m_n_kappa.material.ConcreteTension

class m_n_kappa.material.ConcreteTension(f_cm, E_cm, f_ctm=None, g_f=None, use_tension=True, consider_opening_behaviour=True)

Bases: object

define concrete tensile behaviour

New in version 0.1.0.

Parameters:

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

• E_cm (float) – mean modulus of elasticity of concrete \(E_\mathrm{cm}\)

• f_ctm (float) – mean tensile concrete tensile strength \(f_\mathrm{ctm}\) (Default: None)

• g_f (float) – fracture energy of concrete \(G_\mathrm{f}\) (Default: None)

• use_tension (bool) –

  • True: compute tensile behaviour (Default)

  • False: no tensile behaviour computed

• consider_opening_behaviour (bool) – if True considers the crack opening under tension

Notes

If not given the concrete tensile strength \(f_\mathrm{ctm}\) may be computed according to EN 1992-1-1 [1], Tab. 3.1

(1)\[ \begin{align}\begin{aligned}f_\mathrm{ctm} & = 0.3 \cdot f_\mathrm{ck}^{2/3} \leq C50/50\\f_\mathrm{ctm} & = 2.12 \cdot \ln(1 + 0.1 \cdot f_\mathrm{cm}) > C50/60\end{aligned}\end{align} \]

Stress-strain relationship of concrete under tension

References

[1]

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

[2] (1,2,3)

fib Model Code for Concrete Structures, International Federation for Structural Concrete, Ernst & Sohn GmbH & Co. KG, 2013, p. 78, Eq. 5.1-9

Examples

In case no tension is to be considered ConcreteTension is initialized as follows.

>>> from m_n_kappa.material import ConcreteTension
>>> no_tension = ConcreteTension(f_cm=38, E_cm=33000, use_tension=False)
>>> no_tension.stress_strain()
[[0.0, 10.0]]

The single tension point [[0.0, 10.0]] is needed otherwise the computation fails as soon as the concrete is loaded by tension and effects like redistribution of tensile stresses into rebars.

If the tensile-capacity of the condrete is needed no parameter must be given as use_tension=True is the default.

>>> consider_tension = ConcreteTension(f_cm=38, E_cm=33000)
>>> consider_tension.stress_strain()
[[2.896468153816889, 8.777176223687542e-05], [0.5792936307633778, 0.1723892594303201], [0.0, 0.8619462971516005], [0.0, 10.0]]

Under the hood m_n_kappa automatically computes the concrete tensile strength \(f_\mathrm{ctm}\)

>>> consider_tension.f_ctm
2.896468153816889

Furthermore, the crack opening behaviour according to fib Model Code 2010 [2] is considered. If this shall not be considered ConcreteTension may be initialized as follows.

>>> consider_tension = ConcreteTension(f_cm=38, E_cm=33000, consider_opening_behaviour=False)
>>> consider_tension.stress_strain()
[[2.896468153816889, 8.777176223687542e-05], [0.0, 8.877176223687542e-05], [0.0, 10.0]]

Methods

stress_strain()

stress-strain-relationship of concrete under tension

Attributes

E_cm	mean modulus of elasticity of concrete \(E_\mathrm{cm}\)
consider_opening_behaviour	if True considers the crack opening behaviour according to fib-model-code [2]
f_ck	characteristic cylinder concrete compressive strength \(f_\mathrm{ck}\)
f_cm	mean cylinder concrete compressive strength \(f_\mathrm{cm}\)
f_ctm	concrete tensile strength \(f_\mathrm{ctm}\).
fracture_energy	Fracture energy of concrete \(G_\mathrm{F}\) in N/mm (Newton per millimeter)
use_tension
w	crack-opening at \(0.2 \cdot f_\mathrm{ctm}\)
wu	crack-opening where no tension is transmitted anymore \(w_\mathrm{u} = 5.0 \cdot w\)
yield_strain	strain at peak stresses \(\varepsilon_\mathrm{y} = f_\mathrm{ctm} / E_\mathrm{cm}\)

stress_strain()

stress-strain-relationship of concrete under tension

Return type:

list

property E_cm

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

property consider_opening_behaviour: bool

if True considers the crack opening behaviour according to fib-model-code [2]

property f_ck

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

property f_cm

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

property f_ctm: float

concrete tensile strength \(f_\mathrm{ctm}\). If not given by input \(f_\mathrm{ctm}\) is computed by Formula (1)

property fracture_energy: float

Fracture energy of concrete \(G_\mathrm{F}\) in N/mm (Newton per millimeter)

Notes

The formula assumes that the mean concrete compressive strength \(f_\mathrm{cm}\) is given in N/mm ².

property w: float

crack-opening at \(0.2 \cdot f_\mathrm{ctm}\)

property wu: float

crack-opening where no tension is transmitted anymore \(w_\mathrm{u} = 5.0 \cdot w\)

property yield_strain

strain at peak stresses \(\varepsilon_\mathrm{y} = f_\mathrm{ctm} / E_\mathrm{cm}\)