Material properties for concrete¶

The following functions are related to calculation of material properties of concrete.

Strength¶

structuralcodes.codes.ec2_2004.fcd(fck: float, alpha_cc: float, gamma_c: float) → float[source]¶

The design compressive strength of concrete.

EN 1992-1-1:2004, Eq. (3.15).

Parameters:

fck (float) – The characteristic compressive strength in MPa.
alpha_cc (float) – A factor for considering long-term effects on the strength, and effects that arise from the way the load is applied.
gamma_c (float) – The partial factor of concrete.

Returns:

The design compressive strength of concrete in MPa

Return type:

float

structuralcodes.codes.ec2_2004.fcm(fck: float, delta_f: float = 8) → float[source]¶

The mean compressive strength of concrete.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Keyword Arguments:: delta_f (float) – The difference between the mean and the characteristic strength.
Returns:: The mean compressive strength in MPa.
Return type:: float

structuralcodes.codes.ec2_2004.fctm(fck: float) → float[source]¶

The mean tensile strength of concrete.

EN 1992-1-1: 2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The mean tensile strength in MPa.
Return type:: float

structuralcodes.codes.ec2_2004.fctk_5(fctm: float) → float[source]¶

The 5% fractile of the tensile strength of concrete.

EN 1992-1-1: 2004, Table 3.1.

Parameters:: fctm (float) – The mean tensile strength of concrete in MPa.
Returns:: The 5% fractile of the tensile strength in MPa.
Return type:: float

structuralcodes.codes.ec2_2004.fctk_95(fctm: float) → float[source]¶

The 95% fractile of the tensile strength of concrete.

EN 1992-1-1: 2004, Table 3.1.

Parameters:: fctm (float) – The mean tensile strength of concrete in MPa.
Returns:: The 95% fractile of the tensile strength in MPa.
Return type:: float

Stiffness¶

structuralcodes.codes.ec2_2004.Ecm(fcm: float) → float[source]¶

The secant modulus of concrete.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fcm (float) – The mean compressive strength of concrete in MPa.
Returns:: The secant modulus of concrete in MPa.
Return type:: float

Parameters of constitutive relations¶

structuralcodes.codes.ec2_2004.eps_c1(fcm: float) → float[source]¶

The strain at maximum compressive stress of concrete (fcm) for the Sargin constitutive law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fcm (float) – The mean compressive strength of concrete in MPa.
Returns:: The strain at maximum compressive stress, absolute value, no unit.
Return type:: float

structuralcodes.codes.ec2_2004.eps_cu1(fck: float) → float[source]¶

The ultimate strain for the Sargin constitutive law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The ultimate strain, absolute value, no unit.
Return type:: float

structuralcodes.codes.ec2_2004.eps_c2(fck: float) → float[source]¶

The strain at maximum compressive stress of concrete for the parabolic-rectangular law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The strain at maximum compressive stress, absolute value, no unit.
Return type:: float

structuralcodes.codes.ec2_2004.eps_cu2(fck: float) → float[source]¶

The ultimate strain of the parabolic-rectangular law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The ultimate strain, absolute value, no unit.
Return type:: float

structuralcodes.codes.ec2_2004.eps_c3(fck: float) → float[source]¶

The strain at maximum compressive stress of the bi-linear law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The strain at maximum compressive stress, absolute value, no unit.
Return type:: float

structuralcodes.codes.ec2_2004.eps_cu3(fck: float) → float[source]¶

The ultimate strain of the bi-linear law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The ultimate strain, absolute value, no unit.
Return type:: float

structuralcodes.codes.ec2_2004.n_parabolic_rectangular(fck: float) → float[source]¶

The exponent in the parabolic-rectangular law.

EN 1992-1-1:2004, Table 3.1.

Parameters:: fck (float) – The characteristic compressive strength of concrete in MPa.
Returns:: The exponent n, absolute value, no unit.
Return type:: float

Time development of properties¶

structuralcodes.codes.ec2_2004.beta_cc(t: ArrayLike, s: float) → ArrayLike[source]¶

The time development function for compressive strength of concrete.

