ConcreteSection

class concreteproperties.concrete_section.ConcreteSection(geometry: CompoundGeometry, moment_centroid: tuple[float, float] | None = None, geometric_centroid_override: bool = False)[source]

Bases: object

Class for a reinforced concrete section.

Methods

biaxial_bending_diagram

Generates a biaxial bending diagram.

calculate_cracked_properties

Calculates cracked section properties given a neutral axis angle theta.

calculate_cracked_stress

Calculates cracked stresses.

calculate_cracking_moment

Calculates the cracking moment given a bending angle theta.

calculate_gross_area_properties

Calculates and stores gross section area properties.

calculate_service_stress

Calculates service stresses within the reinforced concrete section.

calculate_ultimate_section_actions

Caclculate ultimate section actions.

calculate_ultimate_stress

Calculates ultimate stresses within the reinforced concrete section.

calculate_uncracked_stress

Calculates uncracked stresses.

cracked_neutral_axis_convergence

Determine the cracked neutral axis convergence.

cracked_section_properties

Calculates cracked section properties.

decode_d_n

Decodes a neutral axis depth given a control point cp.

extreme_bar

Calculates depth to the extreme bar.

get_gross_properties

Returns the gross section properties of the reinforced concrete section.

get_transformed_gross_properties

Transforms gross section properties given a reference elastic modulus.

moment_curvature_analysis

Moment curvature analysis.

moment_interaction_diagram

Generates a moment interaction diagram given a neutral axis angle theta.

plot_section

Plots the reinforced concrete section.

service_normal_force_convergence

Calculates service convergence.

ultimate_bending_capacity

Calculates ultiamte bending capacity.

ultimate_normal_force_convergence

Calculates ultimate convergence.
__init__(geometry: CompoundGeometry, moment_centroid: tuple[float, float] | None = None, geometric_centroid_override: bool = False) → None[source]

Inits the ConcreteSection class.

Parameters:

  • geometry (CompoundGeometry) – sectionproperties CompoundGeometry object describing the reinforced concrete section

  • moment_centroid (tuple[float, float] | None) – If specified, all moments for service and ultimate analyses are calculated about this point. If not specified, all moments are calculated about the gross cross-section centroid, i.e. no material properties applied. Defaults to None.

  • geometric_centroid_override (bool) – If set to True, sets moment_centroid to the geometric centroid i.e. material properties applied (useful for composite section analysis). Defaults to False.

Raises:

ValueError – If steel strand materials are detected, use a PrestressedSection instead

calculate_gross_area_properties() → None[source]

Calculates and stores gross section area properties.

get_gross_properties() → GrossProperties[source]

Returns the gross section properties of the reinforced concrete section.

Returns:

Gross concrete properties object

Return type:

GrossProperties

get_transformed_gross_properties(elastic_modulus: float) → TransformedGrossProperties[source]

Transforms gross section properties given a reference elastic modulus.

Parameters:

elastic_modulus (float) – Reference elastic modulus

Returns:

Transformed concrete properties object

Return type:

TransformedGrossProperties

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

Calculates cracked section properties given a neutral axis angle theta.

Parameters:

theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\)). Defaults to 0.

Raises:

AnalysisError – If the analysis fails

Returns:

Cracked results object

Return type:

CrackedResults

calculate_cracking_moment(theta: float) → float[source]

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[source]

Determine the 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.

Parameters:

  • d_nc (float) – Trial cracked neutral axis

  • cracked_results (CrackedResults) – Cracked results object

Raises:

ValueError – If d_nc is not positive or doesn’t lie within the section

Returns:

Cracked neutral axis convergence

Return type:

float

cracked_section_properties(cracked_results: CrackedResults) → None[source]

Calculates cracked section properties.

Given a list of cracked geometries (stored in cracked_results), determines the cracked section properties and stores in cracked_results.

Parameters:

cracked_results (CrackedResults) – Cracked results object with stored cracked geometries

moment_curvature_analysis(theta: float = 0, n: float = 0, kappa0: float = 0, kappa_inc: float = 1e-07, kappa_mult: float = 2, kappa_inc_max: float = 5e-06, delta_m_min: float = 0.15, delta_m_max: float = 0.3, progress_bar: bool = True) → MomentCurvatureResults[source]

Moment curvature analysis.

