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Eurocode 2 Table of Concrete Design Properties

Description:
Design aid - Table of concrete design properties including strength properties (fck, fcd, fctm, fctd) elastic deformation properties (Ecm), minimum longitudinal reinforcement against brittle failure, and minimum shear reinforcement
According to:
EN 1992-1-1:2004+AC2:2010 Sections 3.1.2, 3.1.3, 9.2.1.1(1)
All Calculations
Input
MPa
Affects minimum reinforcement ratios.
Nationally Defined Parameters
According to EN1992-1-1 §2.4.2.4 and the National Annex. It affects concrete design strengths.
Note: Always verify the validity of the Nationally Defined Parameters. Please inform us of any discrepancy using our Contact Form
Tables
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Concrete Design Properties according to EN1992-1-1 (<i>&gamma;</i><sub>c</sub> = 1.50, <i>f</i><sub>yk</sub> = 500 MPa)
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General material properties for reinforced concrete according to EN1992-1-1 &sect;3.1
Notes
  1. According to EN1992-1-1 §3.1.3(2) the following modifications are applicable for the value of the concrete modulus of elasticity Ecm: a) for limestone aggregates the value should be reduced by 10%, b) for sandstone aggregates the value should be reduced by 30%, c) for basalt aggregates the value should be increased by 20%.
  2. The values of concrete design compressive strength fcd are given as a function of the reduction coefficient αcc as defined in EN1992-1-1 §3.1.6(1)P. Please consult the National Annex about the appropriate value of αcc for each specific design case.
  3. The minimum longitudinal tension reinforcement ratio ρmin corresponds to the notional area btd where bt is the mean width of the tension zone and d is the effective depth of the cross-section.
  4. The minimum longitudinal tension reinforcement ratio ρmin is applicable for tension edges of beams, two-way slabs and principal direction of one-way slabs. This minimum reinforcement is required in order to avoid brittle failure. Typically a larger quantity of minimum longitudinal reinforcement for crack control is required in accordance with EN1992-1-1 §7.3.2. For the secondary reinforcement of one-way slabs the minimum reinforcement is 20% of the primary reinforcement in accordance with EN1992-1-1 §9.3.1.1(2).
  5. According to EN1992-1-1 §9.2.1.1(1) Note 2 for the case of beams where a risk of brittle failure can be accepted, the minimum longitudinal tension reinforcment may be taken as 1.2 times the area required in ULS verification.
  6. The minimum shear reinforcement ratio ρw,min is defined in EN1992-1-1 §9.2.2(5). It is applicable for beams even if design shear reinforcement is not required. For slabs it is applicable only for slabs where design shear reinforcement is required. It corresponds to the notional area bws where bw is the width of the web and s is the spacing of the shear reinforcement along the length of the member.
Details

Design values of concrete material properties according to EN1992-1-1

Unit weight γ

The unit weight of concrete γ is specified in EN1991-1-1 Annex A. For plain unreinforced concrete γ = 24 kN/m3. For concrete with normal percentage of reinforcement or prestressing steel γ = 25 kN/m3.

Characteristic compressive strength fck

The characteristic compressive strength fck is the first value in the concrete class designation, e.g. 30 MPa for C30/37 concrete. The value corresponds to the characteristic (5% fractile) cylinder strength according to EN 206-1. The strength classes of EN1992-1-1 are based on the characteristic strength classes determined at 28 days. The variation of characteristic compressive strength fck(t) with time t is specified in EN1992-1-1 §3.1.2(5).

Characteristic compressive cube strength fck,cube

The characteristic compressive cube strength fck,cube is the second value in the concrete class designation, e.g. 37 MPa for C30/37 concrete. The value corresponds to the characteristic (5% fractile) cube strength according to EN 206-1.

Mean compressive strength fcm

The mean compressive strength fcm is related to the characteristic compressive strength fck as follows:

fcm = fck + 8 MPa

The variation of mean compressive strength fcm(t) with time t is specified in EN1992-1-1 §3.1.2(6).

Design compressive strength fcd

The design compressive strength fcd is determined according to EN1992-1-1 §3.1.6(1)P:

fcd = αccfck / γC

where γC is the partial safety factor for concrete for the examined design state, as specified in EN1992-1-1 §2.4.2.4 and the National Annex.

