Concrete materials¶

Concrete factory¶

structuralcodes.materials.concrete.create_concrete(fck: float, name: str | None = None, density: float = 2400.0, gamma_c: float | None = None, existing: bool = False, design_code: str | None = None, **kwargs) → Concrete | None[source]¶

A factory function to create the correct type of concrete based on the desired design code.

Parameters:

fck (float) – Characteristic strength of concrete in MPa. (if existing it is intended as the mean strength).

Keyword Arguments:

density (float) – Density of Concrete in kg/m3 (default: 2400).
gamma_c (Optional(float)) – The partial factor for concrete.
existing (bool) – Boolean indicating if the concrete is of an existing structure (default: False).
design_code (str) – Optional string (default: None) indicating the desired standard. If None (default) the globally used design standard will be adopted. Otherwise the design standard specified will be used for the instance of the material.
**kwargs – Other valid keyword arguments that are collected and passed to the specific concrete material. Please inspect the documentation of the other concrete materials to see valid arguments.

Raises:

ValueError – if the design code is not valid or does not cover concrete as a material.

Eurocode 2 (2004)¶

Concrete implementation for EC2 2004.

Initializes a new instance of Concrete for EC2 2004.

Parameters:

fck (float) – Characteristic strength in MPa if concrete is not existing.

Keyword Arguments:

name (str) – A descriptive name for concrete.
density (float) – Density of material in kg/m3 (default: 2400).
gamma_c (float, optional) – partial factor of concrete (default is 1.5).
alpha_cc (float, optional) – A factor for considering long-term effects on the strength, and effects that arise from the way the load is applied.
consitutive_law (ConstitutiveLaw | str) – A valid ConstitutiveLaw object for concrete or a string defining a valid constitutive law type for concrete. (valid options for string: ‘elastic’, ‘parabolarectangle’, ‘bilinearcompression’, ‘sargin’, ‘popovics’).
initial_strain (Optional[float]) – Initial strain of the material.
initial_stress (Optional[float]) – Initial stress of the material.
strain_compatibility (Optional[bool]) – Only relevant if initial_strain or initial_stress are different from zero. If True, the material deforms with the geometry. If False, the stress in the material upon loading is kept constant corresponding to the initial strain.
fcm (float, optional) – The mean compressive strength.
fctm (float, optional) – The mean tensile strength.
fctk_5 (float, optional) – The 5% fractile for the tensile strength.
fctk_95 (float, optional) – The 95% fractile for the tensile strength.
Ecm (float, optional) – The mean secant Young’s modulus.
eps_c1 (float, optional) – The strain at peak stress for the Sargin constitutive law.
eps_cu1 (float, optional) – The ultimate strain for the Sargin constitutive law.
k_sargin (float, optional) – The coefficient for the Sargin constitutive law.
eps_c2 (float, optional) – The strain at peak stress for the parabolic rectangular constitutive law.
eps_cu2 (float, optional) – The ultimate strain for the parabolic rectangular constitutive law.
n_parabolic_rectangular (float, optional) – The coefficient for the parabolic rectangular constitutive law.
eps_c3 (float, optional) – The strain at peak stress for the bilinear constitutive law.
eps_cu3 (float, optional) – The ultimate strain for the bilinear constitutive law.

Raises:

ValueError – If fcm is lower than fck.
ValueError – If k_sargin is negative.
ValueError – If n_parabolic_rectangular is negative.
ValueError – If the constitutive law name is not available for the material.
ValueError – If the provided constitutive law is not valid for concrete.
ValueError – If the constitutive law name is unknown.
Warning – If fctm is larger than 0.5 * fck.
Warning – If eps_c1 is larger than 0.1.
Warning – If eps_cu1 is larger than 0.1.
Warning – If eps_c2 is larger than 0.1.
Warning – If eps_cu2 is larger than 0.1.
Warning – If n_parabolic_rectangular is larger than 5.
Warning – If eps_c3 is larger than 0.1.
Warning – If eps_cu3 is larger than 0.1.

fcd() → float[source]¶

Return the design compressive strength in MPa.

Returns:: The design compressive strength of concrete in MPa.
Return type:: float

property fck: float¶: Returns fck in MPa.

property fcm: float¶

Returns fcm in MPa.

