Creep and shrinkage

The following functions are related to calculation of creep and shrinkage.

General

structuralcodes.codes.ec2_2004.t_T(T: ArrayLike, dt: ArrayLike) → float[source]

Calculate the maturity of the concrete.

EN 1992-1-1:2004, Eq. (B.10).

Parameters:

  • T (npt.ArrayLike) – The curing temperature history in degrees Celcius.

  • dt (npt.ArrayLike) – The number of days with temperature T.

Returns:

The maturity of the concrete.

Return type:

float

Note

The two arrays T and dt should have the same length. Each item in dt represents a time interval, and the corresponding item in T represents the average temperature in that time interval.

structuralcodes.codes.ec2_2004.h_0(Ac: float, u: float) → float[source]

Calculate the effective thickness of the cross section.

EN 1992-1-1:2004, Eq. (B.6).

Parameters:

  • Ac (float) – The cross section area.

  • u (float) – The part of the circumference of the cross section subject to drying.

Returns:

The effective thickness.

Return type:

float

Note

The unit of the return will be consistent with the input. E.g. if Ac is mm ** 2 and u is mm, the return is mm.

Creep

structuralcodes.codes.ec2_2004.phi(phi_0: float, beta_c: ArrayLike) → ArrayLike[source]

Calculate the creep number.

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

Parameters:

  • phi_0 (float) – The standardized creep number defined in Eq. B.2.

  • beta_c (npt.ArrayLike) – A factor taking into account the creep development as a function of time after loading defined in Eq. (B.7).

Returns:

The creep number.

Return type:

float

structuralcodes.codes.ec2_2004.phi_0(phi_RH: float, beta_fcm: float, beta_t0: float) → float[source]

Calculate the standardized creep number.

EN 1992-1-1:2004, Eq. (B.2).

Parameters:

  • phi_RH (float) – The effect of relative humidity defined in Eq. B.3.

  • beta_fcm (float) – The effect of the concrete strength defined in Eq. B.4.

  • beta_t0 (float) – The effect of the age at loading defined in Eq. B.5.

Returns:

The standardized creep number.

Return type:

float

structuralcodes.codes.ec2_2004.phi_RH(h_0: float, fcm: float, RH: float, alpha_1: float, alpha_2: float) → float[source]

Calculate the effect of relative humidity on the standardized creep number.

EN 1992-1-1:2004, Eq. (B.3).

Parameters:

  • h_0 (float) – The effective cross sectional thickness in mm, Equation (B.6).

  • fcm (float) – The mean concrete strength in MPa.

  • RH (float) – The relative humidity in percent.

  • alpha_1 (float) – A factor describing the effect of concrete strength defined in Eq. (B.8c).

  • alpha_2 (float) – A factor describing the effect of concrete strength defined in Eq. (B.8c).

Returns:

The calculation parameter (B.3).

Return type:

float

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

Calculate the effect of the concrete strength on the standardized creep number.

EN 1992-1-1:2004, Eq. (B.4).

Parameters:

fcm (float) – The mean concrete strength in MPa.

Returns:

The effect of concrete strength.

Return type:

float

structuralcodes.codes.ec2_2004.beta_t0(t0: float) → float[source]

Calculate the effect of age at loading on the notional creep coefficient.

EN 1992-1-1:2004, Eq. (B.5).

Parameters:

t0 (float) – The age at loading in days.

Returns:

The effect of age at loading.

Return type:

float

structuralcodes.codes.ec2_2004.beta_c(t0: float, t: ArrayLike, beta_H: float) → float[source]

Calculate the factor that describes the creep development as a function of time after loading.

EN 1992-1-1:2004, Eq. (B.7).

Parameters:

  • t0 (float) – The concrete age in days a the time of loading.

  • t (ArrayLike) – The concrete age in days at the evaluated time.

  • beta_H (float) – Parameter defined in (B.8).

Returns:

Parameter defined by Equation (B.7), beta_c.

