the high consequences class.


9.10.2.3(4) Internal ties

The following value is to be applied: The value of q3 is taken as 15 kN/m for the normal conse-

quences class and 30 kN/m for the high consequences class. As a minimum, Ftie should be 40 kN

for the normal consequences class and 80 kN for the high consequences class. The limitation q4 is

not applied in Denmark.

9.10.2.4(2) Horizontal ties to columns and/or walls

The following value is to be applied: For the normal consequences class, the value of the tensile

force, ftie,fac, is taken as 15 kN/m at the top of the wall and as 0 kN/m at the bottom of the wall.

Ftie,col is taken as 80 kN at the top of the column and as 0 kN at the bottom of the column.

For the high consequences class, the value of the tensile force, ftie,fac, is taken as 30 kN/m at the top

and the bottom of the wall. Ftie,col is taken as 160 kN at the top and the bottom of the column.

11.3.5(1)P Design compressive and tensile strengths

The following value is to be applied: αlcc = 1,0.

11.3.5(2)P Design compressive and tensile strengths

The following value is to be applied: αlct = 1,0.


vmin is determined by:

(

)

⁄

⁄


The following value is to be applied:

22006,04,01 (11.6.6N NA)

where ν conforms to the complementary information provided in 5.6.1(3)P.

12.3.1(1) Concrete: additional design assumptions

The following value is to be applied: αcc,pl and αct,pl are taken as 1,0.

C.1(1) General

The fatigue strength of the reinforcement expressed in terms of fatigue properties is to be docu-

mented. For de-coiled rods and tack welded reinforcement to be used in structures where the rein-

forcement is subjected predominantly to static loads, the documentation provided by the manufac-

turer is adequate.

As an alternative, documentation of the fatigue strength may be provided by determining the fatigue

strength R0/+p for 2 x 106 cycles applied with a free impact of a given form, alternating between R0


and R0/+p = 1/3 of the characteristic value of the upper yield strength or the 0,2 % proof strength for

the strength class.

The fatigue strength test is a substitute test the purpose of which is to ensure that the reinforcing

steel is free from notches, brittle zones, etc. As the test is a dynamic test of the reinforcement, it

may also be used as documentation of the fatigue properties of the reinforcement for the test values

given. For concrete structures subjected to dynamic loading where the actions on reinforcement are

outside the test values given, the designer is to prescribe additional fatigue testing in terms of num-

ber of cycles and span such that the additional tests document the fatigue strength of the reinforce-

ment with respect to the actual actions on the reinforcement.

E.1(2) General

Exposure classes are assigned to environmental classes in clause 4.2. 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

of 35 Complementary (non-contradictory) information DS/EN 1992-1-1 DK NA:2013

Complementary (non-contradictory) information

1.2.2 Other reference standards

EN 206-1, Concrete - Part 1: Specification, performance, production and conformity is to be used

together with DS 2426, Concrete - Materials - Rules for application of EN 206-1 in Denmark.

EN 13670, Execution of concrete structures is to be used in Denmark together with DS 2427, Con-

crete execution – Rules for application of EN 13670 in Denmark.

For reinforcement with smooth surfaces EN 10025-1, Hot rolled products of structural steels - Part

1: General technical delivery conditions, and EN 10025-2, Hot rolled products of structural steels -

Part 2: Technical delivery conditions for non-alloy structural steels, apply.

Until EN 10138 is available, prEN10138, Prestressing steels, is used.

2.3.1.4(2) Prestress For unbonded tendons and tendons immersed in oil or equivalent, the methods of analysis adopted

is to reflect that no shear forces are transmitted between reinforcement and concrete.

Unbonded tendons are not allowed where there is a risk of corrosion or frost damage due to pene-

trating water or harmful liquids.

3.1.1(1)P General Crushed concrete shall fulfil the requirements for aggregates according to EN 206-1 and DS 2426.

Crushed concrete shall be divided into coarse and fine fractions.

Crushed concrete from a pure source may be used as aggregate for concrete in the passive environ-

mental class op to strength class C30/37. The crushed concrete shall constitute no more than 20% of

the coarse fraction and 10% of the fine fraction.

NOTE Crushed concrete from a pure source is concrete, excluding reinforcement, containing only materials that can be

referred to current or previously current standards and codes of practice dealing with concrete structures.