Performs a moment curvature analysis given a bending angle theta and applied axial force n. Analysis continues until a material reaches its ultimate strain.

Parameters:

  • theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\)). Defaults to 0.

  • n (float) – Axial force. Defaults to 0.

  • kappa0 (float) – Initial curvature. Defaults to 0.

  • kappa_inc (float) – Initial curvature increment. Defaults to 1e-7.

  • kappa_mult (float) – Multiplier to apply to the curvature increment kappa_inc when delta_m_max is satisfied. When delta_m_min is satisfied, the inverse of this multipler is applied to kappa_inc. Defaults to 2.

  • kappa_inc_max (float) – Maximum curvature increment. Defaults to 5e-6.

  • delta_m_min (float) – Relative change in moment at which to reduce the curvature increment. Defaults to 0.15.

  • delta_m_max (float) – Relative change in moment at which to increase the curvature increment. Defaults to 0.3.

  • progress_bar (bool) – If set to True, displays the progress bar. Defaults to True.

Returns:

Moment curvature results object

Return type:

MomentCurvatureResults

service_normal_force_convergence(eps0: float, kappa: float, moment_curvature: MomentCurvatureResults) → float[source]

Calculates service convergence.

Given a neutral axis depth d_n and curvature kappa, returns the the net axial force.

Parameters:
Returns:

Net axial force

Return type:

float

ultimate_bending_capacity(theta: float = 0, n: float = 0) → UltimateBendingResults[source]

Calculates ultiamte bending capacity.

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

Note

This calculation is code agnostic and no capacity reduction factors are applied. If design capacities are required, use the applicable design_code module or consult your local design code on how to treat nominal axial loads in ultimate bending calculations.

Note

k_u is calculated only for lumped (non-meshed) geometries.

Parameters:

  • theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\)). Defaults to 0.

  • n (float) – Net axial force (nominal axial load). Defaults to 0.

Raises:

AnalysisError – If the analysis fails

Returns:

Ultimate bending results object

Return type:

UltimateBendingResults

ultimate_normal_force_convergence(d_n: float, n: float, ultimate_results: UltimateBendingResults) → float[source]

Calculates ultimate 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 calculated 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: UltimateBendingResults | None = None) → UltimateBendingResults[source]

Caclculate 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_xy and the net axial force n.

Parameters:

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

  • ultimate_results (UltimateBendingResults | None) – Ultimate bending results object

Raises:

ValueError – If d_n is not positive

Returns:

Ultimate bending results object

Return type:

UltimateBendingResults

moment_interaction_diagram(theta: float = 0, limits: list[tuple[str, float]] | None = None, control_points: list[tuple[str, float]] | None = None, labels: list[str] | None = None, n_points: int = 24, n_spacing: int | None = None, max_comp: float | None = None, max_comp_labels: list[str] | None = None, progress_bar: bool = True) → MomentInteractionResults[source]

Generates a moment interaction diagram given a neutral axis angle theta.

limits and control_points accept a list of tuples that define points on the moment interaction diagram. The first item in the tuple defines the type of control points, while the second item defines the location of the control point. Types of control points are detailed below:

Control points

  • "D" - ratio of neutral axis depth to section depth

  • "d_n" - neutral axis depth

  • "fy" - yield ratio of the most extreme tensile bar

  • "N" - net (nominal) axial force

  • "kappa0" - zero curvature compression (N.B second item in tuple is not used)

Parameters:

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

  • limits (list[tuple[str, float]] | None) – List of control points that define the start and end of the interaction diagram. List length must equal two. The default limits range from concrete decompression strain to zero curvature tension, i.e. [("D", 1.0), ("d_n", 1e-6)]. Defaults to None.

  • control_points (list[tuple[str, float]] | None) – List of additional control points to add to the moment interatction diagram. The default control points include the pure compression point (kappa0), the balanced point (fy = 1) and the pure bending point (N=0), i.e. [("kappa0", 0.0), ("fy", 1.0), ("N", 0.0)]. Control points may lie outside the limits of the moment interaction diagram as long as equilibrium can be found. Defaults to None.

