Analysis#

This section of the documentation outlines how to perform analyses in concreteproperties. The Results section outlines how to retrieve and display the results obtained from these analyses.

An analysis in concreteproperties begins by creating a ConcreteSection object from a CompoundGeometry object with assigned material properties.

class ConcreteSection(geometry: CompoundGeometry)[source]

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

Visualising the Cross-Section#

The ConcreteSection object can be visualised by calling the plot_section() method.

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

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

Gross Area Properties#

Upon creating a ConcreteSection object, concreteproperties will automatically calculate the area properties based on the gross reinforced concrete cross-section.

See also

For an application of the above, see the example Calculating Area Properties.

Cracked Area Properties#

The area properties of the cracked cross-section can be determined by calling the calculate_cracked_properties() method. By default the cracked properties are calculated for bending about the x axis, but this can be modified by providing a bending axis angle theta.

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

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

The cracking moment is determines assuming cracking occurs once the stress in the concrete reaches the flexural_tensile_strength. Cracked properties are calculated assuming the concrete is linear elastic and can only resist compression.

See also

For an application of the above, see the example Calculating Cracked Properties.

Moment Curvature Analysis#

A moment curvature analysis can be performed on the reinforced concrete cross-section by calling the moment_curvature_analysis() method. By default the moment curvature analysis is calculated for bending about the x axis, but this can be modified by providing a bending axis angle theta.

ConcreteSection.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[source]

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

This analysis uses the stress_strain_profile given to the Concrete and Steel material properties to calculate a moment curvature response. The analysis is displacement controlled with an adaptive curvature increment controlled by the parameters kappa_inc, delta_m_min and delta_m_max.

See also

For an application of the above, see the example Moment Curvature Analysis.

Ultimate Bending Capacity#

The ultimate bending capacity of the reinforced concrete cross-section can be calculated by calling the ultimate_bending_capacity() method. By default the ultimate bending capacity is calculated for bending about the x axis with zero axial force, but this can be modified by providing a bending axis angle theta and axial force n.

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

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

This analysis uses the ultimate_stress_strain_profile given to the Concrete materials and the stress_strain_profile given to the Steel materials. The ultimate strain profile is determined by setting the strain at the extreme compressive fibre to the ultimate_strain parameter (see Concrete Ultimate Stress-Strain Profiles) and finding the neutral axis which satisfies the equilibrium of axial forces.

Note

The bending neutral axis must lie within the cross-section, if a combination of theta and n is provided to the method that results in the neutral axis angle lying outside the cross-section, the algorithm will not converge and a warning message displayed.

See also

For an application of the above, see the example Ultimate Bending Capacity.

Moment Interaction Diagram#

A moment interaction diagram can be generated for the reinforced concrete cross-section by calling the moment_interaction_diagram() method. By default the moment interaction diagram is generated for bending about the x axis, but this can be modified by providing a bending axis angle theta.

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

The moment interaction diagram is generated by shifting the neutral axis throughout the cross-section from pure bending to the decompression point using n_points. A straight line is generated between the decompression point and the squash load, and the pure bending point and the tensile load.

See also

For an application of the above, see the example Moment Interaction Diagram.

Biaxial Bending Diagram#

A biaxial bending diagram can be generated for the reinforced concrete cross-section, by calling the biaxial_bending_diagram() method. By default the biaxial bending diagram is generated for pure bending, but this can be modified by providing an axial force n.

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

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

The biaxial bending diagram is generated by rotating the bending axis angle through its permissable range \(-\pi \leq \theta \leq \pi\) and calculating the resultant ultimate bending moments about the x and y axes.

See also

For an application of the above, see the example Biaxial Bending Diagram.

Stress Analysis#

concreteproperties allows you to perform four different kinds of stress analysis. Each is detailed separately below.

See also

For an application of stress analysis, see the example Stress Analysis.

Uncracked Stress#

A stress analysis can be performed on the gross reinforced concrete cross-section by calling the calculate_uncracked_stress() method.

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

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

Cracked Stress#

A stress analysis can be performed on the cracked reinforced concrete cross-section by calling the calculate_cracked_stress() method. Prior to calling this method, the cracked properties must be calculated using the calculate_cracked_properties() method and these results passed to calculate_cracked_stress().

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

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

Service Stress#

A service stress analysis can be performed on the reinforced concrete cross-section by calling the calculate_service_stress() method. Prior to calling this method, a moment curvature analysis must be performed by calling the moment_curvature_analysis() method and these results passed to calculate_service_stress().

ConcreteSection.calculate_service_stress(moment_curvature_results: MomentCurvatureResults, m: float, kappa: Optional[float] = 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, 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

Ultimate Stress#

An ultimate stress analysis can be performed on the reinforced concrete cross-section by calling the calculate_ultimate_stress() method. Prior to calling this method, the ultimate bending capacity must be calculated by calling the ultimate_bending_capacity() method and these results passed to calculate_ultimate_stress().

ConcreteSection.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