Crushed concrete from an extra pure source may be used as aggregate for concrete in the passive

environmental class op to the original strength class of the crushed concrete. The crushed concrete

shall constitute no more than 10% of the coarse fraction and 10% of the fine fraction.

NOTE Crushed concrete from an extra pure source is concrete, excluding reinforcement, manufactured according to

applicable codes of practice and standards and manufactured at the place of production where it is recycled.

3.1.3(2) Elastic deformation

Danish concretes according to DS 2426 can normally be considered to correspond to concretes con-

taining quartz aggregate.


3.1.4(2) Creep and shrinkage

For structures where creep does not have a decisive influence on the static behaviour of the struc-

ture, the final creep coefficient, (∞, t0), may as an approximation be taken as 3. Examples of

structures where creep has a decisive influence on the static behaviour include prestressed structures

and the stability of columns and walls.

3.2.1(1)P General

CE Marking and certification

Reinforcing steel shall either be CE marked or manufactured in accordance with the requirements

specified in EN 10080, Annex ZA, and the production/product shall be certified according to the

requirements of Annex ZA in the relevant standard. Where the product is not CE marked, the certi-

fication body and the testing laboratory shall be accredited to the standard concerned by an accredi-

tation body that has signed the Multilateral Agreement of European Co-operation for Accreditation

for the field in question.

After straightening, coils supplied according to EN 10080 shall be certified to the requirements of

EN 10080 for the properties which are changed by the straightening process, in conformity with the

requirements for straightened material in EN 10080.

Application of stainless reinforcement in connection with the use of Eurocode 2

Stainless bars for reinforcement certified to BS 6744, strength class 500 MPa, may be used in ac-

cordance with EN 1992-1-1.

Application of reinforcing steels with indented surfaces

Where reinforcing steels with indented surfaces and with a measured fp fulfil the requirements for fR

for reinforcing steels with ribbed surfaces, reinforcing steels with indented surfaces may be used in

the same manner as reinforcing steels with ribbed surfaces according to Eurocode 2.

Application of reinforcing steels with smooth surfaces

If the requirements specified in this DK NA for reinforcing steels with smooth surfaces are fulfilled,

reinforcing steels with smooth surfaces may be used according to Eurocode 2.

Reinforcing steels with smooth surfaces shall be manufactured as structural steels in accordance

with EN 10025-2 or as reinforcing steels in accordance with EN 10080. Structural steels in accordance with EN 10025-2 shall be steel grades S235, S275 or S355 and be

declared by means of inspection certificate 3.1 in conformity with EN 10204.

3.2.2(3)P Properties The lower limit of 400 MPa does not apply to reinforcing steels with smooth surfaces.

If, for reinforcement with smooth surfaces, transmission of bond forces between concrete and rein-

forcement is assumed, the characteristic yield strength of the reinforcement shall not be taken as

larger than 250 MPa.


3.3.1 General

CE Marking and certification

Prestressing steels are either to be CE marked or manufactured in accordance with the requirements

specified in FprEN 10138-1, Annex ZA, and the production/product is to be certified according to

the requirements of Annex ZA in the relevant standard. Where the product is not CE marked, the

certification body and the testing laboratory are to be accredited to the standard concerned by an

accreditation body that has signed the Multilateral Agreement of European Co-operation for Ac-

creditation for the field in question.

Application of prestressing steels certified to other standards than EN 10138-1 in connection

with the use of Eurocode 2

Prestressing steels with a Zulassungcertifikat may be accepted in the same manner as prestressing

steels certified to the FprEN 10138 series.”

5.2(1)P Geometric imperfections

For buildings where floor diaphragms and shear walls or equivalent strut-and-tie models constitute

the bracing system, the following simplified rules may be used.

The overall effect of geometric imperfections are addressed by designing the building to take ac-

count of equivalent horisontal loads acting at the centre of gravity of the individual floor dia-

phragms. The load is determined according to EN 1992-1-1, 5.2(8), expression (5.4), by replacing

(Nb – Na) with the vertical load acting on the actual floor diaphragm.

For persistent design situations, the horizontal load shall be assumed to act at the same time as wind

actions. When investigating the stability of buildings, it may be assumed for each direction of wind

considered that the effects of geometric imperfections act in the same direction as the wind action.

