Materials#

concreteproperties requires material properties to be defined for the concrete and steel components of the reinforced concrete section. Any number of different material properties can be used for a single cross-section. For example, higher strength precast sections can be topped with lower grade in-situ slabs, and high tensile steel can be used in combination with normal grade reinforcing steel.

The structural behaviour of both concrete and steel materials are described by Stress-Strain Profiles.

Note

In concreteproperties, a positive sign is given to compressive forces, stresses and strains, while a negative sign is given to tensile forces, stresses and strains.

Concrete#

class Concrete(name: str, density: float, stress_strain_profile: ConcreteServiceProfile, ultimate_stress_strain_profile: ConcreteUltimateProfile, alpha_squash: float, flexural_tensile_strength: float, colour: str)[source]

Class for a concrete material.

Parameters

name (str) – Concrete material name
density (float) – Concrete density (mass per unit volume)
stress_strain_profile (ConcreteServiceProfile) – Service concrete stress-strain profile
ultimate_stress_strain_profile (ConcreteUltimateProfile) – Ultimate concrete stress-strain profile
alpha_squash (float) – Factor that modifies the concrete compressive strength at squash load
flexural_tensile_strength (float) – Absolute value of the concrete flexural tensile strength
colour (str) – Colour of the material for rendering

Steel#

class Steel(name: str, density: float, stress_strain_profile: SteelProfile, colour: str)[source]

Class for a steel material.

Parameters

name (str) – Steel material name
density (float) – Steel density (mass per unit volume)
stress_strain_profile – Ultimate steel stress-strain profile
colour (str) – Colour of the material for rendering

Stress-Strain Profiles#

concreteproperties uses stress-strain profiles to define material behaviour for both service and ultimate analyses. A Concrete object requires both a service stress-strain profile (calculation of area properties, moment-curvature analysis, elastic and service stress analysis) and an ultimate stress-strain profile (ultimate bending capacity, moment interaction diagram, biaxial bending diagram, ultimate stress analysis). A Steel object only requires one stress-strain profile which is used for both service and ultimate analyses.

Note

Stress values are interpolated from stresses and strains supplied to the profile. If the strain is outside of the range of the stress-strain profile, the stress is extrapolated based off the closest two points of the stress-strain profile.

class StressStrainProfile(strains: List[float], stresses: List[float])[source]

Abstract base class for a material stress-strain profile.

Implements a piecewise linear stress-strain profile. Positive stresses & strains are compression.

Parameters

strains (List[float]) – List of strains (must be increasing or equal)
stresses (List[float]) – List of stresses

print_properties(fmt: Optional[str] = '8.6e')[source]

Prints the stress-strain profile properties to the terminal.

Parameters: fmt (Optional[str]) – Number format

plot_stress_strain(title: Optional[str] = 'Stress-Strain Profile', **kwargs) → matplotlib.axes.Axes[source]

Plots the stress-strain profile.

Parameters

title (Optional[str]) – Plot title
kwargs – Passed to plotting_context()

Returns

Matplotlib axes object

Return type

matplotlib.axes.Axes

Concrete Service Stress-Strain Profiles#

Note

Unless assigned in the class constructor, the elastic_modulus of the concrete is determined by the initial compressive slope of the stress-strain profile. This elastic_modulus is used in the calculation of area properties and elastic stress analysis.

Generic Concrete Service Profile#

class ConcreteServiceProfile(strains: List[float], stresses: List[float], ultimate_strain: float)[source]

Bases: StressStrainProfile

Abstract class for a concrete service stress-strain profile.

Parameters

strains (List[float]) – List of strains (must be increasing or equal)
stresses (List[float]) – List of stresses
ultimate_strain (float) – Concrete strain at failure

from concreteproperties.stress_strain_profile import ConcreteServiceProfile

ConcreteServiceProfile(
  strains=[-5 / 35e3, -4 / 35e3, -3 / 35e3, 0, 40 / 35e3, 0.003],
  stresses=[0, 0, -3, 0, 40, 40],
  ultimate_strain=0.003,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

ConcreteServiceProfile Stress-Strain Profile#

Linear Concrete Service Profile#

class ConcreteLinear(elastic_modulus: float, ultimate_strain: float = 1)[source]

Bases: ConcreteServiceProfile

Class for a symmetric linear stress-strain profile.