Returns:: The mean compressive strength in MPa.
Return type:: float

Note

The returned value is derived from fck if fcm is not manually provided when initializing the object.

property fctm: float¶

Returns fctm in MPa.

Returns:: The mean tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fck if fctm is not manually provided when initializing the object.

property fctk_5: float¶

Returns fctk_5 in MPa.

Returns:: The lower bound tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fctm if fctk_5 is not manually provided when initializing the object.

property fctk_95: float¶

Returns fctk_95 in MPa.

Returns:: The upper bound tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fctm if fctk_95 is not manually provided when initializing the object.

property Ecm: float¶

Returns Ecm in MPa.

Returns:: The upper bound tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fcm if Ecm is not manually provided when initializing the object.

property gamma_c: float¶: The partial factor for concrete.

property alpha_cc: float¶: The alpha_cc factor.

property eps_c1: float¶

Returns the strain at maximum compressive strength of concrete (fcm) for the Sargin constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from fcm if eps_c1 is not manually provided when initializing the object.

property eps_cu1: float¶

Returns the strain at concrete failure of concrete.

Returns:: The maximum strength at failure of concrete.
Return type:: float

Note

The returned value is derived from fcm if eps_cu1 is not manually provided when initializing the object.

property k_sargin: float¶

Returns the coefficient for Sargin constitutive law.

Returns:: The plastic coefficient for Sargin law.
Return type:: float

Note

The returned value is derived from Ecm, fcm and eps_c1 if k_sargin is not manually provided when initializing the object.

property eps_c2: float¶

Returns the strain at maximum compressive strength of concrete (fcd) for the Parabola-rectangle constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_c2 is not manually provided when initializing the object.

property eps_cu2: float¶

Returns the strain at concrete failure of concrete for the Parabola-rectangle constitutive law.

Returns:: The maximum strain at failure of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_cu2 is not manually provided when initializing the object.

property n_parabolic_rectangular: float¶

Returns the coefficient for Parabola-rectangle constitutive law.

Returns:: The exponent for Parabola-rectangle law.
Return type:: float

Note

The returned value is derived from fck if n_parabolic_rectangular is not manually provided when initializing the object.

property eps_c3: float¶

Returns the strain at maximum compressive strength of concrete (fcd) for the Bi-linear constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from eps_c3 if fck is not manually provided when initializing the object.

property eps_cu3: float¶

Returns the strain at concrete failure of concrete for the Bi-linear constitutive law.

Returns:: The maximum strain at failure of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_cu3 is not manually provided when initializing the object.

property constitutive_law: ConstitutiveLaw¶: Returns the ConstitutiveLaw of the object.

property name¶: Returns the name of the material.

property density¶: Returns the density of the material in kg/m3.

fib Model Code 2010¶

Concrete implementation for MC 2010.

Initializes a new instance of Concrete for MC 2010.

Parameters:

fck (float) – Characteristic strength in MPa if concrete is not existing.

Keyword Arguments:

name (Optional(str)) – A descriptive name for concrete.
density (float) – Density of material in kg/m3 (default: 2400).
gamma_c (Optional(float)) – The partial factor for concrete.
alpha_cc (float, optional) – A factor for considering long-term effects on the strength, and effects that arise from the way the load is applied.
consitutive_law (ConstitutiveLaw | str) – A valid ConstitutiveLaw object for concrete or a string defining a valid constitutive law type for concrete. (valid options for string: ‘elastic’, ‘parabolarectangle’, ‘bilinearcompression’, ‘sargin’, ‘popovics’).
initial_strain (Optional[float]) – Initial strain of the material.
initial_stress (Optional[float]) – Initial stress of the material.
strain_compatibility (Optional[bool]) – Only relevant if initial_strain or initial_stress are different from zero. If True, the material deforms with the geometry. If False, the stress in the material upon loading is kept constant corresponding to the initial strain.
fcm (float, optional) – The mean compressive strength.
fctm (float, optional) – The mean tensile strength.
fctkmin (float, optional) – The minimum tensile strength.
fctkmax (float, optional) – The maximum tensile strength.
Eci (float, optional) – The initial tangent Young’s modulus.
Gf (float, optional) – The tensile fracture energy.
eps_c1 (float, optional) – The strain at peak stress for the Sargin constitutive law.
eps_cu1 (float, optional) – The ultimate strain for the Sargin constitutive law.
k_sargin (float, optional) – The coefficient for the Sargin constitutive law.
eps_c2 (float, optional) – The strain at peak stress for the parabolic rectangular constitutive law.
eps_cu2 (float, optional) – The ultimate strain for the parabolic rectangular constitutive law.
n_parabolic_rectangular (float, optional) – The coefficient for the parabolic rectangular constitutive law.
eps_c3 (float, optional) – The strain at peak stress for the bilinear constitutive law.
eps_cu3 (float, optional) – The ultimate strain for the bilinear constitutive law.