For seismic design situations, the horizontal load due to imperfections is taken to act at the same

time as the seismic load. The horizontal load due to imperfections is assumed to act in the same

direction as the seismic load.

The special analysis corresponding to Figures 5.1 c1) and c2) in EN 1992-1-1, clause 5.2(8), which

applies to eccentricity in opposite directions of isolated vertical structural members across two sto-

reys may be replaced by designing the vertical structural members to resist a horizontal displace-

ment between the structural members at the floors. Imperfection shall be taken as at least e = h 1,

where h is the storey height and 1 = 1/200. Thereby imperfections are accommodated by the effect

of moments in the vertical structural members and no internal forces occur in the overall stabilising

system.

5.6.1(3)P (Plastic analysis) General – General provisions

The determination of internal forces and moments may be based on the theory of plasticity using the

generally acknowledged approximations.

Adoption 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 failure modes such as

instability intervene in a progressing, ductile failure. When applying the theory of plasticity, verifi-

cation of sufficient yield capacity may be omitted if the following conditions are fulfilled:


The distribution of internal forces and moments does not deviate significantly from

that corresponding to the theory of elasticity. An accurate calculation of the distribu-

tion 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 approx-

imation methods. For lower-bound solutions, the following principle may be used:

Where the reinforcement area associated with plastic design at any point of the struc-

ture 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 ful-

filled if 1/3 AsE ≤ AsP ≤ 3 AsE for all points of the structure. The elastic solution may

be assumed to correspond to the plastic solution where the overall design reinforce-

ment 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 Class B and Class C steels according to Annex C of EN 1992-1-1 are used.

A stress-strain curve for the reinforcement is used where it is assumed that stress in-

crements do not occur after the point corresponding to the yield strength. Where a

stress-strain curve is used assuming that stress increments occur after the point corre-

sponding to the yield strength, equilibrium as well as compatibility conditions shall

be fulfilled.

Instability is not a pre-condition for the ultimate limit state.

Satisfactory performance of the structure in the serviceability and ultimate limit states may require

an arrangement of reinforcement that takes account of the actual distribution of internal forces and

moments without redistribution. Where e.g. a plastic solution is adopted disregarding torsional mo-

ments 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 necessary 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 Class B or Class C steels in accord-

ance with Annex C of EN 1992-1-1.

For precast concrete elements covered by a harmonised product standard or subject to third party

surveillance according to EN 13369, Annex E, Class B steel, where εuk ≥ 5,0 % is replaced by εuk ≥

3,3 %, may be used.

Satisfactory performance of the structure at the serviceability limit state may require that the distri-

bution of internal forces and moments obtained 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 in-plane stress conditions, the lower-bound methods of the theory of plasticity, the stringer

method, the strut-and-tie method and division into homogeneous stress fields may be used.

Stringer method

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

stresses are adopted by stringers, while the rectangular shear fields adopt the shear

stresses between the stringers. The extension of the shear fields is defined as the dis-

tance 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 di-

rection of the stringer.

To resist tension in the stringers, the necessary reinforcement is provided. The varia-

tion of the force of the tension stringers should not be greater than a value corre-

sponding 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 stringers

should not exceed vfcd, where the strength reduction factor v should be taken as v =

vm, assuming a section provided with normal reinforcement. The force in the com-

pression reinforcement shall not be assumed to exceed the design compressive force

in the concrete. If the reinforcement is assumed to resist forces exceeding half the

design force resisted in the concrete, lap splices shall not be used.

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

shear fields are calculated using the expressions specified in Annex F. The concrete

compressive stress is controlled by applying the strength reduction factor given be-

low. It is a prerequisite for the applicability of the method that the shear reinforce-

ment is effectively anchored in the stringers. If shear reinforcement is omitted, the

stringers and the nodes related to the shear fields considered should be designed ac-

cording to the rules applying to the strut-and-tie model.

Strength reduction factor

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

cdf , should be used, where is the efficiency factor.


Unless otherwise specified, the values of the strength reduction 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 is determined by:

ckf

2 (fck in MPa) (5.100 NA)

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

In the following it is assumed that actions are referred to an orthogonal coordinate system that coin-

cides with the directions of reinforcement.

