Table of concrete design properties (fcd, fctm, Ecm, fctd) - Eurocode 2 (2024)

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 f_ck

The characteristic compressive strength f_ck 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 f_ck(t) with time t is specified in EN1992-1-1 §3.1.2(5).

Characteristic compressive cube strength f_ck,cube

The characteristic compressive cube strength f_ck,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 f_cm

The mean compressive strength f_cm is related to the characteristic compressive strength f_ck as follows:

f_cm = f_ck + 8 MPa

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

Design compressive strength f_cd

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

f_cd = α_cc ⋅ f_ck / γ_C

where γ_C 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 α_cc 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 f_ctm

f_ctm [MPa] = 0.30⋅f_ck^2/3 for concrete class ≤ C50/60

f_ctm [MPa] = 2.12⋅ln[1+(f_cm / 10 MPa)] for concrete class > C50/60

Formula for 5% fractile tensile strength f_ctk,0.05

f_ctk,0.05 = 0.7⋅f_ctm

Formula for 95% fractile tensile strength f_ctk,0.95

f_ctk,0.95 = 1.3⋅f_ctm

Design tensile strength f_ctd

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

f_ctd = α_ct ⋅ f_ctk,0.05 / γ_C

where γ_C 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 α_ct 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 E_cm

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

E_cm [MPa] = 22000 ⋅ (f_cm / 10 MPa)^0.3

According to EN1992-1-1 §3.1.3(2) for limestone and sandstone aggregates the value of E_cm should be reduced by 10% and 30% respectively. For basalt aggregates the value of E_cm should be increased by 20%. The values of E_cm 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 E_cm(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 ρ_min 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).

A_s,min = max{ 0.26 ⋅ f_ctm / f_yk, 0.0013} ⋅ b_t⋅d

where b_t is the mean width of the tension zone and d is the effective depth of the cross-section, f_ctm is the mean tensile strength of concrete, and f_yk 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, A_s,min may be taken as 1.2 times the area required in ULS verification.

Minimum shear reinforcement ρ_w,min for beams and slabs

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

ρ_w,min = 0.08 ⋅ (f_ck^0.5) / f_yk

where f_ck is the characteristic compressive strength of concrete and f_yk is the characteristic yield strength of steel.

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

ρ_w = A_sw / [ s⋅b_w⋅sin(α) ]

where where b_w 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.