Raises:

ValueError – If fcm is lower than fck.
ValueError – If k_sargin is negative.
ValueError – If n_parabolic_rectangular is negative.
ValueError – If the constitutive law name is not available for the material.
ValueError – If the provided constitutive law is not valid for concrete.
Warning – If Eci is lower than 1e4 or larger than 1e5.
Warning – If fctm is larger than 0.5 * fck.
Warning – If eps_c1 is larger than 0.1.
Warning – If eps_cu1 is larger than 0.1.
Warning – If eps_c2 is larger than 0.1.
Warning – If eps_cu2 is larger than 0.1.
Warning – If n_parabolic_rectangular is larger than 5.
Warning – If eps_c3 is larger than 0.1.
Warning – If eps_cu3 is larger than 0.1.

fcd() → float[source]¶

Return the design compressive strength in MPa.

Returns:: The design compressive strength of concrete in MPa.
Return type:: float

property fck: float¶: Returns fck in MPa.

property fcm: float¶

Returns fcm in MPa.

Returns:: The mean compressive strength in MPa.
Return type:: float

Note

The returned value is derived from fck if fcm is not manually provided when initializing the object.

property Eci: float¶

Returns the modulus of elasticity in MPa at the concrete age of 28 days.

It is assumed a normal concrete with quartzite aggregates (alfa_e = 1)

Returns:: The modulus of elasticity in MPa.
Return type:: float

Note

The returned value is derived from fcm if Eci is not manually provided when initializing the object.

property fctm: float¶

Returns fctm in MPa.

Returns:: The mean tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fck if fctm is not manually provided when initializing the object.

property fctkmin: float¶

Returns fctkmin in MPa.

Returns:: The lower bound tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fctm if fctkmin is not manually provided when initializing the object.

property fctkmax: float¶

Returns fctkmax in MPa.

Returns:: The upper bound tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fctm if fctkmax is not manually provided when initializing the object.

property Gf: float¶

Fracture energy of concrete.

Returns:: The fracture energy in N/m.
Return type:: float

Note

The returned value is derived from fck if Gf is not manually provided when initializing the object.

property gamma_c: float¶: The partial factor for concrete.

property alpha_cc: float¶: The alpha_cc factor.

property eps_c1: float¶

Returns the strain at maximum compressive strength of concrete (fcm) for the Sargin constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_c1 is not manually provided when initializing the object.

property eps_cu1: float¶

Returns the strain at concrete failure of concrete.

Returns:: The maximum strength at failure of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_cu1 is not manually provided when initializing the object.

property k_sargin: float¶

Returns the coefficient for Sargin constitutive law.

Returns:: The plastic coefficient for Sargin law.
Return type:: float

Note

The returned value is derived from fck if k_sargin is not manually provided when initializing the object.

property eps_c2: float¶

Returns the strain at maximum compressive strength of concrete (fcd) for the Parabola-rectangle constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_c2 is not manually provided when initializing the object.

property eps_cu2: float¶

Returns the strain at concrete failure of concrete for the Parabola-rectangle constitutive law.

Returns:: The maximum strain at failure of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_cu2 is not manually provided when initializing the object.

property n_parabolic_rectangular: float¶

Returns the coefficient for Parabola-rectangle constitutive law.

Returns:: The exponent for Parabola-recangle law.
Return type:: float

Note

The returned value is derived from fck if n is not manually provided when initializing the object.

property eps_c3: float¶

Returns the strain at maximum compressive strength of concrete (fcd) for the Bi-linear constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_c3 is not manually provided when initializing the object.

property eps_cu3: float¶

Returns the strain at concrete failure of concrete for the Bi-linear constitutive law.