Pure actions

Pure compressive axial stress

The strength reduction factor for pure compression is denoted νn and is determined by:

bendingbycausedisforceaxialtheifν

forceaxialanbycausedisstressaxialtheif,ν

m

n

01

The strength reduction factor m is determined by:

300500097,0 ckyk

m

ff , but not less than 0,6 (fck and fyk in MPa) (5.101 NA)

For cross-sections provided with normal reinforcement with respect to the bending moment, the

following may be applied:

50098,0 ck

m

f , but not less than 0,6 (fck in MPa) (5.102 NA)

For combined axial force and bending, a weighted average value of n is used, weighting being car-

ried out between the values of pure axial force and pure bending.

Pure shear

The strength reduction factor for pure shear is denoted νv and is determined by

2007,0 ck

v

f , but not less than 0,45 (fck in MPa) (5.103 NA)

The value of νv also applies to beams in cases where inclined reinforcement is used as shear rein-

forcement.


νv applies where shear is produced by a shear action. Where shear is due to torsion, the strength

reduction factor is denoted νt and is determined by:

)200

7,0(7,0 ckt

f (fck in MPa) (5.104 NA)

For pure shear caused by both an external shear force and an external torsional force, a weighted

mean value of vv and vt is applied, weighting being carried out between the values related to pure

shear and pure torsion.

For cross sections subjected to torsion where the individual subwalls constituting the thin-walled

cross section are reinforced by means of closed stirrups along the perimeter and uniformly distribut-

ed longitudinal reinforcement at both sides, vt may be taken as vv. This also applies to reinforced

slabs, provided that shear reinforcement is arranged along edges subjected to torsion.

ν = νt ν = νv

Figure 5.100 NA – Strength reduction factor for pure torsion

For plastic expressions for the resistance of non-shear reinforced members subjected to shear, the

value of the strength reduction factor may be increased, taking into account the favourable influence

of arching action on the concrete strength.

Combined effects for in-plane stress conditions Where concrete struts contribute to the shear capacity, e.g. in the strut-and-tie model, the strength

reduction factor shall as a maximum be taken as ν = νv.

σcd ≤ νvfcd

reinforcement

reinforcement

Figure 5.101 NA – Strength reduction factor for concrete struts contributing to the shear ca-

pacity


For nodes, e.g. in the strut-and-tie models and at supports, the strength reduction factor can general-

ly be taken as ν = 0,8. For nodes where reinforcement is not arranged through the node and node

stress is due solely to an external compression, the strength reduction 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 strength reduction factor is denoted νnr and is determined by:

yd

Ed

nnrf

2,0 (σEd and fyd in MPa) (5.105 NA)

where σEd is the external design tensile axial stress and ρfyd is the design tensile strength perpendicu-

lar to the direction of compression.

σEdσEd

σcd ≤ νnrfcd

σcd

Figure 5.102 NA – Strength reduction factor for compression combined with transverse ten-

sion

For combined shear and axial stresses, a conservative strength reduction factor corresponding to

pure shear may be used. As an alternative, the concrete compressive stress is obtained by fulfilling

the following conditions:

cdxEdx f (5.106 NA)

cdyEdy f (5.107 NA)

))((2

EdycdyEdxcdxEdxy ff (5.108 NA)

cdvEdxy f½ (5.109 NA)

where

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


fcdv is the effective design compressive strength at pure shear, i.e. either fcdv = νv fcd, fcdv = νt fcd or

weighted values of νv fcd and νt fcd, depending on the external action.

fcdx and fcdy are the design compressive strengths of the point in question in the x and y directions,

respectively, assuming that the contribution of the concrete to expressions (5.106 NA) and (5.107

NA) is no more than νnrfcd, while the contribution in expression (5.108 NA) is assumed to be no

more than νn fcd.

For slabs with small reinforcement ratios, i.e. (fyd/fcd) less than approx. 0,1, the strength reduction

factor may be taken as = m when calculating the moment action, viz. the influence of torsion on

the strength reduction factor should be disregarded.

6.2.1(2) General verification procedure

Taking account of the effect of bent-up prestressing tendons in the shear zone, the shear resistance

is determined by:

VRd = VRd,s + Vccd + Vtd + Vpd (6.100 NA)

where Vpd is the force component perpendicular to the longitudinal axis of the capacity of the bent-

up prestressing tendons.

