concreteproperties.prestressed_section.PrestressedSection#

class PrestressedSection(geometry, moment_centroid=None, geometric_centroid_override=True)[source]#

Bases: ConcreteSection

Class for a prestressed concrete section.

Note

Prestressed concrete sections analysed in concreteproperties must be symmetric about their vertical (y) axis, with all flexure assumed to be about the x axis.

Warning

The only meshed geometries that are permitted are concrete geometries.

Inits the ConcreteSection class.

Parameters

geometry (CompoundGeometry) – sectionproperties CompoundGeometry object describing the prestressed 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: True) – If set to True, sets moment_centroid to the geometric centroid i.e. material properties applied

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 an axial loading and bending moment.
`calculate_cracked_stress`	Calculates stresses within the prestressed concrete section assuming a cracked section.
`calculate_cracking_moment`	Calculates the cracking moment given an axial load `n` and internal bending moment `m_int`.
`calculate_gross_area_properties`	Calculates and stores gross section area properties.
`calculate_service_stress`	Calculates service stresses within the prestressed 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 prestressed concrete section.
`calculate_uncracked_stress`	Calculates stresses within the prestressed concrete section assuming an uncracked section.
`cracked_neutral_axis_convergence`	Given a trial cracked neutral axis depth `d_nc`, determines the minimum concrete stress.
`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 an 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 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_cracked_properties(m_ext, n_ext=0)[source]#

Calculates cracked section properties given an axial loading and bending moment.

Parameters

m_ext (float) – External bending moment
n_ext (float, default: 0) – External axial force

Raises

ValueError – If the provided loads do not result in tension within the concrete

Returns

CrackedResults – Cracked results object

calculate_cracking_moment(n, m_int, positive)[source]#

Calculates the cracking moment given an axial load n and internal bending moment m_int.

Parameters

n (float) – Axial load
m_int (float) – Internal bending moment
positive (bool) – If set to True, determines the cracking moment for positive bending, otherwise determines the cracking moment for negative bending

Returns

float – Cracking moment

cracked_neutral_axis_convergence(d_nc, cracked_results)[source]#

Given a trial cracked neutral axis depth d_nc, determines the minimum concrete stress. For a cracked elastic analysis this should be zero (no tension allowed).

Parameters

d_nc (float) – Trial cracked neutral axis
cracked_results (CrackedResults) – Cracked results object

Returns

float – Cracked neutral axis convergence

moment_curvature_analysis(positive=True, n=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 an applied axial force n.

Analysis continues until a material reaches its ultimate strain.

Parameters

positive (bool, default: True) – If set to True, performs the moment curvature analysis for positive bending, otherwise performs the moment curvature analysis for negative bending
n (float, default: 0) – Axial force
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

ultimate_bending_capacity(positive=True, n=0)[source]#

Given axial force n, calculates the ultimate bending capacity.

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

Parameters

positive (bool, default: True) – If set to True, calculates the positive bending capacity, otherwise calculates the negative bending capacity.
n (float, default: 0) – Net axial force

Returns

UltimateBendingResults – Ultimate bending results object

moment_interaction_diagram()[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 – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
limits – 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 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 – 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 – 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 – 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 – If provided, limits the maximum compressive force in the moment interaction diagram to max_comp
max_comp_labels – 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 – If set to True, displays the progress bar

Returns

Moment interaction results object

biaxial_bending_diagram()[source]#

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

Parameters

n – Net axial force
n_points – Number of calculation points
progress_bar – If set to True, displays the progress bar

Returns

Biaxial bending results

calculate_uncracked_stress(n=0, m=0)[source]#

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

Uses gross area section properties to determine concrete, reinforcement and strand stresses given an axial force n and bending moment m.

Parameters

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

Returns

StressResult – Stress results object

calculate_cracked_stress(cracked_results)[source]#

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

Uses cracked area section properties to determine concrete, reinforcement and strand stresses given the actions provided during the cracked analysis.

Parameters: cracked_results (CrackedResults) – Cracked results objects
Returns: StressResult – Stress results object

calculate_service_stress(moment_curvature_results, m, kappa=None)[source]#

Calculates service stresses within the prestressed 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 prestressed concrete section.

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

calculate_gross_area_properties()#

Calculates and stores gross section area properties.

Return type: None

calculate_ultimate_section_actions(d_n, ultimate_results=None)#

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

cracked_section_properties(cracked_results)#

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

decode_d_n(theta, cp, d_t)#

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

extreme_bar(theta)#

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

get_gross_properties()#

Returns the gross section properties of the reinforced concrete section.

Returns: GrossProperties – Gross concrete properties object

get_transformed_gross_properties(elastic_modulus)#

Transforms gross section properties given a reference elastic modulus.

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

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

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

service_normal_force_convergence(eps0, kappa, moment_curvature)#

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_normal_force_convergence(d_n, n, ultimate_results)#

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