Creep and shrinkage

Creep

structuralcodes.codes.mc2010.calc_J(E_ci_t0: float, phi: ArrayLike, E_ci: float) → ndarray

Calculate the creep compliance function.

Defined in fib Model Code 2010, Eq. 5.1-61.

Parameters:

• E_ci_t0 (float) – Modulus of elasticity at time of loading t0, as defined in fib Model Code 2010 (2013), Eq. 5.1-56.

• phi (numpy.typing.ArrayLike) – Creep coefficient, as defined in fib Model Code 2010 (2013), Eq. 5.1-63.

• E_ci (float) – defined in fib Model Code 2010 (2013), Eq. 5.1-21.

Returns:

The creep compliance function.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.phi(phi_bc: ArrayLike, phi_dc: ArrayLike, sigma: float, fcm: float) → ndarray

Calculate the creep coefficient distinguishing between linear and non-linear creep for compressive stresses sigma <= 0.4fcm, and 0.4fcm < sigma <= 0.6fcm, respectively.

Defined in fib Model Code 2010, Eqs. 5.1-63 and 5.1-74.

Parameters:

• phi_bc (numpy.typing.ArrayLike) – Basic creep coefficient, as defined in fib Model Code 2010 (2013), Eq. 5.1-64.

• phi_dc (numpy.typing.ArrayLike) – Drying creep coefficient, as defined in fib Model Code 2010 (2013), Eq. 5.1-67.

• sigma (float) – The compressive stress applied to the concrete at ts in MPa.

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

Returns:

The creep coefficient.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.phi_bc(beta_bc_fcm: float, beta_bc_t: ArrayLike) → ndarray

Calculate the basic creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-64.

Parameters:

• beta_bc_fcm (float) – Multiplication factor that accounts for the influence of the concrete strength of the creep behaviour, as defined in fib Model Code 2010 (2013), Eq. 5.1-65.

• beta_bc_t (numpy.typing.ArrayLike) – Multiplication factor that accounts for the influence of the age of the concrete of the creep behaviour, as defined in fib Model Code 2010 (2013), Eq. 5.1-66.

Returns:

The basic creep coefficient.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.phi_dc(beta_dc_fcm: float, beta_dc_RH: float, beta_dc_t0: float, beta_dc_t: ArrayLike) → ndarray

Calculate drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-67.

Parameters:

• beta_dc_fcm (float) – Multiplication factor that accounts for the effect of the strength of the concrete, as calculated by Eq. 5.1-68.

• beta_dc_RH (float) – Multiplication factor that accounts for the effect of the relative humidity of the environment, as calculated by Eq. 5.1-69.

• beta_dc_t0 (float) – multiplication factor that accounts for the effect of the (temperature corrected) age of the concrete when loading is applied, as calculated by Eq. 5.1-70.

• beta_dc_t (numpy.typing.ArrayLike) – multiplication factor that accounts for the different considered values of time, as calculated by Eq. 5.1-71a.

Returns:

Drying creep coeffcient.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.beta_bc_fcm(fcm: float) → float

Calculate multiplication factor that accounts for the effect of the compressive strength of the concrete to calculate the basic creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-65.

Parameters:

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

Returns:

Multiplication factor beta_bc_fcm.

Return type:

float

structuralcodes.codes.mc2010.beta_bc_t(time: ArrayLike, t0: float, t0_adj: float) → ndarray

Calculate multiplication factor that accounts for the effect of the age of the of the concrete to calculate the basic creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-66.

Parameters:

• time (numpy.typing.ArrayLike) – The different times in days at which the basic creep coefficient is determined.

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

• t0_adj (float) – The temperature corrected age of the concrete when the loading is applied in days, as defined in fib Model Code 2010 (2013). Eq. 5.1-85.

Returns:

Multiplication factors beta_bc_t.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.t_T(t0: ArrayLike, T_cur: ArrayLike, dt: ArrayLike = None) → ndarray

Calculate the temperature corrected concrete age in days at t0.

Defined in fib Model Code 2010 (2013). Eq. 5.1-85 (only for a single time value input, as required in Eq. 5.1-73).

Parameters:

• t0 (np.typing.ArrayLike) – The age of the concrete in days at which the loading is applied.

• T_cur (np.typing.ArrayLike) – The temperature of the environment during curing in degrees Celcius.

Keyword Arguments:

dt (np.typing.ArrayLike) – Number of days at which T_cur prevails. Required when providing a list for T_cur.

Returns:

The temperature corrected age of the concrete in days at loading.