Vpd cannot exceed the value corresponding to utilisation of the prestressing tendons up to the design

yield strength or the 0,2% proof strength. The force is determined taking into account the anchorage

capacity, local crushing and splitting of the concrete at reinforcement bends.

Application of bent longitudinal reinforcement as shear reinforcement in beams requires stirrups to

be used simultaneously and that the stirrup reinforcement corresponds at least to the minimum rein-

forcement.


The influence of arch effect, if any, at supports may be taken into account by the shear capacity

βVRd,c, where the factor β taking into account the effect of arching behaviour at supports, is deter-

mined by β = 2,0d/x ≤ 5, where x is the distance from the edge of the support to the cross section

considered. A lower limit for the factor is β = 1. Application of values of β greater than 1 requires

direct support and adequate anchorage of the reinforcement at the support.

For the length x ≤ 2,0d, the effect of the arching action may be combined with the calculation for

shear reinforced beams and slabs as shear reinforcement is to be provided according to (6.8) for

cross sections where VEd > βVRd,c.

The shear reinforcement intensity required where VEd ≥ βVRd,c, is to be continued to the support.

The above-mentioned rules are not to be used together with 6.2.1(8).


6.2.5(1) Shear at the interface between concrete cast at different times

For indented construction joints the area of the joint is taken as the area of indentation. The area of

indentation is defined as the cross sectional area of teeth at the same side of and parallel to the joint.

The sectional view may be oriented at the root of the teeth to be considered. If the concrete strength

is the same at both sides of the construction joint, the smaller area will determine the strength.

The minimum reinforcement at the interface is determined by:

(6.101 NA)

When the interface is kept effectively together by minimum reinforcement, the specified values of c

and μ may be assumed to apply. Otherwise conservative values of c and μ are to be determined.

6.3.2(6) Design procedure

For the analysis of cross sections subjected to combined actions, an effective cross section analo-

gous to that for pure torsion may be assumed as an alternative, the thickness of the individual sub-

walls being adapted to the relevant actions.

The design internal forces and moments acting on the cross section are converted according to elas-

tic or plastic methods into axial and shear stresses in the effective cross section.

The design method for plane stress specified in Annex F is used to determine the necessary rein-

forcement and the magnitude of the concrete compressive stresses in the effective cross section.

The reinforcement determined according to Annex F may be changed to another statically equiva-

lent reinforcement arrangement, provided that account is taken of the effects of the change in areas

close to beam ends and holes.

For an arbitrary point in the effective cross section it is checked as specified in Annex F that σcd ≤

νfcd, reference being made to 5.6.1(3)P for ν.

7.3.2(1)P Minimum reinforcement areas

As an alternative the following may be applied.

Regardless of the analysis, fulfilment of a specific crack width may require a minimum amount of

reinforcement that exceeds the minimum reinforcement. This reinforcement is denoted minimum

reinforcement for control of crack width. The normal minimum reinforcement secures controlled

cracking.

For structures where it is essential that a defined crack width requirement is not exceeded, e.g. for

water proof structures, the following reinforcement ratio for members exposed to pure tension

should be provided:

(7.100 NA)

kwk

skE

effctf

4

,

sin

02,0

ydf

ncdf


where ϕ is the diameter of the tendons used, fct,eff is the effective concrete tensile strength which

may be taken as 0,5√ , where fck is the cylinder strength in MPa, and wk is the maximum al-

lowed crack width. The expression applies to reinforcement fulfilling the requirements of the stand-

ard for ribbed and indented reinforcement. If reinforcement with a smooth surface is used, the ex-

pression is multiplied by √ . For the fine crack system, k = 1 is assumed, taking k = 2 for the coarse

crack system.

The size of the effective tension area Ac,eff depends on the crack system considered.

For a structure subjected to bending or bending with axial force, Ac,eff is the largest concrete area the

centroid of which coincides with the centroid of the tension reinforcement, see Figure 7.100 NA.

For cross sections subjected to pure tension, Ac,eff for the fine crack system is the sum of the largest

concrete area the centroid of which coincides with the centroid of the reinforcement. For the coarse

crack system, Ac,eff is the entire tension area, see Figure 7.100 NA.