Parameters

elastic_modulus (float) – Elastic modulus of the stress-strain profile
ultimate_strain (Optional[float]) – Concrete strain at failure

from concreteproperties.stress_strain_profile import ConcreteLinear

ConcreteLinear(elastic_modulus=35e3).plot_stress_strain()

(Source code, png, hires.png, pdf)

ConcreteLinear Stress-Strain Profile#

Linear Concrete (No Tension) Service Profile#

class ConcreteLinearNoTension(elastic_modulus: float, ultimate_strain: float = 1)[source]

Bases: ConcreteLinear

Class for a linear stress-strain profile with no tensile strength.

Parameters

elastic_modulus (float) – Elastic modulus of the stress-strain profile
ultimate_strain (Optional[float]) – Concrete strain at failure

from concreteproperties.stress_strain_profile import ConcreteLinearNoTension

ConcreteLinearNoTension(elastic_modulus=35e3).plot_stress_strain()

(Source code, png, hires.png, pdf)

ConcreteLinearNoTension Stress-Strain Profile#

Eurocode Non-Linear Concrete Service Profile#

class EurocodeNonLinear(elastic_modulus: float, ultimate_strain: float, compressive_strength: float, compressive_strain: float, tensile_strength: float, tension_softening_stiffness: float, n_points_1: Optional[int] = 10, n_points_2: Optional[int] = 3)[source]

Bases: ConcreteServiceProfile

Class for a non-linear stress-strain relationship to EC2.

Tension is modelled with a symmetric elastic_modulus until failure at tensile_strength, after which the tensile stress reduces according to the tension_softening_stiffness.

Parameters

elastic_modulus (float) – Concrete elastic modulus (\(E_{cm}\))
ultimate_strain (float) – Concrete strain at failure (\(\epsilon_{cu1}\))
compressive_strength (float) – Concrete compressive strength (\(f_{cm}\))
compressive_strain (float) – Strain at which the concrete stress equals the compressive strength (\(\epsilon_{c1}\))
tensile_strength (float) – Concrete tensile strength
tension_softening_stiffness (float) – Slope of the linear tension softening branch
n_points_1 (Optional[int]) – Number of points to discretise the curve prior to the peak stress
n_points_2 (Optional[int]) – Number of points to discretise the curve after the peak stress

from concreteproperties.stress_strain_profile import EurocodeNonLinear

EurocodeNonLinear(
    elastic_modulus=35e3,
    ultimate_strain=0.0035,
    compressive_strength=40,
    compressive_strain=0.0023,
    tensile_strength=3.5,
    tension_softening_stiffness=7e3,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

EurocodeNonLinear Stress-Strain Profile#

Concrete Ultimate Stress-Strain Profiles#

Note

Unless assigned in the class constructor, the ultimate_strain of the concrete is taken as the largest compressive strain in the stress-strain profile. This ultimate_strain defines the curvature and strain profile used in ultimate analyses.

Warning

concreteproperties currently only supports a single unique ultimate_strain to be used for a given ConcreteSection. While multiple concrete materials, with differing stress-strain profiles, can be used within a given ConcreteSection, the ultimate analysis will use the smallest value of the ultimate_strain amongst the various concrete materials to define the strain profile at ultimate.

Generic Concrete Ultimate Profile#

class ConcreteUltimateProfile(strains: List[float], stresses: List[float], compressive_strength: float)[source]

Bases: StressStrainProfile

Abstract class for a concrete ultimate stress-strain profile.

Parameters

strains (List[float]) – List of strains (must be increasing or equal)
stresses (List[float]) – List of stresses
compressive_strength (float) – Concrete compressive strength

from concreteproperties.stress_strain_profile import ConcreteUltimateProfile

ConcreteUltimateProfile(
  strains=[-20 / 30e3, 0, 20 / 30e3, 30 / 25e3, 40 / 20e3, 0.003],
  stresses=[0, 0, 20, 30, 40, 40],
  compressive_strength=32,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

ConcreteUltimateProfile Stress-Strain Profile#

Rectangular Stress Block#

class RectangularStressBlock(compressive_strength: float, alpha: float, gamma: float, ultimate_strain: float)[source]

Bases: ConcreteUltimateProfile

Class for a rectangular stress block.

