m_n_kappa.Reinforcement#

class m_n_kappa.Reinforcement(f_s=None, f_su=None, failure_strain=None, E_s=200000.0)#

Bases: Steel

Reinforcement material

Parameters:

f_s (float) – Yield strength of the reinforcement \(f_\mathrm{s}\) (Default: None)
f_su (float) – Tensile strength of the reinforcement \(f_\mathrm{su}\) (Default: None)
failure_strain (float) – Tensile strain of the reinforcement \(\varepsilon_\mathrm{su}\) (Default: None)
E_s (float) – Modulus of elasticity of the reinforcement \(E_\mathrm{s}\) (Default: 200000 N/mm ²)

See also

Concrete: material-behaviour of concrete
Steel: material-behaviour of steel

Examples

f_su = None and epsilon_su = None: Linear-elastic behaviour.

>>> from m_n_kappa import Reinforcement
>>> elastic_reinforcement = Reinforcement()
>>> elastic_reinforcement.stress_strain
[StressStrain(stress=-200000.0, strain=-1.0), StressStrain(stress=-0.0, strain=-0.0), StressStrain(stress=200000.0, strain=1.0)]

f_su = None: Bi-linear behaviour where f_su = f_s

>>> bilinear_reinforcement = Reinforcement(f_s=500.0, failure_strain=0.25)
>>> bilinear_reinforcement.stress_strain
[StressStrain(stress=-500.0, strain=-0.25), StressStrain(stress=-500.0, strain=-0.0025), StressStrain(stress=-0.0, strain=-0.0), StressStrain(stress=500.0, strain=0.0025), StressStrain(stress=500.0, strain=0.25)]

All values are not none: Bi-linear behaviour with following stress-strain points (\(f_\mathrm{s}\) | \(\varepsilon_\mathrm{s}\)), (\(f_\mathrm{su}\) | \(\varepsilon_\mathrm{su}\)). Where the strain at yield is computed like \(\varepsilon_\mathrm{s} = f_\mathrm{s} / E_\mathrm{s}\)

>>> reinforcement = Reinforcement(f_s=500.0, f_su=550.0, failure_strain=0.25)
>>> reinforcement.stress_strain
[StressStrain(stress=-550.0, strain=-0.25), StressStrain(stress=-500.0, strain=-0.0025), StressStrain(stress=-0.0, strain=-0.0), StressStrain(stress=500.0, strain=0.0025), StressStrain(stress=550.0, strain=0.25)]

Methods

`get_intermediate_strains`(strain_1[, ...])	determine material points with strains between zero and given strain_value
`get_material_stress`(strain)	gives stress from the stress-strain_value-relationship corresponding with the given strain_value
`sort_strains`([reverse])	sorts stress-strain_value-relationship depending on strains
`sort_strains_ascending`()	sorts stress-strain_value-relationship so strains are ascending
`sort_strains_descending`()	sorts stress-strain_value-relationship so strains are descending
`stress_strain_standard`()	standard stress-strain-relationship

Attributes

`E_a`	modulus of elasticity \(E_\mathrm{a}\)
`E_s`	Modulus of elasticity of the reinforcement \(E_\mathrm{s}\)
`compression_stress_strain`	stress-strain-relationship under compression (negative sign)
`epsilon_y`	yield strength \(f_\mathrm{y}\)
`f_s`	Yield strength of the reinforcement \(f_\mathrm{s}\)
`f_su`	Tensile strength of the reinforcement \(f_\mathrm{su}\)
`f_u`
`f_y`	yield strength \(f_\mathrm{y}\)
`failure_strain`	Failure-strain of reinforcement \(\varepsilon_\mathrm{su}\)
`maximum_strain`	maximum strain_value in the stress-strain_value-relationship
`minimum_strain`	minimum strain_value in the stress-strain_value-relationship
`section_type`	section section_type
`strains`	strains from the stress-strain_value-relationship
`stress_strain`	list of stress-strain_value points
`stress_strain_type`
`stresses`	stresses from the stress-strain_value-relationship
`tension_stress_strain`	stress-strain-relationship under tension (positive sign)

get_intermediate_strains(strain_1, strain_2=0.0, include_strains=False)#

determine material points with strains between zero and given strain_value

Parameters:

strain_1 (float) – 1st strain-value
strain_2 (float) – 2nd strain-value (Default: 0.0)
include_strains (bool) – includes the boundary strain values (Default: False)

Returns:

determine material points with strains between zero and given strain_value

Return type:

list[float]

get_material_stress(strain)#

gives stress from the stress-strain_value-relationship corresponding with the given strain_value

Parameters:: strain (float) – strain_value a corresponding stress value should be given
Returns:: stress corresponding to the given strain-value in the material-model
Return type:: float
Raises:: ValueError – when strain is outside the boundary values of the material-model

sort_strains(reverse=False)#

sorts stress-strain_value-relationship depending on strains

Parameters:

reverse (bool) –

True: sorts strains descending
False: sorts strains ascending (Default)

Return type:

None

sort_strains_ascending()#

sorts stress-strain_value-relationship so strains are ascending

Return type:: None

sort_strains_descending()#

sorts stress-strain_value-relationship so strains are descending

Return type:: None

stress_strain_standard()#

standard stress-strain-relationship

Return type:: list

property E_a: float#: modulus of elasticity \(E_\mathrm{a}\)

property E_s: float#: Modulus of elasticity of the reinforcement \(E_\mathrm{s}\)

property compression_stress_strain: list#: stress-strain-relationship under compression (negative sign)

property epsilon_y: float#: yield strength \(f_\mathrm{y}\)

property f_s: float#: Yield strength of the reinforcement \(f_\mathrm{s}\)

property f_su: float#: Tensile strength of the reinforcement \(f_\mathrm{su}\)

property f_y: float#: yield strength \(f_\mathrm{y}\)

property failure_strain: float#: Failure-strain of reinforcement \(\varepsilon_\mathrm{su}\)

property maximum_strain: float#: maximum strain_value in the stress-strain_value-relationship

property minimum_strain: float#: minimum strain_value in the stress-strain_value-relationship

property section_type#: section section_type

property strains: list#: strains from the stress-strain_value-relationship

property stress_strain: list[m_n_kappa.material.StressStrain]#: list of stress-strain_value points

property stresses: list#: stresses from the stress-strain_value-relationship

property tension_stress_strain: list#: stress-strain-relationship under tension (positive sign)