concreteproperties.concrete_section.ConcreteSection

class ConcreteSection(geometry: CompoundGeometry)

Bases: object

Class for a reinforced concrete section.

Inits the ConcreteSection class.

Parameters

geometry (sectionproperties.pre.geometry.CompoundGeometry) – sectionproperties compound geometry object describing the reinforced concrete section

Methods

biaxial_bending_diagram	Generates a biaxial bending diagram given a net axial force n and n_points calculation points.
calculate_cracked_properties	Calculates cracked section properties given a neutral axis angle theta.
calculate_cracked_stress	Calculates stresses within the reinforced concrete section assuming a cracked section.
calculate_cracking_moment	Calculates the cracking moment given a bending angle theta.
calculate_gross_area_properties	Calculates and stores gross section area properties.
calculate_gross_plastic_properties	Calculates and stores gross section plastic properties.
calculate_service_section_actions	Given a neutral axis depth d_n and curvature kappa, calculates the resultant axial force and bending moment.
calculate_service_stress	Calculates service stresses within the reinforced concrete section.
calculate_ultimate_section_actions	Given a neutral axis depth d_n and neutral axis angle theta, calculates the resultant bending moments m_x, m_y, m_u and the net axial force n.
calculate_ultimate_stress	Calculates ultimate stresses within the reinforced concrete section.
calculate_uncracked_stress	Calculates stresses within the reinforced concrete section assuming an uncracked section.
cracked_neutral_axis_convergence	Given a trial cracked neutral axis depth d_nc, determines the difference between the first moments of area above and below the trial axis.
get_c_local	Returns the elastic centroid location in local coordinates.
get_gross_properties	Returns the gross section properties of the reinforced concrete section.
get_pc_local	Returns the plastic centroid location in local coordinates.
get_transformed_gross_properties	Transforms gross section properties given a reference elastic modulus.
moment_curvature_analysis	Performs a moment curvature analysis given a bending angle theta.
moment_interaction_diagram	Generates a moment interaction diagram given a neutral axis angle theta and n_points calculation points between the decompression case and the pure bending case.
plot_section	Plots the reinforced concrete section.
service_normal_force_convergence	Given a trial neutral axis depth d_n and curvature kappa, determines the difference between the net axial force and the desired axial force.
ultimate_bending_capacity	Given a neutral axis angle theta and an axial force n, calculates the ultimate bending capacity.
ultimate_normal_force_convergence	Given a neutral axis depth d_n and neutral axis angle theta, calculates the difference between the target net axial force n and the axial force.

calculate_gross_area_properties()

Calculates and stores gross section area properties.

calculate_gross_plastic_properties()

Calculates and stores gross section plastic properties.

Calculates the plastic centroid and squash load assuming all steel is at yield and the concrete experiences a stress of alpha_squash * f’c.

Calculates tensile load assuming all steel is at yield and the concrete is entirely cracked.

get_gross_properties() → ConcreteProperties

Returns the gross section properties of the reinforced concrete section.

Returns

Concrete properties object

Return type

ConcreteProperties

get_transformed_gross_properties(elastic_modulus: float) → TransformedConcreteProperties

Transforms gross section properties given a reference elastic modulus.

Parameters

elastic_modulus (float) – Reference elastic modulus

Returns

Transformed concrete properties object

Return type

TransformedConcreteProperties

calculate_cracked_properties(theta: Optional[float] = 0) → CrackedResults

Calculates cracked section properties given a neutral axis angle theta.

Parameters

theta (Optional[float]) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

Returns

Cracked results object

Return type

CrackedResults

calculate_cracking_moment(theta: float) → float

Calculates the cracking moment given a bending angle theta.

Parameters

theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

Returns

Cracking moment

Return type

float

cracked_neutral_axis_convergence(d_nc: float, cracked_results: CrackedResults) → float

Given a trial cracked neutral axis depth d_nc, determines the difference between the first moments of area above and below the trial axis.

Parameters

• d_nc (float) – Trial cracked neutral axis

• cracked_results (CrackedResults) – Cracked results object

Returns

Cracked neutral axis convergence

Return type

float

moment_curvature_analysis(theta: Optional[float] = 0, kappa_inc: Optional[float] = 1e-07, delta_m_min: Optional[float] = 0.15, delta_m_max: Optional[float] = 0.3) → MomentCurvatureResults

Performs a moment curvature analysis given a bending angle theta.

Analysis continues until the steel reaches fracture strain or the concrete reaches its ultimate strain.

Parameters

• theta (Optional[float]) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

• kappa_inc (Optional[float]) – Initial curvature increment

• delta_m_min (Optional[float]) – Relative change in moment at which to double step

• delta_m_max (Optional[float]) – Relative change in moment at which to halve step

Returns

Moment curvature results object

Return type

MomentCurvatureResults

service_normal_force_convergence(d_n: float, kappa: float, moment_curvature: MomentCurvatureResults) → float

Given a trial neutral axis depth d_n and curvature kappa, determines the difference between the net axial force and the desired axial force.

Parameters

• d_nc (float) – Trial cracked neutral axis

• kappa (float) – Curvature

• moment_curvature (MomentCurvatureResults) – Moment curvature results object

Returns

Service normal force convergence

Return type

float

calculate_service_section_actions()

Given a neutral axis depth d_n and curvature kappa, calculates the resultant axial force and bending moment.