Returns:: The maximum strain at failure of concrete.
Return type:: float

Note

The returned value is derived from fck if eps_cu3 is not manually provided when initializing the object.

property constitutive_law: ConstitutiveLaw¶: Returns the ConstitutiveLaw of the object.

property name¶: Returns the name of the material.

property density¶: Returns the density of the material in kg/m3.

Eurocode 2 (2023)¶

class structuralcodes.materials.concrete.ConcreteEC2_2023(fck: float, name: str | None = None, density: float = 2400.0, kE: float = 9500, strength_dev_class: Literal['CS', 'CN', 'CR', 'slow', 'normal', 'rapid'] = 'CN', gamma_c: float | None = None, constitutive_law: Literal['elastic', 'parabolarectangle', 'bilinearcompression', 'sargin', 'popovics'] | ConstitutiveLaw | None = 'parabolarectangle', initial_strain: float | None = None, initial_stress: float | None = None, strain_compatibility: bool | None = None, fcm: float | None = None, fctm: float | None = None, fctk_5: float | None = None, fctk_95: float | None = None, Ecm: float | None = None, eps_c1: float | None = None, eps_cu1: float | None = None, k_sargin: float | None = None, eps_c2: float | None = None, eps_cu2: float | None = None, n_parabolic_rectangular: float | None = None, **kwargs)[source]¶

Concrete implementation for EC2 2023 Concrete.

__init__(fck: float, name: str | None = None, density: float = 2400.0, kE: float = 9500, strength_dev_class: Literal['CS', 'CN', 'CR', 'slow', 'normal', 'rapid'] = 'CN', gamma_c: float | None = None, constitutive_law: Literal['elastic', 'parabolarectangle', 'bilinearcompression', 'sargin', 'popovics'] | ConstitutiveLaw | None = 'parabolarectangle', initial_strain: float | None = None, initial_stress: float | None = None, strain_compatibility: bool | None = None, fcm: float | None = None, fctm: float | None = None, fctk_5: float | None = None, fctk_95: float | None = None, Ecm: float | None = None, eps_c1: float | None = None, eps_cu1: float | None = None, k_sargin: float | None = None, eps_c2: float | None = None, eps_cu2: float | None = None, n_parabolic_rectangular: float | None = None, **kwargs)[source]¶

Initializes a new instance of Concrete for EC2 2023.

Parameters:

fck (float) – Characteristic strength in MPa if concrete is not existing.

Keyword Arguments:

name (str) – A descriptive name for concrete.
density (float) – Density of material in kg/m3 (default: 2400).
kE (float) – Coefficient relating aggregates.
strength_dev_class (str, optional) – Default is CN. Possible values: CS, CN, CR, slow, normal or rapid.
gamma_c (float, optional) – Partial factor of concrete (default is 1.5).
consitutive_law (ConstitutiveLaw | str) – A valid ConstitutiveLaw object for concrete or a string defining a valid constitutive law type for concrete. (valid options for string: ‘elastic’, ‘parabolarectangle’, ‘bilinearcompression’, ‘sargin’, ‘popovics’).
initial_strain (Optional[float]) – Initial strain of the material.
initial_stress (Optional[float]) – Initial stress of the material.
strain_compatibility (Optional[bool]) – Only relevant if initial_strain or initial_stress are different from zero. If True, the material deforms with the geometry. If False, the stress in the material upon loading is kept constant corresponding to the initial strain.
fcm (float, optional) – The mean compressive strength.
fctm (float, optional) – The mean tensile strength.
fctk_5 (float, optional) – The 5% fractile for the tensile strength.
fctk_95 (float, optional) – The 95% fractile for the tensile strength.
Ecm (float, optional) – The mean secant Young’s modulus.
eps_c1 (float, optional) – The strain at peak stress for the Sargin constitutive law.
eps_cu1 (float, optional) – The ultimate strain for the Sargin constitutive law.
k_sargin (float, optional) – The coefficient for the Sargin constitutive law.
eps_c2 (float, optional) – The strain at peak stress for the parabolic rectangular constitutive law.
eps_cu2 (float, optional) – The ultimate strain for the parabolic rectangular constitutive law.
n_parabolic_rectangular (float, optional) – The coefficient for the parabolic rectangular constitutive law.