Return type:

float

structuralcodes.codes.ec2_2004.beta_H(h_0: float, fcm: float, RH: float, alpha_3) → float[source]

Calculate the effect of relative humidity and the effective thickness of the structural element.

EN 1992-1-1:2004, Eq. (B.8a and b).

Parameters:

  • h_0 (float) – The effective cross sectional thickness in mm, Equation (B.6).

  • fcm (float) – The mean concrete strength in MPa.

  • RH (float) – The relative humidity in percent.

  • alpha_3 (float) – A factor describing the effect of concrete strength defined in Eq. B.8c.

Returns:

The effect of humidity and the effective thickness of the element.

Return type:

float

structuralcodes.codes.ec2_2004.alpha_1(fcm: float) → float[source]

Return a factor taking into account the effect of concrete strength.

EN 1992-1-1:2004, Eq. (B.8c).

Parameters:

fcm (float) – The mean concrete strength in MPa.

structuralcodes.codes.ec2_2004.alpha_2(fcm: float) → float[source]

Return a factor taking into account the effect of concrete strength.

EN 1992-1-1:2004, Eq. (B.8c).

Parameters:

fcm (float) – The mean concrete strength in MPa.

structuralcodes.codes.ec2_2004.alpha_3(fcm: float) → float[source]

Return a factor taking into account the effect of concrete strength.

EN 1992-1-1:2004, Eq. (B.8c).

Parameters:

fcm (float) – The mean concrete strength in MPa.

structuralcodes.codes.ec2_2004.t0_adj(t0: float, alpha_cement: float) → float[source]

Calculate the adjusted age of the concrete.

EN 1992-1-1:2004, Eq. (B.9).

Parameters:

  • t0 (float) – The concrete age in days at the time of loading.

  • alpha_cement (float) – Exponent derived from the sement type.

Returns:

The adjusted age of the concrete.

Return type:

float

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

Return an exponent that depends on the cement type.

Parameters:

cement_class (str) – The cement class, either ‘S’, ‘N’ or ‘R’.

Returns:

The exponent that depends on the cement type.

Return type:

float

Raises:

ValueError – If an invalid cement class is provided.

Shrinkage

structuralcodes.codes.ec2_2004.eps_cs(eps_cd: ArrayLike, eps_ca: ArrayLike) → ArrayLike[source]

Calculate the total shrinkage strain.

EN 1992-1-1:2004, Eq. (3.8).

Parameters:

  • eps_cd (npt.ArrayLike) – The drying shrinkage defined in Eq. (3.9).

  • eps_ca (npt.ArrayLike) – The autogenous shrinkage defined in Eq. (3.11).

Returns:

The total shrinkage strain.

Return type:

npt.ArrayLike

Note

In EC2 (2004), the shrinkage strain is calculated as a positive number.

structuralcodes.codes.ec2_2004.eps_cd(beta_ds: ArrayLike, k_h: float, eps_cd_0: float) → ArrayLike[source]

Calculate the drying shrinkage.

EN 1992-1-1:2004, Eq. (3.9).

Parameters:

  • beta_ds (npt.ArrayLike) – A coefficient taking into account the time of drying defined in Eq. (3.10).

  • k_h (float) – A coefficient depending on the effective thickness of the section defined in Tab. 3.3.

  • eps_cd_0 (float) – The nominal value of drying shrinkage defined in Eq. (B.11).

Returns:

The drying shrinkage.

Return type:

npt.ArrayLike

Note

In EC2 (2004), the shrinkage strain is calculated as a positive number.

structuralcodes.codes.ec2_2004.beta_ds(t: ArrayLike, t_s: float, h_0: float)[source]

Calculate the coefficient taking into account the time of drying.

EN 1992-1-1:2004, Eq. (3.10).

Parameters:

  • t (npt.ArrayLike) – The age of the concrete in days.

  • t_s (float) – The age of the concrete in days at the start of drying (normally this is the point in time when curing measures end).

