Table Of Concrete Design Properties (fcd, Fctm, Ecm, Fctd) - Eurocode 2

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 = αcc ⋅ fck / 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 unfavorable 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 concrete class ≤ C50/60

fctm [MPa] = 2.12⋅ln[1+(fcm / 10 MPa)] for concrete 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 = αct ⋅ fctk,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 unfavorable 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 / 10 MPa)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 = max{ 0.26 ⋅ fctm / fyk, 0.0013} ⋅ bt⋅d

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

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 / [ s⋅bw⋅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 reinforcement with perpendicular legs α = 90° and sin(α) = 1.