## 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/m^{3}. For concrete with normal percentage of reinforcement or prestressing steel *γ* = 25 kN/m^{3}.

### 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 0.4*f*_{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.