The coefficient αcc takes into account the long term effects on the compressive strength and of unfavourable effects resulting from the way the load is applied. It is specified in EN1992-1-1 §3.1.6(1)P and the National Annex (for bridges see also EN1992-2 §3.1.6(101)P and the National Annex).

Characteristic tensile strength

The tensile strength under concentric axial loading is specified in EN1992-1-1 Table 3.1. The variability of the concrete tensile strength is given by the following formulas:

Formula for mean tensile strength fctm

fctm [MPa] = 0.30⋅fck2/3 for concete class ≤ C50/60

fctm [MPa] = 2.12⋅ln[1+(fcm / 10MPa)] for concete class > C50/60

Formula for 5% fractile tensile strength fctk,0.05

fctk,0.05 = 0.7⋅fctm

Formula for 95% fractile tensile strength fctk,0.95

fctk,0.95 = 1.3⋅fctm

Design tensile strength fctd

The design tensile strength fctd is determined according to EN1992-1-1 §3.1.6(2)P:

fctd = αctfctk,0.05 / γC

where γC is the partial safety factor for concrete for the examined design state, as specified in EN1992-1-1 §2.4.2.4 and the National Annex.

The coefficient αct takes into account long term effects on the tensile strength and of unfavourable effects, resulting from the way the load is applied. It is specified in EN1992-1-1 §3.1.6(2)P and the National Annex (for bridges see also EN1992-2 §3.1.6(102)P and the National Annex).

Modulus of elasticity Ecm

The elastic deformation properties of reinforced concrete depend on its composition and especially on the aggregates. Approximate values for the modulus of elasticity Ecm (secant value between σc = 0 and 0.4fcm) for concretes with quartzite aggregates, are given in EN1992-1-1 Table 3.1 according to the following formula:

Ecm [MPa] = 22000 ⋅ (fcm / 10MPa)0.3

According to EN1992-1-1 §3.1.3(2) for limestone and sandstone aggregates the value of Ecm should be reduced by 10% and 30% respectively. For basalt aggregates the value of Ecm should be increased by 20%. The values of Ecm given in EN1992-1-1 should be regarded as indicative for general applications, and they should be specifically assessed if the structure is likely to be sensitive to deviations from these general values.

The variation of the modulus of elasticity Ecm(t) with time t is specified in EN1992-1-1 §3.1.3(3).

Poisson ratio ν

According to EN1992-1-1 §3.1.3(4) the value of Poisson's ratio ν may be taken equal to ν = 0.2 for uncracked concrete and ν = 0 for cracked concrete.

Coefficient of thermal expansion α

According to EN1992-1-1 §3.1.3(5) the value of the linear coefficient of thermal expansion α may be taken equal to α = 10⋅10-6 °K-1, unless more accurate information is available.

Minimum longitudinal reinforcement ρmin for beams and slabs

The minimum longitudinal tension reinforcement for beams and the main direction of slabs is specified in EN1992-1-1 §9.2.1.1(1).

As,min = 0.26 ⋅ (fctm / fyk)⋅btd

where bt is the mean width of the tension zone and d is the effective depth of the cross-section, fctm is the mean tensile strength of concrete, and fyk is the characteristic yield strength of steel.

The minimum reinforcement is required to avoid brittle failure. Typically a larger quantity of minimum longitudinal reinforcement for crack control is required in accordance with EN1992-1-1 §7.3.2. Sections containing less reinforcment should be considered as unreinforced.

According to EN1992-1-1 §9.2.1.1(1) Note 2 for the case of beams where a risk of brittle failure can be accepted, As,min may be taken as 1.2 times the area required in ULS verification.

Minimum shear reinforcement ρw,min for beams and slabs

The minimum shear reinforcement for beams and slabs is specified in EN1992-1-1 §9.2.2(5).

ρw,min = 0.08 ⋅ (fck0.5) / fyk

where fck is the characteristic compressive strength of concrete and fyk is the characteristic yield strength of steel.

The shear reinforcement ratio is defined in EN1992-1-1 §3.1.3(5) as:

ρw = Asw / (sbw⋅sin(α))

where where bw is the width of the web and s is the spacing of the shear reinforcement along the length of the member. The angle α corresponds to the angle between shear reinforcement and the longitudinal axis. For typical shear reinforcemnt with perpendicular legs α = 90°.