1. 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 materials is 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.

1.1. Material Classes#

concreteproperties ships with material objects describing the structural behaviour of both concrete and steel. The generic Material class can be used to describe the behaviour of any other material.

By default, all geometries in concreteproperties are meshed to capture strain variation across the section. However, for smaller geometries (such as reinforcement), concreteproperties can treat the area as having a constant strain with a lumped mass, which increases the performance of the analysis with almost no loss in fidelity. The meshing can be switched off by setting the attribute meshed=False.

The SteelBar class has meshing disabled by default and should be used when defining steel reinforcement. On the other hand, the Steel class is meshed by default so should be used when defining larger sections such as strucutral steel sections used in composite sections.

1.1.1. Material#

class Material(name, density, stress_strain_profile, colour, meshed)[source]

Generic class for a concreteproperties material.

Parameters

  • name (str) – Material name

  • density (float) – Material density (mass per unit volume)

  • stress_strain_profile (StressStrainProfile) – Material stress-strain profile

  • colour (str) – Colour of the material for rendering

  • meshed (bool) – If set to True, the entire material region is meshed; if set to False, the material region is treated as a lumped circular mass at its centroid

1.1.2. Concrete#

class Concrete(name, density, stress_strain_profile, colour, ultimate_stress_strain_profile, flexural_tensile_strength)[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

  • flexural_tensile_strength (float) – Absolute value of the concrete flexural tensile strength

  • colour (str) – Colour of the material for rendering

1.1.3. Steel#

class Steel(name, density, stress_strain_profile, colour)[source]

Class for a steel material with the entire region meshed to allow for strain variation across the section, e.g. structural steel profiles.

Parameters

  • name (str) – Steel material name

  • density (float) – Steel density (mass per unit volume)

  • stress_strain_profile (StressStrainProfile) – Steel stress-strain profile

  • colour (str) – Colour of the material for rendering

1.1.4. SteelBar#

class SteelBar(name, density, stress_strain_profile, colour)[source]

Class for a steel bar material, treated as a lumped circular mass with a constant strain.

Parameters

  • name (str) – Steel bar material name

  • density (float) – Steel bar density (mass per unit volume)

  • stress_strain_profile (StressStrainProfile) – Steel bar stress-strain profile

  • colour (str) – Colour of the material for rendering

1.2. 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). All other material objects 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, stresses)[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='8.6e')[source]

Prints the stress-strain profile properties to the terminal.

Parameters

fmt (str, default: '8.6e') – Number format

plot_stress_strain(title='Stress-Strain Profile', fmt='o-', **kwargs)[source]

Plots the stress-strain profile.

Parameters

  • title (str, default: 'Stress-Strain Profile') – Plot title

  • fmt (str, default: 'o-') – Plot format string

  • kwargs – Passed to plotting_context()

Returns

Axes – Matplotlib axes object

1.2.1. 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.

1.2.1.1. Generic Concrete Service Profile#

class ConcreteServiceProfile(strains, stresses, ultimate_strain)[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)

../_images/materials-1.png

ConcreteServiceProfile Stress-Strain Profile#

1.2.1.2. Linear Concrete Service Profile#

class ConcreteLinear(elastic_modulus, ultimate_strain=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 (float, default: 1) – Concrete strain at failure

Warning

This profile is not intended to be used in conjunction with a moment_curvature_analysis() as the concrete can resist large tensile stresses without fracture.

from concreteproperties.stress_strain_profile import ConcreteLinear

ConcreteLinear(elastic_modulus=35e3).plot_stress_strain()

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

../_images/materials-2.png

ConcreteLinear Stress-Strain Profile#

1.2.1.3. Linear Concrete (No Tension) Service Profile#

class ConcreteLinearNoTension(elastic_modulus, ultimate_strain=1, compressive_strength=None)[source]

Bases: ConcreteServiceProfile

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

Parameters

  • elastic_modulus (float) – Elastic modulus of the stress-strain profile

  • ultimate_strain (float, default: 1) – Concrete strain at failure

  • compressive_strength (Optional[float], default: None) – Compressive strength of the concrete

from concreteproperties.stress_strain_profile import ConcreteLinearNoTension

ConcreteLinearNoTension(elastic_modulus=35e3).plot_stress_strain()

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

../_images/materials-3.png

ConcreteLinearNoTension Stress-Strain Profile#

from concreteproperties.stress_strain_profile import ConcreteLinearNoTension

ConcreteLinearNoTension(
  elastic_modulus=35e3,
  ultimate_strain=0.003,
  compressive_strength=40,
).plot_stress_strain()

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

../_images/materials-4.png

ConcreteLinearNoTension Stress-Strain Profile with Compressive Strength#

1.2.1.4. Eurocode Non-Linear Concrete Service Profile#

class EurocodeNonLinear(elastic_modulus, ultimate_strain, compressive_strength, compressive_strain, tensile_strength, tension_softening_stiffness, n_points_1=10, n_points_2=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 (int, default: 10) – Number of points to discretise the curve prior to the peak stress

  • n_points_2 (int, default: 3) – 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)

../_images/materials-5.png

EurocodeNonLinear Stress-Strain Profile#

1.2.2. 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.

1.2.2.1. Generic Concrete Ultimate Profile#

class ConcreteUltimateProfile(strains, stresses, compressive_strength)[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)

../_images/materials-6.png

ConcreteUltimateProfile Stress-Strain Profile#

1.2.2.2. Rectangular Stress Block#

class RectangularStressBlock(compressive_strength, alpha, gamma, ultimate_strain)[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)

../_images/materials-7.png

RectangularStressBlock Stress-Strain Profile#

1.2.2.3. Bilinear Ultimate Profile#

class BilinearStressStrain(compressive_strength, compressive_strain, ultimate_strain)[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)

../_images/materials-8.png

BilinearStressStrain Stress-Strain Profile#

1.2.2.4. Eurocode Parabolic Ultimate Profile#

class EurocodeParabolicUltimate(compressive_strength, compressive_strain, ultimate_strain, n, n_points=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 (int, default: 10) – 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)

../_images/materials-9.png

EurocodeParabolicUltimate Stress-Strain Profile#

1.2.3. Steel Stress-Strain Profiles#

1.2.3.1. Generic Steel Profile#

class SteelProfile(strains, stresses, yield_strength, elastic_modulus, fracture_strain)[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)

../_images/materials-10.png

SteelProfile Stress-Strain Profile#

1.2.3.2. Elastic-Plastic Steel Profile#

class SteelElasticPlastic(yield_strength, elastic_modulus, fracture_strain)[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)

../_images/materials-11.png

SteelElasticPlastic Stress-Strain Profile#

1.2.3.3. Elastic-Plastic Hardening Steel Profile#

class SteelHardening(yield_strength, elastic_modulus, fracture_strain, ultimate_strength)[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)

../_images/materials-12.png

SteelHardening Stress-Strain Profile#