Figure 7.100 NA – Effective tension areas for the calculation of crack widths

The above-mentioned requirement for reinforcement is in particular applied in cases where a structure or

parts thereof to a large or small extent are restrained with respect to shrinkage and/or temperature strains and

where joints are not provided to prevent cracking or where any subsequent repair of single cracks of consid-

erable widths is unacceptable.

7.3.2(3) Minimum reinforcement

The expression (h-x)/3 applies solely to slabs and prestressed members where the depth of the ten-

sile zone may be small.


7.3.4(1) Calculation of crack widths

Expression (7.8) applies to the calculation of crack widths related to the fine crack system. For the

coarse crack system, the crack width can be determined by using (7.8), determining Ac,eff as stated

in Figure 7.100 NA and multiplying the right hand side by ½.


The following value is to be applied: k3 = 3,4(25/c)2/3

(c in mm).


For strain, the following value is applied:

(εsm - εcm) = (εsm - εcm)y + (εsm - εcm)z (7.101 NA)

where (εsm - εcm)y and (εsm - εcm)z are the strain of the reinforcement in the y and z directions, respec-

tively. Account may be taken of tension stiffening by applying (7.9) for each of the two directions.

θ may be calculated as indicated if the reinforcement is determined on the basis of an elastic solu-

tion or an optimum plastic solution. In other cases θ is determined by the expression:

(7.102 NA)

8.3(2) Permissible mandrel diameters for bent bars

Smaller bending diameters are permissible, provided that the resistance of the steel is documented

by a bending test according to EN 10080. For ϕ ≤ 16 mm, the bending diameter is taken as 1,33

times the value determined by bend tests, and for ϕ > 16 mm as 1,16 times the value determined by

bend tests. Lower values that the values given in Table 8.1N may be used only if it has been docu-

mented in the design that the values stated do not result in local crushing of concrete.

For reinforcing steels with smooth surfaces the following applies:

The permissible minimum ratio of D/ϕ where D is the inner diameter (bending diameter) to which

bars with diameter ϕ may be bent is 2 for bars where ϕ ≤ 12 mm and 3 for bars where ϕ > 12 mm.

The bending diameters stated only indicate what the reinforcing steels will withstand.

Rebinding of steels according to EN 10025-2 is permitted for ϕ ≤ 12 mm if the original bending

diameter D is at least twice the minimum bending diameter. In all other cases the properties of the

reinforcement are to be verified after rebending.

The specifications above apply to bending in cold condition which may take place at temperatures

not lower than -5 ⁰C.

0cot3cot4cot

y

Ezy

y

Ey

z

Ez

z

Ezy


8.4.1(2) General

The methods of anchorage do not apply to reinforcing steels with smooth surfaces.

8.4.2(2) Ultimate bond stress

The rules do not apply to reinforcing steels with smooth surfaces.

8.4.3(2) Basic anchorage length

The anchorage length corresponding to the reinforcement being able to carry full loading is denoted

lb.

For reinforcing steels with smooth surfaces, reference is made to the requirements specified in

3.2.2(3)P regarding maximum stress permitted in the reinforcement at anchorages and laps.

The rules below apply to smooth reinforcement.

If the nominal diameter is larger than 10 mm, the reinforcement is to be provided with hooks de-

tailed as shown in Figure 8.100 NA. The anchorage length lb is calculated from the line perpendicu-

lar to the reinforcement and tangential to the outside of the hook, see Figure 8.100 NA.

Figure 8.100 NA – Hooks at anchorages and laps

The basic design anchorage strength fbd is determined by:

r

cc

f

ff cs

yk

ctk

c

s

bd

260

(8.100NA)

where c is the partial factor for reinforcement, s is the partial factor for reinforcement, and κ de-

pends on the surface structure of the reinforcement.

For

sc

,

cc

, Λ and Δr, reference is made to the provisions below.

The expression applies to ϕ ≤ 32 mm.

For smooth reinforcement where ϕ > 10 mm with hooks, κ = 2 is used, and for smooth reinforce-

ment where ϕ ≤ 10 mm, κ = 3 is used.


For a uniform ratio over the entire anchorage length and the stress σs in the reinforcement, the actual

anchorage length lb,net is determined from bd

snetb

f

l

4

,

.