Parameters

compressive_strength (float) – Concrete compressive strength
alpha (float) – Factor that modifies the concrete compressive strength
gamma (float) – Factor that modifies the depth of the stress block
ultimate_strain (float) – Concrete strain at failure

from concreteproperties.stress_strain_profile import RectangularStressBlock

RectangularStressBlock(
    compressive_strength=40,
    alpha=0.85,
    gamma=0.77,
    ultimate_strain=0.003,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

RectangularStressBlock Stress-Strain Profile#

Bilinear Ultimate Profile#

class BilinearStressStrain(compressive_strength: float, compressive_strain: float, ultimate_strain: float)[source]

Bases: ConcreteUltimateProfile

Class for a bilinear stress-strain relationship.

Parameters

compressive_strength (float) – Concrete compressive strength
compressive_strain (float) – Strain at which the concrete stress equals the compressive strength
ultimate_strain (float) – Concrete strain at failure

from concreteproperties.stress_strain_profile import BilinearStressStrain

BilinearStressStrain(
    compressive_strength=40,
    compressive_strain=0.00175,
    ultimate_strain=0.0035,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

BilinearStressStrain Stress-Strain Profile#

Eurocode Parabolic Ultimate Profile#

class EurocodeParabolicUltimate(compressive_strength: float, compressive_strain: float, ultimate_strain: float, n: float, n_points: Optional[int] = 10)[source]

Bases: ConcreteUltimateProfile

Class for an ultimate parabolic stress-strain relationship to EC2.

Parameters

compressive_strength (float) – Concrete compressive strength
compressive_strain (float) – Strain at which the concrete stress equals the compressive strength
ultimate_strain (float) – Concrete strain at failure
n (float) – Parabolic curve exponent
n_points (Optional[int]) – Number of points to discretise the parabolic segment of the curve

from concreteproperties.stress_strain_profile import EurocodeParabolicUltimate

EurocodeParabolicUltimate(
    compressive_strength=40,
    compressive_strain=0.00175,
    ultimate_strain=0.0035,
    n=2,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

EurocodeParabolicUltimate Stress-Strain Profile#

Steel Stress-Strain Profiles#

Generic Steel Profile#

class SteelProfile(strains: List[float], stresses: List[float], yield_strength: float, elastic_modulus: float, fracture_strain: float)[source]

Bases: StressStrainProfile

Abstract class for a steel stress-strain profile.

Parameters

strains (List[float]) – List of strains (must be increasing or equal)
stresses (List[float]) – List of stresses
yield_strength (float) – Steel yield strength
elastic_modulus (float) – Steel elastic modulus
fracture_strain (float) – Steel fracture strain

from concreteproperties.stress_strain_profile import SteelProfile

SteelProfile(
  strains=[-0.05, -0.03, -0.02, -500 / 200e3, 0, 500 / 200e3, 0.02, 0.03, 0.05],
  stresses=[-600, -600, -500, -500, 0, 500, 500, 600, 600],
  yield_strength=500,
  elastic_modulus=200e3,
  fracture_strain=0.05,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

SteelProfile Stress-Strain Profile#

Elastic-Plastic Steel Profile#

class SteelElasticPlastic(yield_strength: float, elastic_modulus: float, fracture_strain: float)[source]

Bases: SteelProfile

Class for a perfectly elastic-plastic steel stress-strain profile.

Parameters

yield_strength (float) – Steel yield strength
elastic_modulus (float) – Steel elastic modulus
fracture_strain (float) – Steel fracture strain

from concreteproperties.stress_strain_profile import SteelElasticPlastic

SteelElasticPlastic(
  yield_strength=500,
  elastic_modulus=200e3,
  fracture_strain=0.05,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

SteelElasticPlastic Stress-Strain Profile#

Elastic-Plastic Hardening Steel Profile#

class SteelHardening(yield_strength: float, elastic_modulus: float, fracture_strain: float, ultimate_strength: float)[source]

Bases: SteelProfile

Class for a steel stress-strain profile with strain hardening.

Parameters

yield_strength (float) – Steel yield strength
elastic_modulus (float) – Steel elastic modulus
fracture_strain (float) – Steel fracture strain
ultimate_strength (float) – Steel ultimate strength

from concreteproperties.stress_strain_profile import SteelHardening

SteelHardening(
  yield_strength=500,
  elastic_modulus=200e3,
  fracture_strain=0.05,
  ultimate_strength=600,
).plot_stress_strain()

(Source code, png, hires.png, pdf)

SteelHardening Stress-Strain Profile#