Return type:

np.ndarray

structuralcodes.codes.mc2010.t0_adj(t_T: float, cem_class: Literal['32.5 N', '32.5 R', '42.5 N', '42.5 R', '52.5 N', '52.5 R']) → float

Calculate the modified age at loading (t0) to account for the effect of the type of cement and curing temperature on the degree of hydration and - in turn - on creep.

Defined in fib Model Code 2010 (2013), Eq. 5.1-73.

Parameters:

• t_T (float) – Temperature adjusted concrete age in days.

• cem_class (str) – The cement strength class that is used. The choices are: ‘32.5 N’, ‘32.5 R’, ‘42.5 N’, ‘42.5 R’, ‘52.5 N’, ‘52.5 R’.

Returns:

The temperature corrected age of the concrete in days at loading, accounting for the effect of the cement type. For slow hardening concrete, the creep coefficient is increased due to the lower modified age at loading.

Return type:

float

structuralcodes.codes.mc2010.beta_dc_fcm(fcm: float) → float

Calculate multiplication factor that accounts for the effect of the strength of the concrete to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-68.

Parameters:

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

Returns:

Multiplication factor beta_dc_fcm.

Return type:

float

structuralcodes.codes.mc2010.beta_dc_RH(rh: float, notional_size: float) → float

Calculate multiplication factor that accounts for the effect of the relative humidity of the environment to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-69.

Parameters:

• rh (float) – The relative humidity of the environment. Value can be provided as percentage (i.e. 40–100), or as ratio (i.e. 0.4–1).

• notional_size (float) – The notional size of the considered element in mm, defined as 2A/u.

Returns:

Multiplication factor beta_RH.

Return type:

float

structuralcodes.codes.mc2010.beta_dc_t(time: ArrayLike, t0: float, beta_h: float, gamma_t0: float) → ndarray

Calculate multiplication factor that accounts for the different considered values of time. Used to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-71a.

Parameters:

• time (numpy.typing.ArrayLike) – The different times in days at which the drying creep coefficient is determined.

• t0 (float) – The age of the concrete concrete when the loading is applied in days.

• beta_h (float) – Multiplication factor that accounts for the effect of the notional size, as calculated by Eq. 5.1-71c

• gamma_t0 (float) – Exponent that accounts for the effect of the (temperature corrected) age of the concrete when loaded, as calculated by Eq. 5.1-71b.

Returns:

Multiplcation factor beta_dc_t for the considered values of time.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.beta_dc_t0(t0_adj: float) → float

Calculate multiplication factor that accounts for the effect of the (temperature corrected) age of the concrete when loading is applied to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-70.

Parameters:

t0_adj (float) – The temperature corrected age of the concrete when the loading is applied in days, as defined in fib Model Code 2010 (2013). Eq. 5.1-85.

Returns:

Multiplication factor beta_dc_t0.

Return type:

float

structuralcodes.codes.mc2010.beta_h(notional_size: float, alpha_fcm: float) → float

Calculate multiplication factor that accounts for the effect of the notional size of the to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-71c

Parameters:

• notional_size (float) – The notional size of the considered element in mm, defined as 2A/h.

• alpha_fcm (float) – Multiplication factor that accounts for the effect of the strength of the concrete on the drying creep coefficient.

Returns:

Multiplication factor beta_h.

Return type:

float

structuralcodes.codes.mc2010.gamma_t0(t0_adj: float) → float

Calculate exponent that accounts for the effect of the (temperature corrected) age of the concrete when loaded. Used to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-71b.

Parameters:

t0_adj (float) – The temperature corrected age of the concrete when the loading is applied in days, as defined in fib Model Code 2010 (2013). Eq. 5.1-85.

Returns:

Exponent gamma_t0.

Return type:

float

structuralcodes.codes.mc2010.alpha_fcm(fcm: float) → float

Calculate multiplication factor that accounts for the effect of the strength of the concrete to calculate the drying creep coefficient.

Defined in fib Model Code 2010 (2013), Eq. 5.1-71d.

Parameters:

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

Returns:

Multiplication factor alpha_fcm.

Return type:

float

structuralcodes.codes.mc2010.k_sigma(sigma: float, fcm: float) → float

Calculate the ratio between the applied stress and the mean concrete compressive strength.

Defined in fib Model Code 2010 (2013), Eq. 5.1-74.

Parameters:

• sigma (float) – The compressive stress applied to the concrete at ts in MPa.

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

Returns:

Absolute value of the ratio between the stress in the concrete and the mean concrete strength.