When calculating the anchorage capacity, conditions are assumed to be uniform over the anchorage

length concerned. If this is not the case, the length is divided into sub-lengths of uniform conditions

and the anchorage capacity is calculated for each sub-length. The total anchorage capacity is calcu-

lated as the sum of anchorage capacities of the individual sub-lengths. The capacity of the individu-

al sub-length of length l is πϕlfbd.

cs is the width parallel to the concrete surface provided for the anchored bar, i.e. the sum of half the

distance, ½s, to adjacent reinforcement which is anchored, or the distance to the edge cc.

For

sc

> 12,

sc

= 12 is assumed and for

s> 12,

s= 12 is assumed, see Figure 8.101

NA.

For beams sp

s

n

bc

, is assumed, where b is the width of the beam and nsp is the number of bars

anchored in the same layer, provided that the requirements for

sc

,

s and

cc

are met.

cc is the smallest distance from the free surface to the central bar, see Figure 8.101 NA. For

cc

>

6,

cc

= 6 is assumed.

Figure 8.101 NA - Definition of geometric parameters

Λ is the transverse reinforcement ratio given by:

ctk

ck

ctk

ydt

sp

sss

f

f

f

f

n

nn3,1

10

2

(8.101 NA)

where ϕt is the diameter of the stirrup reinforcement perpendicular to the edge, fyd is the design yield

strength for stirrups, and ns is the number of stirrups along the anchorage length enclosing the nsp


bars to be anchored. For the stirrup to be regarded as effective for the anchorage capacity of the

reinforcement concerned, it is to be provided within the distance cs. nss specifies the number of sec-

tions in stirrups, see Figure 8.102 NA.

Figure 8.102 NA - Definition of number of sections in stirrups and number of stirrups

For the anchorage of bars subjected to tension, anchorage lengths smaller than 10 may not be

used, assuming a minimum length of 100 mm.

takes into account anchorages or laps, where η = 1 is applied for anchorages and η = 2 for laps.

For the anchorage of bars subjected to compression, anchorage lengths smaller than 15 may not

be used, assuming a minimum length of 150 η mm.

At bearings, a favourable contribution from transverse compression may be included. The allow-

ance Δr is determined by

ctk

Sdss

f

rcLr

06,0

(8.102 NA)

where rSd is the external design reaction stress (transverse compression), and Ls and b are the sizes

of the supporting area in the direction of and perpendicular, respectively, to the beam axis, see Fig-

ure 8.103 NA. The transverse compression Sdr is not to be taken as larger than 0,7 fcd. When includ-

ing the effect for transverse compression, cs /ϕ cannot be assumed to be larger than 3.


Figure 8.103 NA – Transverse compression at bearings

Sufficient transverse reinforcement is to be provided at anchorages and laps in tension and com-

pression reinforcement in boundary zones. In order to be effective the transverse reinforcement is to

be placed in the concrete cover of the longitudinal reinforcement, and may e.g. consist of stirrups.

The transverse reinforcement is to be evenly distributed over the anchorage or lap length.

At anchorages and laps in longitudinal reinforcement in beams and similar structural members,

transverse reinforcement should be provided, and it should be uniformly distributed over the an-

chorage or lap length and fulfil the requirement

2

,

55 t

netb

s

ln

(8.103 NA)

or be expressed in terms of the transverse reinforcement ratio

netb

sp

ss

ctk

yd l

n

n

f

f,

550

1

(8.104 NA)

where fyd is the design yield strength of the transverse reinforcement.

Stirrups taken into account as shear reinforcement may also be used as transverse reinforcement.

For reinforcement bent with a small diameter, it is recommended that transverse reinforcement be

provided to prevent splitting.

Wire fabrics of smooth reinforcement are to be anchored and lapped as non-welded reinforcement.

8.4.4 Design anchorage length

The rules do not apply to reinforcement with a smooth surface. Reference is made to 8.4.3(2).

8.7.3 Lap length

The rules do not apply to reinforcement with a smooth surface. Reference is made to 8.4.3(2).


8.9 Bundled bars

The rules do not apply to reinforcement with a smooth surface.