Raises:

ValueError – If the provided strength development class is invalid.
ValueError – If gamma_c is less than zero.
ValueError – If fcm is less than fck.
ValueError – If k_sargin is negative.
ValueError – If n_parabolic_rectangular is negative.
ValueError – If the constitutive law name is not available for the material.
ValueError – If the provided constitutive law is not valid for concrete.
Warning – If eps_c1 is larger than 0.1.
Warning – If eps_cu1 is larger than 0.1.
Warning – If eps_c2 is larger than 0.1.
Warning – If eps_cu2 is larger than 0.1.

fcd(t_ref: float = 28, t0: float = 91, fck_ref: float = 40) → float[source]¶

Computes the value of the design compressive strength of concrete.

Parameters:

t_ref (float,optional) – The reference time in days (default is 28 days).
t0 (float, optional) – Age at loading in days (default is 91 days).
fck_ref (float, optional) – The reference compressive strength in MPa (default is 40 MPa).

Returns:

The design compressive strength of concrete in MPa.

Return type:

float

Raises:

ValueError – If fck_ref is less or equal to 0.
ValueError – If t_ref is less than 0.
ValueError – If t0 is less than 0.

fctd(t_ref: float = 28) → float[source]¶

Computes the value of the design tensile strength of concrete.

Parameters:: t_ref (float, optional) – The reference time in days (default is 28 days).
Returns:: The design tensile strength of concrete in MPa.
Return type:: float
Raises:: ValueError – If t_ref is less than 0.

property fck: float¶: Returns fck in MPa.

property fcm: float¶

Returns the mean strength of concrete.

Returns:: The mean compressive strength in MPa.
Return type:: float

Note

The returned value is derived from fck if fcm is not manually provided when initializing the object.

property fctm: None¶

Returns the mean concrete tensile strength.

Returns:: The mean concrete tensile strength.
Return type:: float

Note

The returned value is derived from fck if fctm is not manually provided when initializing the object.

property fctk_5: float¶

Returns the 5% fractile for the concrete tensile strength.

Returns:: The 5% fractile for the concrete tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fctm if fctk_5 is not manually provided when initializing the object.

property fctk_95: float¶

Returns the 95% fractile for the concrete tensile strength.

Returns:: The 5% fractile for the concrete tensile strength in MPa.
Return type:: float

Note

The returned value is derived from fctm if fctk_95 is not manually provided when initializing the object.

property Ecm: float¶

Returns the secant modulus.

Returns:: The secant concrete modulus in MPa.
Return type:: float

Note

The returned value is derived from fcm and kE if Ecm is not manually provided when initializing the object.

property gamma_c: float¶: The partial factor for concrete.

property eps_c1: float¶

Returns the strain at maximum compressive strength of concrete (fcm) for the Sargin constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is derived from fcm if eps_c1 is not manually provided when initializing the object.

property eps_cu1: float¶

Returns the strain at concrete failure of concrete.

Returns:: The maximum strength at failure of concrete.
Return type:: float

Note

The returned value is derived from fcm if eps_cu1 is not manually provided when initializing the object.

property k_sargin: float¶

Returns the k coefficient for Sargin constitutive law.

Returns:: k coefficient for Sargin constitutive law.
Return type:: float

Note

The returned value is derived from Ecm, fcm, and eps_c1 if k_sargin is not manually provided when initializing the object.

property eps_c2: float¶

Returns the strain at maximum compressive strength of concrete (fcd) for the Parabola-rectangle constitutive law.

Returns:: The strain at maximum compressive strength of concrete.
Return type:: float

Note

The returned value is the default value in the design code if not manually provided when initializing the object.

property eps_cu2: float¶

Returns the strain at concrete failure of concrete for the Parabola-rectangle constitutive law.

Returns:: The maximum strain at failure of concrete.
Return type:: float

Note

The returned value is the default value in the design code if not manually provided when initializing the object.

property n_parabolic_rectangular: float¶

Returns the coefficient for Parabola-rectangle constitutive law.

Returns:: The exponent for Parabola-recangle law.
Return type:: float

Note

The returned value is the default value in the design code if not manually provided when initializing the object.

property constitutive_law: ConstitutiveLaw¶: Returns the ConstitutiveLaw of the object.

property name¶: Returns the name of the material.

property density¶: Returns the density of the material in kg/m3.