Return type:

float

Shrinkage

structuralcodes.codes.mc2010.eps_cbs(eps_cbs0: float, beta_bs: ArrayLike) → ndarray

Calculate the basic shrinkage.

Defined in fib Model Code 2010 (2013), Eqs. 5.1-76.

Parameters:

• eps_cbs0 (float) – Notional basic shrinkage, as defined in fib Model Code 2010 (2013), Eq. 5.1-78.

• beta_bs (numpy.typing.ArrayLike) – Time function for basic shrinkage, as defined in fib Model Code 2010 (2013), Eq. 5.1-79.

Returns:

The basic shrinkage strains for the given times.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.eps_cds(eps_cds0: float, beta_ds: ArrayLike, beta_rh: float) → ndarray

Calculate the drying shrinkage of the concrete element.

Defined in fib Model Code 2010 (2013), Eqs. 5.1-77.

Parameters:

• eps_cds0 (float) – The notional drying shrinkage, no units, as defined in fib Model Code 2010 (2013), Eq. 5.1-80.

• beta_ds (numpy.typing.ArrayLike) – Multiplication factor used for calculating the drying shrinkage as a function of time, as defined in fib Model Code 2010 (2013), Eq. 5.1-82.

• beta_rh (float) – Multiplication factor used when calculating the drying shrinkage.

Returns:

The drying shrinkage strains for the given times, no units.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.eps_cbs0(fcm: float, cem_class: Literal['32.5 N', '32.5 R', '42.5 N', '42.5 R', '52.5 N', '52.5 R']) → float

Calculate the notional basic shrinkage.

Defined in fib Model Code 2010 (2013), Eq. 5.1-78.

Parameters:

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

• cem_class (str) – The cement strength class that is used. The choices are: ‘32.5 N’, ‘32.5 R’, ‘42.5 N’, ‘42.5 R’, ‘52.5 N’, ‘52.5 R’.

Returns:

The notional basic shrinkage, no units.

Return type:

float

structuralcodes.codes.mc2010.beta_bs(time: ArrayLike) → ndarray

Calculate multiplication factor beta_bs which is used to determine the basic shrinkage.

Defined in fib Model Code 2010 (2013), Eq. 5.1-79.

Parameters:

time (numpy.typing.ArrayLike) – The different times in days at which the basic strain is determined.

Returns:

Multiplication factor that is used to determine the basic shrinkage.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.eps_cds0(fcm: float, cem_class: Literal['32.5 N', '32.5 R', '42.5 N', '42.5 R', '52.5 N', '52.5 R']) → float

Calculate the notional drying shrinkage.

Defined in fib Model Code 2010 (2013), Eq. 5.1-80.

Parameters:

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

• cem_class (str) – The cement strength class that is used. The choices are: ‘32.5 N’, ‘32.5 R’, ‘42.5 N’, ‘42.5 R’, ‘52.5 N’, ‘52.5 R’.

Returns:

The notional drying shrinkage, no units.

Return type:

float

structuralcodes.codes.mc2010.beta_ds(time: ArrayLike, ts: float, notional_size: float) → ndarray

Calculate the multiplication factor beta_ds.

Defined in fib Model Code 2010 (2013), Eq. 5.1-82.

Parameters:

• time (numpy.typing.ArrayLike) – The different times in days at which the shrinkage strain is determined.

• ts (float) – Age of the concrete when exposed to the environment.

• notional_size (float) – The notional size of the considered element in mm, defined as 2A/u.

Returns:

Multiplication factor used for calculating the drying shrinkage as a function of time.

Return type:

numpy.ndarray

structuralcodes.codes.mc2010.beta_RH(rh: float, beta_s1: float) → float

Calculate the multiplication factor beta_RH.

Defined in fib Model Code 2010 (2013), Eq. 5.1-81

Parameters:

• rh (float) – The relative humidity of the environment. Value can be provided as percentage (i.e. 40–100), or as ratio (i.e. 0.4–1).

• beta_s1 (float) – Multiplication factor as calculated in the fib Model Code 2010 (2013), Eq. 5.1-83.

Returns:

Multiplication factor used when calculating the drying shrinkage.

Return type:

float

structuralcodes.codes.mc2010.beta_s1(fcm: float) → float

Calculate the correction factor beta_s1.

Defined in fib Model Code 2010 (2013), Eq. 5.1-83.

Parameters:

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

Returns:

Multiplication factor used when calculating the drying shrinkage.

Return type:

float