9.10.3(3) Continuity and anchorage of ties

Laps of reinforcement in joints between precast units may be used provided that the lap in the joint

is surrounded by a cover at least equivalent to the diameter of the reinforcement. The cover is to be

no less than the maximum aggregate size and always at least 10 mm.

C.1(1) General

The requirement for shear strength, cf. the requirement for Fw in EN 10080, does not apply. The

requirements specified in this standard for the properties of reinforcement cannot normally be as-

sumed to be met at the same time as fulfilment of the requirement for shear strength. The shear

strength value, Fw, may be specified if documentation can be provided that the reinforcement after

welding continues to meet the requirements specified in this standard for the properties of rein-

forcement.

Tack welded reinforcement of nominal diameter is to withstand bending through an angle of 60º

around a mandrel having a diameter as given in Table C100 NA.

Table C100 NA – Bend testing of tack welded reinforcement

Tack welded reinforcing steel

Requirement for mandrel diameter D

Reinforcement diameter ≤ 12 mm > 12 mm

Ribbed steel and indented reinforcing

steel 4 8

Smooth reinforcing steel 2 3

The bend test is carried out across the weld with the weld in the tension zone. After testing, the base

metal of test pieces of tack welded reinforcing steel is not to be fractured or cracked, whereas total

or partial detachment of the cross bar due to fracture of the welded metal or fusion line is accepta-

ble. Visual evaluation is carried out.

The Annex applies to reinforcing steels with ribbed surfaces. With the exception of requirements

for anchorage, yield strength range and bendability, the Annex also applies to reinforcing steels

with smooth surfaces according to EN 10080 and EN 10025-2.

Smooth bars of hot-rolled non-alloy structural steels of grades S235, S275 and S355 in accordance

with EN 10025-2 are applicable. The properties appear from EN 10025-2. The requirements speci-

fied in EN 10025-2 are to be fulfilled.

The characteristic value of the yield strength is assumed to be equal to the minimum yield strength

value given in EN 10025-2 for the type concerned.

The properties of reinforcement with a smooth surface according to EN 10080 are to conform to the

Annex with the exception of surface geometry and yield strength range. The characteristic yield

strength fyk is to be less than 500 MPa.


C.3(1)P Bendability

The clause applies to reinforcing steels conforming to EN 10080 only. For the purpose of the test

for suitability for bending of reinforcement with a smooth surface, Table 4 of EN 10080 is omitted

and replaced by the following:

Reinforcing steel of nominal diameter ø is to be bent through 180⁰ around a mandrel having a di-

ameter, D, equal to ø for bars of ø ≤ 12 mm and equal to 2ø for bars of ø > 12 mm. After the test,

the test piece no fracture or cracks are allowed. Visual examination is carried out without the aid of

optical instruments.

For steels according to EN 10025-2 no further testing is required with the exception of identifica-

tion.

NOTE For the purpose of a rebend test, the bend angle is 90º and the rebend angle is 20 º. It is not equivalent to

straightening of the bar, and a passed rebend test does not constitute documentation to substantiate that the bar may be

subjected to 90 degree bending and subsequent straightening.

F. 1(4)

For Class A steels, the reinforcement is to be determined using (F.2)-(F.7). For Class B or Class C

steels, (F.8)-(F.10) may be used.

Annex 1

Design of certain 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 col-

umn. The approximate calculation may be used provided:

that λ < 90, the free column length being taken as 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 unilaterally in two directions

from 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 is to have approx-

imately the same stiffness on either side of the column. Otherwise, calculation is per-

formed as under a or c, respectively;

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


Annex 2

Verification of robustness

For structures of low consequences classes and for housing structures of normal consequences clas-

ses comprising 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 Euro-

codes.

For buildings of normal consequences classes 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 Claue 9.10 of EN 1992-1-1 and this National Annex to EN

1992-1-1.

For buildings of high consequences classes where the main structure of the building consists of

connected walls and floors that following collapse as stated in the National Annex to EN 1990 can

be assumed to constitute a stable static system, the requirements for robustness can normally be

assumed to be fulfilled by the requirements for ties described in clause 9.10 of EN 1992-1-1 and

this National Annex to EN 1992-1-1.

For other structures, robustness verification according to the National Annex to EN 1990 in addition

to the verification of the requirements for ties is required.

national annex to eurocode 2: design of concrete...

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