  • h_0 (float) – The effective cross section thichkness in mm.

Returns:

The coefficient taking into account the time of drying.

Return type:

npt.ArrayLike

structuralcodes.codes.ec2_2004.k_h(h_0: float) → float[source]

Calculate the coefficient depending on the notional size.

EN 1992-1-1:2004, Tab. 3.3.

Parameters:

h_0 (float) – The notional size of the cross-section in mm.

Returns:

The coefficient depending on the notional size.

Return type:

float

structuralcodes.codes.ec2_2004.eps_cd_0(alpha_ds1: float, alpha_ds2: float, fcm: float, beta_RH: float, fcm_0: float = 10) → float[source]

Calculate the nominal value of drying shrinkage.

EN 1992-1-1:2004, Eq. (B.11).

Parameters:

  • alpha_ds1 (float) – A coefficient depending on the cement type, defined in EC2 (2004), Sec. B.2.

  • alpha_ds2 (float) – A coefficient depending on the cement type, defined in EC2 (2004), Sec. B.2.

  • fcm (float) – The mean compressive strength in MPa.

  • beta_RH (float) – A factor describing the effect of relative humidity, defined in Eq. (B.12).

Keyword Arguments:

fcm_0 (float) – A reference strength in MPa, default 10 MPa.

Returns:

The nominal value of drying shrinkage.

Return type:

float

structuralcodes.codes.ec2_2004.alpha_ds1(cement_class: Literal['S', 'N', 'R']) → float[source]

Return a coefficient depending on the cement class.

EN 1992-1-1:2004, Sec. B.2.

Parameters:

cement_class (str) – The cement class, either ‘S’, ‘N’ or ‘R’.

Returns:

The exponent that depends on the cement type.

Return type:

float

Raises:

ValueError – If an invalid cement class is provided.

structuralcodes.codes.ec2_2004.alpha_ds2(cement_class: Literal['S', 'N', 'R']) → float[source]

Return a coefficient depending on the cement class.

EN 1992-1-1:2004, Sec. B.2.

Parameters:

cement_class (str) – The cement class, either ‘S’, ‘N’ or ‘R’.

Returns:

The exponent that depends on the cement type.

Return type:

float

Raises:

ValueError – If an invalid cement class is provided.

structuralcodes.codes.ec2_2004.beta_RH(RH: float, RH_0: float = 100) → float[source]

Calculate the factor describing the effect of relative humidity.

EN 1992-1-1:2004, Eq. (B.12).

Parameters:

RH (float) – The relative humidity in percent.

Keyword Arguments:

RH_0 (float) – The reference relative humidity, default: 100%.

Returns:

The factor taking into account the relative humidity.

Return type:

float

structuralcodes.codes.ec2_2004.eps_ca(beta_as: ArrayLike, eps_ca_inf: float) → ArrayLike[source]

Calculate the autogenous shrinkage.

EN 1992-1-1:2004, Eq. (3.11).

Parameters:

  • beta_as (npt.ArrayLike) – A factor describing the autogenous shrinkage development.

  • eps_ca_inf (float) – The final autogenous shrinkage.

Returns:

The autogenous shrinkage.

Return type:

npt.ArrayLike

Note

In EC2 (2004), the shrinkage strain is calculated as a positive number.

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

Calculate the final autogenous shrinkage.

EN 1992-1-1:2004, Eq. 3.12.

Parameters:

fck (float) – The characteristic compressive strength in MPa.

Returns:

The final autogenous shrinkage.

Return type:

float

structuralcodes.codes.ec2_2004.beta_as(t: ArrayLike) → ArrayLike[source]

Calculate the factor describing the development of autogenous shrinkage.

EN 1992-1-1:2004, Eq. (3.13).

Parameters:

t (npt.ArrayLike) – The age of the concrete in days.

Returns:

The factor describing the development of autogenous shrinkage.

Return type:

npt.ArrayLike