  • labels (list[str] | None) – List of labels to apply to the limits and control_points for plotting purposes. The first two values in labels apply labels to the limits, the remaining values apply labels to the control_points. If a single value is provided, this value will be applied to both limits and all control_points. The length of labels must equal 1 or 2 + len(control_points). Defaults to None.

  • n_points (int) – Number of points to compute including and between the limits of the moment interaction diagram. Generates equally spaced neutral axis depths between the limits. Defaults to 24.

  • n_spacing (int | None) – If provided, overrides n_points and generates the moment interaction diagram using n_spacing equally spaced axial loads. Note that using n_spacing negatively affects performance, as the neutral axis depth must first be located for each point on the moment interaction diagram. Defaults to None.

  • max_comp (float | None) – If provided, limits the maximum compressive force in the moment interaction diagram to max_comp. Defaults to None.

  • max_comp_labels (list[str] | None) – Labels to apply to the max_comp intersection points, first value is at zero moment, second value is at the intersection with the interaction diagram

  • progress_bar (bool) – If set to True, displays the progress bar. Defaults to True.

Raises:

  • ValueError – Length of limits must equal 2

  • ValueError – Length of labels must be 1 or 2 + len(control_points)

  • ValueError – If max_comp is greater than the maximum axial capacity

Returns:

Moment interaction results object

Return type:

MomentInteractionResults

biaxial_bending_diagram(n: float = 0, n_points: int = 48, progress_bar: bool = True) → BiaxialBendingResults[source]

Generates a biaxial bending diagram.

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

Parameters:

  • n (float) – Net axial force. Defaults to 0.

  • n_points (int) – Number of calculation points. Defaults to 48.

  • progress_bar (bool) – If set to True, displays the progress bar. Defaults to True.

Returns:

Biaxial bending results

Return type:

BiaxialBendingResults

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

Calculates uncracked stresses.

Calculates stresses within the reinforced concrete section assuming an uncracked section. Uses gross area section properties to determine concrete and reinforcement stresses given an axial force n, and bending moments m_x and m_y.

Parameters:

  • n (float) – Axial force. Defaults to 0.

  • m_x (float) – Bending moment about the x-axis. Defaults to 0.

  • m_y (float) – Bending moment about the y-axis. Defaults to 0.

Returns:

Stress results object

Return type:

StressResult

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

Calculates cracked stresses.

Calculates stresses within the reinforced concrete section assuming a cracked section. Uses cracked area section properties to determine concrete and reinforcement 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 (float) – Axial force. Defaults to 0.

  • m (float) – Bending moment. Defaults to 0.

Returns:

Stress results object

Return type:

StressResult

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

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, a curvature can be provided which overrides the supplied moment.

Parameters:

  • moment_curvature_results (MomentCurvatureResults) – Moment-curvature results objects

  • m (float) – Bending moment

  • kappa (float | None) – Curvature, if provided overrides the supplied bending moment and calculates the stress at the given curvature. Defaults to None.

Raises:

AnalysisError – If the stress analysis fails

Returns:

Stress results object

Return type:

StressResult

calculate_ultimate_stress(ultimate_results: UltimateBendingResults) → StressResult[source]

Calculates ultimate stresses within the reinforced concrete section.

Parameters:

ultimate_results (UltimateBendingResults) – Ultimate bending results objects

Returns:

Stress results object

Return type:

StressResult

extreme_bar(theta: float) → tuple[float, float][source]

Calculates depth to the extreme bar.

Given neutral axis angle theta, determines the depth of the furthest lumped reinforcement from the extreme compressive fibre and also returns its yield strain.

Parameters:

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

Returns:

Depth of furthest bar and its yield strain

Return type:

tuple[float, float]

decode_d_n(theta: float, cp: tuple[str, float], d_t: float) → float[source]

Decodes a neutral axis depth given a control point cp.

Parameters:

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

  • cp (tuple[str, float]) – Control point to decode

  • d_t (float) – Depth to extreme tensile fibre

Raises:
Returns:

Decoded neutral axis depth

Return type:

float

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

Plots the reinforced concrete section.

Parameters:

  • title (str) – Plot title. Defaults to "Reinforced Concrete Section".

  • background (bool) – If set to True, uses the plot as a background plot. Defaults to False.

  • kwargs – Passed to plotting_context()

Returns:

Matplotlib axes object

Return type:

matplotlib.axes.Axes