m_n_kappa.material.ConcreteCompressionBiLinear

class m_n_kappa.material.ConcreteCompressionBiLinear(f_cm)

Bases: ConcreteCompression

bi-linear behaviour of concrete under compression according to EN 1992-1-1 [1]

New in version 0.1.0.

Parameters:

f_cm (float) – mean concrete cylinder compressive strength \(f_\mathrm{cm}\)

See also

ConcreteCompressionNonlinear

Describes non-linear behaviour of concrete under compression

ConcreteCompressionParabolaRectangle

Describes parabola rectangle behaviour of concrete under compression

Notes

Strain at peak stress \(\varepsilon_\mathrm{c}\) and strain at failure \(\varepsilon_\mathrm{cu}\) are computed as follows according to EN 1992-1-1 [1], Tab. 3.1

(1)\[ \begin{align}\begin{aligned}\varepsilon_\mathrm{c}(Permil) & = 1.75 + 0.55 \cdot \frac{f_\mathrm{ck} - 50.0}{40.0} \leq 1.75\\\varepsilon_\mathrm{cu}(Permil) & = 2.6 + 35.0 \cdot \left(\frac{90.0 - f_\mathrm{ck}}{100} \right)^{4} \leq 3.5\end{aligned}\end{align} \]

Bi-linear stress-strain relationship of concrete by EN 1992-1-1 [1], Fig. 3.4

References

[1] (1,2,3)

EN 1992-1-1: Eurocode 2 - Design of concrete structures - Part 1-1: General rules and rules for buildings, European Committee of Standardization (CEN), April 2004

Examples

The stress-strain relationship of concrete under compression is computed as follows.

>>> from m_n_kappa.material import ConcreteCompressionBiLinear
>>> f_cm = 30.0 # mean concrete compressive strength
>>> E_cm = 33000 # modulus of elasticity of concrete
>>> concrete = ConcreteCompressionBiLinear(f_cm=f_cm)
>>> concrete.stress_strain()
[[-22.0, -0.00175], [-22.0, -0.0035]]

Methods

stress(strain)	computation of stresses according to formula (1)
stress_strain()	stress-strain points of the material

Attributes

E_cm	mean elasticity modulus of concrete \(E_\mathrm{cm}\)
c	strain at peak stress \(\varepsilon_\mathrm{c}\) (see Formula (1))
cu	failure strain of concrete \(\varepsilon_\mathrm{cu}\) (see Formula (2))
f_ck	characteristic concrete cylinder compressive strength \(f_\mathrm{ck}\)
f_cm	mean concrete cylinder compressive strength \(f_\mathrm{cm}\)
strains	Strain-values where stresses are computed.
yield_strain	strain up to which the concrete is assumed to be linear-elastic \(\varepsilon_\mathrm{y}\)

stress(strain)

computation of stresses according to formula (1)

Parameters:

strain (float) – strain to compute corresponding stress

Returns:

stress to the given strain

Return type:

float

stress_strain()

stress-strain points of the material

Return type:

list

property E_cm: float

mean elasticity modulus of concrete \(E_\mathrm{cm}\)

property c: float

strain at peak stress \(\varepsilon_\mathrm{c}\) (see Formula (1))

property cu: float

failure strain of concrete \(\varepsilon_\mathrm{cu}\) (see Formula (2))

property f_ck: float

characteristic concrete cylinder compressive strength \(f_\mathrm{ck}\)

property f_cm: float

mean concrete cylinder compressive strength \(f_\mathrm{cm}\)

property strains: list

Strain-values where stresses are computed.

Current strain-values are:

• \(\varepsilon_\mathrm{c}\)

• \(\varepsilon_\mathrm{cu}\)

property yield_strain: float

strain up to which the concrete is assumed to be linear-elastic \(\varepsilon_\mathrm{y}\)