AnalysisSection#

class concreteproperties.analysis_section.AnalysisSection(geometry: CPGeom)[source]#

Bases: object

Class for an analysis section to perform a fast analysis on meshed sections.

Methods

`calculate_meshed_area`	Calculates the area of the analysis section based on the generated mesh.
`get_elastic_stress`	Given section actions and section propreties, calculates elastic stresses.
`get_service_stress`	Determines the service stresses.
`get_ultimate_stress`	Determines the ultimate stresses.
`plot_mesh`	Plots the finite element mesh.
`plot_shape`	Plots the coloured shape of the mesh with no outlines on `ax`.
`service_analysis`	Performs a service analysis on the section.
`ultimate_analysis`	Performs an ultimate analysis on the section.

__init__(geometry: CPGeom) → None[source]#

Inits the AnalysisSection class.

Parameters:: geometry (CPGeom) – Geometry object

calculate_meshed_area() → float[source]#

Calculates the area of the analysis section based on the generated mesh.

Returns:: Meshed area (un-weighted by elastic modulus)
Return type:: float

get_elastic_stress(n: float, m_x: float, m_y: float, e_a: float, cx: float, cy: float, e_ixx: float, e_iyy: float, e_ixy: float) → tuple[ndarray, float, float, float][source]#

Given section actions and section propreties, calculates elastic stresses.

Parameters:

n (float) – Axial force
m_x (float) – Bending moment about the x-axis
m_y (float) – Bending moment about the y-axis
e_a (float) – Axial rigidity
cx (float) – x-Centroid
cy (float) – y-Centroid
e_ixx (float) – Flexural rigidity about the x-axis
e_iyy (float) – Flexural rigidity about the y-axis
e_ixy (float) – Flexural rigidity about the xy-axis

Returns:

Elastic stresses, net force and distance from neutral axis to point of force action

Return type:

tuple[ndarray, float, float, float]

service_analysis(ecf: tuple[float, float], eps0: float, theta: float, kappa: float, centroid: tuple[float, float]) → tuple[float, float, float, float, float][source]#

Performs a service analysis on the section.

Parameters:

ecf (tuple[float, float]) – Global coordinate of the extreme compressive fibre
eps0 (float) – Strain at top fibre
theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
kappa (float) – Curvature
centroid (tuple[float, float]) – Centroid about which to take moments

Returns:

Axial force, section moments and min/max strain

Return type:

tuple[float, float, float, float, float]

get_service_stress(kappa: float, ecf: tuple[float, float], eps0: float, theta: float, centroid: tuple[float, float]) → tuple[ndarray, float, float, float][source]#

Determines the service stresses.

Given the neutral axis depth d_n and curvature kappa determines the service stresses within the section.

Parameters:

kappa (float) – Curvature
ecf (tuple[float, float]) – Global coordinate of the extreme compressive fibre
eps0 (float) – Strain at top fibre
theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
centroid (tuple[float, float]) – Centroid about which to take moments

Returns:

Service stresses, net force and distance from centroid to point of force action

Return type:

tuple[ndarray, float, float, float]

ultimate_analysis(point_na: tuple[float, float], d_n: float, theta: float, ultimate_strain: float, centroid: tuple[float, float]) → tuple[float, float, float][source]#

Performs an ultimate analysis on the section.

Parameters:

point_na (tuple[float, float]) – Point on the neutral axis
d_n (float) – Depth of the neutral axis from the extreme compression fibre
theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
ultimate_strain (float) – Concrete strain at failure
centroid (tuple[float, float]) – Centroid about which to take moments

Returns:

Axial force and resultant moments about the global axes

Return type:

tuple[float, float, float]

get_ultimate_stress(d_n: float, point_na: tuple[float, float], theta: float, ultimate_strain: float, centroid: tuple[float, float]) → tuple[ndarray, float, float, float][source]#

Determines the ultimate stresses.

Given the neutral axis depth d_n and ultimate strain, determines the ultimate stresses with the section.

Parameters:

d_n (float) – Neutral axis depth
point_na (tuple[float, float]) – Point on the neutral axis
theta (float) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))
ultimate_strain (float) – Concrete strain at failure
centroid (tuple[float, float]) – Centroid about which to take moments

Returns: