concreteproperties.concrete_section.ConcreteSection#

class ConcreteSection(geometry, moment_centroid=None, geometric_centroid_override=False)[source]#

Bases: object

Class for a reinforced concrete section.

Inits the ConcreteSection class.

Parameters

geometry (CompoundGeometry) – sectionproperties CompoundGeometry object describing the reinforced concrete section
moment_centroid (Optional[Tuple[float, float]], default: 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.
geometric_centroid_override (bool, default: False) – If set to True, sets moment_centroid to the geometric centroid i.e. material properties applied (useful for composite section analysis)

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.
`cracked_section_properties`	Given a list of cracked geometries (stored in `cracked_results`), determines the cracked section properties and stores in `cracked_results`.
`decode_d_n`	Decodes a neutral axis depth given a control point `cp`.
`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` and applied axial force `n`.
`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`	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.

Return type: None

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

cracked_section_properties(cracked_results)[source]#

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
Return type: None

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

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, default: 0) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
n (float, default: 0) – Axial force
kappa0 (float, default: 0) – Initial curvature
kappa_inc (float, default: 1e-07) – Initial curvature increment
kappa_mult (float, default: 2) – 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.
kappa_inc_max (float, default: 5e-06) – Maximum curvature increment
delta_m_min (float, default: 0.15) – Relative change in moment at which to reduce the curvature increment
delta_m_max (float, default: 0.3) – Relative change in moment at which to increase the curvature increment
progress_bar (bool, default: True) – If set to True, displays the progress bar

Returns

MomentCurvatureResults – Moment curvature results object

service_normal_force_convergence(eps0, kappa, moment_curvature)[source]#

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

Parameters

eps0 (float) – Strain at top fibre
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

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 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 (nominal axial load)

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, limits=[('D', 1.0), ('d_n', 1e-06)], control_points=[('kappa0', 0.0), ('fy', 1.0), ('N', 0.0)], labels=None, n_points=24, n_spacing=None, max_comp=None, max_comp_labels=None, progress_bar=True)[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, default: 0) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
limits (List[Tuple[str, float]], default: [('D', 1.0), ('d_n', 1e-06)]) – 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.
control_points (List[Tuple[str, float]], default: [('kappa0', 0.0), ('fy', 1.0), ('N', 0.0)]) – 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). Control points may lie outside the limits of the moment interaction diagram as long as equilibrium can be found.
labels (Optional[List[str]], default: 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).
n_points (int, default: 24) – Number of points to compute including and between the limits of the moment interaction diagram. Generates equally spaced neutral axis depths between the limits.
n_spacing (Optional[int], default: 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.
max_comp (Optional[float], default: None) – If provided, limits the maximum compressive force in the moment interaction diagram to max_comp
max_comp_labels (Optional[List[str]], default: 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, default: True) – If set to True, displays the progress bar

Returns

MomentInteractionResults – Moment interaction results object

biaxial_bending_diagram(n=0, n_points=48, progress_bar=True)[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
progress_bar (bool, default: True) – If set to True, displays the progress bar

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

decode_d_n(theta, cp, d_t)[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

Returns

float – Decoded neutral axis depth

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