EN 1992-1-1:2004, Eq. (3.2).

Parameters:

t (ArrayLike) – The time in days to evaluate the development function for.
s (float) – The scale factor in the exponent for the time development function. s = 0.20 for class R, 0.25 for class N, and 0.38 for class N.

Returns:

The value of the time development function.

Return type:

ArrayLike

structuralcodes.codes.ec2_2004.beta_ct(t: ArrayLike, s: float) → ArrayLike[source]¶

The time development function for tensile strength of concrete.

EN 1992-1-1:2004, part of Eq. (3.4).

Parameters:

t (ArrayLike) – The time in days to evaluate the development function for.
s (float) – The scale factor in the exponent for the time development function. s = 0.20 for class R, 0.25 for class N, and 0.38 for class N.

Returns:

The value of the time development function.

Return type:

ArrayLike

structuralcodes.codes.ec2_2004.beta_E(t: ArrayLike, s: float) → ArrayLike[source]¶

The time development function for Young’s modulus of concrete.

EN 1992-1-1:2004, part of Eq. (3.5).

Parameters:

t (ArrayLike) – The time in days to evaluate the development function for.
s (float) – The scale factor in the exponent for the time development function. s = 0.20 for class R, 0.25 for class N, and 0.38 for class N.

Returns:

The value of the time development function.

Return type:

ArrayLike

structuralcodes.codes.ec2_2004.s_time_development(cement_class: Literal['S', 'N', 'R']) → float[source]¶

Return the scale factor for the exponent for the time development function.

EN 1992-1-1:2004, Eq. (3.2).

Parameters:: cement_class (str) – The cement class, either ‘S’, ‘N’ or ‘R’.
Returns:: The scale factor that depends on the cement type.
Return type:: float
Raises:: ValueError – If an invalid cement class is provided.

structuralcodes.codes.ec2_2004.fcm_time(fcm: float, beta_cc: ArrayLike) → ArrayLike[source]¶

Calculate the compressive strength as function of time.

EN 1992-1-1:2004, Eq. (3.1).

Parameters:

fcm (float) – The reference value for the compressive strength.
beta_cc (ArrayLike) – The value(s) of the time development function.

Returns:

The calculated value(s) of the compressive strength.

Return type:

ArrayLike

Note

The value of beta_cc should be calculated with the function beta_cc.

structuralcodes.codes.ec2_2004.fctm_time(fctm: float, beta_cc: ArrayLike, alpha: ArrayLike) → ArrayLike[source]¶

Calculate the tensile strength as function of time.

EN 1992-1-1:2004, Eq. (3.4).

Parameters:

fctm (float) – The reference value for the tensile strength.
beta_cc (ArrayLike) – The value(s) of the time development function.
alpha (ArrayLike) – An exponent for the time development function. It should be set to 1 for t < 28, and 2/3 else.

Returns:

The calculated value(s) of the tensile strength.

Return type:

ArrayLike

Note

The value of beta_cc should be calculated with the function beta_cc. Alternatively, the time development function for the tensile strength could be calculated directly with the function beta_ct.

structuralcodes.codes.ec2_2004.Ecm_time(fcm: float, fcm_time: ArrayLike, Ecm: float) → ArrayLike[source]¶

Calculate the Young’s modulus as function of time.

EN 1992-1-1:2004, Eq. (3.5).

Parameters:

fcm (float) – The reference value for the compressive strength.
fcm_time (float) – The value(s) of the compressive strength at the point(s) in time.
Ecm (float) – The reference value for the Young’s modulus.

Returns:

The calculated value(s) of the Young’s modulus.

Return type:

ArrayLike

Note

The value of fcm_time should be calculated with the function fcm_time. Alternatively, the time development function for the Young’s modulus could be calculated directly with the function beta_E.