Parameters

• d_n (float) – Depth of the neutral axis from the extreme compression fibre

• kappa (float) – Curvature

• moment_curvature (Optional[MomentCurvatureResults]) – Moment curvature results object

Returns

Moment curvature results object

Return type

MomentCurvatureResults

ultimate_bending_capacity(theta: Optional[float] = 0, n: Optional[float] = 0) → results.UltimateBendingResults

Given a neutral axis angle theta and an axial force n, calculates the ultimate bending capacity.

Parameters

• theta (Optional[float]) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

• n (Optional[float]) – Net axial force

Returns

Ultimate bending results object

Return type

UltimateBendingResults

ultimate_normal_force_convergence(d_n: float, n: float, ultimate_results: results.UltimateBendingResults) → float

Given a neutral axis depth d_n and neutral axis angle theta, calculates the difference between the target net axial force n and the axial force.

Parameters

• d_n (float) – Depth of the neutral axis from the extreme compression fibre

• n (float) – Net axial force

• ultimate_results (UltimateBendingResults) – Ultimate bending results object

Returns

Axial force convergence

Return type

float

calculate_ultimate_section_actions(d_n: float, ultimate_results: Optional[res.UltimateBendingResults] = None) → results.UltimateBendingResults

Given a neutral axis depth d_n and neutral axis angle theta, calculates the resultant bending moments m_x, m_y, m_u and the net axial force n.

Parameters

• d_n (float) – Depth of the neutral axis from the extreme compression fibre

• ultimate_results (Optional[UltimateBendingResults]) – Ultimate bending results object

Returns

Ultimate bending results object

Return type

UltimateBendingResults

moment_interaction_diagram(theta: Optional[float] = 0, m_neg: Optional[bool] = False, n_points: Optional[int] = 24) → MomentInteractionResults

Generates a moment interaction diagram given a neutral axis angle theta and n_points calculation points between the decompression case and the pure bending case.

Parameters

• theta (Optional[float]) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

• m_neg (Optional[bool]) – If set to true, also calculates the moment interaction for \(\theta = \theta + \pi\), i.e. sagging and hogging

• n_points (Optional[int]) – Number of calculation points between the decompression point and the pure bending point

Returns

Moment interaction results object

Return type

MomentInteractionResults

biaxial_bending_diagram(n: Optional[float] = 0, n_points: Optional[int] = 48) → BiaxialBendingResults

Generates a biaxial bending diagram given a net axial force n and n_points calculation points.

Parameters

• n (Optional[float]) – Net axial force

• n_points (Optional[int]) – Number of calculation points between the decompression

Returns

Biaxial bending results

Return type

BiaxialBendingResults

calculate_uncracked_stress(n: Optional[float] = 0, m_x: Optional[float] = 0, m_y: Optional[float] = 0) → StressResult

Calculates stresses within the reinforced concrete section assuming an uncracked section.

Uses gross area section properties to determine concrete and steel stresses given an axial force n, and bending moments m_x and m_y.

Parameters

• n (Optional[float]) – Axial force

• m_x (Optional[float]) – Bending moment about the x-axis

• m_y (Optional[float]) – Bending moment about the y-axis

Returns

Stress results object

Return type

StressResult

calculate_cracked_stress(cracked_results: CrackedResults, n: Optional[float] = 0, m: Optional[float] = 0) → StressResult

Calculates stresses within the reinforced concrete section assuming a cracked section.

Uses cracked area section properties to determine concrete and steel stresses given an axial force n and bending moment m about the bending axis stored in cracked_results.

Parameters

• cracked_results (CrackedResults) – Cracked results objects

• n (Optional[float]) – Axial force

• m (Optional[float]) – Bending moment

Returns

Stress results object

Return type

StressResult

calculate_service_stress(moment_curvature_results: MomentCurvatureResults, m: float, kappa: Optional[float] = None) → StressResult

Calculates service stresses within the reinforced concrete section.

Uses linear interpolation of the moment-curvature results to determine the curvature of the section given the user supplied moment, and thus the stresses within the section. Otherwise, can provided a curvature which overrides the supplied moment.

Parameters

• moment_curvature_results (MomentCurvatureResults) – Moment-curvature results objects

• m (float) – Bending moment

• kappa (Optional[float]) – Curvature, if provided overrides the supplied bending moment and plots the stress at the given curvature

Returns

Stress results object

Return type

StressResult

calculate_ultimate_stress(ultimate_results: UltimateBendingResults) → StressResult

Calculates ultimate stresses within the reinforced concrete section.

Parameters

ultimate_results (UltimateBendingResults) – Ultimate bending results objects

Returns

Stress results object

Return type

StressResult

get_c_local(theta: float) → Tuple[float]

Returns the elastic centroid location in local coordinates.

Parameters

theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

Returns

Elastic centroid in local coordinates (c_u, c_v)

Return type

Tuple[float]

get_pc_local(theta: float) → Tuple[float]

Returns the plastic centroid location in local coordinates.

Parameters

theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))

Returns

Plastic centroid in local coordinates (pc_u, pc_v)

Return type

Tuple[float]

plot_section(title: Optional[str] = 'Reinforced Concrete Section', background: Optional[bool] = False, **kwargs) → matplotlib.axes.Axes

Plots the reinforced concrete section.

Parameters

• title (Optional[str]) – Plot title

• background (Optional[bool]) – If set to True, uses the plot as a background plot

• kwargs – Passed to plotting_context()

Returns

Matplotlib axes object

Return type

matplotlib.axes.Axes