concreteproperties.concrete_section.ConcreteSection#

class ConcreteSection(geometry)[source]#

Bases: object

Class for a reinforced concrete section.

Inits the ConcreteSection class.

Parameters: geometry (CompoundGeometry) – sectionproperties CompoundGeometry 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_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_xy` 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.
`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.
`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`	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 neutral axis depth `d_n` and curvature `kappa`, returns the the net 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 calculated axial force.

calculate_gross_area_properties()[source]#: Calculates and stores gross section area properties.

get_gross_properties()[source]#

Returns the gross section properties of the reinforced concrete section.

Returns: GrossProperties – Gross concrete properties object

get_transformed_gross_properties(elastic_modulus)[source]#

Transforms gross section properties given a reference elastic modulus.

Parameters: elastic_modulus (float) – Reference elastic modulus
Returns: TransformedGrossProperties – Transformed concrete properties object

calculate_cracked_properties(theta=0)[source]#

Calculates cracked section properties given a neutral axis angle theta.

Parameters: theta (float, default: 0) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
Returns: CrackedResults – Cracked results object

calculate_cracking_moment(theta)[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: float – Cracking moment

cracked_neutral_axis_convergence(d_nc, cracked_results)[source]#

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

float – Cracked neutral axis convergence

moment_curvature_analysis(theta=0, kappa_inc=1e-07, delta_m_min=0.15, delta_m_max=0.3)[source]#

Performs a moment curvature analysis given a bending angle theta.

Analysis continues until a material reaches its ultimate strain.

Param

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

Parameters

kappa_inc (float, default: 1e-07) – Initial curvature increment
delta_m_min (float, default: 0.15) – Relative change in moment at which to double step
delta_m_max (float, default: 0.3) – Relative change in moment at which to halve step

Returns

MomentCurvatureResults – Moment curvature results object

service_normal_force_convergence(d_n, kappa, moment_curvature)[source]#

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

Parameters

d_nc – Trial cracked neutral axis
kappa (float) – Curvature
moment_curvature (MomentCurvatureResults) – Moment curvature results object

Returns

float – Net axial force

ultimate_bending_capacity(theta=0, n=0)[source]#

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

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

Parameters

theta (float, default: 0) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
n (float, default: 0) – Net axial force

Returns

UltimateBendingResults – Ultimate bending results object

ultimate_normal_force_convergence(d_n, n, ultimate_results)[source]#

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

float – Axial force convergence

calculate_ultimate_section_actions(d_n, ultimate_results=None)[source]#

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 (Optional[UltimateBendingResults], default: None) – Ultimate bending results object

Returns

UltimateBendingResults – Ultimate bending results object

moment_interaction_diagram(theta=0, control_points=[('kappa0', 0.0), ('D', 1.0), ('fy', 1.0), ('N', 0.0), ('d_n', 1e-06)], labels=[None], n_points=[4, 12, 12, 4], max_comp=None, max_comp_labels=[None, None])[source]#

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 (float, default: 0) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
control_points (List[Tuple[str, float]], default: [('kappa0', 0.0), ('D', 1.0), ('fy', 1.0), ('N', 0.0), ('d_n', 1e-06)]) – List of control points over which to generate the interaction diagram. Each entry in control_points is a Tuple with the first item the type of control point and the second item defining the location of the control point. Acceptable types of control points are "D" (ratio of neutral axis depth to section depth), "d_n" (neutral axis depth), "fy" (yield ratio of the most extreme tensile bar), "N" (axial force) and "kappa" (zero curvature compression - must be at start of list, second value in tuple is not used). Control points must be defined in an order which results in a decreasing neutral axis depth (decreasing axial force). The default control points define an interaction diagram from the decompression point to the pure bending point.
labels (List[Optional[str]], default: [None]) – List of labels to apply to the control_points for plotting purposes, length must be the same as the length of control_points. If a single value is provided, will apply this label to all control points.
n_points (Union[int, List[int]], default: [4, 12, 12, 4]) – Number of neutral axis depths to compute between each control point. Length must be one less than the length of control_points. If an integer is provided this will be used between all control points.
max_comp (Optional[float], default: None) – If provided, limits the maximum compressive force in the moment interaction diagram to max_comp
max_comp_labels (List[Optional[str]], default: [None, 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

Raises

ValueError – If control_points, labels or n_points is invalid

Returns

MomentInteractionResults – Moment interaction results object

biaxial_bending_diagram(n=0, n_points=48)[source]#

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

Parameters

n (float, default: 0) – Net axial force
n_points (int, default: 48) – Number of calculation points between the decompression

Returns

BiaxialBendingResults – Biaxial bending results

calculate_uncracked_stress(n=0, m_x=0, m_y=0)[source]#

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, default: 0) – Axial force
m_x (float, default: 0) – Bending moment about the x-axis
m_y (float, default: 0) – Bending moment about the y-axis

Returns

StressResult – Stress results object

calculate_cracked_stress(cracked_results, n=0, m=0)[source]#

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, default: 0) – Axial force
m (float, default: 0) – Bending moment

Returns

StressResult – Stress results object

calculate_service_stress(moment_curvature_results, m, kappa=None)[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 (Optional[float], default: None) – Curvature, if provided overrides the supplied bending moment and calculates the stress at the given curvature

Returns

StressResult – Stress results object

calculate_ultimate_stress(ultimate_results)[source]#

Calculates ultimate stresses within the reinforced concrete section.

Parameters: ultimate_results (UltimateBendingResults) – Ultimate bending results objects
Returns: StressResult – Stress results object

extreme_bar(theta)[source]#

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: Tuple[float, float] – Depth of furthest bar and its yield strain

plot_section(title='Reinforced Concrete Section', background=False, **kwargs)[source]#

Plots the reinforced concrete section.

Parameters

title (str, default: 'Reinforced Concrete Section') – Plot title
background (bool, default: False) – If set to True, uses the plot as a background plot
kwargs – Passed to plotting_context()

Returns

Axes – Matplotlib axes object